Answers
Answer:
[tex]\left(x\:+\:1\right)^2\:+\:y^2=25[/tex]
Step-by-step explanation:
The equation of a circle with radius r and center at (a, b) is given by
(x - a)² + (y - b)² = r²
Let's first find the radius
The circle intersects the x axis at two points (-6, 0) and (4, 0)
The diameter is therefore the absolute difference between the x values:
|-6 - 4| same as |4 - (-6)| = 10
The radius r = 5 (half of diameter)
Now, let's find the center point of the circle. This will lie midway between (-6, 0) and (4, 0)
Midpoint (xm, ym) between two points(x1, y) and (x2, y2) :
xm = (x1 + x2)/2 = (-6 + 4)/2 = -1
ym = (y1 + y2)/2 = (0 + 0)/2 = 0
So the center (a, b) = (-1, 0) with a = -1, b = 0
The equation of the circle therefore is
(x - a)² + (y - b)² = r²
( x - (-1) )² + (y - 0)² = 25
(x + 1)² + y² = 25
To find a and b take any point (x, y) and plug these
Related Questions
Find the radius of the circle with equation x² + y² = 19²
r=0
Submit Answer
Answers
The radius of the circle of equation x² + y² = 19² is given as follows:
r = 19 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.
The equation of the circle in this problem is given as follows:
x² + y² = 19².
Hence the radius is obtained as follows, comparing to the general equation:
r² = 19²
r = 19 units.
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. Y
=
−
16
x
2
+
180
x
+
63
y=−16x 2
+180x+63
Answers
The maximum height reached by the rocket is approximately 504.6 feet.
To find the maximum height reached by the rocket, we need to determine the vertex of the parabola represented by the given quadratic equation: y = -16x^2 + 180x + 63.
The x-coordinate of the vertex can be found using the formula x = -b / 2a, where a = -16 and b = 180.
x = -180 / (2 * -16) = 180 / 32 = 5.625
Now, we'll plug the x-coordinate back into the equation to find the y-coordinate (maximum height).
y = -16(5.625)^2 + 180(5.625) + 63
y ≈ 504.6
The maximum height reached by the rocket is approximately 504.6 feet.
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Plsssssssss answer quick need this NOWWW
Answers
Answer:
Step-by-step explanation:
A= 1/2 b h b=6 h=2.5
= 7.5
Answer:
7.5 inches squared
Step-by-step explanation:
If only distances are provided, there are two methods to find the area of a triangle. Which method to use depends on which lengths are provided:
Method 1: Base * Height (one leg and the corresponding height)Method 2: Heron's Formula (all three legs are known)Method 1: Base * Height
For any triangle, a line segment from one vertex that terminates perpendicularly to the leg across from it is considered a "height," and the leg that the "height" intersects is "base". If both quantities are known, then the area of the triangle is base times height divided by 2 (sometimes stated as 1/2 times base times height).
In an equation format: [tex]Area_{triangle}=\frac{1}{2}base*height[/tex], often abbreviated as [tex]A_{triangle}=\frac{1}{2}bh[/tex]
For this example, the base at the bottom "6 in" has a corresponding height of "2.5 in", so
[tex]A_{triangle}=\frac{1}{2}(2.5~\text{in})(6~\text{in})[/tex]
[tex]A_{triangle}=7.5\text{ in}^2[/tex]
Method 2: Heron's Formula
If you are not provided any of the heights, but only the three legs of the triangle, Heron's formula provides a method of finding the area of the triangle. It is significantly more complicated, and should only be used if one doesn't have one of the heights given.
Heron's formula gives the area of a triangle using the following formula:[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] where a, b, and c, are the side lengths of the triangle, and "s" is the "semi-perimeter" (one half of the perimeter) of the triangle: [tex]s=\dfrac{a+b+c}{2}[/tex]
To be consistent, let's let a=3 in, b=5 in, and c=6 in.
Calculating the semi-perimeter of the given triangle first:
[tex]s=\dfrac{a+b+c}{2}=\dfrac{(3~\text{in})+(5~\text{in})+(6~\text{in})}{2}=\dfrac{14~\text{in}}{2}=7~\text{in}[/tex]
Calculating the area:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]A=\sqrt{(7~\text{in})((7~\text{in})-(3~\text{in}))((7~\text{in})-(5~\text{in}))((7~\text{in})-(6~\text{in}))}[/tex]
[tex]A=\sqrt{(7~\text{in})(4~\text{in)(2~\text{in})(1~\text{in})}[/tex]
[tex]A=\sqrt{56~\text{in}^4}[/tex]
[tex]A=7.48331477355...~\text{in}^2[/tex]
[tex]A\approx7.5~\text{in}^2[/tex]
Side note: The 2.5 inches that they gave you in the problem isn't exactly 2.5 inches. They rounded to one decimal place there.
Sam built a circular fenced-in section for some of his animals. The section has a circumference of 55 meters. What is the approximate area, in square meters, of the section? Use 22/7 for π.
Answers
The approximate area of the circular fenced-in section is 950.5 square meters.
The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. We are given that the circumference of the fenced-in section is 55 meters, so we can set up the equation:
2πr = 55
We can solve for r by dividing both sides by 2π:
r = 55/(2π)
We are asked to find the area of the section, which is given by the formula A = πr². Substituting our expression for r, we get:
A = π(55/(2π))²
Simplifying, we get:
A = (55²/4)π
Using the approximation 22/7 for π, we get:
A ≈ (55²/4)(22/7)
A ≈ 950.5
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If the expressions (3x)² (5x6) is written in aa
axb
form what is the value of a + b?
Answers
The value of the expression a+b = 45+8 = 53
Expression calculation.
To write (3x)² (5x⁶) in the form of ax^b, we need to simplify the expressions and multiply the coefficients and the variables separately:
(3x)² (5x⁶) = 9x² × 5x⁶ = 45x^(2+6) = 45x^8
So, the expression (3x)² (5x⁶) can be written as 45x^8 in the form of ax^b, where a=45 and b=8.
Therefore, a+b = 45+8 = 53
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PLEASE HELP ( I CAN GIVE BRAINLIEST)
Answers
Answer:
x = √(6^2 + 18^2) = √(36 + 324) = √360
= 6√10
Answer:
[tex]x = 6\sqrt{10}[/tex]
Step-by-step explanation:
You can find the height using [tex]c^2 = a^2 + b^2[/tex] formula.
[tex](6\sqrt{2})^2 = 6^2 + b^2.[/tex]
[tex]b^2 = 72-36=36.[/tex]
[tex]b=6.[/tex]
You can find x using the same formula.
[tex]x^2 = 6^2 + 18^2 = 360.[/tex]
[tex]x = 6\sqrt{10}[/tex]
Find the sum of the first 10 terms of the following series, to the nearest integer.
8,20/3,50/9
Answers
The sum of the first 10 terms of the given series 8,20/3,50/9... is 140.
Given series: 8,20/3,50/9...
The given series is not in a standard form, but it appears to be an arithmetic sequence with a common difference of 4/3. To check this, we can find the difference between consecutive terms:
20/3-8=4/3
50/9-20/3=4/3
Thus, the common difference is indeed [tex]\frac{4}{3}[/tex].
We notice that each term of the series can be written as:
a_n=a+(n-1)d
a_n=8+(n-1)(4/3)
where n is the index of the term, and 4/3 is the common difference between the consecutive terms.
To find the sum of the first 10 terms of the series, we use the formula for the sum of an arithmetic series:
S=(n/2)[2a_1+(n-1)d]
where S is the sum of the series, a_1 is the first term of the series, d is the common difference, and n is the number of terms to be added.
Substituting the given values, we get:
S=(10/2)[2*8+(10-1)(4/3)]
Simplifying the expression:
S=5[16+9(4/3)]
S=5[16+12]=5(28)=140
Therefore, the sum of the first 10 terms of the series is 140.
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Nolan is following his family's macaroni and and cheese recipe. The recipe calls 6 cups of shredded cheese 4 tablespoons of milk. He wants to make a smaller batch, so he uses only 3 cups of shredded cheese
Answers
Nolan is making a smaller batch of his family's macaroni and cheese recipe, and as a result, he has reduced the amount of shredded cheese to 3 cups. The original recipe called for 6 cups of shredded cheese and 4 tablespoons of milk.
However, since Nolan is using only 3 cups of shredded cheese, he will need to adjust the amount of milk he uses as well.
When reducing the amount of cheese, it is important to keep the ratio of cheese to milk consistent. Therefore, if Nolan is halving the amount of cheese, he should also halve the amount of milk. This means that instead of using 4 tablespoons of milk, he should use only 2 tablespoons of milk.
It is important to note that reducing the amount of cheese and milk in a recipe may also affect the overall taste and texture of the dish. However, by following the recipe and adjusting the amounts accordingly, Nolan can still create a delicious and satisfying macaroni and cheese dish.
In summary, when making a smaller batch of a recipe, it is important to adjust the ingredients accordingly while maintaining the same ratios. Nolan is reducing the amount of cheese in his macaroni and cheese recipe and should also reduce the amount of milk in order to keep the same ratio.
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Water began leaking from a holes in a bucket at a constant rate. Here is a Table of how many ounces were in the bucket at
different times. 10 am:
304 ounces
Noon :
228 ounces
3 pm :
114 ounces
there are more then one question to answer
What is the amount of water that leaks from the bucket each hour?
How many ounces of water were in the bucket at 8 am. ?\
At what time will the bucket be empty. ?
Write the equation of this function in slope intercept form. Use x for the amount of time in hours since the leak began and y for the amount of water in the buck
Answers
The amount of water that leaks from the bucket each hour is 38 ounces/hour.
The amount of water in the bucket at 8 am would have been 380 ounces. The bucket will be empty after 8 hours, or at 6 pm.
To find the amount of water that leaks from the bucket each hour, we can use the information that the leak is at a constant rate. We can find the total amount of water that leaked out of the bucket from 10 am to 3 pm, which is 304 - 114 = 190 ounces.
This is over a time period of 5 hours (from 10 am to 3 pm), so the amount of water that leaks from the bucket each hour is:
190 ounces ÷ 5 hours = 38 ounces/hour
To find how many ounces of water were in the bucket at 8 am, we need to estimate the amount of water that leaked out from 8 am to 10 am. We know that the bucket loses 38 ounces of water every hour, so from 8 am to 10 am (2 hours), the amount of water that leaked out would be:
38 ounces/hour x 2 hours = 76 ounces
Therefore, the amount of water in the bucket at 8 am would have been:
304 ounces + 76 ounces = 380 ounces
To find at what time the bucket will be empty, we can assume that the leak rate remains constant at 38 ounces/hour. We know that the bucket starts with 304 ounces, so we can set up the equation:
y = 304 - 38x
where y is the amount of water in the bucket and x is the time in hours since the leak began. When the bucket is empty, y will be zero, so we can solve for x:
0 = 304 - 38x
38x = 304
x = 8
Therefore, the bucket will be empty after 8 hours, or at 6 pm.
The equation for the amount of water in the bucket as a function of time can be written in slope-intercept form as:
y = -38x + 304
where the slope (m) is -38 (the rate at which water is leaking out of the bucket) and the y-intercept (b) is 304 (the initial amount of water in the bucket).
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Find the area of a parallelogram with the given vertices: p(3, 3), q(5, 3), r(7, 7), s(9, 7). a. 16 units2 b. 8 units2 c. 4 units2 d. none of these
Answers
The area of the parallelogram is 8 units², which is option (b).
To find the area of a parallelogram, we need to use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we can use the distance formula to find the base and height.
Base = distance between points P and Q
= √[(5-3)² + (3-3)²]
= √4
= 2 units
Height = distance between point P and the line containing points R and S. We can find the equation of this line by first finding its slope:
slope = (y2 - y1)/(x2 - x1)
= (7 - 7)/(9 - 7)
= 0
Since the slope is 0, the line is horizontal and has an equation of y = 7. Therefore, the height is the distance between point P and this line, which is:
Height = distance from point P to line y = 7
= |3 - 7|
= 4 units
Now we can plug in the values of b and h into the formula A = bh:
A = 2 x 4
= 8 units²
Therefore, the area of the parallelogram is 8 units², which is option (b).
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Use the given sample data to find each of the listed values. In your answer, include both numerical answers and an explanation, in complete sentences, for the steps necessary to find the data values. Complete your work in the space provided.
62 52 52 52 64 69 69 76 54 58 61 67 73
Range _____
Q1 _____
Q3 _____
IQR _____
Answers
Using the given sample data, the data values are:
Range 24
Q1 52
Q3 69
IQR 17
1. Arrange the data in ascending order:
52, 52, 52, 54, 58, 61, 62, 64, 67, 69, 69, 73, 76
2. Calculate the range (highest value - lowest value):
Range = 76 - 52 = 24
3. Find the first quartile (Q1) - the median of the first half of the data:
Since there are 13 data points, we'll take the median of the first 6 numbers: (52 + 52) / 2 = 52
Q1 = 52
4. Find the third quartile (Q3) - the median of the second half of the data:
We'll take the median of the last 6 numbers: (69 + 69) / 2 = 69
Q3 = 69
5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 69 - 52 = 17
So, the requested values are:
Range = 24
Q1 = 52
Q3 = 69
IQR = 17
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Please help it would be amazing if you knew this
Answers
Answer: 5x + 5
Step-by-step explanation:
You combine the two functions togther, and add the like terms.
2x +3 +3x +2
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Ellus
These prisms are similar. Find the surface
area of the larger prism in decimal form.
5 m
7 m
Surface Area
90 m2
Surface Area = [? ] m2
please helppp. :)
Answers
If two prisms are similar, their corresponding dimensions are proportional.
Let's assume that the ratio of the corresponding lengths of the smaller prism to the larger prism is k:1, where k is a constant.
Then the ratio of the corresponding surface areas of the smaller prism to the larger prism is [tex](k^2):1[/tex], because the surface area of a prism is proportional to the square of its length.
In this problem, the surface area of the smaller prism is not given.
However, we can find the ratio of the corresponding lengths of the smaller prism to the larger prism using the fact that they are similar.
The height of the smaller prism can be found as follows:
[tex]7/5 = h/L[/tex]
where h is the height of the smaller prism and L is the length of the larger prism.
Solving for h, we get:
[tex]h = (7/5)L[/tex]
The ratio of the corresponding lengths of the smaller prism to the larger prism is 7:5.
The ratio of the surface areas of the smaller prism to the larger prism is:
[tex](7/5)^2 : 1 = 49/25 : 1[/tex]
We know that the surface area of the larger prism is [tex]90 m^2.[/tex]
Let's denote the surface area of the smaller prism by A. Then we can set up an equation:
(49/25)A = 90
Solving for A, we get:
A = (25/49) * 90 = 45/7 ≈ 6.4
The surface area of the smaller prism is approximately [tex]6.4 m^2.[/tex]
(Note: The units of the surface area are not provided for the smaller prism, so I assumed the same units as the larger prism.
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Type the correct answer in the box.
Answers
The given equation, V = 1/3 πr²h, solved for h is:
h = 3V / πr²
Subject of formulae: Solving the equation for hFrom the question, we are to solve the give equation for h
From the given information,
The given equation is
V = 1/3 πr²h
To solve the equation for h, we will isolate h
Solving the equation for h
V = 1/3 πr²h
Multiply both sides of the equation by 3
3 × V = 3 × 1/3 πr²h
3V = πr²h
Divide both sides of the equation by πr²
3V / πr² = πr²h / πr²
3V / πr² = h
This can be written as
h = 3V / πr²
Hence, the equation solved for h is:
h = 3V / πr²
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Jim walks 3 miles per hour slower than his friend Steve runs. Steve runs 4 miles per hour slower than his friend Matt rides his bike. Jim walks 25 miles in the same time Matt rides his bike miles. Steve runs 16 miles in the same time Matt rides his bike 24 miles.
Part A: Write an equation to calculate Jim's speed
Answers
Let's start by assigning variables to the unknowns in the problem:
- Let j be Jim's speed in miles per hour (in other words, the rate at which he walks).
- Let s be Steve's speed in miles per hour (in other words, the rate at which he runs).
- Let m be Matt's speed on his bike in miles per hour.
From the first sentence of the problem, we know that:
s = m + 4 (Steve runs 4 miles per hour slower than Matt rides his bike)
And from the second sentence, we know that:
j = s - 3 (Jim walks 3 miles per hour slower than Steve runs)
We want to find out how long it takes Jim to walk 25 miles and how long it takes Matt to ride his bike x miles. We can use the formula:
time = distance / rate
For Jim, we have:
time = 25 / j
For Matt, we have:
time = x / m
We also know that Steve runs 16 miles in the same time that Matt rides his bike 24 miles, so we can write:
16 / s = 24 / m
Substituting s = m + 4 and solving for m, we get:
16 / (m + 4) = 24 / m
16m = 24(m + 4)
16m = 24m + 96
8m = 96
m = 12
So Matt rides his bike at a speed of 12 miles per hour.
Now we can use the equations we set up earlier to solve for j and x:
j = s - 3
s = m + 4
j = (m + 4) - 3
j = m + 1
j = 13
x / m = 25 / j
x / 12 = 25 / 13
x = (25 * 12) / 13
x = 300 / 13
x ≈ 23.08
So it takes Jim 25 / 13 ≈ 1.92 hours to walk 25 miles, and it takes Matt 23.08 hours to ride his bike x = 300 / 13 ≈ 23.08 miles.
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The circumference of a wheel is 320.28 centimeters.
a) Determine the radius of the wheel.
b) Determine the area of the wheel.
Answers
Answer:
radius is 50.95
area is 8158.55
Step-by-step explanation:
cirumference = 2pi×r
or,320.28=2×(22/7)×r
or, r=320.28/(2×(22/7))
r=50.95 cm
area=(22/7)r^2
=8158.55
‘Vehicles approaching a certain road junction from town A can either turn left, turn right or go straight on. Over time it has been noted that of the vehicles approaching this particular junction from town A, 55% turn left, 15% turn right and 30% go straight on. The direction a vehicle takes at the junction is independent of the direction any other vehicle takes at the junction.
(i) Find the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right. ’
Answers
To solve this problem, we can use the multiplication rule of probability, which states that the probability of two or more independent events occurring together is the product of their individual probabilities.
Let L, R, and S be the events that a vehicle turns left, turns right, and goes straight on, respectively. We want to find the probability of the following event:
E: One vehicle goes straight on and the other two either both turn left or both turn right.
We can break down event E into two sub-events: one vehicle goes straight on and the other two vehicles both turn left or both turn right. Let's calculate the probabilities of these sub-events separately:
- Probability that one vehicle goes straight on: P(S) = 0.3
- Probability that the other two vehicles both turn left or both turn right: P((LL) or (RR)) = P(LL) + P(RR)
To find P(LL) and P(RR), we can use the multiplication rule again. Since the events are independent, we can multiply their individual probabilities:
- Probability that two vehicles both turn left: P(LL) = P(L) × P(L) = 0.55 × 0.55 = 0.3025
- Probability that two vehicles both turn right: P(RR) = P(R) × P(R) = 0.15 × 0.15 = 0.0225
Therefore, the probability of event E is:
P(E) = P(S) × P((LL) or (RR))
= 0.3 × (P(LL) + P(RR))
= 0.3 × (0.3025 + 0.0225)
= 0.0975
So the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right is 0.0975 or approximately 0.1 (rounded to one decimal place).
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Find the mean and the mean absolute deviation of each data set
Answers
To find the mean and mean absolute deviation of a data set, you need to follow these steps:
1. Find the mean: To find the mean of a data set, add up all of the values in the set and then divide that sum by the number of values in the set. For example, if your data set is {2, 4, 6, 8, 10}, you would add up all of the values (2+4+6+8+10=30) and then divide that sum by the number of values (5). So the mean of this data set is 30/5 = 6.
2. Find the mean absolute deviation:
To find the mean absolute deviation of a data set, you first need to find the absolute deviation of each value in the set from the mean.
To do this, subtract the mean from each value in the set (for example, if your data set is {2, 4, 6, 8, 10} and the mean is 6, you would subtract 6 from each value: 2-6=-4, 4-6=-2, 6-6=0, 8-6=2, 10-6=4).
Then, take the absolute value of each of these differences (|-4|=4, |-2|=2, |0|=0, |2|=2, |4|=4). Finally, find the mean of these absolute deviations by adding them up and dividing by the number of values in the set.
For the example data set above, the mean absolute deviation is (4+2+0+2+4)/5 = 2.4.
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Marina has learned that it typically rains 43% of the days in August in the city where she lives.
Assuming that the probability of rain on each day is independent, find the variance in the number of rainy days in Marina's city in two weeks during the month of August.
Round your answer to three significant figures
Answers
The variance in the number of rainy days in Marina's city in two weeks during the month of August is approximately 3.96.
We know that the probability of rain on any given day is0.43, and we want to find the friction in the number of stormy days in two weeks, which is 14 days.
The friction of a binomial distribution is given by the formula
Var( X) = npq
where n is the number of trials,
p is the probability of success on each trial,
and q is the probability of failure on each trial( q = 1- p).
In this case, n = 14,
p = 0.43, and
q = 0.57.
Substituting these values, we get
Var( X) = npq
Var( X) = 14 x0.43 x0.57
Var( X) = 3.9642
Rounding to three significant numbers, we get Var( X) = 3.96
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Select all the polygons that can be formed by the intersection of a plane and a cylinder, either parallel or perpendicular to the base?
Answers
The intersection of a plane and a cylinder can result in the following polygons when the plane is either parallel or perpendicular to the base:
Oa Rectangle
Oc Square
Od Triangle
What are the polygons that can be formedThe angle and position of the plane relative to the cylinder intersect determines a myriad of shapes not limited to just one. Herein are the descriptions for a few that may arise:
Rectangle: If a plane intersects the cylinder but remains parallel to its base, the resulting outline shall be rectangular. This is due to the aforementioned plane cutting through the lateral surface of the circumference, forming two equal lines--thereby shaping a closed loop in an angular fashion.
Square: The intersection of a plane perpendicularly bisecting the base of a cylindrical object will conjure up a square shape congruent to the cylinders. In other words, a perfectly squared compartment matching with the pre-existing edges of the bottom curve of the cylinder.
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I need help, answers and explanations
Answers
The length of the top of the ladder from the ground is 10m and the distance from wall to the bottom of ladder is 1.5m
Given that an ladder leans against a wall.
We have to find the length of the top of the ladder from the ground.
We know that tan function is the ratio of opposite side and adjacent side
Let x be the opposite side
tan 68 = x/4
2.475 = x/4
x= 4×2.475
x=9.9 m
x=10 m
So, the length of the top of the ladder from the ground is 10m.
Now let us find the distance from wall to the bottom of ladder
cosine function is the ratio of adjacent side and hypotenuse
Cos 68 = x/4
0.374 =x/4
x=0.374×4
x=1.5m
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Suppose p(c) = .048 , p(m cap c)=.044 and p(m cup c)=.524 . find the indicated probability p(m)
Answers
To find the probability of p(m) given the information provided, we can use the formula:
p(m) = p(m cap c') + p(m cap c)
where c' represents the complement of c, or everything that is not c.
First, we need to find the probability of c' by using the formula:
p(c') = 1 - p(c)
p(c') = 1 - 0.048
p(c') = 0.952
Next, we can find the probability of p(m cap c') by using the formula:
p(m cap c') = p(m) - p(m cap c)
p(m cap c') = p(m cup c) - p(c)
p(m cap c') = 0.524 - 0.048
p(m cap c') = 0.476
Finally, we can substitute these values into the formula for p(m) and solve:
p(m) = 0.476 + 0.044
p(m) = 0.52
Therefore, the indicated probability of p(m) is 0.52.
In simpler terms, p(m) is the probability of event m occurring. To find this probability, we first need to find the probability of event c not occurring, or c'. Then, we can use this information to find the probability of event m occurring but c not occurring, or m cap c'.
Finally, we add this probability to the probability of event m occurring and c occurring, or m cap c, to get the overall probability of event m occurring, or p(m). In this case, the indicated probability of p(m) is 0.52.
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A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius 5. If the density function is 8(x, y) = 2xy, find the mass of the wire.
Answers
The mass of the wire is 500.
To find the mass of the wire, we need to integrate the density function over the surface area of the wire.
First, we need to parameterize the curve. The equation of the circle with center at the origin and radius 5 is:
x^2 + y^2 = 25
We can parameterize this curve by letting:
x = 5cos(t)
y = 5sin(t)
where t varies from 0 to pi/2 (the first quadrant).
Next, we need to find the surface area element. We can do this using the formula:
dS = sqrt(1 + (dz/dx)^2 + (dz/dy)^2) dA
where dz/dx and dz/dy are the partial derivatives of the height function z = f(x,y) (in this case, z = 0 since the wire is a curve in the xy-plane).
Since dz/dx = dz/dy = 0, we have:
dS = dA
where dA is the area element in the xy-plane, which is given by:
dA = |(dx/dt)(dy/ds) - (dx/ds)(dy/dt)| dt ds
Plugging in our parameterization, we have:
dA = 5 dt ds
Now we can integrate the density function over the surface area of the wire:
m = ∫∫ 8(x,y) dS
= ∫∫ 2xy dA
= ∫[0,pi/2] ∫[0,5] 2(5cos(t))(5sin(t)) (5 dt ds)
= 500
Therefore, the mass of the wire is 500.
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f(x,y) = x2 + y² + xy {(x, y) : x2 + y2 < 1}
"Find the maxima and minima, and where they are reached, of the
following function. Find the locals and absolutes. Identify the
critical points inside the disk if any."
Answers
The given function f(x,y) = x^2 + y^2 + xy has a maximum value of 3/4 at (x,y) = (1/2,1/2) and a minimum value of -1/4 at (x,y) = (-1/2,1/2) inside the disk x^2 + y^2 < 1. There are no critical points inside the disk.
To find the critical points, we need to take partial derivatives of the function with respect to x and y and solve the resulting equations simultaneously.
fx = 2x + y = 0
fy = 2y + x = 0
Solving these equations, we get the critical point at (x,y) = (-1/2,-1/2) outside the disk. Hence, we do not consider it further.
Next, we need to find the boundary points of the disk, which is the circle x^2 + y^2 = 1. We can parameterize this circle as x = cos(t) and y = sin(t), where t ranges from 0 to 2π.
Substituting these values in the given function, we get:
f(cos(t), sin(t)) = cos^2(t) + sin^2(t) + cos(t)sin(t)
= 1/2 + 1/2sin(2t)
Now, we need to find the maximum and minimum values of this function. Since sin(2t) ranges from -1 to 1, the maximum value of the function is 3/4 when sin(2t) = 1, i.e., when t = π/4 or 5π/4. At these points, x = cos(π/4) = 1/2 and y = sin(π/4) = 1/2.
Similarly, the minimum value of the function is -1/4 when sin(2t) = -1, i.e., when t = 3π/4 or 7π/4. At these points, x = cos(3π/4) = -1/2 and y = sin(3π/4) = 1/2.
Therefore, the function has a maximum value of 3/4 at (x,y) = (1/2,1/2) and a minimum value of -1/4 at (x,y) = (-1/2,1/2) inside the disk x^2 + y^2 < 1. There are no critical points inside the disk.
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Find the slope from the data below
Answers
Answer:
m = -4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-3,12) (-2,8)
We see the y decrease by -4, and the x increase by 1, so the slope is
m = -4
So, the slope of the line representing by the data is -4.
2. If Q(-5, 1) is the midpoint of PR and R is located
at (-2.-4), what are the coordinates of P?
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad R(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +x}{2}~~~ ,~~~ \cfrac{ -4 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE Q} }{(-5~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -2 +x }{2}=-5\implies -2+x=-10\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -4 +y }{2}=1\implies -4+y=2\implies \boxed{y=6}[/tex]
Answer:
The answer is (-8,6)
are 4(5k – 3) and 14k – 8 equivalent
help please
Answers
Answer: No they are not
Step-by-step explanation:
Distribute the 4 from the left equation into the parenthesis.
you would get 20k - 12
that is not equivalent to 14k - 8
Larry sold 300 items in his sports memorabilia shop. 5 of the items sold 6 were football items. 20% of the other items sold were baseball items. What percent of the total items sold were baseball items?
Answers
Approximately 21.3 percent of the total items sold were baseball items.
Out of the 300 items sold, 5 of them were football items, so the number of non-football items sold is:
300 - 5 = 295
We know that 20% of the non-football items sold were baseball items, so the number of baseball items sold is:
0.20 * 295 = 59
Therefore, the total number of baseball and football items sold is:
59 + 5 = 64
The percentage of total items sold that were baseball items is:
(64 / 300) * 100% = 21.3%
Therefore, approximately 21.3 percent of the total items sold were baseball items.
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Height of 10th grade boys is normally distributed with a mean of 63. 5 in. And a standard deviation of 2. 9 in. The area greater than the z-score is the probability that a randomly selected 14-year old boy exceeds 70 in. What is the probability that a randomly selected 10th grade boy exceeds 70 in. ?Use your standard normal table.
Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard deviation of 2. 9 in. Find the z-score associated with the 96th percentile. Find the height of a 16-year-old boy in the 96th percentile. State your answer to the nearest inch
Answers
The probability that a randomly selected 10th grade boy exceeds 70 in is approximately 0.0127 or 1.27%.
The height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
For the first question, we need to find the z-score for a height of 70 inches using the formula:
z = (x - μ) / σ
where x is the height of 70 inches, μ is the mean of 63.5 inches, and σ is the standard deviation of 2.9 inches.
z = (70 - 63.5) / 2.9 = 2.241
Using a standard normal table, we can find the area to the right of this z-score, which represents the probability that a randomly selected 10th grade boy exceeds 70 inches. The area to the right of 2.24 is 0.0127. Therefore, the probability is approximately 0.0127 or 1.27%.
For the second question, we need to find the z-score associated with the 96th percentile using a standard normal table. The 96th percentile is the point below which 96% of the data falls and above which 4% of the data falls. This corresponds to a z-score of approximately 1.75.
To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:
x = μ + z * σ
where x is the height we want to find, μ is the mean of 68.3 inches, σ is the standard deviation of 2.9 inches, and z is the z-score we just found.
x = 68.3 + 1.75 * 2.9 = 73.28
Therefore, the height of a 16-year-old boy in the 96th percentile is approximately 73 inches.
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As Nancy's small insurance agency has grown, the spreadsheets they use to track income and expenses have become increasingly complex. Which feature of an AIS (Accounting Information System) would help Nancy to better manage income and expenses?
Answers
The income statement and Accounting Information System, along with the balance sheet and cash flow statement, help you understand your company's financial health.
MIS employs non-financial data, but AIS exclusively uses financial data.
MIS indirectly to other external users.
The income management account is most likely affected by Selling, General, and Administrative Expenses.
In accounting, an instrument that provides the data needed to effectively manage an organization and make decisions is a management information system (MIS).
It is used to locate, collect, process, and distribute economic data about a company to a variety of users (AIS).
MIS concentrates on the financial and accounting aspects of a business, diagnosing problems and proposing solutions. The former management system, that occasionally relied on intuition and unscientific approaches and was arbitrarily constructed, has been replaced with MIS.
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