Answers
Her next step in obtaining the area of the triangle is replacing the numeric values of h and y into the area formula.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The dimensions for this problem are given as follows:
Base of b = y.Height of h.Hence the formula is:
A = 0.5yh.
Hence the actual values of y and h must be inserted into the formula to obtain the area of the triangle.
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Related Questions
Given the circle below with secants
�
�
�
‾
KLM
and
�
�
�
‾
ONM
. If
�
�
=
13
,
�
�
=
12
LM=13,NM=12 and
�
�
KL is
3
3 less than
�
�
ON, find the length of
�
�
‾
ON
. Round to the nearest tenth if necessary.
Answers
The length of ON for the intersecting secants is derived to be equal to 14
What is the intersecting secant theoremThe intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
MK × KL = MO × MN
note that KL = (ON - 3) so;
[13 + (ON - 3)] × 13 = (12 + ON) × 12
13(10 + ON) = 144 + 12ON
130 + 13ON = 144 + 12ON
13ON - 12ON = 144 - 130 {collect like terms}
ON = 14
Therefore, the length of ON for the intersecting secants is derived to be equal to 14
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College Level Trigonometry Question Any Help will do
Answers
The expression of angle in radian is -0.071.
What is the measure of angles in radian?Angles can be measured in two units: degrees and radians.
Radian is a unit of measurement for angles, and it is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
To be more precise, an angle of one radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
The expression of angle in radian is calculated as follows;
θ = tan⁻¹ (-0.071)
θ = -0.071
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The vertices of AABC are A (-3, -6), B (-3,5), and C (5,5).
What is the area of AABC?
Answers
Answer:
44 units²-----------------------------
AB is vertical with same x-coordinates, and BC is horizontal with same y-coordinates.
Hence this is a right triangle.
Its area is:
A = 1/2 × AB × BCA = 1/2(5 - (-6))(5 - (-3)) = 1/2(11)(8) = 44 units²The wolf population in a certain region was monitored over several years for a project aimed at
boosting the number of wolves. The number of wolves can be modeled by the function
f(x)=41x +7 where x is the number of years since 2005. Using algebraic techniques, find the
value of x so that f(x) = 89.
Answers
Answer:
x=2
Step-by-step explanation:
f(x) is 89
f(x)=41x+7
89=41x+7
41x+7=89
41x=89-7
41x=81
x=81/41
x=2
PLEASE HELP ME WITH THE WHOLE PROBLEM PLEASEEEE
Answers
The probability of getting blue or green is 1/3, the probability of getting blue is 3/4 and there are 8 blue marbles.
What is the probability in each case?a) If the probability of getting a yellow marble is 2/3, then the probability of getting a blue or green marble is:
P(blue or green) = 1 - P(yellow) = 1 - 2/3 = 1/3
b) If the probability of getting a green marble is 1/4, then the probability of getting a blue marble is:
P(blue) = 1 - P(green) = 1 - 1/4 = 3/4
c) The total number of marbles in the bag is 24. Let x be the number of blue marbles. Then the number of yellow marbles is 2x, and the number of green marbles is 24 - x - 2x = 24 - 3x. We know that:
2x/24 = 2/3 (probability of getting a yellow marble is 2/3)
=> x = 8
Therefore, there are 8 blue marbles in the bag.
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find x, y, and z
will give brainly
Answers
Answers:
[tex]z=12\sqrt{3} \\y=12\\x=12\sqrt2[/tex]
PLEASE HELP!!!
The surface area of a triangular pyramid is 400 square meters. The surface area of a similar triangular pyramid is 25 square meters.
What is the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid?
Enter your answer by filling in the boxes.
Answers
Answer:
can i get a picture\
Step-by-step explanation:
thanks
Answer:
Step-by-step explanation:
1:4
) In the figure below, two secants are drawn to a circle from exterior point U.
Suppose that UW=40, UY=64, and UX= 8. Find UZ.
U
Answers
Applying the Intersecting Secants and Tangents Theorem, the measures are: CD = 19.5 units; UZ = 12.8 units
How to Apply the Intersecting Secants and Tangents Theorem?a. Apply the intersecting secant-tangent theorem to create the equation below:
EG² = EC * ED
Plug in the values:
13² = 6.5 * (6.5 + CD)
169 = 42.25 + 6.5CD
169 - 42.25 = 6.5CD
126.75/6.5 = CD
CD = 19.5 units
b. Apply the intersecting secants theorem to create the equation below:
UX * UY = UZ * UW
Plug in the values:
8 * 64 = UZ * 40
512/40 = UZ
UZ = 12.8
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what is equilivent to 28/2
Answers
Answer:
14
Step-by-step explanation:
28/2 is equivalent to 14. This is because when you divide a number by 2, you are essentially cutting it in half. So, 28/2 is the same as cutting 28 into two equal parts, which is 14.
Answer:
28
2
looks like a fraction but it is actually the whole number 14.
There is an infinity number of equivalent fractions to 28
2
.
To find an equivalent fraction to 28
2
, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:
By dividing the original fraction by 2, we get:
28 ÷ 2
2 ÷ 2
= 14
1
By multiplying the original fraction by 2, we get:
28 × 2
2 × 2
= 56
4
Here is the full list of equivalent fractions to 28
2
.
14
1
, 28
2
, 42
3
, 56
4
, 70
5
, 84
6
, 98
7
, 112
8
, 126
9
, 140
10
, 154
11
, 168
12
, 182
13
, 196
14
, 210
15
, 224
16
, 238
17
, 252
18
, 266
19
, 280
20
...
Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
g(x)
(Table)
0 1 2 3 4
1/2 1 2 4 8
A.They have the same y-intercept.
B.They have the same asymptote.
c. They have the same range.
D.They have the same domain.
Answers
The functions have the following characteristics:
A. They have the same y-intercept.
D. They have the same domain.
How to compare the graphs of the functionsWhen a function f(x) is transformed by multiplying its input by a constant "a", it results in a new function g(x) = f(ax). In this case, f(x) = 2x, so when we multiply x by a constant "a", we get g(x) = f(ax) = 2ax.
Therefore, the functions f(x) = 2x and g(x) = 2ax have the same y-intercept (0,0) and the same domain (-∞, +∞).
The range of g(x) is determined by the value of "a", which is different from the range of f(x), so option C is not correct. Asymptotes are not relevant for linear functions, so option B is not correct.
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A company sells cereal in two different-sized boxes. The smaller box has the dimensions shown below. The height of the smaller box is 80% of the height of the larger box, while the other two dimensions are the same for both boxes. What is the volume of the two boxes?
Answers
Since the other two dimensions are the same for both boxes, we only need to compare the volumes based on their height.
Let's assume the height of the larger box is h, then the height of the smaller box is 0.8h.
The volume of the larger box is:
V1 = lwh = (8)(11)(h) = 88h
The volume of the smaller box is:
V2 = lwh = (8)(11)(0.8h) = 70.4h
Therefore, the volume of the larger box is 88h and the volume of the smaller box is 70.4h.
Let H be the height of the larger box. Then the height of the smaller box is 0.8H.
The volume of the larger box is given by:
V_large = L × W × H
The volume of the smaller box is given by:
V_small = L × W × 0.8H
Since the length and width are the same for both boxes, we can factor them out:
V_large = L × W × H
= (L × W × 1) × H
= A × H
V_small = L × W × 0.8H
= (L × W × 0.8) × H
= 0.8A × H
where A = L × W is the area of the base of each box.
Therefore, the volume of the smaller box is 0.8 times the volume of the larger box.
We can also write this as:
V_small/V_large = 0.8
So, if we know the volume of one of the boxes, we can find the volume of the other box by multiplying by 0.8.
Without specific information about the dimensions of the boxes, we cannot calculate their volumes.
Find the value of 11 3/8 -7/8
Answers
The value of 11 3/8 -7/8 is 10 1/2
What is subtraction?Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60
Solving 11 3/8 -7/8
= 91/8 - 7/8
= (91-7)/8
= 84/8
= 21/2
= 10 1/2
Therefore the value of 11 3/8 -7/8 is 10 1/2
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In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows:
Company A: 9.3; 8.8; 6.8; 8.7; 8.5; 6.7; 8.0; 6.5; 9.2; 7.0
Company B: 11.0; 9.8; 9.9; 10.2; 10.1; 9.7; 11.0; 11.1; 10.2; 9.6
i. Calculate the sample mean and median for the data for the two companies.
ii. Plot the data for the two companies on the same line/chart and give your impression regarding any apparent differences between the two.
iii. Is there any relation between the two companies? Compare using the 90% confidence interval of the mean.
iv. Which company you will recommend
Answers
i. The sample mean and median for the data for the two companies are 8.1 and 8.25 respectively.
ii. The line graph of the data is illustrated below.
iii. Yes, The steel rods supplied by Company B may be more flexible than those supplied by Company A.
iv. If you are looking for steel rods with higher flexibility, I would recommend Company B based on the higher median, the apparent differences in the box and whisker plot, and the confidence interval indicating a higher mean flexibility for their rods.
For Company A, the sample mean can be calculated by adding all the values and dividing by the number of values:
Mean of Company A = (9.3 + 8.8 + 6.8 + 8.7 + 8.5 + 6.7 + 8.0 + 6.5 + 9.2 + 7.0) / 10 = 8.1
To find the median, we first need to arrange the data in ascending order:
6.5, 6.7, 6.8, 7.0, 8.0, 8.5, 8.7, 8.8, 9.2, 9.3
Since there are an even number of values, the median is the average of the two middle values:
Median of Company A = (8.0 + 8.5) / 2 = 8.25
For Company B, the sample mean can be calculated similarly:
Mean of Company B = (11.0 + 9.8 + 9.9 + 10.2 + 10.1 + 9.7 + 11.0 + 11.1 + 10.2 + 9.6) / 10 = 10.2
Arranging the data in ascending order, we get:
9.6, 9.7, 9.8, 9.9, 10.1, 10.2, 10.2, 10.2, 11.0, 11.1
Since there are an odd number of values, the median is the middle value:
Median of Company B = 10.2
Next, let's plot the data for both companies on the same chart and observe any apparent differences. We can use a box and whisker plot to do this.
Looking at the box and whisker plot, we can see that the median of Company B (represented by the line in the middle of the box) is higher than the median of Company A. Additionally, the box for Company B is taller than the box for Company A, indicating that the range of values for Company B is greater than that of Company A. These observations suggest that the steel rods supplied by Company B may be more flexible than those supplied by Company A.
To determine if there is a significant difference between the means of the two companies, we can use a 90% confidence interval of the mean. This interval gives us a range within which we can be 90% confident that the true population mean lies.
Using a t-distribution with 18 degrees of freedom (10 + 10 - 2), we can find the 90% confidence interval for the difference between the means of the two companies. The formula for the confidence interval is:
Difference in means ± (t-value x standard error of difference in means)
The t-value for a 90% confidence interval with 18 degrees of freedom is approximately 1.734.
Now, we can calculate the margin of error by multiplying the t-value (1.734) by the standard error:
Margin of Error = 1.734 * 0.393 ≈ 0.682
Finally, we can construct the 90% confidence interval for the difference in means as:
Difference in means ± Margin of Error
Calculating the difference in means (mean of Company B - mean of Company A), we have:
Difference in means = 10.2 - 8.1 = 2.1
Therefore, the 90% confidence interval is:
2.1 ± 0.682
This means that we can be 90% confident that the true population mean difference between the two companies' steel rods lies between 1.418 and 2.782.
Based on this analysis, we can conclude that Company B tends to supply steel rods that are more flexible compared to Company A. However, it's important to note that this study was conducted on a small sample size, so further investigation with larger sample sizes would be beneficial to confirm the findings.
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HOW TO SOLVE LINEAR REGRESSIONS
Answers
A good rule of thumb is to save 10 percent of what you earn, and have at least three months' worth of living expenses saved up in case of an emergency.
False
True
Answers
Answer:
False
Step-by-step explanation:
you have to save at least 20 percent
2. Ricky wants to make rice cream. Of 1 kilogram of rice, milk2/5 is rice and 1/6 is sugar. Find the quantity of rice and sugar needed for 1 kg of rice milk.
Answers
The quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
To solve the above problem, we can use the following equation:
Rice + Milk + Sugar = 1 kg
Rice = 2/5 (1 kg) = 0.4 kg
Milk = 2/5 (1 kg) = 0.4 kg
Sugar = 1/6 (1 kg) = 0.167 kg
Therefore, the quantities of rice, milk and sugar needed for 1 kg of rice milk are 0.4 kg, 0.4 kg and 0.167 kg respectively.
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The slope of the line whose equation is 5x - 3y = 4 is 4/5 5/3 -3/5
Answers
The slope of the relation with the equation 5x - 3y = 4 is 5/3
Calculating the slope of the relationTo find the slope of the line whose equation is 5x - 3y = 4, we need to rearrange the equation to be in slope-intercept form, y = mx + b, where m is the slope of the line.
First, we'll subtract 5x from both sides:
-3y = -5x + 4
Next, we'll divide both sides by -3 to isolate y:
y = (5/3)x - 4/3
Now we can see that the slope of the line is 5/3.
So the correct answer is: 5/3
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Correct answer gets brainliest!!!!
Answers
Answer: 5
Step-by-step explanation:
They are the points
There are 5 points so answer is 5
Step 1: Understand the Problem
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 190 miles per week to commute to work. With gas prices currently at $
2.9 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 18 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $
770 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $
6,500 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $
10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
Step 3: Apply Quantitative Tools
Use computational and algebraic tools to quantify the total costs (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Scenario
Total Cost for Three Years
Keep the old car
$
Number
Buy the fuel-efficient used car
$
Number
Answers
Total cost of keeping the old car = (Gas cost + Maintenance cost) x 3 years
Total cost of buying the used car = (Purchase price + Gas cost + Maintenance cost) + (Interest on loan)
Using the given information, we can calculate the total cost for each scenario:
Total cost of keeping the old car = ($2.9/gallon x 190 miles/18 miles per gallon + $770) x 3 = $10,768
Total cost of buying the used car = ($6,500 + $2.9/gallon x 190 miles/32 miles per gallon + $10 per month) + (Interest on loan) = $9,425 + (Interest on loan)
Based on the given information, buying the used car would be the better financial decision as it would cost less over three years. However, without knowing the interest rate on the loan, we cannot accurately calculate the total cost of buying the used car.
PLEASE HELP ME!!!!!
Write the expression of the graph the function represents.
Answers
The expression of the function which is represented by the given graph is given by,
xy = -8
The given figure is a rectangular hyperbola.
So the equation of the given graphed curve be, xy = c, where c is a constant.
We can clearly see that the curve passes through the point with coordinates (-2, 4). So it must satisfy the equation of the curve.
Substituting the point (-2, 4) in the equation of the curve xy = c we get,
(-2)*4 = c
c = -8
Hence the expression for the graph the function represents is given by,
xy = -8.
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Rafael finished the Boston Marathon ( 26.2 miles) in 4.75 hours. At this pace, how long would it take him to run a 50 mile marathon in Washington D.C?
Answers
The time taken by the runner is equal to 9.064 hours.
How to determine the time taken by a runner
In this problem we find the case of runner taking a time (t), in hours, to run a certain distance (d), in miles, at constant speed (v), in miles per hour. The kinematic equation is now introduced:
v = d / t
Now we proceed to determine the missing time:
(26.2 mi) / (4.75 hours) = (50 mi) / t
t = 9.064 h
The runner takes a time of 9.064 hours to run a distance of 50 miles.
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If cosθ=-1/3 and θ is in quadrant III, find the exact values of sinθ,tanθ,secθ,cscθ,and cotθ. You can use the identities or x, y, r.
Answers
The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
Given: cosθ = -1/3 and θ is in quadrant III.
This means that sinθ = ± √(1 - (cosθ)2).
We know that cosθ is negative, so sinθ will be negative.
Therefore, sinθ = -√(1 - (-1/3)2 )
sinθ = - √(1 - 1/9)
sinθ = -√8/9
tanθ = sinθ/cosθ
tanθ = (-√8/9)/-1/3
tanθ = √8/3
secθ = 1/cosθ
secθ = 1/-1/3
secθ = -3
cscθ = 1/sinθ
cscθ = 1/-√8/9
cscθ = -√9/8
cotθ = cosθ/sinθ
cotθ = -1/3/-√8/9
cotθ = √9/8
Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.
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Brent starts with 16 identical white socks in his sock drawer. Imagine he receives 2 identical black socks as a gift and mixes them in with his 16 white socks. If he draws one sock without looking to put on his left foot, then draws a second sock without looking to put on his right foot, what is the probability that he draws mismatched socks?
Answers
The probability that Brent draws mismatched socks is approximately 31/153.
After adding 2 identical black socks, Brent has a total of 18 socks in his drawer. The probability of drawing a white sock on the first draw is 16/18 (since there are 16 white socks out of 18 total socks).
After drawing a white sock on the first draw, there are 15 white socks and 2 black socks left in the drawer. The probability of drawing a black sock on the second draw is 2/17 (since there are 2 black socks out of 17 total socks left). So the probability of drawing a white sock followed by a black sock is;
(16/18) × (2/17) = 32/306
Similarly, the probability of drawing a black sock followed by a white sock is;
(2/18) × (15/17) = 30/306
However, the probability of drawing mismatched socks is;
32/306 + 30/306 = 62/306
= 31/153
Therefore, the probability will be 31/153.
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A woman earned wages of 33,900 receive 2600 and interest from savings account and contributed 3600 to tax deferred retirement plan she was entitled to a personal exemption of 3500 and her deductions totaling 5440 find her gross income adjusted income and taxable income
Answers
The woman's gross income, adjusted income and taxable income are:
gross income - $ 36, 500adjusted income - $ 32, 900taxable income -$ 23, 960How to find the types of income ?The gross income to the woman is:
= Wages + interest
= 33, 900 + 2, 600
= $ 36, 500
The adjusted gross income :
= Gross income - Retirement plan contribution
= 36, 500 - 3, 600
= $ 32, 900
The taxable income ;
= AGI - Personal exemption - Deductions
= 32, 900 - 3, 500 - 5, 440
= $ 23, 960
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Find the exact value of each of the following:
a)4sin(π/6)+tan(π/4)
b)cos(4π/3) tan(330°)-sin(3π/4)
Answers
The exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
How to solvea) In order to ascertain the precise value of 4sin(π/6) + tan(π/4), we must first evaluate the trigonometric functions involved: sin(π/6) = 1/2 and tan(π/4) = 1.
Now, by substituting these values in the equation, we get
4(1/2) + 1 = 2 + 1 = 3.
b) To calculate cos(4π/3) tan(330°) - sin(3π/4), it is necessary to convert 330° into radians: (330 * π) / 180 = 11π/6.
After setting this conversion, evaluate the trigonometric functions present: cos(4π/3) = -1/2, tan(11π/6) = √3, and sin(3π/4) = √2/2.
When these values are used within the equation, the result is (-1/2)(√3) - (√2/2) which equals -√3/2 - √2/2.
Ergo, the exact values for both equations are as follows:
a) 3
b) -√3/2 - √2/2
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what are the answers to these questions?
Answers
The height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.
The total surface area of the can is therefore:
A = 2πr² + 2πrh
We know that the volume of the can is 810 cm³, which is given by:
V = πr²h
We can solve this equation for h to get:
h = V/(πr²)
Substituting this expression for height h into the equation for the surface area, we get:
A = 2πr² + 2πr(V/(πr²))
Simplifying, we get:
A = 2πr² + 2V/r
Now we have an equation for the surface area of the can in terms of the radius, r.
To minimize the surface area, we need to take the derivative of this equation with respect to r, set it equal to zero, and solve for r.
dA/dr = 4πr - 2V/r² = 0
Solving for radius r, we get:
[tex]r = (810/\pi)^1^/^3[/tex]
r=∛810/3.14
r=6.35 cm
Now find h:
h = 810/πr²
h=810/3.14×6.35²
h=810/126.6
h=6.39 cm
Hence, the height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.
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The formula v= √√2gh gives the velocity v, in feet per second, of an object after it falls h feet accelerated by gravity g, in feet
per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 96 feet
per second.
Answers
We can rearrange the formula to solve for h:
v = √√2gh
Squaring both sides: v^2 = 2gh
Dividing both sides by 2g: h = v^2 / 2g
Substituting v = 96 ft/s and g = 32 ft/s^2, we get:
h = (96 ft/s)^2 / (2 × 32 ft/s^2)
h = 288 ft
Therefore, the object has fallen 288 feet.
Alexander deposits $3,200 into a savings account that has a simple interest rate of 1%. If interest is calculated quarterly, which statement is true?
Select one:
a.
He will earn $8 in interest each quarter, totaling $32 in interest for the year
b.
He will earn $32 in interest at the end of one year
c.
He will earn $0.80 in interest each quarter, totaling $3.20 in interest for the year
d.
He will earn $3.20 in interest at the end of one year
Answers
The TRUE statement about Alexander's deposit of $3,200 into a savings account that has a simple interest rate of 1% calculated quarterly is a. He will earn $8 in interest each quarter, totaling $32 in interest for the year.
What is the simple interest?Simple interest describes an interest system that does not compound the interest.
Compounding involves charging interest on both interest and principal.
For the simple interest system, the interest amount is computed only on the principal, using the following SI formula.
Principal deposit, P = $3,200
Interest rate, R = 1%
Interest period, P = 1 year
Interest system = Simple interest quarterly
Simple interest (SI) formula = P x R x T
Simple interest for each quarter = $8 ($3,200 x 0.01 x 1/4)
Simple interest for the year = $32 ($3,200 x 0.01)
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A tunnel is shaped in the form of a semi-ellipse. The width of the tunnel is 20 feet and the height of the tunnel is 12 feet. A train is 10 feet wide and centered in the tunnel. Determine whether a 10-foot high train would have clearance to pass through. If so, by how much? If not, by how much? (Nearest inch.)
Answers
(x^2 / a^2) + (y^2 / b^2) = 1
where "a" is the horizontal radius (half of the width) and "b" is the vertical radius (half of the height).
In this case, we have:
a = 20/2 = 10 feet
b = 12/2 = 6 feet
We can assume that the train is centered in the tunnel, so we need to find the height of the semi-ellipse at the center (i.e., the value of "y" when "x" is 0).
Plugging in the values for "a" and "b", we get:
(0^2 / 10^2) + (y^2 / 6^2) = 1
Simplifying, we get:
y^2 / 36 = 1
y^2 = 36
y = ±6 feet
Therefore, the height of the semi-ellipse at the center is 6 feet.
To determine whether a 10-foot high train would have clearance to pass through, we need to check whether the height of the semi-ellipse at the sides is greater than or equal to 10 feet.
Plugging in the values for "a" and "b" and solving for "y" when "x" is 5 feet (half of the train's width), we get:
(5^2 / 10^2) + (y^2 / 6^2) = 1
Simplifying, we get:
y^2 / 36 = 0.75
y^2 = 27
y ≈ ±5.2 feet
Since the height of the semi-ellipse at the sides is about 5.2 feet, a 10-foot high train would not have clearance to pass through. The clearance is less than 5.2 - 5 = 0.2 feet (or about 2.4 inches).
Therefore, the train would not fit through the tunnel with 10 feet of clearance.
Find the slope of the line represented
by the data below.
x 2 4 6 8
-3 39
3
9 15
y|-3
Simplify completely.
Slope = [?
Hint: The slope of a line is the
Change in y
Change in x
Answers
3 - (-3) / 4 - 2
3+3/2
6/2 = 3
Slope is 3