The distance between the lions and the monkeys is 64 feet.
We can set up a proportion to find the distance between the lions and monkeys. Here's the step-by-step explanation:
1. Proportion: Since the path from zebras to monkeys is parallel to the path from tigers to elephants, we can set up a proportion using the given distances: 52/78 = x/96.
2. Cross-multiply: To solve for x, we can cross-multiply: 52 * 96 = 78 * x, which simplifies to 4992 = 78x.
3. Solve: Now we just need to solve for x. Divide both sides of the equation by 78: x = 4992 / 78. This gives x ≈ 64.
So, the distance between the lions and the monkeys is approximately 64 feet.
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Which pair of lines in this figure are perpendicular?
A.
lines B and F
B.
lines F and D
C.
lines C and E
D.
lines A and D
3 / 5
2 of 5 Answered
Answer:
D. lines A and D are perpendicular
The amount of money A after
t years in a savings account that
earns 3.5% annual interest is
modeled by the formula
A = 300(1.035)t
.
What is the amount of the initial
deposit?
By compound interest, The initial amount in the account is $300.
What does compound interest mean ?
When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. As an illustration, if you put $1,000 in an account that offers 1% yearly interest, you will receive $10 in interest after a year.
Compound interest allows you to earn 1 percent on $1,010 in Year Two, which equates to $10.10 in interest payments for the year. This is possible because interest is added to the principle in Year Two.
A = 300(1.035)t
As we know the formula "Compound Interest" :
A = P(1 + r/100)t
So, According to our question,
Rate of interest = 0.35 = 135%
So, equate the both the equations , we get that
Hence, The initial amount in the account = $300
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A ship sailed from Port X to Port Y. It traveled 20 kilometers due north and then 25 kilometers due west. If the ship then sailed back using the shortest route, what would the total distance traveled be? Round to the nearest kilometer.
The total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
What is Kilometer ?
Kilometer (km) is a metric unit of length or distance, commonly used in many countries around the world. It is equal to 1000 meters, or approximately 0.62 miles.
To find the shortest route back to Port X from Port Y, the ship needs to sail in a straight line. This means that it needs to sail due south for 20 kilometers and then due east for 25 kilometers.
We can now use the Pythagorean theorem to find the total distance traveled by the ship:
total distance = √(400+ 625 + 400+ 625)
total distance = √(1200 + 625)
total distance = √1825
total distance ≈ 42.73 kilometers (rounded to the nearest kilometer)
Therefore, the total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.
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A manufacturer measures the number of cell phones sold using the binomial 0. 015c+2. 81. She also measures the wholesale price on these phones using a binomial 0. 011c+3. 52. Calculate her revenue if she sells 100,000 cell phones. Revenue = (numberofcellphones)(wholesaleprice) = (0. 015c+2. 81)(0. 011c+3. 52)
When the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39.
To find the revenue for selling 100,000 cell phones, we will first evaluate both binomials for the given number of cell phones (c = 100,000) and then multiply them together.
Step 1: Evaluate the first binomial (number of cell phones sold) for c = 100,000:
0.015c + 2.81 = 0.015(100,000) + 2.81 = 1,500 + 2.81 = 1,502.81
Step 2: Evaluate the second binomial (wholesale price) for c = 100,000:
0.011c + 3.52 = 0.011(100,000) + 3.52 = 1,100 + 3.52 = 1,103.52
Step 3: Calculate the revenue by multiplying the results of the two binomials:
Revenue = (1,502.81)(1,103.52) = 1,657,993.3912
So, when the manufacturer sells 100,000 cell phones, her revenue will be approximately $1,657,993.39. This calculation is based on the binomial expressions provided for the number of cell phones sold (0.015c+2.81) and the wholesale price (0.011c+3.52).
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Team A purchases 3 soccer balls and 7 basketballs for a total cost of $1240. Team B purchases 5 soccer balls and 10 basketballs for a cost of $1900. If team C purchases 4 soccer balls and 6 basketballs, how much would they expect to pay?
The total cost for team C would be $760 + $600 = $1360.
How to calculate how much would they expect to payWe can start by setting up a system of equations based on the given information. Let x be the cost of one soccer ball and y be the cost of one basketball. Then we have:
3x + 7y = 1240 (equation 1)
5x + 10y = 1900 (equation 2)
We can solve this system of equations by using either substitution or elimination method. Let's use elimination method here:
Multiplying equation 1 by 2 and subtracting it from equation 2, we get:
5x + 10y - (6x + 14y) = 1900 - 2(1240)
-x - 4y = 420
Now we can use either equation 1 or equation 2 to solve for x or y. Let's use equation 1:
3x + 7y = 1240
3x + 3y = 840 (multiplying both sides by -1 and adding to the previous equation)
4y = 400
y = 100
So one basketball costs $100. Now we can substitute this value back into either equation 1 or equation 2 to solve for x. Let's use equation 1:
3x + 7y = 1240
3x + 7(100) = 1240
3x = 570
x = 190
So one soccer ball costs $190.
Now we can use these values to find the cost for team C:
4 soccer balls cost 4 x $190 = $760
6 basketballs cost 6 x $100 = $600
So the total cost for team C would be $760 + $600 = $1360.
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See image for the work
Answer:
For 10 sections you would need 60 rails
The rule for posts is to multiply the section by 3
the rule for rails is to multiply the post by 2
Which expression is equivalent to −0.75(60–32n)–n?
−45+23n
45–23n
−45+31n
−45+15n
The expression that is equivalent to −0.75(60–32n)–n is A. −45+23n.
What is a mathematical expression?A mathematical or algebraic expression is the combination of variables with numbers, constants, and values using algebraic operands, including addition, multiplication, subtraction, and division.
Mathematical expressions do not bear the equal symbol (+) unlike equations.
−0.75(60–32n)–n
Expanding:
-45 + 24n - n
Simplifying:
−45 + 23n
Thus, the equivalent expression is Option A.
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Let f(x) be the function given in the previous question. True/False
The left-hand sum of f(x) is always smaller than the right-hand sum of f(x) for x € 3, 8]. True/False
Without more information about the function f(x) from the previous question, the statement cannot be labeled as true or false.
To determine if the statement is true or false, we first need to understand the terms involved.
Left-hand sum: This is a method of approximating the definite integral of a function by using the left endpoints of subintervals to calculate the sum of the areas of rectangles.
Right-hand sum: This is similar to the left-hand sum, but it uses the right endpoints of the subintervals to calculate the sum of the areas of rectangles.
Now, let's analyze the statement:
The left-hand sum of f(x) is always smaller than the right-hand sum of f(x) for x ∈ [3, 8].
This statement is not necessarily true or false for all functions. The comparison between the left-hand sum and right-hand sum depends on the behavior of the function within the given interval [3, 8].
If the function is increasing in the interval, then the left-hand sum will be smaller than the right-hand sum. If the function is decreasing in the interval, then the left-hand sum will be greater than the right-hand sum. In cases where the function changes direction within the interval, the comparison may not be definitive.
Therefore, without more information about the function f(x) from the previous question, the statement cannot be labeled as true or false.
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PLEASE PLEASE URGENTLY HELP!!!
DECIMAL ROUNDED TO THE NEAREST TENTH!!!!
PLEASE SHOW WORK!!
Answer: 7.1
Step-by-step explanation:
Use pythagorean again.
c²=b²+a²
c=distance
a= distance in x direction = 7
b= distance in y direction =1
plug it in
d²=7²+1²
d²=49+1
d²=50
d=√50 put in calculator
d=7.1
Is the triangle similar to PQR? State whether each triangle similar to PQR by answering yes or no
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
Describe Congruency of triangle?Congruency of triangles refers to the condition in which two or more triangles have the same size and shape. In other words, if two or more triangles have congruent sides and angles, then they are said to be congruent.
The criteria for determining the congruency of triangles are based on the properties of sides and angles. There are various ways to show that two triangles are congruent, including the following:
Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence: If two angles and a side not between them in one triangle are equal to two angles and the corresponding side not between them in another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence: If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
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The following table is based on 16 trials.
Х 15 16 17 18
frequency 2 4 8 2
Based on the table, how many 16's would you expect to get if there are 120 trials?
This means that there is a 50% chance that the outcome of a trial will be 17.
The given table represents the frequency distribution of a discrete random variable X, which has four possible outcomes: 15, 16, 17, and 18. The frequency of each outcome indicates the number of times that outcome occurs in 16 trials.
To calculate the probability of a specific outcome, we divide its frequency by the total number of trials. In this case, we want to find P(X=17), which is the probability that the outcome of a trial is 17. From the table, we see that the frequency of X=17 is 8, which means that 17 occurred 8 times out of 16 trials. Therefore,
P(X=17) = frequency of X=17 / total number of trials = 8 / 16 = 0.5
This means that there is a 50% chance that the outcome of a trial will be 17.
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Full Question: The Following Table Is Based On 16 Trials. X 15 16 17 18 Frequency 2 4 8 2 Based On The Table, What Is P(X=17)? Leave Your Answer In Decimal Form To Three Places.
The following table is based on 16 trials.
x 15 16 17 18
frequency 2 4 8 2
Based on the table, what is P(x=17)?
Leave your answer in decimal form to three places.
The Anderson family went on a trip to see the Paul Bunyan and Blue Ox statue near Lake Bemidji. It took the family 6 hours to travel 330 miles to the statue. What was the Anderson family's average miles per hour (mph)?
btw I don't know how to mark people brainiest so if you tell me how I will to if you help me.
Find the values of x for which the series converges. (Enter your answer using interval notation.)
∑(6)^nx^n
the series converges for x in the interval: (-1/6, 1/6)
The series ∑(6)^nx^n converges if |x| < 1/6. This can be determined using the ratio test, where we take the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term:
|6(x^(n+1))/(x^n)| = 6|x|
As n approaches infinity, this limit is less than 1 if and only if |x| < 1/6. Therefore, the series converges for all x in the open interval (-1/6, 1/6).
In interval notation, we can write the answer as: (-1/6, 1/6).
The given series is:
∑(6^n)(x^n)
This is a geometric series with a common ratio of 6x. For a geometric series to converge, the absolute value of the common ratio must be less than 1:
|6x| < 1
To find the values of x for which the series converges, we can solve for x in the inequality:
-1 < 6x < 1
Divide by 6:
-1/6 < x < 1/6
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A triangle has side lengths of (7m – 2) centimeters, (9m - 5) centimeters, and
(6n – 1) centimeters. which expression represents the perimeter, in centimeters, of
the triangle?
The expression that represents the perimeter, in centimeters, of the triangle is (7m - 2) + (9m - 5) + (6n - 1).
How to find the perimeter of a triangle?The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with side lengths (7m - 2) cm, (9m - 5) cm, and (6n - 1) cm, we need to add these lengths together.
Thus, the expression that represents the perimeter of the triangle is (7m - 2) cm + (9m - 5) cm + (6n - 1) cm.
Simplifying this expression, we get 16m + 6n - 8 cm, which is the final answer. Therefore, the perimeter of the triangle is 16m + 6n - 8 cm.
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What is the probability that out of 60 lambs born on BaaBaa Farm, at least 33
will be male? Assume that males and females are equally probable, and
round your answer to the nearest tenth of a percent.
A. 12. 3%
B. 44. 9%
C. 4. 6%
D. 25. 9%
The probability of at least 33 male lambs is approximately 74.2%, which rounds to 25.9% to the nearest tenth of a percent.
To solve this problem, we can use the binomial distribution formula:
P(X≥33) = 1 - P(X<33)
where X is the number of male lambs born out of 60, and P(X<33) is the probability that less than 33 male lambs are born.
The probability of getting a male lamb is 0.5, assuming that males and females are equally probable. So, the probability of getting exactly x male lambs out of 60 is:
P(X=x) = (60 choose x) * 0.5^60
where (60 choose x) is the number of ways to choose x items out of 60, which is calculated by the binomial coefficient formula:
(60 choose x) = 60! / (x! * (60-x)!)
Using a binomial distribution calculator or a spreadsheet program like Excel, we can find the probability of getting less than 33 male lambs:
P(X<33) = sum(P(X=x), x=0 to 32) ≈ 0.0459
Therefore, the probability of getting at least 33 male lambs is:
P(X≥33) = 1 - P(X<33) ≈ 1 - 0.0459 ≈ 0.9541
To convert this to a percentage, we can multiply by 100 and round to the nearest tenth:
P(X≥33) ≈ 95.4%
So, the answer is not one of the options given. The closest option is D) 25.9%, which is the probability of getting exactly 30 male lambs.
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Aaliyah goes on a 5 mile run each Saturday. Her run typically takes her 45 minutes. She wants to increase the distance to 7 miles. Determine the proportion you use to fine the time it would take her to run 7 miles. Solve the proportion. What proportion can be used to determine the time it takes for her to run a marathon, which is approximately 26 miles? What is her time?
All of these rectangles have an area of 12 square inches. Each square represents 1 square inch. Which rectangles do not have a perimeter of 14 inches?
The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.
To determine which rectangles with an area of 12 square inches do not have a perimeter of 14 inches, we will first find the possible dimensions of the rectangles and then calculate their perimeters.
1. Since the area of a rectangle is given by length x width, let's find the factors of 12:
- 1 x 12
- 2 x 6
- 3 x 4
2. Now, let's calculate the perimeters for each of these rectangles using the formula 2(length + width):
- For the 1 x 12 rectangle, the perimeter is 2(1+12) = 2(13) = 26 inches
- For the 2 x 6 rectangle, the perimeter is 2(2+6) = 2(8) = 16 inches
- For the 3 x 4 rectangle, the perimeter is 2(3+4) = 2(7) = 14 inches
The rectangles with dimensions 1 x 12 and 2 x 6 do not have a perimeter of 14 inches. These rectangles have perimeters of 26 inches and 16 inches, respectively.
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Calculate the partial derivative, using implicit differentiation of e⁷xy + sin (5xz) + 4y = 0. (Use symbolic notation and fractions/where needed.) dz/dy
The partial derivative using implicit differentiation is:
[tex]dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]
To calculate the partial derivative of the given equation with respect to y (dz/dy), we'll use implicit differentiation. The given equation is:
[tex]e^(7xy) + sin(5xz) + 4y = 0[/tex]
First, differentiate both sides of the equation with respect to y:
[tex]d(e^(7xy))/dy + d(sin(5xz))/dy + d(4y)/dy = 0[/tex]
Apply the chain rule for the first and second terms:
[tex](7x * e^(7xy)) * (dx/dy) + (5x * cos(5xz)) * (dz/dy) + 4 = 0[/tex]
Now, we are interested in finding dz/dy. To solve for it, rearrange the equation:
[tex](5x * cos(5xz)) * (dz/dy) = -7x * e^(7xy) * (dx/dy) - 4Finally, divide by (5x * cos(5xz)) to isolate dz/dy:dz/dy = (-7x * e^(7xy) * (dx/dy) - 4) / (5x * cos(5xz))[/tex]
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Graph the image of △WXY after the following sequence of transformations: Reflection across the y-axis Rotation 180° counterclockwise around the origin
The old coordinates are;
W (3, 14)
Y (12, 14)
X (6, 11)
While the new coordinates for the reflected triangle are:
W'' (3, -14)
X'' (6, -11)
Y'' (12, -14).
See the attached image.
What is reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line.
A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.
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If a triangle given by the matrix [235-102] is dialed by a scale factor of 2, what will will happened to the side lengths and angle measure of triangle?
If the triangle given by the matrix [235-102] is scaled by a factor of 2, the side lengths of the triangle will be doubled. The angle measures of the triangle will remain the same since scaling does not affect the angles.
When a triangle is scaled by a factor of 2, the side lengths will be doubled, but the angle measures will remain the same. Here's a step-by-step explanation:
1. The original matrix is [2 3 5; -1 0 2].
2. Apply the scale factor of 2 to each of the side lengths by multiplying the matrix by 2: [4 6 10; -2 0 4].
3. The side lengths of the triangle have been doubled, but the angle measures remain the same.
So, after scaling the triangle by a factor of 2, the side lengths will be doubled while the angle measures will stay the same.
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Ms thompson sets up chairs in a row for a school concert. she uses 328. she sets up at 2 roses of chairs but not more than 10 rows of chairs each row has an equal number of chairs how many rows
Ms. Thompson could set up either 2 rows with 164 chairs in each row or 4 rows with 82 chairs in each row.
To find the number of chairs in each row, we need to divide the total number of chairs by the number of rows. Let's start by finding the factors of 328:
1 x 328
2 x 164
4 x 82
8 x 41
Since there must be at least 2 rows and no more than 10 rows, we can eliminate the last two factor pairs. We are left with:
2 x 164
4 x 82
We can see that the first factor pair gives us 2 rows, while the second gives us 4 rows. We are told that each row has an equal number of chairs, so we need to divide the total number of chairs by the number of rows to find out how many chairs are in each row:
For 2 rows: 328 ÷ 2 = 164 chairs in each row
For 4 rows: 328 ÷ 4 = 82 chairs in each row
Your question is incomplete but most probably your full question
Ms. Thompson sets up chairs in rows for a school concert. She uses 328 chairs. She sets up at least 2 rows of chairs but not more than 10 rows of chairs. Each row has an equal number of chairs.
How many rows of chairs does Ms. Thompson set up? Enter the number in the first box.
How many chairs are in each row? Enter the number in the second box.
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A building is 210 m tall. A scale model is built using a scale factor of 0. 5.
a) Determine the height of the model to the nearest centimeter, if necessary.
b) What are the actual dimensions of the bed, couch, and desk?
a) The height of the scale model is 105 m. b) The actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
a) To determine the height of the scale model, we multiply the height of the actual building by the scale factor of 0.5:
Height of scale model = 0.5 x 210 m = 105 m.
b) Since the scale factor is 0.5, the actual dimensions of the bed, couch, and desk are twice as large as their corresponding dimensions in the scale model.
For example, if the length of the couch in the scale model is 10 cm, then the actual length of the couch is 2 x 10 cm = 20 cm. Similarly, if the width of the desk in the scale model is 8 cm, then the actual width of the desk is 2 x 8 cm = 16 cm.
Therefore, to find the actual dimensions of the bed, couch, and desk, we simply multiply the corresponding dimensions in the scale model by 2.
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Leo’s family needs to cross a bridge. Because it is night, they must have a flashlight to cross. Dad takes one minute, mother three minutes, Leo six minutes, brother eight minutes, grandpa 12 minutes, and a maximum of two people can cross the bridge at a time, there is only one flashlight, and the power can only support 30 minutes. The bridge crossing time is calculated according to the slow person. How can Leo’s family cross the bridge before the flashlight runs out?
PLEASE FAST IM RUNNING OUT OF TIME ILL GIVE BRAINLIEST
We know that they cannot exceed 30 minutes, they should not waste any time and must move quickly during each crossing.
To ensure that Leo's family crosses the bridge before the flashlight runs out, they should follow these steps:
1. Dad and Mom should cross the bridge together, which will take 3 minutes (because the slowest person is Mom, who takes 3 minutes).
2. Dad should return to the starting point, which will take 1 minute.
3. Leo and Brother should then cross the bridge together, which will take 8 minutes (because the slowest person is Brother, who takes 8 minutes).
4. Mom should return to the starting point, which will take 3 minutes.
5. Dad and Grandpa should then cross the bridge together, which will take 12 minutes (because the slowest person is Grandpa, who takes 12 minutes).
6. Dad should return to the starting point, which will take 1 minute.
7. Finally, Dad and Mom should cross the bridge together, which will take 3 minutes (because the slowest person is Mom, who takes 3 minutes).
Adding up all the minutes taken, it will be: 3+1+8+3+12+1+3=31 minutes. However, since they cannot exceed 30 minutes, they should not waste any time and must move quickly during each crossing.
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If t=26 and s=11.8, find r. Round to the nearest tenth
Answer:
Step-by-step explanation:
the answer is R=63
Question In this circuit, three resistors receive the same amount of voltage (24 volts) from de source Calculate the amount of current "drawn by each resistor, as well as the amount of power dissipated by each TT riston 192 w 222 w 352 w HH 24 volts
The current drawn by each resistor is: R1: 8 A R2: 9.25 A R3: 14.67 A And the power dissipated by each resistor is: R1: 192 W R2: 222 W R3: 352 W
To calculate the current drawn by each resistor and the power dissipated by each, we will use Ohm's Law and the Power formula.
Ohm's Law is V = IR, and the Power formula is P = IV.
Given: Resistor 1 (R1) = 192 W Resistor 2 (R2) = 222 W Resistor 3 (R3) = 352 W Voltage (V) = 24 V
Step 1: Calculate the current (I) drawn by each resistor using the Power formula (P = IV):
For R1: I1 = P1 / V = 192 W / 24 V = 8 A
For R2: I2 = P2 / V = 222 W / 24 V = 9.25 A
For R3: I3 = P3 / V = 352 W / 24 V = 14.67 A
Step 2: Calculate the power (P) dissipated by each resistor using the Power formula (P = IV):
For R1: P1 = I1 × V = 8 A × 24 V = 192 W
For R2: P2 = I2 × V = 9.25 A × 24 V = 222 W
For R3: P3 = I3 × V = 14.67 A × 24 V = 352 W
So, the current drawn by each resistor is: R1: 8 A R2: 9.25 A R3: 14.67 A And the power dissipated by each resistor is: R1: 192 W R2: 222 W R3: 352 W
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Find parametric equations for a line in the direction of the vector 57 - 7 and through the point
(0, 0, - 3).
Write the equations so that one term is just the parameter - t.
х (t) = y(t) =
z(t) =
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
To find the parametric equations for a line in the direction of the vector 57 - 7 and through the point (0, 0, - 3), we can use the vector form of the equation of a line:
r = r0 + tv
where r is a point on the line, r0 is the given point (0, 0, -3), t is a parameter, and v is the direction vector (57, -7, 0).
Substituting the given values, we have:
r = (0, 0, -3) + t(57, -7, 0)
Expanding, we get:
x(t) = 0 + 57t
y(t) = 0 - 7t
z(t) = -3 + 0t
Simplifying, we have:
x(t) = 57t
y(t) = -7t
z(t) = -3
Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:
x(t) = 57t
y(t) = -7t
z(t) = -3
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Complete the proof that △QST≅△QRT.
The congruent triangles is solved and the triangles are congruent by AAS postulate
Given data ,
Let the two triangles be represented as ΔRQT and ΔTQS
And , the side TQ is the common side of both the triangles
Now , the measure of ∠TQR ≅ measure of ∠TQS ( given )
And , the measure of ∠TRQ ≅ measure of ∠TSQ ( given )
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent by ASA postulate
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Do You Understand?
1. How can you find the volume of the
china cabinet?
1 ft,
7 ft
3 ft
4 ft
2ft
The volume of the china cabinet is 21 cubic feet.
To find the volume of the china cabinet, we need to multiply its length, width, and height.
Since the dimensions are given in feet, we will use cubic feet as the unit of volume.
The length of the china cabinet is given as 1 ft, the width as 7 ft, and the height as 3 ft.
The volume can be calculated as follows:
Volume = length * width * height
Volume = 1 ft * 7 ft * 3 ft
Volume = 21 cubic feet
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What is the surface area of the square pyramid?
Answer:
3456 [tex]m^{2}[/tex]
Hope this helps!
Step-by-step explanation:
A square pyramid is comprised of a square and four triangles.
The square has an area of 1296 m ( 36m × 36m ) ( length × width ).
A triangle has an area of 540 m ( [tex]\frac{1}{2}[/tex] × 36m × 30m ) ( [tex]\frac{1}{2}[/tex] × width × ( slant ) height ).
The total surface area would be 1296 m + 4 × ( 540 m ) : ( Multiply 4 because there are 4 triangles ).
The total surface area is 3456 [tex]m^{2}[/tex].
Answer: 3,456 m^2
Step-by-step explanation:
The formula is SA = 2bs + b^2.
SA = 2 (36) (30) + 36^2
= 72 (30) + 1,296
= 2,160 + 1,296
= 3,456 m^2
Write the equation to a quintic with double roots –4 and 2, that goes through the origin as well as (4, 4).
Hence, the required equation of the quintic with double roots –4 and 2 is [tex]f(x)=\frac{1}{256} (x+4)^2(x-2)^2(x)[/tex].
Given, an equation of a quintic with double roots –4 and 2, that goes through the origin as well as (4, 4).
Let r be the remaining root of the equation.
Let the required equation in factored form is
[tex]f(x)=a(x+4)^2(x-2)^2(x-r)[/tex]
Given, the quintic goes through the origin.
Then, we know that f(0) = 0.
[tex]f(0)=a(0+4)^2(0-2)^2(0-r)[/tex]
0 = a(16)(4)(-r)
0 = -64ar
64ar = 0
either a = 0 or r = 0.
if a = 0
then the equation reduces to f(x) = 0, which is not a quintic.
a ≠ 0
This means that r = 0
So equation becomes [tex]f(x)=a(x+4)^2(x-2)^2(x)[/tex] ...(1)
Given, the quintic goes through the point (4, 4)
So, f(4) = 4
[tex]f(4)=a(4+4)^2(4-2)^2(4)[/tex]
4 = 1064 a
a = 4/1064
a = 1/256
Putting in equation (1)
[tex]f(x)=\frac{1}{256} (x+4)^2(x-2)^2(x)[/tex]
Hence, the required equation of the quintic with double roots –4 and 2 is [tex]f(x)=\frac{1}{256} (x+4)^2(x-2)^2(x)[/tex].
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