Find two vectors in opposite directions that are orthogonal to the vector u.
u = 1/4 i - 4/5j

Answers

Answer 1

Two  vectors in opposite directions that are orthogonal to u are v = 5i + 4j and w = -4i + 5j.

To find two vectors in opposite directions that are orthogonal to u, we need to use the cross product. The cross product of two vectors is a vector that is perpendicular to both of them. We can choose any two non-collinear vectors as long as they are orthogonal to each other and the given vector.

Let's find the cross product of u and a vector v. The cross product of two vectors a and b is given by:

a x b = |a| |b| sinθ n

where |a| and |b| are the magnitudes of the vectors, θ is the angle between them, and n is a unit vector perpendicular to both a and b in the direction given by the right-hand rule.

Since we want v to be orthogonal to u, we need to choose v such that u x v = 0. This means that the angle between u and v is either 0 or 180 degrees, and |v| is arbitrary.

Let v = 5i + 4j. Then, we have:

u x v = (1/4 i - 4/5j) x (5i + 4j)

= (-16/20)i - (5/20)j + (1/20)k

= (-4/5)i - (1/4)j + (1/20)k

Since u x v is not equal to zero, v is not orthogonal to u. To find another vector that is orthogonal to u, we can take the cross product of u and w, where w = -4i + 5j. Then, we have:

u x w = (1/4 i - 4/5j) x (-4i + 5j)

= (-5/20)i + (16/20)j + (1/20)k

= (-1/4)i + (4/5)j + (1/20)k

Since u x w is also not equal to zero, we need to adjust the signs of v and w to make them orthogonal to u. We can do this by taking the opposite of v and w. Therefore, two vectors in opposite directions that are orthogonal to u are v = 5i + 4j and w = -4i + 5j.

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Related Questions

An oil tank is the shape of a right rectangular prism. The inside of the tank is 36. 5 cm long, 52 cm wide, and 29 cm


high. If 45 liters of oil have been removed from the tank since it was full, what is the current depth of oil left in the


tank?

Answers

The current depth of oil left in the tank is approximately 4.64 cm.

The volume of the oil tank can be found by multiplying its length, width, and height:

Volume of the oil tank = length x width x height

= 36.5 cm x 52 cm x 29 cm

= 53,854 cubic cm

If 45 liters of oil have been removed from the tank, the current volume of oil in the tank is:

Current volume of oil = Total volume of tank - Volume of oil removed

= 53,854 cubic cm - 45,000 cubic cm (1 liter = 1000 cubic cm)

= 8,854 cubic cm

Let's assume that the depth of oil left in the tank is x cm. Then the volume of oil left in the tank can be found by multiplying the length, width, and depth of oil:

Volume of oil left in tank = length x width x depth of oil

= 36.5 cm x 52 cm x x cm

= 1906x cubic cm

Now we can set up an equation to find the value of x:

1906x = 8,854

Dividing both sides by 1906, we get:

x = 4.64 cm

Therefore, the current depth of oil left in the tank is approximately 4.64 cm.

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Chris wants to order DVD's over the internet. Each DVD costs $15. 99 and shipping the entire order costs $9. 99. If he can spend no more than $100, how many DVD's could he buy?

Answers

Since Chris can only buy whole DVDs, he can purchase a maximum of 5 DVDs within his $100 budget.

Each DVD costs $15.99, and the shipping for the entire order is $9.99.

We can use the following inequality to represent Chris's budget constraint:

15.99x + 9.99 ≤ 100

Here, x represents the number of DVDs he can buy.

To find the maximum value of x, we can rearrange the inequality:

x ≤ (100 - 9.99) / 15.99 x ≤ 90.01 / 15.99 x ≤ 5.63

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Jack starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2. 1% interest, compounded annually. What is the future value of this investment, rounded to the nearest dollar, when Jack is ready to purchase the vacation home?



$11,000



$11,231



$44,000



$44,924

Answers

The future value of the investment when Jack is ready to purchase the vacation home is $44,924.

To solve this problem, we can use the formula for future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

Where:

Pmt = $1000 (quarterly contribution)
r = 0.021 (annual interest rate)
n = 40 (number of quarters until Jack turns 50)

Plugging in the numbers, we get:

FV = $1000 x [(1 + 0.021)^40 - 1] / 0.021
FV = $44,924.38

Therefore, the future value of Jack's investment, rounded to the nearest dollar, is $44,924. So the correct answer is $44,924.

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For a certain company , the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0. 5x^2.

a) set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces (hint: it is a quadratic polynomial)

b) find two values of x that will create a profit of $300

c) is it possible for the company to make a profit of $15,000​

Answers

Answer:

Step-by-step explanation:

a)  Profit = Revenue - Cost = (90x - 0.5x²) - (50x + 300)

= -0.5x² + 90x - 50x - 300

= -0.5x² + 40x - 300

b)  -0.5x² + 40x - 300 = 300

-0.5x² + 40x - 600 = 0

use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -600):

x = 20, 60

c)  -0.5x² + 40x - 300 = 15000

-0.5x² + 40x - 15300 = 0

use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -15300):

x = 40±10√290i

Not possible to make a profit of $15,000

Evaluate the integral. 8 Vi s dt Vi 8V1 ſ Vi dt=U Help me solve this Ca

Answers

The integral evaluates to (16/3)s³/² + C.

What is power rule of integration?

The power rule of integration is a method for finding the indefinite integral of a function of the form f(x) = x^n, where n is any real number except for -1. The rule states that the indefinite integral of f(x) is (x^(n+1))/(n+1) + C, where C is an arbitrary constant of integration.

To evaluate the integral 8√(s) ds, follow these steps:


1. Rewrite the integral with a rational exponent: ∫8s¹/² ds
2. Apply the power rule for integration: ∫sⁿ ds = (sⁿ⁺¹/(n+1) + C, where n ≠ -1
3. Substitute n=1/2: (s³/²)/(3/2) + C
4. Multiply by 8: 8*(s³/²)/(3/2) + C
5. Simplify the expression: (16/3)s³/² + C

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northview swim club has a number of members on monday. on tuesday, 22 new members joined the swim clun on wednesday 17 members cancled their membership or left the swim clun northview swim club has 33 members on thursday morning the equation m+22-17=33 repersents the situation solve the equation

Answers

There were 28 members in the Northview Swim Club on Monday before any new members joined or any current members left.

What is the solution of the equation?

The equation "m+22-17=33" represents the situation where "m" is the number of members in the Northview Swim Club on Monday.

To solve the equation, we can start by simplifying it:

m + 5 = 33

Next, we can isolate "m" on one side of the equation by subtracting 5 from both sides:

m = 33 - 5

m = 28

Thus, the solution of the equation for the Northview Swim Club on Monday before any new members joined is determined as 28 members.

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Calculate A. ∂z and ∂x
B. ∂z and ∂y
at the point
(5, 17, 1)
where z is defined implicitly by the equation
z4 + z2x2 − y − 9 = 0

Answers

At the point (5, 17, 1), the partial derivatives of z with respect to x and y are -12.5 and 0.25, respectively, as calculated using implicit differentiation. At the point (5, 17, 1), the partial derivatives of z with respect to z and y are 0.16 and -1.

To find the partial derivatives, we need to use the implicit differentiation.

To find ∂z/∂x, we differentiate the equation with respect to x, treating y and z as functions of x

4z^3(dz/dx) + 2z^2x^2 - 0 - 0 = 0

Simplifying, we get

4z^3(dz/dx) = -2z^2x^2

(dz/dx) = -1/2x^2z

At the point (5, 17, 1), we have

(dz/dx) = -1/2(5)^2(1) = -12.5

To find ∂z/∂y, we differentiate the equation with respect to y, treating x and z as functions of y

4z^3(dz/dy) - 1 - 0 + 0 = 0

Simplifying, we get

4z^3(dz/dy) = 1

(dz/dy) = 1/4z^3

At the point (5, 17, 1), we have

(dz/dy) = 1/4(1)^3 = 0.25

To find ∂z and ∂y at the point (5, 17, 1), we need to take partial derivatives with respect to z and y, respectively, of the implicit equation

z^4 + z^2x^2 - y - 9 = 0

Taking the partial derivative with respect to z, we get

4z^3 + 2z^2x^2(dz/dz) - dy/dz = 0

Simplifying and solving for ∂z, we get

∂z = dy/dz = 8z^3/(2z^2x^2) = 4z/x^2

At the point (5, 17, 1), we have

z = 1, x = 5

So, ∂z at the point (5, 17, 1) is

∂z = 4z/x^2 = 4(1)/(5^2) = 0.16

To find ∂y, we take the partial derivative with respect to y, keeping x and z constant

-1 = ∂y

Therefore, ∂y at the point (5, 17, 1) is -1.

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A 40 -degree angle is translated 5 inches along a vector. What is the angle measurement, in degrees, of the image?

Answers

The angle measurement would remain as 40 degrees

Does angle change when translated?

No, when a geometric figure, such as a line or an angle, is translated (moved) to a new position without being rotated, reflected, or scaled, its shape and size do not change, and therefore its angle measure remains the same.

This property is a fundamental concept in geometry and is known as the "invariance of angle measure under translation". It means that if two angles are congruent (have the same measure) in their original position, they will remain congruent after being translated to a new position.

Hence The angle measurement would remain as 40 degrees

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HELP MARKING BRAINLEIST IF CORRECT

Answers

Answer:

21.5

Step-by-step explanation:

First we can solve for c using the pythagoreom theorem. (probably didn't spell that right)

A squared + B squared =  C squared

9 squared + 3 squared = c squared

81+9= c squared

90=c squared

90 square root is (rounded to the nearest tenth) 9.5

c=9.5

Then we can add 9.5+9+3= 21.5

Jenelle draws one from a standard deck of 52 cards. Determine the probability of drawing either a two or a ten? Write your answer as a reduced fraction. Answer= Determine the probability of drawing either a two or a club? Write your answer as a reduced fraction. Answer=

Answers

The probability of drawing either a two or a ten is (4+4)/52, which simplifies to 2/13.
The probability of drawing either a two or a club is (3+13)/52, which simplifies to 4/13.


For the first question: In a standard deck of 52 cards, there are four 2s and four 10s. The probability of drawing either a two or a ten is the number of successful outcomes (drawing a 2 or a 10) divided by the total number of possible outcomes (52 cards). So, the probability is (4+4)/52 = 8/52. This can be reduced to the fraction 2/13.

For the second question: There are four 2s and thirteen clubs in a standard deck of 52 cards. Since one of the 2s is a club, there are three additional 2s that are not clubs. The probability of drawing either a two or a club is the number of successful outcomes (3 additional 2s + 13 clubs) divided by the total number of possible outcomes (52 cards). So, the probability is (3+13)/52 = 16/52. This can be reduced to the fraction 4/13.

Therefore,
1) Probability of drawing either a two or a ten: 2/13
2) Probability of drawing either a two or a club: 4/13

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Find the value of x such that the data set has the given mean.

102​, 120​, 103​, 112​, 110​, ​x; mean 108

Answers

The value of x in the data set is 101.

How to find mean?

The mean of a data set is the sum of all the data divided by the count n.

Therefore, let's find the mean of the data set as follows:

The mean is  the sum of the data divided by the total number of data.

Hence, let's find the value of x using the mean

108  = 102 + 120 + 103 + 112 + 110 + x  / 6

108 = 547 + x / 6

Cross multiply

108 × 6 = 547 + x

648 = 547 + x

x = 648 - 547

x = 101

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Carlos spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. the plane maintains a constant altitude of 7275 feet. carlos initially measures an angle of elevation of 20°

to the plane at point aa. at some later time, he measures an angle of elevation of 37°

to the plane at point bb. find the distance the plane traveled from point aa to point bb. round your answer to the nearest foot if necessary.

Answers

The distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.

Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.

At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.

Using trigonometry, we can set up the following equations:

tan(20 degrees) = 7275 / x,

tan(37 degrees) = 7275 / y.

We can rearrange these equations to solve for x and y:

x = 7275 / tan(20 degrees),

y = 7275 / tan(37 degrees).

Using a calculator, we can evaluate these expressions:

x ≈ 20246.71 feet,

y ≈ 14046.99 feet.

Therefore, the distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:

Distance ≈ 6201 feet.

To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.

Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.

At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.

Using trigonometry, we can set up the following equations:

tan(20 degrees) = 7275 / x,

tan(37 degrees) = 7275 / y.

We can rearrange these equations to solve for x and y:

x = 7275 / tan(20 degrees),

y = 7275 / tan(37 degrees).

Using a calculator, we can evaluate these expressions:

x ≈ 20246.71 feet,

y ≈ 14046.99 feet.

Therefore, the distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:

Distance ≈ 6201 feet.

Therefore, the distance the plane traveled from point A to point B is approximately 6201 feet.

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Consider the governing equation of a system. The coefficient 'a' in the equattion is a positive constant.First, let a=4. What is the value of x in steady state? Suppose that coefficient has changed to a=2. What is the new value of x in the steady state?

Answers

To answer this question, we need to know the specific governing equation of the system. Without this information, we cannot determine the value of x in steady state for either case.

However, we do know that the coefficient 'a' in the equation is a positive constant. When a=4, we can solve for x in steady state using the given equation and the value of a=4. When a=2, we can solve for x in steady state using the same equation and the new value of a=2.

In general, the value of x in steady state will depend on the specific equation and the values of its coefficients.
Hi there! To help you with your question, I need more information about the governing equation of the system. Please provide the complete equation with 'x' and the coefficient 'a'. Once I have that information, I can help you find the steady-state values of x for a=4 and a=2.

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given a standard deck of cards, what is the probability of choosing a diamond, then a heart, then a black card if no replacement is made

Answers

Answer:The probability of both is 1/4*13/51.

Step-by-step explanation:

There are 52 cards in the deck, 13 hearts and 13 spades. The probability of getting a heart is 13/52 or 1/4. Given an initial heart there are 51 cards remaining; the probability of a spade is now 13/51

A recipe for banana pudding calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. How many cups of sugar in all is required to make the banana pudding?

Answers

Answer: To find the total amount of sugar required to make the banana pudding, we need to add the amount of sugar needed for the flour mixture to the amount of sugar needed for the meringue topping.

The recipe calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. To add these two fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can convert these fractions to twelfths:

2/3 = 8/12

1/4 = 3/12

Now we can add these two fractions:

8/12 + 3/12 = 11/12

So the total amount of sugar required to make the banana pudding is 11/12 of a cup.

For this problem, a table has been started for you based on the information given in the problem. use inductive reasoning to complete the table.



an electronics store finds that over a period of three months, sales of stereos decreased. in march, the store sold 325 stereos. in april, the store sold 280 stereos, and in may, the store sold 235 stereos.



month



stereos sold



march



325



april



280



may



235



june



july



august



incorrect feedback has been removed from the screen.


type your answers and then click or tap done.




make a conjecture about the number of stereos sold in june. fill in the blank text field 1


190



make a conjecture about the number of stereos sold in july.



make a conjecture about the number of stereos sold in august.

Answers

Using inductive reasoning, we can observe a pattern in the given data: the number of stereos sold decreases by 45 each month.

We can apply this pattern to make conjectures about the number of stereos sold in June, July, and August.

June: 235 (May's sales) - 45 = 190 stereos
July: 190 (June's sales) - 45 = 145 stereos
August: 145 (July's sales) - 45 = 100 stereos

So, the conjectures for the number of stereos sold are:
June: 190
July: 145
August: 100

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How many 4-digit numbers have the second digit even and the fourth digit at least twice the second digit?

Answers

There are 1350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.

To form a 4-digit number, we have 10 choices for each digit, except the first digit, which can't be 0. Hence, there are 9 choices for the first digit.

For the second digit, there are 5 even digits (0, 2, 4, 6, 8) to choose from.

For the third digit, there are 10 choices.

For the fourth digit, we can choose any of the even digits we picked for the second digit, or any of the larger odd digits 4, 6, 8.

Hence, the number of 4-digit numbers that meet the given criteria is

9 × 5 × 10 × 3 = 1350.

Therefore, there are 1,350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.

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CAN SOMEONE HELP ME PLEASEEEEEEEEEEEEEE I NEED HELP :( ​

Answers

Answer:

for the first three, divide the number by 2

for the second three, multiply by 2

9 and 11. divide the number by 2 and plug into the formula 2 * pi * radius, radius is number/2

10. plug 7 into formula 2 * pi * radius, radius = 7

Step-by-step explanation:

radius is half the length of the circle, diameter is the full length, circumference is 2 * pi * radius

Al has a cylindrical storage container 30 centimeters tall with a diameter of 22 centimeters. How much bird food in cubic centimeters will fit in the container? Use the formula V = Bh and approximate π using 3.14. Round your answer to the nearest tenth.

Answers

The amount of  bird food in cubic centimeters will fit in the container is

11, 398. 2 cubic centimeters

How to determine the volume

The formula that is used for calculating the volume of a cylinder is expressed with the equation;

V = π(d/2)²h

Such that the parameters of the given equation are;

V is the volume of the cylinder.d is the diameter of the cylinderh is the height of the cylinder

Now, substitute the values into the formula, we have;

Volume = 3.14 (22/2)² 30

divide the values

Volume = 3.14(121)30

Now, multiply the values and expand the bracket

Volume = 11, 398. 2 cubic centimeters

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Please help this is for a test and i need a good grade lollll

"the wind force f on a sail varies jointly as the area al of the sall and the square of the wind speed w.
the force on a sail with area an area of 500 p? is 64.8 pounds when the wind speed is 18 mph. what
would be the force for a sail with an area of 250 f12 with a wind speed of 35 mph"

please show step by step work tysmmmm <3

Answers

The force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.

How to find force on sail?

We are given that the wind force F on a sail varies jointly as the area A and the square of the wind speed W. We can represent this relationship mathematically using the equation:

F = k * A * W²

where k is a constant of proportionality.

We are also given that the force on a sail with an area of 500 p and wind speed of 18 mph is 64.8 pounds. We can use this information to solve for k:

64.8 = k * 500 * 18²

Solving for k, we get:

k = 64.8 / (500 * 18²)

k = 0.0000768

Now, we can use the equation to find the force for a sail with an area of 250 f12 and a wind speed of 35 mph:

F = 0.0000768 * 250 f12 * 35²

F = 108.72 pounds

Therefore, the force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.

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Breck has 22 dimes and nickels. The total value of the coins is $1. 45. How many dimes and how many nickels does Breck have?

Answers

Let x be the number of dimes and y be the number of nickels that Breck has. We know that he has 22 coins in total so

x + y = 22

We also know that the total value of the coins is $1.45, which is equivalent to 145 cents. Since dimes are worth 10 cents and nickels are worth 5 cents, we can write another equation:

10x + 5y = 145

We can simplify this equation by dividing both sides by 5:

2x + y = 29

Now we have two equations:

x + y = 22
2x + y = 29

We can solve for y by subtracting the first equation from the second equation:

2x + y - (x + y) = 29 - 22
x = 7

Now that we know x, we can substitute it back into either equation to solve for y:

x + y = 22
7 + y = 22
y = 15

Therefore, Breck has 7 dimes and 15 nickels.

What is the image of (5,−4) after a dilation by a scale factor of 4 centered at the origin?

Answers

The image of (5,−4) after a dilation by a scale factor of 4 centered at the origin is (20,−16)

What is the image after a dilation centered at the origin?

From the question, we have the following parameters that can be used in our computation:

Point = (5,−4)

Scale factor of 4 centered at the origin

The image after a dilation centered at the origin is

Image = Point  * Scale factor

Substitute the known values in the above equation, so, we have the following representation

image = (5,−4) * 4

Evaluate

image = (20,−16)

Hence, the image after a dilation centered at the origin is (20,−16)

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If there are 30 people in a classroom, what is the probability that at least two have the same birthday

Answers

The probability that at least two people in a group of 30 have the same birthday is about 0.7063 or 70.63%.

To calculate the probability that at least two people in a group of 30 have the same birthday, we can use the complement rule:

P(at least 2 people have the same birthday) = 1 - P(all people have different birthdays)

The probability that the first person has a unique birthday is 1 (since there are no other people to share with yet).

The probability that the second person also has a unique birthday is 364/365 (since there are now 364 days left out of 365 that they could have a different birthday from the first person).

Similarly, the probability that the third person has a unique birthday is 363/365, and so on. So, we can write:

P(all people have different birthdays) = 1 x 364/365 x 363/365 x ... x 336/365

Using a calculator or computer program, we can evaluate this expression to be approximately 0.2937.

Therefore,

P(at least 2 people have the same birthday) = 1 - 0.2937 = 0.7063

So the probability that at least two people in a group of 30 have the same birthday is about 0.7063 or 70.63%.

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A scale drawing of a famous statue uses a scale factor of 240:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?

288 feet
241.2 feet
238.8 feet
200 feet

Answers

The height of the statue is 288 feet.

The scale factor is 240:1

Or, the ratio of the height of the statue to the height of the drawing = 240:1.

This means, for 1 unit height of drawing, the height of the statue = 240 units

Or, for 1 feet height of the drawing, the height of the statue = 240 feet.

Let us suppose the actual height of the statue to be x.

The height of the drawing = 1.2 feet    (given)

So, the ratio of the height of the statue to the height of the drawing = x/1.2

But, the scale factor  = 240:1 = 240/1

240/1=x/1.2

⇒x=240×1.2

x=288

Hence, the height of the statue is 288 feet.

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A circle is circumscribed around a regular octagon with side lemgths of 10 feet. Another circle is inscribed inside the octagon. Find the area. Of the ring created by the two circles. Round the respective radii of the circles to two decimals before calculating the area

Answers

The area of the ring is 1,462.81 square feet, under the condition that a circle is circumscribed around a regular octagon with side lengths of 10 feet.

The area of the ring formed by the two circles can be evaluated using the formula for the area of a ring which is

Area of ring = π(R² - r²)

Here
R = radius of the larger circle
r = smaller circle radius

The radius of the larger circle is equal to half the diagonal of the octagon which is 10 feet. Applying Pythagoras theorem, we can evaluate that the length of one side of the octagon is 10/√2 feet.
Radius of the larger circle is

R = 5(10/√2)
= 25√2/2 feet
≈ 17.68 feet

Staging these values into the formula for the area of a ring,

Area of ring = π(17.68² - 10²) square feet

Area of ring ≈ 1,462.81 square feet
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Every winter, students at Camden Middle School go on a class ski trip.
For every inch of snow that falls, an additional 25 students sign up.
Write an expression showing the total number of students going on the trip, using only a variable to represent the additional students

Now write a different expression to show the total number of students going on the trip, using an expression consisting of a variable and a number to represent the students

Answers

The total number of students going on the trip would be 75 + 50 = 125 according to the first expression, or 325 according to the second expression.

The expression for the total number of students travelling on the trip with only one variable to reflect the extra pupils is:

25x + b

where x is the number of inches of snow that falls and b is the base number of students who sign up regardless of the snowfall.

Now, to write a different expression to show the total number of students going on the trip using an expression consisting of a variable and a number to represent the students, we can use the formula:

N = 25x + 250

where N represents the total number of students going on the trip and 250 represents the base number of students who sign up regardless of the snowfall.

Let's say that 3 inches of snow have fallen. Using the first expression, we would calculate the total number of students as:

25(3) + b = 75 + b

Now, let's say that the base number of students who signed up is 50. Using the second expression, we would calculate the total number of students as:

N = 25(3) + 250 = 325

Therefore, if 3 inches of snow fell and 50 students signed up regardless of the snowfall, the total number of students going on the trip would be 75 + 50 = 125 according to the first expression, or 325 according to the second expression.

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Show your work for multiplying the polynomials below and put your answer in standard form in the box below: (No work loses points)
(x+6)(x2−3x−4)

Answers

The polynomials are multiplied to give the expression x³ + 3x² - 22x - 24

How to determine the product

We need to know that algebraic expressions are described as expressions that are composed of terms, variables, their coefficients, factors and constants.

Also, these expressions are made up of mathematical operations. They are listed as;

SubtractionMultiplicationDivisionAddition BracketParentheses

From the information given, we have the expression;

(x+6)(x2−3x−4)

expand the bracket, we get;

x³ - 3x² - 4x + 6x² - 18x - 24

add the like terms, we get;

x³ + 3x² - 22x - 24

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Integrate fover the given curve. f(x,y) = x+ y, C: x^2 + y^2 = 4 in the first quadrant from
(2,0) to (0,2)

Answers

The integral of f(x, y) = x + y over the given curve is 8.

To integrate the function f(x, y) = x + y over the curve C: x² + y² = 4 in the first quadrant from (2, 0) to (0, 2), we will use the line integral. Since the curve is a circle, we can parameterize it using polar coordinates as follows:

x = 2cos(θ)
y = 2sin(θ)

Now, let's find the derivatives:

dx/dθ = -2sin(θ)
dy/dθ = 2cos(θ)

Next, we substitute x and y in f(x, y):

f(x, y) = 2cos(θ) + 2sin(θ)

Now, we can set up the line integral:

∫[f(x, y) * ||dr/dθ||]dθ

Since ||dr/dθ|| = sqrt((-2sin(θ))^2 + (2cos(θ))^2) = 2, the line integral becomes:

∫[2cos(θ) + 2sin(θ)] * 2 dθ

To find the limits of integration, we can use the points (2, 0) and (0, 2). In polar coordinates, these points correspond to θ = 0 and θ = π/2.

So, the line integral becomes:

∫[4cos(θ) + 4sin(θ)]dθ from 0 to π/2

Now, we can integrate and evaluate:

[4sin(θ) - 4cos(θ)] from 0 to π/2 = [4(1) - 4(0)] - [4(0) - 4(1)] = 8

Thus, the integral of f(x, y) = x + y over the given curve is 8.

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Bill is walking up the steps in the Washington Monument at a rate of 30 feet per minute and Joe is walking down at the rate of 45 feet per minute. Bill is 75 feet from the bottom at the same moment that Joe is 325 feet from the bottom. Which of the following systems of equations can be used to determine the number of minutes t, from now and height, ℎ (in feet), at which they will pass each other?

Answers

The equation that can be used to determine the number of minutes t, from now and height, ℎ (in feet), at which they will pass each other is 75t = h.

What is the time taken for them to pass each other?

The time taken for them to pass each other is calculated as follows;

Apply the rules of relative velocity;

(V₂ - V₁)t = h

where;

V₂ is the velocity of the BillV₁ is the velocity of the Joet is the time taken for them to meeth is the distance between them

(30 ft/min - ( -45 ft/min )t = h

75t = h

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Help me please I don’t know what to do

Answers

Answer:

179.3 square units

Step-by-step explanation:

We have to find the area of the rectangle and area of semicircle using the formula and then add the areas.

Area of rectangle:

                  length = 14 units

                   width = 10 units

          [tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]

                                             = 14 * 10

                                             = 140 square units

Area of semicircle:

                diameter of semicircle = width of the rectangle

                                                 d =  10 units

                                                 r = d ÷ 2

                                                    = 10 ÷ 2

                                                    = 5 units

                     [tex]\boxed{\text{\bf Area of semicircle = $\dfrac{1}{2}\pi r^2$}}[/tex]

                                                       [tex]\sf = \dfrac{1}{2}*3.14*5*5\\\\ = 39.26\\\\ = 39.3 \ square \ units[/tex]

Area of the figure = area of rectangle +  area of semicircle

                             = 140 + 39.3

                             = 179.3 square units

                 

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