An architect uses a scale of 3 4 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?

Answers

Answer 1

Answer:

The length of the line on the blueprint of the wall will be 18 inches.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

An architect uses a scale of 3/4 inches to represent 1 foot on a blueprint for a building.

Then the scale factor of the blueprint will be

Scale factor = 3/4 inches per foot

If the east wall of the building is 24 feet long.

Then the length of the line on the blueprint of the wall will be

Length = 24 feet x scale factor

Length = 24 x (3/4)

Length = 6 x 3

Length = 18 inches

Thus, the length of the line on the blueprint of the wall will be 18 inches.

More about the dilation link is given below.

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Answer 2

Answer:

16 in.

Step-by-step explanation:

We have the ratio

How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of

Now we need to know how many inches there would be if the number of feet is 24:

Cross multiply to get

3x = 48 so

x = 16 in.

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Three-fourths of a number is at least -18

Answers

Answer:

x ≥ - 24

Step-by-step explanation:

Let's solve this with an equal sign and then decide how to handle the at least part.

3/4 x = -18 Multiply by 4

3/4 * 4 x = -18*4 Cancel the left, multiply the right.

3x = -72 Divide by 3

x ≥ -24

You need the greater than to indicate that 3/4 of a number can give something larger than - 18.

You need the equal sign to fulfill at least.

At least, in this question means "get larger."

so x > - 24

Answer:

3/4*X < -18

( put a line underneath the less than sign ) ( Astric's means multiplication )

Step-by-step explanation:

Hope this helped, Have a Wonderful Day!!

Suppose f(x,y)=xy, P=(−4,−4) and v=2i+3j. A. Find the gradient of f. ∇f= i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇f)(P)= i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf= Note: Your answer should be a number D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u= i+ j Note: Your answers should be numbers

Answers

Answers:

Gradient of f: $\nabla f = y\hat{i} + x\hat{j}$

Gradient of f at point p: $\nabla f = -4\hat{i} -4\hat{j}$

Directional derivative of f and P in direction of v: $\nabla f(P)v = -20\n$

The maximum rate of change of f at P: $| \nabla f(P)| = 4√(2)$

The (unit) direction vector in which the maximum rate of change occurs at P is: $v = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}$

Step by step solutions:

Given that:

$f(x,y) = xy$

$P = (-4,4)\n$

$v = 2i + 3j$

A: Gradient of f

$\nabla f = ((\partial f)/(\partial x), (\partial f)/(\partial y)) = (y,x) = y\hat{i} + x\hat{j}$

B: Gradient of f at point P:

Just put the coordinates of p in above formula:

$\nabla f = -4\hat{i} -4\hat{j}$

C: The directional derivative of f and P in direction of v:

The directional derivative is found by dot product of $\nabla f(P) \: \rm and \: \rm v$ :

$\nabla f(P)v = [-4,4][2,3]^T = -20\n$

D: The maximum rate of change of f at P is calculated by evaluating the magnitude of gradient vector at P:

$| \nabla f(P)| = √((-4)^2 + (-4)^2) = 4√(2)$

E: The (unit) direction vector in which the maximum rate of change occurs at P is:

$v = ((-4)/(4√(2)), (-4)/(4√(2))) = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}$

That vector v is the needed unit vector in this case.

we divided by $4√(2)$ to make that vector as of unit length.

Learn more about vectors here:

brainly.com/question/12969462

Answer:

a) The gradient of a function is the vector of partial derivatives. Then

$\nabla f=((\partial f)/(\partial x), (\partial f)/(\partial y))=(y,x)=y\hat{i} + x\hat{j}$

b) It's enough evaluate P in the gradient.

$\nabla f(P)=(-4,-4)=-4\hat{i} - 4 \hat{j}$

c) The directional derivative of f at P in direction of V is the dot produtc of $\nabla f(P)$ and v.

$\nabla f(P) v=(-4,-4)\left[\begin{array}{ccc}2\n3\end{array}\right] =(-4)2+(-4)3=-20$

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

$||\nabla f(P)||=√((-4)^2+(-4)^2)=√(32)=4√(2)$

e) The maximum rate of change occurs in the direction of the gradient. Then

$v=(1)/(4√(2))(-4,-4)=((-1)/(√(2)),(-1)/(√(2)))= (-1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}$

is the direction vector in which the maximum rate of change occurs at P.

Consider the optimization problem where A m × n , m ≥ n , and b m . a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

Answers

Answer:

Answer for the question :

Consider the optimization problem where A m × n , m ≥ n , and b m .

a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

is explained din the attachment.

Step-by-step explanation:

4x (7+8) = (4x _) + (4x _)

Answers

Answer:

4x (7+8)=(4x3) + (4x4)

4x(7+8)=(4x7) +(4x8)

Step-by-step explanation:

Im not sure with one tho

What is the length of AC?

Answers

The length of AC found using the Pythagorean Theorem is C) 120.

The length of AC can be found using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is AC, and the other two sides are AB and BC.

AB = 60 units

BC = 80 units

Plugging these values into the Pythagorean Theorem, we get:

$AC^2$ = $AB^2$ + $BC^2$

$AC^2$ = $60^2$ + $80^2$

$AC^2$ = 3600 + 6400

$AC^2$ = 10000

AC = $\sqrt{$ (10000)

AC = 100 * $\sqrt{$ (10)

AC = 120 units

Therefore, the length of AC is C) 120.

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B I think and I hope it’s right!

Raquel kicks a football. The height in feet canbe modeled by the equation
h(x) = -16x2 + 64x.
How long in seconds before the ball reaches
its maximum height? Show work.
What is the maximum height of the ball? Show work.

answer fast please

Answers

Answer:

the answer is 0

Step-by-step explanation:

16x2 + 64x.

Answer:

Step-by-step explanation:

i agree with bigmack0

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