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3 years ago

After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6,3), B'(-2, 1)

Mathematics

1 answer:

Fed [463]3 years ago

8 0

Answer:

A(3, -6)
B(1, 2)
C(7, -1)

Step-by-step explanation:

Rotation by -90° about the origin is the transformation ...

(x, y) ⇒ (y, -x)

So, your pre-image points are ...

A'(6, 3) ⇒ A(3, -6)

B'(-2, 1) ⇒ B(1, 2)

C'(1, 7) ⇒ C(7, -1)

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Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Vikki [24]

Answer:

Height: 3/2 inches

Length: 12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

The new length of the cardboard = 15 -2x (because we cut from 4 corners)
The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = $4x^3 -44x^2 +105x$

To maximum volume, we use the first derivative of the volume

$\dfrac{dV}{dx} = 0$

<=> $12x^2-88x+105=0$

<=> $\left(2x-3\right)\left(6x-35\right) = 0$

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

$\dfrac{d^2V}{dx^2}$ = 24x -88

If x = 3/2, we have:

$\dfrac{d^2V}{dx^2}$ = 24(3/2) -88 = -52

If x = 35/6, we have:

$\dfrac{d^2V}{dx^2}$ = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0

3 years ago

PLEASE HURRY IT'S URGENT!!!!!

kramer

Answer:

none of those answers are right, because the base of the triangle at 7/24 ft (or 0.29 ft) is smaller than the height 1/3 ft (or 0.33 ft)

Step-by-step explanation:

7/24 - 1/3 =

7/24 - 8/24 = -1/24

5 0

3 years ago

Read 2 more answers

I need help with number 2 please.

Vedmedyk [2.9K]

The answer is 73.33333333 (repeated). You can also write it as 73 or 73.3 with a line over the 3 (after the decimal point) to indicate it being repeated.

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3 years ago

Determine f^-1(2) given the following: f(1 = -3f(2) = -2f(-1) = 2f(3) = -1

lana [24]

We assume that the function is as follows:

$f^{-1_{}}(2)=?$

Then, we have that:

$f^{-1}(x)=\frac{1}{f(x)}$

Thus, if we have that:

$f(2)=-2\Rightarrow f^{-1^{}_{}}(x)=\frac{1}{f(x)}\Rightarrow f^{-1}(2)=\frac{1}{f(2)}=\frac{1}{-2}\Rightarrow f^{-1}(2)=-\frac{1}{2}$

Therefore, the value for the function is f^-1(2) = -1/2 or

$f^{-1}(2)=-\frac{1}{2}$

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1 year ago

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Sav [38]

It represents simulations

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