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The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. Th

Orlov [11]

The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

<h3>How to determine the length</h3>

The cosine rule is given as;

$c = \sqrt{a^2 + b^2 - 2ab cos \alpha }$

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

$c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}$

$c = \sqrt{533 - 308 * 0. 7660}$

$c = \sqrt{533 - 235. 93}$

$c = \sqrt{297. 072}$

$c = 17. 24$ feet

Using sine rule

$\frac{a}{sin A } = \frac{c}{sin C}$

$\frac{a}{sin 70} = \frac{17. 24}{sin 40}$

Cross multiply

$a$ × $sin 60$ = $c$ × $sin 70$

$a$ × $0. 8660$ = $17. 24$ × $0. 9397$

$a = \frac{16. 20}{0. 8660}$

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

Learn more about isosceles trapezoid here:

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5 0

2 years ago

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

The perimeter of a rectangle is 48 m. The area of the rectangle is 128 square meters. Find the dimensions of the rectangle.

Andreas93 [3]

Answer:

l = 16, w = 8

Step-by-step explanation:

Let l = length

Let w = width

Area = w * l

128 = w * l

w = 128/l

Perimeter = 2w + 2l

48 = 2w + 2l

48 = 2(128/l) +2l

48 = 256/l +2l

Multiply everything by l

48l = 256 + 2l^2

l^2 + 128 = 24l

l^2 + 128 -24l = 0

(l-16)(l-8)= 0

L = 16

L = 8

If you try them out, and test it, l = 16 would work:

2(16) + 256/16 = 48

32 + 16 =48

16 * 128/16 = 128

16 * 8= 128

128 = 128

Since I'm not sure if you are in advanced math or not, I will do it simple with guess and check

Try w is

3 0

3 years ago

I give brainliest!!!!

Elza [17]

Answer:

(3，2) i hope this answer will help you

7 0

3 years ago

Read 2 more answers

Which is the coefficient in the algebraic expression 12x + z^4 ?

love history [14]

I think the coefficient is the 12, before the variable

8 0

3 years ago

Read 2 more answers