40 plus 26!!!!!!!! Like legit
Answer:
8.06 inches
Step-by-step explanation:
The diagram shows a rectangle with width of 4 inches and area of 28 square inches.
Use area formula:

So,

By the Pythagorean theorem,

Hi there!
So we are given that:-
- tan theta = 7/24 and is on the third Quadrant.
In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.
Since we want to find the value of cos theta. cos must be less than 0 or in negative.
To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.
<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>I</u><u>d</u><u>e</u><u>n</u><u>t</u><u>i</u><u>t</u><u>y</u>

Substitute tan theta = 7/24 in.

Evaluate.

Reminder -:

Hence,

Because in QIII, cos<0. Hence,

<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>P</u><u>y</u><u>t</u><u>h</u><u>a</u><u>g</u><u>o</u><u>r</u><u>e</u><u>a</u><u>n</u><u> </u><u>T</u><u>h</u><u>e</u><u>o</u><u>r</u><u>e</u><u>m</u>

Define c as our hypotenuse while a or b can be adjacent or opposite.
Because tan theta = opposite/adjacent. Therefore:-

Thus, the hypotenuse side is 25. Using the cosine ratio:-

Therefore:-

Because cos<0 in Q3.

Hence, the value of cos theta is -24/25.
Let me know if you have any questions!
Answer:
Step-by-step explanation:
The the area of the rectangular pen be A = LW
L is the length
W is the width
Given
A = 3136ft²
3136 = LW..........1
Given the perimeter P = 2L+2W....... 2
From 1; L = 3136/W
Substitute into 2
P = 2(3136/W)+2W
P = 6272/W + 2W
In order to minimize the amount of material needed, then dP/dW = 0
dP/dW = -6272/W² + 2
0 = -6272/W² + 2
6272/W² = 2
cross multiply
6272 = 2W²
W² = 3136
W = √3136
W = 56ft
Since A = LW
3136 = 56L
L = 3136/56
L = 56ft
Hence the dimensions of the rectangular pen that minimize the amount of material needed is 56ft by 56ft