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kvv77 [185]
3 years ago
6

Find the Perimeter and Area of the following:

Mathematics
1 answer:
Lynna [10]3 years ago
5 0
Peramter 7 and area 49
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An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne
lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

3 0
3 years ago
SHOW YOUR WORK!!<br><br> What is the distance between point A (-3, -2) and Point B (4, -7)?
gulaghasi [49]

Answer: \bold{\sqrt{74}}

<u>Step-by-step explanation:</u>

\text{Use the distance formula: }d_AB=\sqrt{(x_A-x_B)^2+(y_A-y_B)^2}\\where\ (X_A, y_A)=(-3, -2)\\and\ (x_B,y_B)=(4, -7)\\\\\\d_AB=\sqrt{(-3-4)^2+[-2-(-7)]^2}\\\\.\quad =\sqrt{(-7)^2+(5)^2}\\\\.\quad =\sqrt{49+25}\\\\.\quad =\boxed{\sqrt{74}}

3 0
3 years ago
A swimming pool has a length of 12 feet, a width of 8 feet, and a depth of 9 feet. What is the volume of the pool in cubic feet?
Umnica [9.8K]

Answer:

V=864 cubic feet

Step-by-step explanation:

Volume of a rectangular prism is Length x width x depth

So V=12x8x9

V=864 Cubic feet

6 0
2 years ago
what is the inverse of the conditional statement? If a polygon the has five angles, then it is a Pentagon
den301095 [7]

Answer:  The inverse f the given statement is

"If a polygon is not a Pentagon, then it does not have five sides".

Step-by-step explanation:  We are given to write the inverse of the following conditional statement:

"If a polygon the has five angles, then it is a Pentagon".

<u>INVERSE of a conditional statement :</u>

If the conditional statement is

"If p, then q",

then its inverse statement is given by

"If not q, then not p".

Therefore, the inverse of the given statement is

"If a polygon is not a Pentagon, then it does not have five sides".

9 0
3 years ago
Read 2 more answers
Pls need this for today (geometry) all the info I have for the question
Nezavi [6.7K]

Answer:

Step-by-step explanation:

the triangles are similar, also is a right triangle

therefore

16/8=10/x

x=(8*10)/16=5

x=5

3 0
2 years ago
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