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Rzqust [24]
3 years ago
7

How are the surface area and volume of a rectangular prism related to each other?

Mathematics
1 answer:
MatroZZZ [7]3 years ago
7 0
The surface area of a rectangular prism is equal to the volume of a rectangular prism on their cooresponding sides.
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The perimeter of a rectangular baking sheet is 58 inches and its area is 201.25 in.2. What are the length and width of the bakin
anzhelika [568]

Answer:

Length=17.5\ in\\\\Width=11.5\ in

Step-by-step explanation:

The formula for calculate the Area of a rectangle is:

A=lw

Where "l" is the lenght and "w" is the width.

And the formula for calculate the peimeter of a rectangle is:

P=2l+2w

Where "l" is the lenght and "w" is the width.

We know that the perimeter of the rectangular baking sheet is 58 inches and its area is 201.25 in². Then:

A=201.25\ in^2\\\\P=58\ in

<u>The steps are:</u>

1. Solve for the "l" from the formula A=lw:

A=lw\\\\l=\frac{A}{w}\\\\\l=\frac{201.25}{w}

2. Substitute l=\frac{201.25}{w} into the formula P=2l+2w and solve for "w":

58=2(\frac{201.25}{w})+2w\\\\58=\frac{402.5}{w}+2w\\\\58=\frac{402.5+2w^2}{w}\\\\58w=402.5+2w^2\\\\2w^2-58w+402.5=0

Applying the Quadratic formula x=\frac{-b\±\sqrt{b^2-4ac}}{2a}, we get:

x=w=\frac{-(-58)\±\sqrt{(-58)^2-4(2)(402.5)}}{2(2)}\\\\w_1=17.5\\\\w_2=11.5

3.  Substitute w_1=17.5 into l=\frac{201.25}{w}:

l=\frac{201.25}{17.5}=11.5

4. Substitute w_2=11.5 into l=\frac{201.25}{w}:

l=\frac{201.25}{11.5}=17.5

Therefore, since the value of the lenght of a rectangle must be greater that the value of the width, we can conclude that the lenght and the width of the rectangular baking sheet are:

l=17.5\ in\\\\w=11.5\ in

8 0
4 years ago
Suppose that during it's flight, the elevation `e` (in feet) of a certain airplane and its time `t,` in minutes since takeoff, a
kifflom [539]

Answer:

Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time ... since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. ... Unit 3; Linear Relationships Lesson 9: Slopes Don't Have to be Positive.

Step-by-step explanation:

8 0
3 years ago
18 Points! K12 Student struggling with deadline!
Liula [17]

Answer:

B.

Step-by-step explanation:

The easiest way is to substitute 8 for x in the first equation,

5 0
3 years ago
A function f defined by f(x) = x² + px + q is such that f(3) = 6 and f¹(3) = 0. Find the value of q.
CaHeK987 [17]

Answer:

q = 15

Step-by-step explanation:

Given

f(x) = x² + px + q , then

f(3) = 3² + 3p + q = 6 , that is

9 + 3p + q = 6 ( subtract 9 from both sides )

3p + q = - 3 → (1)

---------------------------------------

f'(x) = 2x + p , then

f'(3) = 2(3) + p = 0, that is

6 + p = 0 ( subtract 6 from both sides )

p = - 6

Substitute p = - 6 into (1)

3(- 6) + q = - 3

- 18 + q = - 3 ( add 18 to both sides )

q = 15

5 0
3 years ago
Expand &amp; simplify: (x + 1)(x + 3)
Sindrei [870]

Answer:

368

Step-by-step explanation:

5 0
4 years ago
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