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3 years ago

Find the slope of the line that contains the points (-9, 4) and (-7, -2).

Mathematics

1 answer:

Nataliya [291]3 years ago

3 0

Answer:

-3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-2-4)/(-7-(-9))

m=-6/(-7+9)

m=-6/2

m=-3

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Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large

Debora [2.8K]

Answer:

x = 1,6 in ( the side of the corner squares )

V(max) = 67,58 in³

Step-by-step explanation:

The cardboard is:

L = 12 in w = 8 in

Let´s call "x" the side of the square from the corner:

Then the sides of the base of the open box are:

( L - 2*x ) and ( w - 2*x ) and x is the height

( 12 - 2*x ) and ( w - 2*x )

V(ob) = (L - 2*x ) * ( - 2*x ) * x

Wich is a function of x

V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x

V(x) = ( 96 - 24*x - 16*x + 4*x²) * x

V(x) = 96*x - 40*x² + 4*x³

Tacking derivatives on both sides of the equation

V´(x) = 12*x² - 80*x + 96

V´(x) = 0 12*x² - 80*x + 96 = 0

Solving for x

x₁,₂ = 80 ± √ 6400 - 4608 / 24

x₁,₂ = 80 ± 42,33 / 24

x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20

ant this value is bigger than 8 inches

x₂ = 1,60 in

Therefore dimensions of the box

a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in

b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in

And the volume of the open box is:

V(max) = 8,8*4,8*1,6

V(max) = 67,58 in³

How do we Know that is the maximun value for V?

We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6

3 0

3 years ago

The length of a rectangle is represented by the function L(x) = 5x. The width of that same rectangle is represented by the funct

Mazyrski [523]

Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.

In this case, we could say (where $A(x)$ is the area of the rectangle):

$A(x) = L(x) \cdot W(x)$

Substituting the values the problem gave us for $L(x)$ and $W(x)$ , we can find the formula for $A$ in terms of $x$ , which is:

$A(x) = (5x) \cdot (2x^2 - 4x + 13) = (10x^3 - 20x^2 + 65x)$

The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.

3 0

3 years ago

Read 2 more answers

If 14x = ^13√14, what value of x makes this equation true?

Andrews [41]

The value of x is 1/13 (4th choice)

Step-by-step explanation:

${a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} }$

If 14^x = ¹³√14, what value of x makes this equation true?

$\sqrt[13]{14} = {14}^{x} \\ \sqrt[13]{14} = {14}^{ \frac{1}{13} }$

So, the value of x is 1/13 (4th choice)

Hope it helpful and useful :)

6 0

3 years ago

480 is what percent greater than 160

MrMuchimi

160 is 100% of 160, 480 is 4 times that. So 400%

7 0

3 years ago

Read 2 more answers

A plane made a trip to Miami and back. It flew 400mph on the way there and flew 450mph on the return trip. How long did the trip

quester [9]

Answer:

equation: 400 + ( 450×10)= h

h= 4900.

4 0

3 years ago