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3 years ago

Given AC with A(3, 4) and C(-9, -2), if B

Mathematics

1 answer:

babymother [125]3 years ago

6 0

Answer:

B = (- 4, $\frac{1}{2}$ )

Step-by-step explanation:

Using the Section formula

$x_{B}$ = $\frac{7(-9)+5(3)}{7+5}$ = $\frac{-63+15}{12}$ = $\frac{-48}{12}$ = - 4

$y_{B}$ = $\frac{7(-2)+5(4)}{7+5}$ = $\frac{-14+20}{12}$ = $\frac{6}{12}$ = $\frac{1}{2}$

Thus coordinates of B = (- 4, $\frac{1}{2}$ )

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An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from e

laila [671]

Answer:

x=4 Inch

Step-by-step explanation:

Length of the Square = 24 Inches

If a Square of Length x cm is cut out from each corner

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Simplifying

V(x)=4x(12-x)(12-x)

To determine the value of x at which V is largest, we take the derivative of V(x) and solve for the critical points.

V(x)=4x(12-x)(12-x)

$V^{'}(x)=12(x-12)(x-4)$

Set the derivative equal to zero to obtain the critical points

$V^{'}(x)=12(x-12)(x-4)=0\\Since \: 12\neq 0\\(x-12)(x-4)=0\\x-12=0 \:or\: x-4=0\\x=12 \:or\: x=4$

x cannot be equal to 12 as it divides the length of the square cardboard into exactly two equal parts.

When x=4

V(4)=4*4(12-4)(12-4)=16*8*8=1024 Cubic Inches

When x=4 Inch, the volume, V of the open box is largest.

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3 years ago