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2 years ago

5

You own a townhome valued at $232,088, but still owe $165,111 on the loan. You also have $7,342 in savings and a balance of $2,1

45 on his credit cards. There is a balance of $22,260 owed on your car which is valued at $31,034. What is your net worth

1 answer:

olya-2409 [2.1K]2 years ago

4 0

232088-165111+7342-2145-22260+31034=$89048

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

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How do I find the area of a triangle

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Answer:

Area of triangle = ½ × base × height

Step-by-step explanation:

(A = ½ × b × h)

This formula is mainly used to find the area of the triangle.

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Given f(x) = x^2 - 5x, find f(x-3)

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Answer:

f(x-3)= x^2 -11x +24

Step-by-step explanation:

We want to find an equivalent expression for f(x-3)

To do this, we can simply substitute every 'x' variable in f(x) by 'x-3'

Therefore f(x-3)= (x-3)^2 -5*(x-3)

Lets re arrange the expression by grouping terms.

f(x-3)=x^2 - 6x +9 -5x + 15

f(x-3)= x^2 -11x +24

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Answer:

Step-by-step explanation:

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If f(x) =4x-2 and g(x) =2x+8, what is h (x) when h (x) =f (x) +g(x)

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Answer:

h(x)=4x_2+2x+8

h(x)=6x+6

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