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3 years ago

Help me with this one pls

Mathematics

2 answers:

larisa [96]3 years ago

5 0

Answer:

C) $9x^2+24x+16$

Step-by-step explanation:

$\left(3x+4\right)^2$

Use Perfect Square Formula :

$\left(a+b\right)^2=a^2+2ab+b^2$

$\left(3x\right)^2+2\cdot \:3x\cdot \:4+4^2$

$9x^2+24x+16$

OAmalOHopeO

Effectus [21]3 years ago

4 0

Expand it, so you will get 9x^2 + 24x + 16

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Answer: 1/4

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3 years ago

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What is the slope of a line that contains the points (1 -2) and (4, -3).

Naddika [18.5K]

Answer:

$-\frac{1}{3}$

Step-by-step explanation:

Use the definition of slope:

$m=\frac{y_2-y_1}{x_2-x_1}\\$

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$m=\frac{-3-(-2)}{4-1} \\m=\frac{-1}{3}\\m=-\frac{1}{3}$

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2 years ago

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

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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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3 years ago

What is the volume of the cylinder below?

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Answer:

Step-by-step explanation:

It is C.

Volume-πr^2h

r-11

h-15

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