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3 years ago

The formula for the bowline of a sphere is V=4/3πr^3. solve for r

Mathematics

1 answer:

Tpy6a [65]3 years ago

5 0

Answer:

$r=\sqrt[3]{\frac{3V}{4\pi}}$

Step-by-step explanation:

$v= \frac{4}{3} \pi r^3$

We need to isolate 'r'

To isolate 'r' , first multiply by 3 on both sides

$3v=4* \pi r^3$

divide by 4pi on both sides

$\frac{3V}{4\pi} = r^3$

Take cube root on both sides

$\sqrt[3]{\frac{3V}{4\pi}}= r$

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Find the value of x. Round the length to the nearest tenth.

Mamont248 [21]

From right triangle trigonometry, we have the following:

$\displaystyle{ tan(35^o)= \frac{opposite \ side }{adjacent \ side }$ ,

where the "opposite side" means the opposite side to angle with measure $35^o$ , and "adjacent side" means the adjacent side to angle with measure $35^o$ .

$tan(35^o)$ is a constant which can be found using a calculator.

In the calculator of the pc press: view - scientific - 35 - tan.

This gives $tan(35^o)=0.7$

Thus, back in the equation $\displaystyle{ tan(35^o)= \frac{opposite \ side }{adjacent \ side }$ we substitute as follows and solve:

$\displaystyle{0.7= \frac{x }{12 }\\\\$

$x=0.7\cdot12=8.4$

Answer: 8.4 cm

5 0

2 years ago

Read 2 more answers

1 If 2x+2 = 32, then x =

VashaNatasha [74]

The answer would be x=15

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3 years ago

A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides

ivolga24 [154]

Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

=(15-2x)(10-2x)x cubic inches

=(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ , here a=12, b= -100 and c=15

$x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}$

$\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}$

$\Rightarrow x=0.1528,8.18$

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, $V''|_{x=0.1528}=24(0.1528)-100$

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.

4 0

3 years ago

What information does the ordered pair (3, 87) represent?

mafiozo [28]

<span>The 3 (x-coordinate) indicates that from the origin (0,0) in the cartesian plane, you have traveled four units to the right along the x-axis(the horizontal axis). </span>

<span>The 87 indicates that you traveled 87 units up in the y-axis(vertical axis), in line with the point 3 in the x-axis.This number is the y-coordinate, the second number in the ordered pair. </span>

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2 years ago

100pts: Why was obsidian used to make scalpels?

Margaret [11]

Answer:

Research also confirms that incisions carried out with obsidian produce narrower scars and fewer inflammatory cells. This is because on cellular level, obsidian knife cuts between cells rather than tearing it in case of a steel knife, hence, a sharper cut allows the wound to heal more easily with negligible scarring.

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2 years ago

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