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2 years ago

6) The quotient of seven and a number. added to ten w

Mathematics

1 answer:

Andreyy892 years ago

5 0

Ten more than a number. X + 10 ... Eleven added to a number. A number minus seven x + 2 added to x + 11. Subtraction

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Round your answer to the nearest whole. use Pie as 3.14

sladkih [1.3K]

To find the volume of a cylinder you must use the formula:

πr^2h

1) Plug in your variables
π(3)^2•(11)

2) Solve
~ 311.01 cm^3

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3 years ago

Rafael deposits $5000 into and account that pays simple interest at an annual 5%. He does not make anymore deposits. He makes no

nekit [7.7K]

Answer:

Step-by-step explanation:

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2 years ago

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A car moves a distance of 100m in 12 seconds. what is the average speed in km/h

Maksim231197 [3]

Answer:

30km/h.

Step-by-step explanation:

100m/12s = 0.1km/12s

There are 3600 seconds in an hour.

0.1km/12s = 30km/h.

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3 years ago

Find the mass and the center of mass of a wire loop in the shape of a helix (measured in cm: x = t, y = 4 cos(t), z = 4 sin(t) f

Sholpan [36]

Answer:

Mass

$\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)$

Center of mass

Coordinate x

$\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Coordinate y

$\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Coordinate z

$\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Step-by-step explanation:

Let W be the wire. We can consider W=(x(t),y(t),z(t)) as a path given by the parametric functions

x(t) = t

y(t) = 4 cos(t)

z(t) = 4 sin(t)

for 0 ≤ t ≤ 2π

If D(x,y,z) is the density of W at a given point (x,y,z), the mass m would be the curve integral along the path W

$m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt$

The density D(x,y,z) is given by

$D(x,y,z)=x^2+y^2+z^2=t^2+16cos^2(t)+16sin^2(t)=t^2+16$

on the other hand

$||W'(t)||=\sqrt{1^2+(-4sin(t))^2+(4cos(t))^2}=\sqrt{1+16}=\sqrt{17}$

and we have

$m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt=\\\\\sqrt{17}\displaystyle\int_{0}^{2\pi}(t^2+16)dt=\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)$

The center of mass is the point $(\bar x,\bar y,\bar z)$

where

$\bar x=\displaystyle\frac{1}{m}\displaystyle\int_{W}xD(x,y,z)\\\\\bar y=\displaystyle\frac{1}{m}\displaystyle\int_{W}yD(x,y,z)\\\\\bar z=\displaystyle\frac{1}{m}\displaystyle\int_{W}zD(x,y,z)$

We have

$\displaystyle\int_{W}xD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}t(t^2+16)dt=\\\\=\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)$

$\bar x=\displaystyle\frac{\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

$\displaystyle\int_{W}yD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}4cos(t)(t^2+16)dt=\\\\=16\sqrt{17}\pi$

$\bar y=\displaystyle\frac{16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

$\displaystyle\int_{W}zD(x,y,z)=4\sqrt{17}\displaystyle\int_{0}^{2\pi}sin(t)(t^2+16)dt=\\\\=-16\sqrt{17}\pi$

$\bar z=\displaystyle\frac{-16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

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2 years ago

ABC is a right triangle. If AB = 3 and AC = 7, find BC. Leave your answer in simplest radical form.

aivan3 [116]

1. Suppose that BC is hypotenuse, then by Pythagorean theorem:
$BC^2=AC^2+AB^2, \\ BC^2=3^2+7^2, \\ BC^2=9+49, \\ BC^2=58, \\ BC= \sqrt{58}$ .
2. If BC is not hypotenuse, then BC is a leg and AC is hypotenuse (because AC>AB). Hence by Pythagorean theorem:
$AC^2=AB^2+BC^2, \\ 7^2=3^2+BC^2, \\ BC^2=49-9, \\ BC^2=40, \\ BC= \sqrt{40} =2 \sqrt{x10}$ .

8 0

3 years ago

Read 2 more answers