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mars1129 [50]
3 years ago
8

Convert the equation into slope-intercept form 2x+3y=9

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
8 0
Convert the equation into slope-intercept form 2x+3y=9

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( h -3 )2 for h = 5 what is it
Nookie1986 [14]

Answer: 4

Step-by-step explanation:

Substitute the value of the <u><em>variable</em></u> into the <u><em>equation</em></u> and simplify.

I evaluate and found the exact value: 4

( h -3 )2 \\h = 5

If you want me to Find the Linearization at h=5: Use the formula L(x)=f(a)+f'(a) (x-a)  to find the linearization.

Answer(Find the Linearization at h=5): L(x)=2x-6

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What would be the answer to this question?
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2 years ago
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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:

<u>Mass</u>

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

<u>Center of mass</u>

<em>Coordinate x</em>

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

<em>Coordinate y</em>

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

<em>Coordinate z</em>

\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)

so

\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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Write a word problem that can be solved by ordering three decimals to thousandths. Include a solution.
kolbaska11 [484]

Problem:

Jacob purchased a water plant. While testing, he found that in 1 ml of water, a particular salt content was 0.0078 grams. Find the salt content in 1 ltr of water.

Solution:

Salt content in 1 mil of water = 0.0078 g.

Salt content in 1000 ml of water = 0.0078(1000)

                                                      = 7.8 g.

7 0
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