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dimaraw [331]
3 years ago
6

- 2x - 147 = 123 + 7x

Mathematics
2 answers:
k0ka [10]3 years ago
7 0
-2x - 147 = 123 + 7x
Add 147 on both sides
-2x = 270 + 7x
Subtract 7x on both sides
-9x = 270
Divide -9x on both sides
X = -30
worty [1.4K]3 years ago
6 0

Answer:

<h2>x = -30</h2>

Step-by-step explanation:

-2x-147=123+7x\qquad\text{add 147 to both sides}\\\\-2x-147+147=123+147+7x\\\\-2x=270+7x\qquad\text{subtract }\ 7x\ \text{from both sides}\\\\-2x-7x=270+7x-7x\\\\-9x=270\qquad\text{divide both sides by (-9)}\\\\\dfrac{-9x}{-9}=\dfrac{270}{-9}\\\\x=-30

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Answer:

r = 5.848cm, h = 11.696cm

Step-by-step explanation:

Surface area: SA=2\pi rh+2\pi r^2

Volume: V=\pi r^2h

Therefore, the height of a cylinder given its volume would be h=\frac{V}{\pi r^2}, thus:

SA=2\pi r(\frac{V}{\pi r^2})+2\pi r^2\\\\SA=\frac{2V}{r}+2\pi r^2\\\\SA=\frac{2(400\pi)}{r}+2\pi r^2\\\\SA=\frac{800\pi}{r}+2\pi r^2

We now find the derivative of the surface area of the cylinder with respect to its radius and set it equal to 0, solving for the radius:

\frac{d(SA)}{dr}=-\frac{800\pi}{r^2}+4\pi r

0=-\frac{800}{r^2}+4\pi r

0=800\pi+4\pi r^3

-800\pi=4\pi r^3

-200=r^3

r\approx5.848

If 0If [tex]r>5.848, then the surface area of the cylinder increases

Therefore, the surface area is minimized when the radius is r=5.848cm, making the minimum height h=\frac{V}{\pi r^2}=\frac{400\pi}{\pi(5.848)^2}\approx11.696cm.

In conclusion, the 2nd option is correct.

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3 years ago
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So, we need to figure out how much times the body size of the flea it can jump. First, we need to figure out the size of the flea: <em>2^-4=0.0625</em>

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After we figure out the size of the flea, we need to divide 8 by .0625 because it is inverse operations to multiplication: <em>8/.0625=128</em>

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4 years ago
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We are to solve for the vertical and horizontal component of the force he is pulling with.

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Question 1:

If Jason is pulling with a force of 19 Newtons and his arm is at an angle of 30° with the horizontal.

By resolving Jason's force of pull in the vertical direction, Fy = 19 × Sin 30° = 9.5 Newtons.

The <em>vertical</em> component of Jason's force is 9.5 Newtons.

Question 2:

Also,If Jason is pulling with a force of 14 Newtons and his arm is at an angle of 79° with the <em>horizontal</em>.

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By resolving Jason's force of pull in the <em>vertical</em> direction, Fy = 23 × Sin 30° = 11.5Newtons.

The vertical component of Jason's force of pull is, 11.5Newtons.

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By treating up as the +ve vertical direction and down as the -ve vertical direction,

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Therefore, the net force in the vertical direction is = 11.5Newtons + (-24Newtons)

Therefore, the net force in the vertical direction is -12.5Newtons.

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If there are two forces at right angles to eachother, one of magnitude, 68 and the other of magnitude, 24.

The resultant force on the object can be obtained by Pythagoras theorem (Triangle law of forces).

Resultant, R = √(68²+24²) = √5200.

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