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Olin [163]
4 years ago
9

Quick plz help asap marking brainliest for first answer as long as you include steps !!!

Mathematics
1 answer:
Akimi4 [234]4 years ago
7 0

Answer:

a=2.48

c=9.52

Step-by-step explanation:

a+c=12

4a+7.5c=72.5 Given


a+c=12

-4a-7.5c=-72.5 multiply the equation by negative 1


-3a-6.5c=-60.5 simplify


-3a=-60.5+6.5c add 6.5c to both sides


a=-20.17+2.17c divide it by 3

now you would take that equation and plug it into an equation you already have since you have something to plug in for a, the easiest one to do is a+c=12

(-20.17+2.17c)+c=12 plug in the equation


-20.17+3.17c=12 simplify by solving for c


3.17c=30.17 add 20.17 to both sides


c=9.52 divide both sides by 3.17

now since you have found c, you can plug it in to you equation to solve for a now (use the ones from the second step).  I am using the equation a+c=12.

a+9.52=12 plug in the variable and solve for a


a=2.48 subtract 9.52 to both sides


a=2.48

c=9.52

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Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = sqrt(25x) and y = x^2/25. Find V b
Westkost [7]

Explanation:

Let f(x) = \sqrt{25x} and g(x) = \frac{x^2}{25}. The differential volume dV of the cylindrical shells is given by

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\displaystyle V = 2\pi\int{x[f(x) - g(x)]}dx

To determine the limits of integration, we equate the two functions to find their solutions and thus the limits:

\sqrt{25x} = \dfrac{x^2}{25}

We can clearly see that x = 0 is one of the solutions. For the other solution/limit, let's solve for x by first taking the square of the equation above:

25x = \dfrac{x^4}{(25)^2} \Rightarrow \dfrac{x^3}{(25)^3} = 1

or

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Since we are rotating the functions around the y-axis, we are going to use the x = 25 solution as one of the limits. So the expression for the volume of revolution around the y-axis is

\displaystyle V = 2\pi\int_0^{25}{x\left(\sqrt{25x} - \frac{x^2}{25}\right)}dx

\displaystyle\:\:\:\:=10\pi\int_0^{25}{x^{3/2}}dx - \frac{2\pi}{25}\int_0^{25}{x^3}dx

\:\:\:\:=\left(4\pi x^{5/2} - \dfrac{\pi}{50}x^4\right)_0^{25}

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4 0
3 years ago
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elixir [45]

Answer:

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Step-by-step explanation:

4 - 5x < 22 - 2x rearrange the expression so like terms will be in the same sides of inequation

4 - 22 < -2x + 5x

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3 years ago
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.........................

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Answer:

Step-by-step explanation:

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7 0
3 years ago
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gtnhenbr [62]
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2c + 2d = 4.60
----------------
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-----------------add
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c = 4.10 - 2.70
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4 years ago
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