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2 years ago

60 POINTS!!!! PLEASE HELP URGENT

Mathematics

1 answer:

sammy [17]2 years ago

3 0

Using linear combination method to solve the system of equations 3x - 8y = 7 and x + 2y = -7 is (x, y) = (-3, -2)

<h3><u>Solution:</u></h3>

Given that, a system of equations are:

3x – 8y = 7 ⇒ (1) and x + 2y = - 7 ⇒ (2)

We have to solve the system of equations using linear combination method and find their solution.

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.

Now, let us multiply equation (2) with 4 so that y coefficients will be equal numerically.

4x + 8y = -28 ⇒ (3)

Now, add (1) and (3)

3x – 8y = 7

4x + 8y = - 28

----------------

7x + 0 = - 21

7x = -21

x = - 3

Now, substitute "x" value in (2)

(2) ⇒ -3 + 2y = - 7

2y = 3 – 7

2y = - 4

y = -2

Hence, the solution for the given two system of equations is (-3, -2)

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If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

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Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$

Then

$\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.$

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