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3 years ago

What is the solution to the equation below? Round your answer to two decimal places. 2^3x=91

2 answers:

tatiyna3 years ago

4 0

11.38
(I’m not sure if this was the equation you asked for or not. Sorry if it isn’t ❤️)

2^3 = 8

So:

9x = 91

Divide both sides by 9

x = 91/9
x = 11.38

~~hope this helps~~

Flauer [41]3 years ago

4 0

Answer:

The solution of the equation is $x=2.169..$

Step-by-step explanation:

Given : Equation $2^{3x}=91$

To find : What is the solution to the equation below?

Solution :

Equation $2^{3x}=91$

Taking log both side,

$\log(2^{3x})=\log(91)$

Apply logarithmic property, $\log a^x=x\log a$

$3x\log(2)=\log(91)$

$3x=\frac{\log(91)}{\log(2)}$

$x=\frac{\log(91)}{3\log(2)}$

$x=2.169..$

Therefore, The solution of the equation is $x=2.169..$

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S_A_V [24]

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2 years ago

Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

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

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
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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

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