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Marat540 [252]
3 years ago
14

What is the volume of a sphere with a radius of 6mm

Mathematics
1 answer:
sertanlavr [38]3 years ago
8 0
Approximately 904.78
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Andrej [43]

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Choose the answer. 1. (1 pt) use any model you choose to solve the story problem. a fisherman separated of his catch into 2 equa
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3 years ago
For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?
Bond [772]
Given that r=\theta, then r'=1

The slope of a tangent line in the polar coordinate is given by:

m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}

Thus, we have:

m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}



Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

\sin\theta+\theta\cos\theta=0 \\  \\ \theta\cos\theta=-\sin\theta \\  \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

</span><span>θ = 0

</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488



Part B:

For vertical tangent lines, \frac{1}{m} =0

Thus, we have:

\cos\theta-\theta\sin\theta=0 \\  \\ \Rightarrow\theta\sin\theta=\cos\theta \\  \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

</span>θ = <span>4.91718592528713</span>
3 0
3 years ago
IM GIVING BRAINIEST TO THE FIRST CORRECT ANSWER !!! HURRY.
dexar [7]

Answer:

-1,3

Step-by-step explanation:

1 left and 3 up

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The ratio of oil to vinegar is 8:5 how much oil blended with 7 liters vinegar for recipe
Ugo [173]
Write and solve an equation of ratios:

oil       8          x
---- = ---- = -----------
vin      5      7 liters

Then 5x = 56, and x = 56/5 liters (of vinegar)
3 0
3 years ago
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