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polet [3.4K]
3 years ago
10

What is 90,090,010 in expanded form​

Mathematics
1 answer:
tester [92]3 years ago
3 0

Answer:

90,000,000 + 90,000 + 10


I hope this helped!

Step-by-step explanation:


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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>
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3 years ago
The difference of two numbers is equal to 0.6. Their quotient is also 0.6. What are the numbers? There are 4
Makovka662 [10]
Let the two numbers be represented by x and y. The problem statement gives rise to two sets of equations.
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or
  x/y = 0.6 . . . . . . . assuming y has the larger magnitude

The solution of the first pair of equations is
  (x, y) = (1.5, 0.9)

The solution of the first and last equations is
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The pairs of numbers could be {0.9, 1.5} or {-1.5, -0.9}.
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3 years ago
A. What is 50% of R1,00?
gladu [14]

Answer:

1000÷50%=2000

Step-by-step explanation:

hope it helps

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spayn [35]

Answer:

Step-by-step explanation:

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CD is a perpendicular bisector of chord AB and a chord through CD passes through the center of a circle. Find the diameter of th
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Answer:

12\frac{1}{5} in

Step-by-step explanation:

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