1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
NeX [460]
3 years ago
9

I need 33. B) find the exact time when the radius reaches 10 inches 100 points! Plz help

Mathematics
1 answer:
stealth61 [152]3 years ago
3 0

Step-by-step explanation:

You have found a function r(V(t)). We can see that this function is a one variable function. The variable is time.

So in this specific function we can call r(v(t)), r(t).

So:

r(t) =  \sqrt[3]{ \frac{3 \times (10 + 20t)}{4\pi} }

If α is the moment that the radius is 10 inches and since the function above gives radius in inches we have to solve the equation:

r( \alpha ) = 10

Which is the same as:

\sqrt[3]{ \frac{3 \times (10 + 20 \alpha )}{4\pi} }  = 10 \\  \frac{3 \times (10 + 20 \alpha )}{4\pi}  = 1000 \\ (10 + 20 \alpha ) =  \frac{4000\pi}{3}  \\ 20 \alpha  =  \frac{(4000\pi - 30)}{3} \\  \alpha  =  \frac{(4000\pi - 30)}{60}

You might be interested in
How do you solve this?
puteri [66]

Answer:

Width: 7

Length: 14

Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let x represent the width.

Since the length is 7 feet longer, we can represent the length by x+7.

Now that we have our values for the length and the width we can multiply them together to find our area.

(x)(x+7)=x^{2} +7x

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

(x+7)(x+14)

And multiply our area by 3.

3(x^{2} +7x)

set these equal to each other to find your new equation.

(x+7)(x+14)=3(x^{2} +7x)

Now you need to solve for x. To do this first muliply (x+7) and (x+14).

(x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98

Then multiply 3(x^{2} +7x)

3(x^{2} +7x)=\\3x^{2} +21x

Now you can begin solving for x.

x^{2} +21x+98=3x^{2} +21x

Subtract x^{2} from both sides.

21x+98=2x^{2} +21x

Subtract 21x from both sides.

98=2x^{2}

Divide by 2.

49=x^{2}

And finally take the sqaure root of both sides.

\sqrt{x^{2} }=\sqrt{49}\\x=7

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.

Now that we have the value of x, we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

7 0
3 years ago
What is the standard form of twenty-one and six hundred thirty-four thousandths
bija089 [108]

Answer:

21,634 is the answer im pretty sure

Step-by-step explanation:

i think

4 0
3 years ago
Where should she place the top-left corner of the left-most plaque? 9feet high 11 feet wide 6in of space 2 wide
labwork [276]

Answer:

78

Step-by-step explanation:

8 0
3 years ago
"All parallelograms have two pairs of parallel sides. All rectangles are parallelograms with four right angles. All squares are
Lorico [155]
A. Yes, since a square is a type of rectangle, but it has four congruent and parallel side.
B. Yes, since a square is also a type of parallelogram. Therefore it has 2 pairs of parallel sides.
C. No, they have 2 pairs of congruent sides.
Hope this helps :D
4 0
3 years ago
Read 2 more answers
The lifespan (in days) of the common housefly is best modeled using a normal curve having mean 22 days and standard deviation 5.
Natasha_Volkova [10]

Answer:

Yes, it would be unusual.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If Z \leq -2 or Z \geq 2, the outcome X is considered unusual.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1

Would it be unusual for this sample mean to be less than 19 days?

We have to find Z when X = 19. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{19 - 22}{1}

Z = -3

Z = -3 \leq -2, so yes, the sample mean being less than 19 days would be considered an unusual outcome.

7 0
3 years ago
Other questions:
  • Simplify the fraction ​
    14·1 answer
  • What is the number 1 2 3 and 4
    6·1 answer
  • What is the difference when the product of 0.3 and 0.4 is subtracted from the sum of 0.3 and 0.4?​
    5·1 answer
  • How long will it take 4000 to grow to 9000 if it is invested at 7% compounded monthly
    9·1 answer
  • The multiplication property of equality could be used to solve which of the following equations?
    13·1 answer
  • Refer previous problem. Suppose that you wish to estimate the difference between the mean acidity for rainfalls at two different
    14·1 answer
  • Solve the following proportion for x.
    12·2 answers
  • The smallest number that has 3,7 and 11 as prime factors
    8·1 answer
  • A 9,000-gallon silo of wheat is being drained at a rate of 500 gallons per hour. A 7,000-gallon silo of wheat is being filled at
    10·1 answer
  • Find x in the diagram below.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!