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2 years ago

5. Skylar has pool toys shaped like a sphere

Mathematics

1 answer:

slega [8]2 years ago

6 0

Answer:

128π or 402.12

Step-by-step explanation:

Vol of a sphere = 4/3πr³

Sub 2 into ^

Multiply by 12 to find vol of all 12 shapes

This is the volume of water needed

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Ex 4.8 14) integrate 3^(2x-1)

sesenic [268]

Take the integral:

$\large\begin{array}{l} \mathsf{\displaystyle\int\!3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\int\!\frac{1}{2}\cdot 2\cdot 3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^{2x-1}\cdot 2\,dx\qquad(i)} \end{array}$

$\large\begin{array}{l} \textsf{Substitute}\\\\ \mathsf{2x-1=u\quad\Rightarrow\quad 2\,dx=du}\\\\\\ \textsf{so (i) becomes}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^u\,du}\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{1}{\ell n\,3}\,3^u+C}\\\\ =\mathsf{\dfrac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}$

$\large\begin{array}{l} \boxed{\begin{array}{c}\mathsf{\displaystyle\int\!3^{2x-1}\,dx=\frac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}}\qquad\checkmark \end{array}$

If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154165

$\large\textsf{I hope it helps. :-)}$


Tags: integrate indefinite integral substitution exponential base logarithm log ln composite integral calculus

4 0

3 years ago

The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5600. The distributi

pshichka [43]

Answer:

$E(\bar{x}) = 28520$

Standard error of mean = 689

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $28,520

Standard Deviation, σ = $5600

Mean of sampling distribution =

$E(\bar{x}) = \mu = 28520$

As per Central Limit Theorem, if the sample size is large enough, then the sampling distribution of the sample means follow approximately a normal distribution.

Sample size, n = 66

Since the sample size is large, we can use normal distribution for approximation.

Standard error of mean =

$\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{5600}{\sqrt{66}} = 689.31 \approx 689$

7 0

2 years ago

Please help! If possible please show your work :D Thank you! Solve.

nataly862011 [7]

Equation at the end of step1: (7x + 18) (4) - 4x = 0 2 STEP2:Equation at the end of step 2 2 • (7x + 18) - 4x = 0 STEP3:STEP4:Pulling out like terms

4.1 Pull out like factors :

10x + 36 = 2 • (5x + 18)

Equation at the end of step4: 2 • (5x + 18) = 0 STEP5:Equations which are never true:

5.1 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2 Solve : 5x+18 = 0

Subtract 18 from both sides of the equation :

5x = -18

Divide both sides of the equation by 5:

x = -18/5 = -3.600

6 0

2 years ago

Please help me on this

emmainna [20.7K]

I got 1/81

hope this helps.

8 0

2 years ago

Read 2 more answers

What are the soulutions of x^2+6x-6=10?

tia_tia [17]

Answer:x= -8 or 2

Step-by-step explanation:

6 0

3 years ago