<img src="https://tex.z-dn.net/?f=%5Cint%5C%7B-2%2B%28x%5E%7B2%7D%20%2B3x%29%5E%286%2F5%29%20-%20x%5E3%7D%20%5C%2C%20dx" id="Tex

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3 years ago

Formula1" title="\int\{-2+(x^{2} +3x)^(6/5) - x^3} \, dx" alt="\int\{-2+(x^{2} +3x)^(6/5) - x^3} \, dx" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

gogolik [260]3 years ago

3 0

Apply sum rule:

- 2dx + (x^2 +3x) 6/5dx = x^3dx

2dx = 2x

(x^2 + 3x) 6/5dx = 6/5 (x^3/3 + 3x^2/2)

x^3dx = x^4/4

-2x + 6/5 (x^3/3 + 3x^2/2) - x^4/4

Add constant

-2x + 6/5 (x^3/3 + 3x^2/2) - x^4/4 + c

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If the height of a cone is 7.5 cm and the radius is 2 cm, find the approximate volume of the cone.

larisa86 [58]

Volume: h • pi r^2

Volume: (7.5) • pi (2)^2

Volume: 94.247796

Just round to your teacher’s liking

6 0

3 years ago

I neeeeeeeeeeeeeed help

masya89 [10]

9514 1404 393

Answer:

14 +2i

Step-by-step explanation:

For this sort of problem, you can treat i as though it were a variable. Combine like terms.

(8 -7i) +(6 +9i) = (8 +6) +(-7 +9)i

= 14 +2i

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3 years ago

What is The simple interest earned on a deposit of $3000 at 6% for five years

Norma-Jean [14]

Answer: $900

Step-by-step explanation:

The simple interest is calculated using the formula:

(P × R × T)/100

where,

P = Principal = $3000

R = Rate = 6%

T = Time = 5 years

Simple Interest = (P × R × T)/100

= ($3000 × 6 × 5)/100

= 90000/100

= $900

Therefore, the simple interest is $900

4 0

3 years ago

You estimated the average rental cost of a 2 bedroom apartment in Denton. A random sample of 16 apartments was taken. The sample

Zigmanuir [339]

Answer:

The new sample size required in order to have the same confidence 95% and reduce the margin of erro to $60 is:

n=28

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=160)$

And the distribution for $\bar X$ is:

$\bar X \sim N(\mu, \frac{160}{\sqrt{n}})$

We know that the margin of error for a confidence interval is given by:

$Me=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The next step would be find the value of $\z_{\alpha/2}$ , $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$

Using the normal standard table, excel or a calculator we see that:

$z_{\alpha/2}=\pm 1.96$

If we solve for n from formula (1) we got:

$\sqrt{n}=\frac{z_{\alpha/2} \sigma}{Me}$

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And we have everything to replace into the formula:

$n=(\frac{1.96(160)}{78.4})^2 =16$

And this value agrees with the sample size given.

For the case of the problem we ar einterested on Me= $60, and we need to find the new sample size required to mantain the confidence level at 95%. We know that n is given by this formula:

$n=(\frac{z_{\alpha/2} \sigma}{Me})^2$

And now we can replace the new value of Me and see what we got, like this:

$n=(\frac{1.96*160}{60})^2 =27.32$

And if we round up the answer we see that the value of n to ensure the margin of error required $Me=\pm 60$ $ is n=28.

5 0

3 years ago

Help me please show ur work

Lisa [10]

Let the length of the patio is x and width is 3/4x
So according to the equation x.3/4x = 432
x^2. 3/4 =432
x^2 =432 times 4/3
x^2 =1728/3 =576
x= 24

The length is 24 ft

5 0

3 years ago