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3 years ago

Hello please help i’ll give brainliest

Mathematics

1 answer:

Margarita [4]3 years ago

5 0

Answer:

Explanation:

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Find the derivative with respect to x of the integral from 2 to x^3 of ln(x^2)dx

strojnjashka [21]

The derivative follows from the fundamental theorem of calculus:

$\displaystyle\frac{\mathrm d}{\mathrm dx}\int_c^{g(x)}f(t)\,\mathrm dt=f(g(x))\dfrac{\mathrm dg}{\mathrm dx}$

where $c$ is any constant in the domain of $f$ .

We have

$g(x)=x^3\implies\dfrac{\mathrm dg}{\mathrm dx}=3x^2$

$\displaystyle\frac{\mathrm d}{\mathrm dx}\int_2^{x^3}\ln(t^2)\,\mathrm dt=3x^2\ln((x^3)^2)=18x^2\ln x$

(applying the property $\ln a^b=b\ln a$ )

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3 years ago

If x=(y+2)^2 and y= -7 then what is the value of x

vova2212 [387]

Answer:

Step-by-step explanation:

(y+2)^2=x

(-7+2)^2=x

(-5)^2=x

(-5)(-5)=x

25=x

Hope that helps :)

8 0

3 years ago

Read 2 more answers

A USA Today/CNN/Gallup survey of 369 working parents found 200 who said they spend too little time with their children because o

KengaRu [80]

Answer: a. 0.542

b. 0.051

c. $(0.491,\ 0.593)$

Step-by-step explanation:

Let p be the population proportion of parents spend too little time with their children because of work commitments

As per given , we have

n= 369

$\hat{p}=\dfrac{200}{369}=0.542005420054\approx0.542$

Since the sample proportion is the best estimate for the population proportion.

So , the point estimate of the proportion of the population of working parents who feel they spend too little time with their children because of work commitments = 0.542

z-value for 95% confidence interval : $z_{\alpha/2}=1.96$

Margin of error : $E=z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$E=(1.96)\sqrt{\dfrac{0.542(1-0.542)}{369}}\\\\=0.0508364564574\approx0.051$

The margin of error = 0.051

Confidence interval : $\hat{p}\pm E$

$0.542\pm0.051\\\\=(0.542-0.051,\ 0.542+0.051)\\\\=(0.491,\ 0.593)$

95% confidence interval estimate of the population proportion of working parents who feel they spend too little time with their children because of work commitments : $(0.491,\ 0.593)$

6 0

3 years ago

Find the scale factor of the small triangle to the large triangle.

Korvikt [17]

Answer:

scale factor is: 2.25

Step-by-step explanation:

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3 years ago

A sphere has a volume of 4500pi cubic feet what is the radius of the sphere

Fofino [41]

Answer:

S = $900\pi in^2$

Step-by-step explanation:

$V = 4\pi r^3 /3\\\\\\13500\pi = 4\pi r^3\\\\\\r^3 = \frac{13500\pi }{4\pi } \\\\\\r^3 = 3375\\\\\\r = 15 in\\\\\\S = 4\pi r^2\\\\S = 4\pi 15^2\\\\S = 900 \pi in^2$

5 0

4 years ago

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