All categories

4 years ago

Give an example of a number that is a perfect square and also a perfect cube.

Mathematics

2 answers:

Vanyuwa [196]4 years ago

6 0

Answer:

Step-by-step explanation:

$\sqrt{64} \\$ =8

$\sqrt[3]{64}$ =4

scoundrel [369]4 years ago

3 0

The answer is 64 and 729

You might be interested in

Find the values of the Vertex and Axis of symmetry.

Ipatiy [6.2K]

Answer:

it is none of my business ～(つˆДˆ)つ｡☆～(つˆДˆ)つ｡☆(っ.❛ ᴗ ❛.)っ(っ.❛ ᴗ ❛.)っ(っ.❛ ᴗ ❛.)っ

4 0

3 years ago

Evaluate the integral Integral from (5 comma 2 comma 4 )to (7 comma 9 comma negative 3 )y dx plus x dy plus 3 dz by finding para

padilas [110]

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{(5,2,4)}^{(7,9,-3)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz$

Parameterize the line segment (call it $C$ ) by

$\vec r(t)=(1-t)(5\,\vec\imath+2\,\vec\jmath+4\,\vec k)+t(7\,\vec\imath+9\,\vec\jmath-3\,\vec k)$

$\vec r(t)=(2t+5)\,\vec\imath+(7t+2)\,\vec\jmath+(4-7t)\,\vec k$

with $0\le t\le1$ . Then

$\vec r'(t)=2\,\vec\imath+7\,\vec\jmath-7\,\vec k$

and the line integral is

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1((7t+2)\,\vec\imath+(2t+5)\,\vec\jmath+3\,\vec k)\cdot\vec r'(t)\,\mathrm dt$

$=\displaystyle\int_0^1((2t+5)+2(7t+2)-21)\,\mathrm dt$

$=\displaystyle\int_0^1(28t+18)\,\mathrm dt=\boxed{32}$

Alternatively, if we can show that $\vec F$ is conservative, then we can apply the fundamental theorem of calculus. We need to find $f$ such that $\nabla f=\vec F$ , which requires

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

Integrating both sides of the first equation with respect to $x$ gives

$f(x,y,z)=xy+g(y,z)$

Differentiating both sides wrt $y$ gives

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

Differentiating wrt $z$ gives

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}$

$\implies h(z)=3z+C$

So we have

$f(x,y,z)=xy+3z+C$

and $\vec F$ is conservative. By the FTC, we find

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=f(7,9,-3)-f(5,2,4)=\boxed{32}$

5 0

3 years ago

A high school statistics class wants to estimate the average number of chocolate chips in a generic brand of chocolate chip cook

Viktor [21]

Answer:

Correct option:

We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie.

Step-by-step explanation:

The general formula for the (1 - α)% confidence interval for population mean is:

$CI=\bar x\pm CV \times SE_{\bar x}$

Here:

$\bar x$ = sample mean

CV = critical value

$SE_{\bar x}$ = standard error of mean.

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence interval for the mean number of chocolate chips per cookie is (18.6, 21.3).

This 95% confidence interval implies that there is a 0.95 probability that the true mean number of chocolate chips per cookie is between 18.6 and 21.3.

Thus, the correct option is:

"We are 95% certain that the confidence interval of 18.6 to 21.3 includes the true average number of chocolate chips per cookie. "

6 0

3 years ago

Shortest to longest in order 1 mm, 1m, 1cm, 1 km

DanielleElmas [232]

Answer:

1mm, 1cm, 1m, 1km.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Please with full explanation please it's urgent

anyanavicka [17]

Answer:

u have some very good handwriting

3 0

3 years ago