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3 years ago

A slide and its ladder form a right triangle with the ground, with the

Mathematics

1 answer:

zhuklara [117]3 years ago

8 0

Answer:

15.6 ft

Step-by-step explanation:

Let's call

a: distance from the top of the ladder to the ground = 10 ft

b: distance from the bottom of the ladder to the bottom of the slide = 12 ft

c: length of the slide

From Pythagorean theorem:

c² = a² + b²

c = √(10² + 12²)

c = 15.6 ft

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Evaluate c (y + 7 sin(x)) dx + (z2 + 9 cos(y)) dy + x3 dz where c is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (hin

saw5 [17]

Treat $\mathcal C$ as the boundary of the region $\mathcal S$ , where $\mathcal S$ is the part of the surface $z=2xy$ bounded by $\mathcal C$ . We write

$\displaystyle\int_{\mathcal C}(y+7\sin x)\,\mathrm dx+(z^2+9\cos y)\,\mathrm dy+x^3\,\mathrm dz=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r$

with $\mathbf f=(y+7\sin x,z^2+9\cos y,x^3)$ .

By Stoke's theorem, the line integral is equivalent to the surface integral over $\mathcal S$ of the curl of $\mathbf f$ . We have

$\nabla\times\mathbf f=(-2z,-3x^2,-1)$

so the line integral is equivalent to

$\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\mathrm d\mathbf S$
$=\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv$

where $\mathbf s(u,v)$ is a vector-valued function that parameterizes $\mathcal S$ . In this case, we can take

$\mathbf s(u,v)=(u\cos v,u\sin v,2u^2\cos v\sin v)=(u\cos v,u\sin v,u^2\sin2v)$

with $0\le u\le1$ and $0\le v\le2\pi$ . Then

$\mathrm d\mathbf S=\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv=(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv$

and the integral becomes

$\displaystyle\iint_{\mathcal S}(-2u^2\sin2v,-3u^2\cos^2v,-1)\cdot(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv$
$=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}u-6u^4\sin^3v-4u^4\cos v\sin2v\,\mathrm du\,\mathrm dv=\pi$ <span />

4 0

3 years ago

Which of the following is an irrational number? -7 , 7/101, -1/3, pi

Damm [24]

Answer:

Step-by-step explanation:

An irrational number cannot be expressed by two integers.

4 0

3 years ago

What is In 7 days, a group of workers can plant 21 acres. What is their rate in acres per day?

FromTheMoon [43]

So do 21/7 to give you how much they do in a day. The answer is three so they do 3 aceres in a day.

8 0

3 years ago

What is y=-2/3 x + 4 in standard form?

maxonik [38]

Answer:

2x + 3y = 12

Step-by-step explanation:

Standard form is Ax + By = C, A, B and C must be intergers, cannot be fractions or decimals

y = -2/3x + 4 First we want to get rid of the fractions. There is only one, so if we multiply both sides by 3 that should do it.

3y = -2x + 12 Now make the constant be on one side by itself

2x + 3y = 12

5 0

3 years ago

Read 2 more answers

Simplify. (-5.12) - (-4.7) (7.021)

aksik [14]

First, you should do the product first:
(-4.7)* (7.021)= -32.9987

Then, let's do the subtraction:
(-5.12)- (-32.9987)
= (-5.12)+ 32.9987
= 27.8787

Final answer: 27.8787

Hope this would help~

7 0

3 years ago

Read 2 more answers