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2 years ago

A car drives with a constant speed of 20 km/h. How long will it take to travel a distance of 160 kilometers?

Mathematics

1 answer:

harkovskaia [24]2 years ago

5 0

ANSWER:

We know that,

Speed = Distance/Time

So, Time taken = 20kmh-¹/160km

1/8h or 7.5min.

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Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

4 0

2 years ago

the cost of 5 cans of dog food is $4.35. at this price how much do 11 cans of dog food cost explain your reasoning. ASAP

mestny [16]

Answer:

Cost of 11 cans of Dog food is $9.57

Step-by-step explanation:

Cost of 5 cans of dog food = $4.35

So to find out the cost of 11 cans of dog food at the same price, we need to calculate the price of 1 can of dog food.

Calculation for finding out cost of 1 can of dog food

The price $4.35 which is given is the price of 5 cans

So to find the cost of 1 can, we need to divide the given price by 5

5 Cans of dog food = $4.35

1 can of dog food = 4.35 ÷ 5

1 can of dog food = $0.87

Now to find out the price of 11 cans, we will multiply the price of 1 can with 11

Cost of 11 cans = 11 × $0.87

= $9.57

6 0

2 years ago

An incoming airplane is x miles due north from the control tower at an airport. A second incoming airplane is y miles due east o

MAVERICK [17]

Answer:

B. Square root

Step-by-step explanation:

using distance formula:

x = √z^2 - y^2

y = √z^2 - x^2

=> z = √x^2 + y^2

5 0

3 years ago

Read 2 more answers

I need help showing steps to solve 36v-12=12

Ad libitum [116K]

36v - 12 = 12 .....add 12 to both sides
36v - 12 + 12 = 12 + 12...simplify
36v = 24...divide both sides by 36
(36/36)v = 24/36
v = 2/3 <===

8 0

3 years ago

Read 2 more answers

1\3 generate equivalent fractions

Llana [10]

Multiply 1/3 by any number higher than 2 and you can have equivalent fractions.
Ex:
1/3×3/3=3/9

8 0

3 years ago