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2 years ago

What is the value of x

Mathematics

1 answer:

jok3333 [9.3K]2 years ago

8 0

Answer:

Step-by-step explanation:

x = (1/2)(172 - 52)

x = (1/2)(120)

x = 60

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A car’s stopping distance in feet is modeled by the equation d(v)=2.15vsquared over 58.4f, where v is the initial velocity of th

frutty [35]

According to your description, you can simply plug in all the numbers:

d(47) = 2.15 * 45^2 / (58.4*0.34) = 219.27 m

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2 years ago

Read 2 more answers

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

Tomtit [17]

Apparently my answer was unclear the first time?

The flux of F across S is given by the surface integral,

$\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S$

Parameterize S by the vector-valued function r(u, v) defined by

$\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k$

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2. Then the surface element is

dS = n • dS

where n is the normal vector to the surface. Take it to be

$\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}$

The surface element reduces to

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv$

so that it points toward the origin at any point on S.

Then the integral with respect to u and v is

$\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS$

$=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS$

$=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}$

4 0

3 years ago

Can someone please help me with this problem? <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%28%20x%5E%7B2%7D%20%2B8x%2

hodyreva [135]

First, factor the expression on the top. What two numbers add to get 8 and multiply to 15? 5 and 3! so the top expression factors to (x+3)(x+5). You can cancel the x+3 from the denominator and end up with x+5. Make sense?

7 0

2 years ago

What are the zeros of the function <img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%202x%20%5E%7B2%7D%20-8x%20-%2010" id="Tex

allsm [11]

Hello there!

To find the zeroes or the roots of a function, you just need to set the function equal to 0 then solve for x

f(x) = 2x² - 8x - 10

Set function equal to 0

2x² - 8x - 10 = 0

Now we can factorize the left side

2(x + 1)(x - 5) = 0

Then set factors equal to 0

x + 1 = 0 or x - 5 = 0

x = 0 - 1 or x = 0 + 5

x = -1 or x = 5

Thus,

The roots are -1 and 5

Let me know if you have any questions. As always, it is my pleasure to help students like you~!

7 0

2 years ago

Help me out guys!!!!!!!

Dmitrij [34]

Answer:

$\frac{5 \sqrt{11} }{11}$

you are correct !!

3 0

1 year ago