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LekaFEV [45]
3 years ago
13

Toby wants to buy 2 concert tickets that cost $19 each. His makes $4.75 an hour while he mows lawns. How many hours will he need

to mow lawns in order to buy the two tickets?
8


10


12
Mathematics
1 answer:
nikitadnepr [17]3 years ago
8 0
Cost of a ticket = $19
So, cost of two tickets = 19 * 2 = $38

Now, he makes, $4.75 in an hour.
Let, the number of hours for that much money = x

It would be: 4.75x = 38
x = 38 / 4.75
x = 8 hours

In short, Your Answer would be 8 hours

Hope this helps!
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Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the o
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Speed=\frac{y}{x}

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y2=80x

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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2
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The Jacobian for this transformation is

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with determinant |J| = 12, hence the area element becomes

dA = dx\,dy = 12 \, du\,dv

Then the integral becomes

\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv

where R' is the unit circle,

\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1

so that

\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}

Then

\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}

3 0
2 years ago
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