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MrMuchimi
3 years ago
8

Ismael has a set of 5 solar panels and Ben has a set of 6 smaller solar panels. Each set of panels produce the same amount of en

ergy. 3 of Ismael's panels are on and producing energy. 4 of Ben's are on and producing more energy. Whose solar panels are producing more energy? Explain.
Mathematics
1 answer:
eimsori [14]3 years ago
5 0

9514 1404 393

Answer:

  Ben's

Step-by-step explanation:

If E is the amount of energy that each full set of panels produces, then ...

  3 of Ismael's 5 panels produce 3/5E

  4 of Ben's 6 panels produce 4/6E

We can compare these fractions when they have a common denominator.

  3/5E = 18/30E . . . . energy from Ismael's panels

  4/6E = 20/30E . . .  energy from Ben's panels

  18/30 < 20/30 . . . . so Ben's panels are producing more energy

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cluponka [151]

Under the given transformation, the Jacobian and its determinant are

\begin{cases}x=uv\\y=u^2\end{cases}\implies J=\begin{bmatrix}v&u\\2u&0\end{bmatrix}\implies|\det J|=2u^2

so that

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\iint_{D'}\frac{2u^2}{u^2}\,\mathrm du\,\mathrm dv=2\iint_{D'}\mathrm du\,\mathrm dv

where D' is the region D transformed into the u-v plane. The remaining integral is the twice the area of D'.

Now, the integral over D is

\displaystyle\iint_D\frac{\mathrm dx\,\mathrm dy}y=\left\{\int_0^6\int_{x^2/2}^{x^2}+\int_6^{12}\int_{x^2/2}^{6x}\right\}\frac{\mathrm dx\,\mathrm dy}y

but through the given transformation, the boundary of D' is the set of equations,

\begin{array}{l}y=x^2\implies u^2=u^2v^2\implies v^2=1\implies v=\pm1\\y=\frac{x^2}2\implies u^2=\frac{u^2v^2}2\implies v^2=2\implies v=\pm\sqrt2\\y=6x\implies u^2=6uv\implies u=6v\end{array}

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\displaystyle2\iint_{D'}\mathrm du\,\mathrm dv=2\int_1^{\sqrt2}\int_0^{6v}\mathrm du\,\mathrm dv=\boxed6

4 0
3 years ago
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kenny6666 [7]

Answer:

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Order of Operations: BPEMDAS

Step 1: Translate (z - 6)

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- = difference

6 = six

(z - 6) = The difference between a number <em>z</em> and 6

Step 2: Translate 8(z - 6)

(z - 6) = The difference between a number <em>z</em> and 6

Since we are distributing the 8, we are multiplying.

8 times the difference of a number <em>z</em> and 6

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3 years ago
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Answer:

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Step-by-step explanation:

1. You want to find the volume of the box. (Length x width x height)

2.5 x 2 x 1.5 = 7.5

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prohojiy [21]

Answer:

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Then we can write two equations:

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Now we can take the quotient of these two equations to get:

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Solving this for x, we get:

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