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babymother [125]
3 years ago
6

Here is the region of integration of the integral Integral from negative 6 to 6 Integral from x squared to 36 Integral from 0 to

36 minus y dz dy dx. Rewrite the integral as an equivalent integral in the following orders. a. dy dz dx by. dy dx dz c. dx dy dz d. dx dz dy e. dz dx dy
Mathematics
1 answer:
Soloha48 [4]3 years ago
3 0

Answer:

a) ∫_{-6}^{6} ∫_{0}^{36} ∫_{x²}^{36} (-y) dy dz dx

b)  ∫_{0}^{36} ∫_{-6}^{6} ∫_{x²}^{36} (-y) dy dx dz

c)  ∫_{0}^{36} ∫_{x²}^{36} ∫_{-6}^{6} (-y) dx dy dz

e) ∫_{x²}^{36} ∫_{-6}^{6} ∫_{0}^{36} (-y) dz dx dy

Step-by-step explanation:

We write the equivalent integrals for given integral,

we get:

a) ∫_{-6}^{6} ∫_{0}^{36} ∫_{x²}^{36} (-y) dy dz dx

b)  ∫_{0}^{36} ∫_{-6}^{6} ∫_{x²}^{36} (-y) dy dx dz

c)  ∫_{0}^{36} ∫_{x²}^{36} ∫_{-6}^{6} (-y) dx dy dz

e) ∫_{x²}^{36} ∫_{-6}^{6} ∫_{0}^{36} (-y) dz dx dy

We changed places of integration, and changed boundaries for certain integrals.

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Answer: $9 per hour at his job as a cashier and $8 per hour at his job delivering newspapers.

Step-by-step explanation:

1. Let's call the amount he got paid per hour at his job as a cashier: x.

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2. Keeping on mind the information given in the problem above, you can make the following system of equations:

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3. You can solve it by applying the Substitution method, as following:

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5x+4y=77\\5x=77-4y\\x=\frac{77-4y}{5}=15.4-0.8y

Then:

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Therefore he got paid $9 per hour at his job as a cashier and $8 per hour at his job delivering newspapers.

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