Step by step explanation of y-10=9(x+8), written in standard form

Write five other iterated integrals that are equal to the given iterated integral. 8 0 x2 0 y f(x, y, z) dz dy dx 0

mash [69]

An iterated integral is the outcome of taking integrals toward a function of more than one variable in such a way that part of the variables is treated as constants for each of the integrals.

From the given parameters, we are to write out five iterations for a triple integral;

$\mathbf{\int ^8_0\ \int^{x^2}_{0} \ \int^y_0 \ \ f(x, y, z) \ dz dy dx }$

where;

the region is bounded by 0 ≤ z ≤ y, 0 ≤ y ≤ x², 0 ≤ x ≤ 8.

Thus, since x, y, z are functions of at least one variable, we can have the following iterations:

$\mathbf{\int^{64}_{0} \ \int^{8}_{\sqrt{y}} \ \int^{y}_{0} \ \ f(x,y,z) dz dxdy}$

$\mathbf{\int^{64}_{0} \ \int^{y}_{0} \ \int^{8}_{\sqrt{y}} \ \ f(x,y,z)\ dxdzdy}$

$\mathbf{\int^{64}_{0} \ \int^{64}_{z} \ \int^{8}_{\sqrt{y}} \ \ f(x,y,z)\ dxdydz}$

$\mathbf{\int^{8}_{0} \ \int^{x^2}_{0} \ \int^{x^2}_{z} \ \ f(x,y,z)\ dydzdx}$

$\mathbf{\int^{64}_{0} \ \int^{8}_{\sqrt{z}} \ \int^{x^2}_{z} \ \ f(x,y,z)\ dydxdz}$

Learn more about iterated integrals here:

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4 0

2 years ago

Evaluate.<br><br> 102 ÷ 25 • 20 + 4 ÷ 2 – 14

vredina [299]

Answer: 30.8

Step-by-step explanation:

if you follow the rules of PEMDAS you'll get 30.8

4 0

3 years ago

Read 2 more answers

Shianne is looking up at the flag on the top of the sailboat she is sailing on. She is sitting 16 feet from the bottom

storchak [24]

Answer:

height of the flag from the bottom of the boat ≈ 32 ft (nearest foot)

Step-by-step explanation:

She is on her boat and the angle of elevation to the top of the flag is 58°. Her eyes her 6 ft above the bottom of the boat she is sailing on. The height of the flag from the bottom of the boat is the sum of the height of the flag and the remaining height from the horizontal line of sight upward to the flag top.

A right angle triangle was formed Shianne line of sight. The angle from her line of sight is 58° from the horizontal. Therefore,

the adjacent side of the triangle formed is 16 ft which is the distance from the boat to the flag.

adjacent side = 16 ft

opposite angle = ?

using tangential ratio

tan 58° = opposite/adjacent

tan 58° = h/16

cross multiply

h = 16 × 1.60033452904

h = 25.6053524647

height of the flag from the bottom of the boat = 25.6053524647 + 6 = 31.6053524647

height of the flag from the bottom of the boat ≈ 32 ft(nearest foot)

7 0

3 years ago

The Montegro Flooring Company can replace 200 square feet of carpet with tile in one day They accept a job replacing carpet with

choli [55]

It will take 5 days for Montegro Flooring Company to complete this job

<u>Solution:</u>

Given, The Montegro Flooring Company can replace 200 square feet of carpet with tile in one day

They accept a job replacing carpet with tile in an apartment that measures 977.5 square feet

We have to find how many days will it take the Montegro Flooring Company to complete this job?

Now, according to given information,

200 square feet ⇒ 1 day

Then, 977.5 square feet ⇒ n days

Now, by chris cross method

$\begin{array}{l}{200 \times n=1 \times 977.5} \\\\ {200 n=977.5} \\\\ {n=\frac{977.5}{200}=4.8875}\end{array}$

Hence, the company requires 5 days approximately.

5 0

4 years ago

Complementary angles are two angles that have measures with a sum of 90°. Angles P and Q are complementary and the measure of an

Pachacha [2.7K]

Answer:

P = 62° Q = 28°

Step-by-step explanation:

Let x = measure of angle Q

then y = measure of angle P

Now x + y = 90 and 2x + 6 = y

Substituting 2x + 6 from the second equation in for y in the first equation, we get x + 2x + 6 = 90 since the two angles are complementary.

3x + 6 = 90

3x = 84

x = 28

y = 2(28) + 6 = 56 + 6 = 62

Check: 28 + 62 = 90

4 0

3 years ago