Find solution to the equation x+4=7 if the replacement set us (1,2,3,4,5)

Use cylindrical coordinates to evaluate the triple integral ∭ where E is the solid bounded by the circular paraboloid z = 9 - 16

4vir4ik [10]

Answer:

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

Step-by-step explanation:

The Cylindrical coordinates are:

x = rcosθ, y = rsinθ and z = z

From the question, on the xy-plane;

$9 -16 (x^2 + y^2) = 0 \\ \\ 16 (x^2 + y^2) = 9 \\ \\ x^2+y^2 = \dfrac{9}{16}$

$x^2+y^2 = (\dfrac{3}{4})^2$

where:

0 ≤ r ≤ $\dfrac{3}{4}$ and 0 ≤ θ ≤ 2π

∴

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} \int ^{9-16r^2}_{0} \ r \times rdzdrd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 z|^{z= 9-16r^2}_{z=0} \ \ \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 ( 9-16r^2}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} ( 9r^2-16r^4}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( \dfrac{9r^3}{3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3r^3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) d \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) \theta |^{2 \pi}_{0}$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{64}}-\dfrac{243}{320}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{160}})2 \pi$

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

4 0

2 years ago

Which polynomial is a perfect square trinomial? (4 points) 9x2 − 12x + 4 36b2 − 24b + 16 16x2 − 24x − 9 4a2 − 10a − 25ynomial is

o-na [289]

Answer:

9x² − 12x + 4

Step-by-step explanation:

A perfect square trinomial:

a² + 2ab +b²= (a + b)²

a² - 2ab +b²= (a - b)²

9x² − 12x + 4 = (3x)² - 2*(3x)*2 + 2² = (3x - 2)²

36b² − 24b + 16

16x² − 24x − 9

4a² − 10a − 25

8 0

2 years ago

Read 2 more answers

Solve absolute value equation 2|x-3|-8=2

Semmy [17]

Answer:

$x=8, -2$

Step-by-step explanation:

$2|x-3|-8=2$

$2|x-3|=10$

$|x-3|=5$ $|x-3|=-5$

$x-3=5$ $x-3=-5$

$x=8$ $x=-2$

7 0

2 years ago

Can anyone help me with this?

Maurinko [17]

Answer:

D. -6m²n² + 10m²n + 8mn² - 10mn

Step-by-step explanation:

(-7mn + 8mn² - 8m²n²) + (10m²n + 2m²n² - 3mn)

Apply the distributive property to remove the parentheses

-7mn + 8mn² - 8m²n² + 10m²n + 2m²n² - 3mn

Combine like terms together and arrange in standard form

-7mn + 8mn² - 8m²n² + 10m²n + 2m²n² - 3mn

-8m²n² + 2m²n² + 10m²n + 8mn² - 7mn - 3mn

-6m²n² + 10m²n + 8mn² - 10mn

5 0

2 years ago

Can somebody please help me with this question?

meriva

What, this is math right?

7 0

2 years ago