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3 years ago

B Which pair of lines are skew? CAE, DH ET, EH BC, CG AG, FE FE, BC

Mathematics

1 answer:

deff fn [24]3 years ago

7 0

Answer:

I think CAE, DH is the answer not sure

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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

3 years ago

What is the product of <br><br> 2x+3 and 4x^2-5x+6 .

stira [4]

Answer:

Explanation:

We have:

(

)

(

−

)

Now let's distribute this piece by piece:

(

)

(

)

(

)

(

−

)

−

(

)

(

)

(

)

(

)

(

)

(

−

)

−

(

)

(

)

And now we add them all up (I'm going to group terms in the adding):

−

And now simplify:

−

18Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

a class conduct a survey of 1000 students At one point 6% of the students forgot their locker combination, how many forgot their

jek_recluse [69]

You need to multiply 1000 by 0.06 (6% in decimal form) to get the answer. When you multiply you get 60 so the answer is 60 students forgot their locker combination.

4 0

3 years ago

Three fair dice are rolled, one red, one green and one blue. What is the probability that the upturned faces of the three dice a

r-ruslan [8.4K]

Answer: $\dfrac{5}{9}$

Step-by-step explanation:

When we throw a die , Total outcomes =6

When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]

Given : Three fair dice are rolled, one red, one green and one blue.

Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed

By Permutations , the number of favorable outcomes = $^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120$

The probability that the upturned faces of the three dice are all of different numbers = $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$=\dfrac{120}{216}=\dfrac{5}{9}$

The probability that the upturned faces of the three dice are all of different numbers is $\dfrac{5}{9}$ .

7 0

3 years ago

What is the measure of the exterior angle at D?

coldgirl [10]

Answer:

360-63

=297 my guy

7 0

4 years ago