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Contact [7]

Answer:

We can say that

3x + x + 8 = 32

So:

3x + x + 8 = 32

4x = 32 - 8

4x = 24

x = 24/4

x = 6

6 0

3 years ago

If x-2 is one of the factors of x^4-kx^2+4, find the value of k.

Andrei [34K]

Step-by-step explanation:

Given expression is x⁴-kx²+4 =0

x−2 is a factor of the given expression.

So, x=2

Substitute in the equation, we get

2⁴-k(2)²+4

⇒16+4k+4=0

⇒4k=−20

⇒k=−5

8 0

3 years ago

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

Aidan looked at how many people ride the morning

SashulF [63]

Answer:

Average number of people ride ferry boat = 62 or 63 people

Step-by-step explanation:

Given:

Number of people ride ferry boat

58 59 60 61 62 63 64 65 66 67

Find:

Average number of people ride ferry boat

Computation:

Average mean = Sum of all observation / Number of observation

Average number of people ride ferry boat = [58 + 59 + 60 + 61 + 62 + 63 + 64 + 65 + 66 + 67] / 10

Average number of people ride ferry boat = [625] / 10

Average number of people ride ferry boat = 62.5

Average number of people ride ferry boat = 62 or 63 people

5 0

3 years ago

The minute hand of a clock is 1010 inches long and moves from 12 to 33 o'clock. How far does the tip of the minute hand move?

kenny6666 [7]

Answer: 2929 π inch

Step-by-step explanation:

Circumference is given by= 2πr

Here r= 1010 inches

So Tip of minute hand moves= 2π (1010inch)

= 2020 π inch for an hour

Now it comes from 12 to 33 o'clock= 1.45 hour so,

Tip of minute hand moves= 2020 π inch x 1.45

Tip of minute hand moves= 2929 π inch

5 0

3 years ago