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garik1379 [7]
3 years ago
5

I have 45 cents in nickels.

Mathematics
1 answer:
pentagon [3]3 years ago
5 0

Answer:

135

Step-by-step explanation:

43 times 3 is 135

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What expression is equal to 6(-3m) times 4
ololo11 [35]

Answer:

-18x4

Step-by-step explanation:

8 0
3 years ago
Evaluate the surface integral. S xz dS S is the boundary of the region enclosed by the cylinder y2 + z2 = 16 and the planes x =
bagirrra123 [75]

If you project S onto the (x,y)-plane, it casts a "shadow" corresponding to the trapezoidal region

T = {(x,y) : 0 ≤ x ≤ 10 - y and -4 ≤ y ≤ 4}

Let z = f(x, y) = √(16 - y²) and z = g(x, y) = -√(16 - y²), each referring to one half of the cylinder to either side of the plane z = 0.

The surface element for the "positive" half is

dS = √(1 + (∂f/∂x)² + (∂f/dy)²) dx dy

dS = √(1 + 0 + 4y²/(16 - y²)) dx dy

dS = √((16 + 3y²)/(16 - y²)) dx dy

The the surface integral along this half is

\displaystyle \iint_T xz \,dS = \int_{-4}^4 \int_0^{10-y} x \sqrt{16-y^2} \sqrt{\frac{16+3y^2}{16-y^2}} \, dx \, dy

\displaystyle \iint_T xz \,dS = \int_{-4}^4 \int_0^{10-y} x \sqrt{16+3y^2}\, dx \, dy

\displaystyle \iint_T xz \,dS = \frac12 \int_{-4}^4 (10-y)^2 \sqrt{16+3y^2} \, dy

\displaystyle \iint_T xz \,dS = 416\pi

You'll find that the integral over the "negative" half has the same value, but multiplied by -1. Then the overall surface integral is 0.

8 0
3 years ago
Convert from rectangular to polar coordinates:Note: Choose r and θ such that r is non-negative and 0 ≤ θ < 2πa. (6,0)b. (9,9/
Anuta_ua [19.1K]

Answer:

The polar coordinates are as follow:

a. (6,2π)

b. (18, π/3)

c. (2√2 , 3π/4)

d. (2, 5π /6)

Step-by-step explanation:

To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .

To calculate r, we use Pythagorean theorem:

r = \sqrt{ x^{2} +y^{2} } ---- (1)

To calculate the θ, first we will find out the θ '  using the inverse of cosine as it is easy to calculate.

So,    θ '  = cos ⁻¹  (x/r)

If  y  ≥  0  then  θ  =  ∅

If  y  <  0  then  θ  =  2 π  −  ∅

For a. (6,0)

Sol:

Using the formula in equation (1). we get the value of r as:

r = \sqrt{6^{2} + 0^{2}  }

r = 6

And ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (6/6)

∅  =cos ⁻¹   (1) = 2π

As If  y  ≥  0  then  θ  =  ∅

So ∅ = 2π

The polar coordinates are (6,2π)

For a. (9,9/\sqrt{3})

Sol:

r = 9 + 3(3) = 18

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (9/18)

∅ = cos ⁻¹   (1/2) = π/3

As  If  y  ≥  0  then  θ  =  ∅

then θ  = π/3

The polar coordinates are (18, π/3)

For (-2,2)

Sol:

r =√( (-2)²+(2)² )

r = 2 √2

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (-2/ 2 √2)

∅ = 3π/4

As  If  y  ≥  0  then  θ  =  ∅

then   θ  = 3π/4

The polar coordinates are (2√2 , 3π/4)

For (-√3, 1)

Sol:

r = √ ((-√3)² + 1²)

r = 2

and ∅  = cos ⁻¹  (x/r)

∅  = cos ⁻¹ ( -√3/2)

∅  = 5π /6

As  If  y  ≥  0  then  θ  =  ∅

So  θ  = 5π /6

The polar coordinates are (2, 5π /6)

6 0
3 years ago
"if the standard deviation of a group of 20 scores is 15, what is the variance?"
DerKrebs [107]

We have been given that the standard deviation of a group of 20 scores is 15 and we are asked to find variance.

Since we know variance is square of standard deviation. In order to find out the variance of the given data we have to take the square of 15.

\text{ Variance}=\sigma^{2}\\&#10;=15^{2}=225

Therefore, our variance is 225.


7 0
3 years ago
A high school student named David Merrell did a study of how music affects the ability of rats to run a maze. He trained 71 rats
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