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3 years ago

State whether each pair of terms are like terms. (so yes or no)

Mathematics

1 answer:

Rom4ik [11]3 years ago

7 0

Answer: 4xy and 3xy are, 2s and 5s are, but -10 and -10b aren't.

Step-by-step explanation: 4xy and 2xy have the same terms. 2s and 5s have the same terms but -10a and -10b have different variables.

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To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s

inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

5 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago

PLEASE GIVE THE COMPLETE FACTORED FORM OF THE FOLLOWING: (4 POINTS EACH)

stepan [7]

Answer:

The answer is in pictures.

hope it helps:)

7 0

2 years ago

Find the x-intercept and y-intercept of the liné. - 6x + 5y = 21

Hunter-Best [27]

Answer:

x=-3.5 or -7/2 (same thing)

y=21/5

Step-by-step explanation:

x intercept is when y=0

y intercept is when x=0

x intercept is

-6x=21

x=21/-6

x=-3.5

y intercept is

5y=21

y=21/5

7 0

3 years ago

Find the prime factorization of each number: 11. 29 12. 168

Ray Of Light [21]

29 is a prime number.
Factors of 29: 1 , 29

168 is a composite number, therefore you can find the prime factorization for it. Divide prime factors until what is left is a prime number. Use the tree factor. See attached picture:

Prime factorization of 168: 2, 2, 2, 3, 7

7 0

3 years ago