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kkurt [141]
2 years ago
9

LMNP is rotated 180 degrees clockwise around the origin. What are the coordinates of L?

Mathematics
1 answer:
Alona [7]2 years ago
4 0

\huge\boxed{L^\prime(0, -1)}

To rotate a point around the origin by 180 degrees, multiply both parts of the coordinate point by -1. (This means you go from (x, y) to (-x, -y).)

L(0, 1)

L^\prime(0*(-1), 1*(-1))\\\boxed{L^\prime(0, -1)}

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A circular cylindrical container, open at the top, and having a capacity of 24pi cubic inches, is to be manufactured. If the cos
otez555 [7]

Answer: radius r = 2 inches

height h = 6 inches

Step-by-step explanation:

Given;

Volume V = 24πin3

Volume of a cylinder is given by

V = πr^2h

h = V/πr^2. ....1

Where, h = height and r = radius of cylinder

For the surface area of the cylinder with open top. we have,

S = 2πrh + πr^2

For the cost of materials used, let k represent the cost of materials used for the body of the cylinder.

Then, for the bottom will be 3k

Total cost will be represented by C, which gives

C = 2πrhk + 3πr^2k. .....2

Substituting eqn 1 to 2, we have;

C = 2πrVk/πr^2 + 3πr^2k

C = 2Vk/r + 3πr^2k

The material cost is minimum at dC/dr = 0

dC/dr = -2Vk/r^2 + 6πrk =0

6πrk = 2Vk/r^2

r^3 = 2V/6π

r = (2×24π/6π)^-3

r = (8)^-3

r = 2

Substituting r = 2 into eqn1

h = 24π/π(2^2)

h = 24/4 = 6

h = 6

5 0
3 years ago
Answer this!!!!!!!!!
muminat

Surface area = area of 2 triangular sides + area of the roof + area of the base.

= 2 * 1/2 * 6 * 4 + 2 * 5*7 + 6 * 7

= 24 + 70 + 42

= 136 units^2

8 0
3 years ago
Find the domain and range of f(x) = 2 square root of x-2
Neporo4naja [7]
f(x)=2\sqrt{x-2}\\\\The\ domain:\\x-2\geq0\to x\geq2\\\boxed{x\in[2;\ \infty)}\\\\The\ range:\\\boxed{y\in[0;\ \infty)}

If\ f(x)=2\sqrt{x}-2,\ then\\\\The\ domain:\boxed{x\in[0;\ \infty)}\\\\The\ range:\boxed{y\in[-2;\ \infty)}
5 0
3 years ago
Divide z4 by z-3<br><br>A. z1<br>B. z7<br>C. z-12<br>D. z12<br>E. z-7
lakkis [162]
If you mean z to the powers given the answer will be B
5 0
3 years ago
Eva has £6.05 in her moneybox.
PIT_PIT [208]

Answer:

11 of 20p, 22 of 10p and 33 of 5p

Step-by-step explanation:

Eva has 20p, 10p and 5p coins, total of £6.05 = 605p

Let 20p=x, 10p=y, 5p=z

<u>Then</u>:

  • 20x + 10y + 5z = 605
  • y : x = 2 : 1 ⇒ x= y/2
  • y : z = 2 : 3 ⇒ z= 3y/2

<u>Rewriting the first equation considering next two:</u>

  • 10y + 10y + 7.5y = 605
  • 27.5y = 605
  • y= 605/27.5
  • y= 22
  • x= y/2 = 22/2 = 11
  • z = 3y/2 = 3*11 = 33

<u>Answer:</u> 11 of 20p coins, 22 of 10p coins and 33 of 5p coins

3 0
3 years ago
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