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3 years ago

7000 is 10 times as much as

Mathematics

1 answer:

Rzqust [24]3 years ago

6 0

7,000=10x -- divide by. 10
x=700

7000 is 10x as much as 700.

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An assembly line produces 20 items per hour. If the line runs 24 hours per day, 7 days week, how many items are made by this mac

Margaret [11]

20x24x30 = 14,400
14,400 items

7 0

4 years ago

Solve the following equation:

Rama09 [41]

Complete the square.

$z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0$

$\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4$

Use de Moivre's theorem to compute the square roots of the right side.

$w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)$

$\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2$

Now, taking square roots on both sides, we have

$z^2 + \dfrac12 = \pm w^{1/2}$

$z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2$

Use de Moivre's theorem again to take square roots on both sides.

$w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)$

$\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}$

$w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)$

$\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}$

3 0

2 years ago

What is the area of the triangle in the diagram?

amm1812

Answer:

I think the answer is B. Let me know if im right

Step-by-step explanation:

l*w*1/2 is the same as 1/2*y*(x2-x1)

7 0

3 years ago

Read 2 more answers

Find the gradient of the line segment between the points (-1,3) and (1,-2).

RideAnS [48]

The answer is -5/2, hope this helps you!

4 0

3 years ago

If f(x) = 2x – 1 and g(x) = ^ – 2, find [g ◦ f](x).

Viefleur [7K]

Answer:

The value of [g ◦ f](x) = $4x^{2} -4x-1$

Step-by-step explanation:

If f(x) = 2x - 1

g(x) = $x^{2} -2$

we need to find the value of [g ◦ f](x).

which means that g(f(x))

g(f(x)) = $(2x-1)^{2} -2$

g(f(x)) = $4x^{2} -4x+1 -2$

g(f(x)) = $4x^{2} -4x-1$

The value of [g ◦ f](x) = $4x^{2} -4x-1$

6 0

4 years ago