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1 year ago

A deep-sea diver dives from the surface to 131 feet below the

Mathematics

1 answer:

Darina [25.2K]1 year ago

8 0

Answer:

146 feet below the surface

Step-by-step explanation:

$-131+8-18-28+23=-146$

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Complex numbers & DeMoivre's theory<br> If z=-1-√3 i and z^6=a+bi, a=_____ and b=_____

Mice21 [21]

Convert $z$ to exponential/polar/trigonometric form:

$r=|z|=\sqrt{(-1)^2+(-\sqrt 3)^2}=2$

$\tan\theta=\dfrac{-\sqrt3}{-1}\implies\theta=\dfrac{4\pi}3$

$\implies z=-1-\sqrt3\,i=2e^{4\pi/3\,i}=2\left(\cos\dfrac{4\pi}3+i\sin\dfrac{4\pi}3\right)$

By DeMoivre's theorem,

$z^6=\left(2e^{4\pi/3\,i}\right)^6=2^6e^{24\pi/3\,i}=64e^{8\pi\,i}$

$z^6=64\left(\cos8\pi+i\sin8\pi)=64$

so that $a=64$ and $b=0$ .

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3 years ago

Write an equation of a line that passes through the point (7, 3) and is parallel to the line y = negative 2 over 3x + 3.

alexandr1967 [171]

Parallel lines have the same slope, but different y-intercepts

The slope of both lines is -2/3

To find the equation that passes through (7, 3) we can use the point-slope formula: y - y1 = m (x - x1)

y - (3) = (-2/3) (x - (7))

y - 3 = -2/3x + 4 and 2/3

y = -2/3x + 7 and 2/3

y = -2/3x + 7.67

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2 years ago

in a sale there is twenty five per cent off all prices a bed cost £33 in the sale how much was it before the sale ?

goldfiish [28.3K]

The original price was 100% and the sale was -25%
100% - 25% = 75%
This means 75% = £33
75% = 3/4
If we divide the sale amount by 3 and them multiply by 4, we will get the original amount.
£33 / 3 = £11
£11 x 4 = £44

5 0

2 years ago

Fill in the numbers to find a Sum

Alekssandra [29.7K]

Answer:

The numbers are -15 and 100

$\frac{2}{10} +\frac{-15}{100} =\frac{5}{100}$

Step-by-step explanation:

we have

$\frac{2}{10} +\frac{x}{100} =\frac{5}{y}$

Solve the left side

$\frac{2}{10} +\frac{x}{100} =\frac{20+x}{100}$

$\frac{20+x}{100}=\frac{5}{y}$

equate the numerators and the denominators

20+x=5 ------> x=5-20=-15

100=y -------> y=5

therefore

The numbers are -15 and 100

$\frac{2}{10} +\frac{-15}{100} =\frac{5}{100}$

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3 years ago

A road construction crew paves 1/5 mile every day. How much would they pave in 2 days?

Helen [10]

Answer: 0.4 miles

Step-by-step explanation:

You can use the equation y=1/5x to help you figure it out where x is the days and y is the length. y=1/5(2). y=2/5 or 0.4 miles. Please vote my answer as brainliest

7 0

2 years ago

Read 2 more answers