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4 years ago

(-2-4i) + (1+6i) how do you do this question

1 answer:

6 0

For this equation you would need to combine like terms
Step 1: -2+1= -1
Step 2: -4i+6i= 2i
so your answer to this question would be -1+2i

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Write an expression to represent: the product of 5 and a number decreased by 3.

Maru [420]

Answer:

(n) (5) - 3

5n - 3

7 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

Heights of male students in the eighth grade are normally distributed with a mean of 57.2 in. and standard deviation of 2.4 in.

romanna [79]

In statistics finding percentiles relates to the standard deviation and something called a z-score. For normally distributed data the z-score represents how many standard deviations above or below the mean that group is a part of. The z-score for normally distributed data for the 90th percentile is 1.28. The standard deviation is then multiplied by the z-score to find, in this case, the shotlrtest height needed to be in the 90th percentile of this population. In this case to be in the 90th percentile your height must be 60.27 inches.

3 0

3 years ago

Albert's hourly pay is $8.10. He has an hourly pay of $12.15 when he works more than 40 hours. He worked 45 hours last week. Wha

Sedaia [141]

Answer:

$384.75

Step-by-step explanation:

Albert's hourly pay is $8.10

When he works for more than 40 hours, his hourly pay will increase to $12.15.

Last week, Albert worked for 45 hours, his hourly pay would be:

First 40 hours = $8.10 * 40 = $324

Remaining 5 hours =

$12.15 * 5 = $60.75

Albert gross pay for this period will be calculated as:

$324 + $60.75 = $384.75

Therefore, Albert gross pay for this period = $384.75

3 0

4 years ago

Use the net to find the surface area of the regular pyramid. plz, help I'm stuck.

Zepler [3.9K]

Answer:

178.3 mm²

Step-by-step explanation:

Surface area = Base area + 3 x side triangles area

Sₐ = 43.3 + 3 x (1/2 x (10 x 9)) = 43.3 + (3 x 45) = 178.3

5 0

3 years ago