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Akimi4 [234]
3 years ago
9

A concrete pillar has the shape of a cylinder. It has a radius of 6 meters and a height of 4 meters. If concrete costs $82 per c

ubic meter, how much did the concrete cost for the pillar? Use 3.14 for π, and do not round your answer.

Mathematics
2 answers:
wel3 years ago
7 0

Answer: $37077.12

Step-by-step explanation:

Please see the attachment below

suter [353]3 years ago
3 0

Answer:

The answer is $37,077.12

Step-by-step explanation: First we will calculate the volume of the cylindrical pillar. We use the formula:

πr^2h.

Where:

π = 3.14

r = 6m

h = 4m.

We calculate thus:

3.14 X 6^2 x 4

= 452.16m^3.

Having gotten the volume of the pillar. We proceed to calculate the cost. We have the cost as $82 per cubic meter, and the pillar is 452.16 cubic meters. We therefore multiply the volume of the pillar by the cost per cubic meter, thus:

82 X 452.16 = 37,077.12

Therefore it costs $37,077.12 to build the concrete pillar.

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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by
WARRIOR [948]

Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\

z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]

3 0
3 years ago
Most college-bound students take either the SAT(Scholastic Assessment Test) or the ACT (which originally stood for American coll
Jlenok [28]

Answer:

Luis would need to have a SAT score of 574.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Nicole's z-score:

ACT scores have a mean of about 21 with a standard deviation of about 5, which means that \mu = 21, \sigma = 5

Nicole gets a score of 24, which means that X = 24. Her z-score is:

Z = \frac{X - \mu}{\sigma}

Z = \frac{24 - 21}{5}

Z = 0.6

What score would Luis have to have on the SAT to have the same standardized score(z-score) as Nicole's standardized score on the ACT?

Luis would have to get a score with a z-score of 0.6, that is, X when Z = 0.6.

SAT scores have a mean of about 508 with a standard deviation of about 110, which means that \mu = 508, \sigma = 110.

The score is:

Z = \frac{X - \mu}{\sigma}

0.6 = \frac{X - 508}{110}

X - 508 = 0.6*110

X = 574

Luis would need to have a SAT score of 574.

8 0
3 years ago
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