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Vladimir [108]
3 years ago
12

Find the area of the region under the graph of f on [a, b]. f(x) = x2 − 8x + 17; [−1, 2]

Mathematics
1 answer:
Harman [31]3 years ago
5 0

Answer:

The area is 42 area units.

Step-by-step explanation:

The area of a function f(x) on an interval [a,b] is given by:

A = \int\limits^a_b {f(x)} \, dx

Applying to this question:

A = \int\limits^-1_2 {x^2 - 8x + 17} \, dx

Then

F(x) = \frac{x^{3}}{3} - 4x^{2} + 17x

A = F(2) - F(-1)

F(2) = frac{2^{3}}{3} - 4*2^{2} + 17*2 = \frac{8}{3} + 18 = \frac{8 + 3*18}{3} = \frac{62}[3}

F(-1) = frac{(-1)^{3}}{3} - 4*(-1)^{2} + 17*(-1) = -\frac{1}{3} - 21 = \frac{-1 - 21*3}{3} = -\frac{64}[3}

A = F(2) - F(-1) = \frac{62}[3} - (-\frac{64}[3}) = \frac{62+64}{3} = 42

The area is 42 area units.

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X- 18 = 0<br> Number of real number solutions
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Answer:

X= 18

Step-by-step explanation:

18-18=0

x=18

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3 years ago
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The number of stamps that kaye and alberto had were in the ratio 5 : 3, respectively. after kaye gave alberto 10 of her stamps,
Gala2k [10]
K:A
5:3 (before)
15:9

since the total number of stamps didn't change, the total ratio should be the same.

7:5(after)
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so this means 1 unit is 10stamps.

14-10=4
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Kaye have 40 more stamps than Alberto.
4 0
3 years ago
the flag pole in front of the school casts a shadow 40 feet long when the measurement of the angle of elevation to the sun is 31
san4es73 [151]

Answer:

I would say that the flag pole is about 120 feet long. Recall that this is an estimation.

Step-by-step explanation:

8 0
3 years ago
What is 117/320 simplified to a mixed fraction
Alex

Answer:

hope this helps 229 999 0523

117 /320 ≈ 0.366

Step-by-step explanation:

Step 1 of 1: Simplify.

Simplify

117 over 320

117

320

Step 1 of 1: Simplify, sub-step a: Reduce fraction to lowest terms.

Reduce fraction to lowest terms

1 is the greatest common divisor of 117 and 320. The result can't be further reduced.

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The mean of a certain set of measurements is 27 with a standard deviation of 14. The distribution of the
Talja [164]

Answer:

Exactly 16%.

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.

The mean of a certain set of measurements is 27 with a standard deviation of 14.

This means that \mu = 27, \sigma = 14

The proportion of measurements that is less  than 13 is

This is the p-value of Z when X = 13, so:

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

Z = \frac{13 - 27}{14}

Z = -1

Z = -1 has a p-value of 0.16, and thus, the probability is: Exactly 16%.

8 0
3 years ago
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