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2 years ago

H(t)= (t+3)^2 + 5

Mathematics

1 answer:

oee [108]2 years ago

5 0

Answer:

The average rate of change for the given function in the interval (-5, -1) is 0 (zero)

Step-by-step explanation:

The average rate of change of a function over an interval is the quotient between the difference between the function evaluated at the ends of the interval divided by the length of the interval. That is for our case:

the average rte of change of h(t) in the interval (-5, -1) is:

$\frac{h(-1)-h(-5)}{-1+5}$

so we find:

$h(-1)=(-1+3)^2+5=2^2+5=4+5=9\\and\\h(-5)=(-5+3)^2+5=(-2)^2+5=4+5=9$

then the average rate of change becomes:

$\frac{h(-1)-h(-5)}{-1+5}=\frac{9-9}{4} =\frac{0}{4} =0$

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Answer:

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Step-by-step explanation:

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3 years ago

A man weighing 800 N is hanging from a 2 mm diameter titanium wire with a cross-section of 3 x 10^-6 m^2. Will the wire break?

DENIUS [597]

Answer:

Since stress is greater than ultimate strength, the wire will break.

Step-by-step explanation:

The titanium wire is experimenting an axial load. Ultimate strength equals $2.20\times 10^{8}\,Pa$ . The wire shall break if and only if stress is at least equal to ultimate strength. The equation for axial stress ( $\sigma$ ), measured in pascals, in the wire with circular cross-section is:

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Where:

$F$ - Axial force, measured in newtons.

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Please notice that axial force is the weight of the man hanging from wire.

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2 years ago

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6. What ar

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Answer:

The minimum value of the bill that is greater than 95% of the bills is $37.87.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 28, \sigma = 6$