What is the answer for this equation?

A small island is 3 kilometers from the nearest point p on the straight shoreline of a large lake. if a woman on the island can

yKpoI14uk [10]

The distance walked will be (12-x) km
the distance rowed will be (9+x²) km
A] The function T(x) will be given by:
Time=distance/speed
thus we shall have:
T(x)=[√(9+x²)]/2.5+(12-x)/4

B] To get the distance x=c that minimizes the time travel, we differentiate the above.
T'(x)=(1/2.5)[1/(2.5√9+x²)*2x-1/4]
this should give us 0 for x=c, thus
c/[2.5*√(9+c²)]-1/4=0
⇒c/[2.5*√(9+c²)]=1/4
c/√(9+c²)=2.5/4
squaring both sides we get:
c²/(9+c²)=5/8
8c²=5(9+c²)
8c²=45+5c²
3c²=45
c²=15
c=3.87 km

c] The least travel time is
T(c)=[√(9+c²)]/2.5+(12-c)/4
this will give us:
T(c)=[√(9+3.87²)]/2.5+(12-3.87)/4
T(c)=3.9999209~4 hours

d] The second derivative will be:
T"(x)=1/[2.5√(9+x²)]-x²/[2.5(9+x²)^(3/2)]
but
x=c=3.87
T"(x)=0.01668 hours/ mile²
Given that T(c)=0, while T(x)<0 for x<c and T(x)>0 for x>c proves that T(x) decreases for x<c and increases for x>c, so there is a minimum at x=c

4 0

3 years ago

Jika suku pertama suatu barisan geometri = 16 dan suku ketiga = 36, maka besar suku kelima adalah …..

morpeh [17]

Answer:

Suku yang kelima adalah 56

4 0

3 years ago

The first figure is dilated to form the second figure.

coldgirl [10]

This is clearly a reduction meaning the copy got smaller. This indicates that the scale factor IS less than 1 and the only answer choice less than 1 is the first statement.

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Answer : The scale factor is 0.25.

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I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

7 0

3 years ago

Read 2 more answers

Please help me with this problem

ser-zykov [4K]

Answer:

d=−bc+a/0.5bc

Step-by-step explanation:

Let's solve for d.

a=0.5bcd+bc

Step 1: Flip the equation.

0.5bcd+bc=a

Step 2: Add -bc to both sides.

0.5bcd+bc+−bc=a+−bc

0.5bcd=−bc+a

Step 3: Divide both sides by 0.5bc.

0.5bcd/0.5bc = −bc+a/0.5bc

d=−bc+a/0.5bc

7 0

3 years ago

Suppose monthly rental prices for a one-bedroom apartment in a large city has a distribution that is skewed to the right with a

omeli [17]

Answer:

a) Nothing, beause the distribution of the monthly rental prices are not normal.

b) 1.43% probability that the sample mean rent price will be greater than $900

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?

Nothing, beause the distribution of the monthly rental prices are not normal.

(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Now we can apply the Central Limit Theorem.

$\mu = 880, \sigma = 50, n = 30, s = \frac{50}{\sqrt{30}} = 9.1287$