How do you solve dy/dx=(y−1)(y+1) if the solution passes through the point (x,y)=(4,0)(x,y)=(4,0)?

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year

Roman55 [17]

Answer:

The required equation is $y = 18(1.15)^x$ .

Step-by-step explanation:

Consider the provided information.

The Initial value of poster = $ 18

After 1 year amount of increase = $ 20.70

With the rate of 15% = 0.15

Let future value is y and the number of years be x.

$y = 18(1.15)^x$

Now verify this by substituting x=1 in above equation.

$y = 18(1.15)^1=20.7$

Which is true.

Hence, the required equation is $y = 18(1.15)^x$ .

7 0

2 years ago

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Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the

natulia [17]

Answer:

C. JKM is not a right triangle because KM ≠ 15.3.

Step-by-step explanation:

We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.

In order to triangle JKM be a right triangle $KM^{2}=JK^{2}+JM^{2}$ .

We will find length of side KM using our right triangles JLM and JLK as $KM=KL+LM$ .

Using Pythagorean theorem in triangle JLM we will get,

$LM=\sqrt{JM^{2}-JL^{2}}$

$LM=\sqrt{8^{2}-5^{2}}$

$LM=\sqrt{64-25}$

$LM=\sqrt{39}=6.244997998\approx 6.24$

Now let us find length of side KL.

$KL=\sqrt{JK^{2}-JL^{2}}$

$KL=\sqrt{13^{2}-5^{2}}$

$KL=\sqrt{169-25}$

$KL=\sqrt{144}=12$

Now let us find length of KM by adding lengths of KL and LM.

$KM=12+6.24=18.24$

Now let us find whether JKM is right triangle or not using Pythagorean theorem.

$KM^{2}=JK^{2}+JM^{2}$

$18.24^{2}=13^{2}+8^{2}$

$18.24^{2}=169+64$

$18.24^{2}=233$

Upon taking square root of both sides of equation we will get,

$18.24\neq 15.264337522473748$

$18.2\neq 15.3$

We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.

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2 years ago

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Melanie is very concerned with avoiding late fees. The table shows her choices for paying her bills. Method Bill Payment Methods

pshichka [43]

Answer:

3

Step-by-step explanation:

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2 years ago

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Doris put $4000 in a 5year CD paying 6% interest compounded monthly. After 2 years, she withdrew all her money, and as an early

sp2606 [1]

For APEX it is going to be 4261.93

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2 years ago

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The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard d

Bezzdna [24]

Answer:

0% probability that it would take exactly 3.7 hours to construct a soapbox derby car

Step-by-step explanation:

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.

Also, the probability of finding an exact value in the normal probability distribution is 0.

So

0% probability that it would take exactly 3.7 hours to construct a soapbox derby car

3 0

2 years ago