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Mathematics High School

Given the following sequence, find the 25th term: 0, 1, 2, 3, 4, . . .

Given the following sequence, find the 25th term: 0, 1, 2, 3, 4, . . . A. 24 B. 25 C. 26 D. 27

2 months ago

Solution 1

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Guest #6877836

2 months ago

The answer for this question would be 24 because 0 is included.

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Calculus question!

Solution 1

First, some rewriting:

$\dfrac{\mathrm d}{\mathrm dx}(5x)^{-4x}=\dfrac{\mathrm d}{\mathrm dx}\exp\left(\ln(5x)^{-4x}\right)=\dfrac{\mathrm d}{\mathrm dx}\exp\left(-4x\ln(5x)\right)$

Now taking the derivative is just a matter of applying the chain rule. Since $\dfrac{\mathrm d}{\mathrm dx}e^{f(x)}=\dfrac{\mathrm df(x)}{\mathrm dx}e^{f(x)}$ , you end up with

$\dfrac{\mathrm d}{\mathrm dx}(5x)^{-4x}=\dfrac{\mathrm d}{\mathrm dx}[-4x\ln(5x)]\exp\left(-4x\ln(5x)\right)=\dfrac{\mathrm d}{\mathrm dx}[-4x\ln(5x)](5x)^{-4x}$

The product rule tells you that

$\dfrac{\mathrm d}{\mathrm dx}[-4x\ln(5x)]=-4x\dfrac{\mathrm d}{\mathrm dx}[\ln(5x)]+\ln(5x)\dfrac{\mathrm d}{\mathrm dx}[-4x]=-4x\times\dfrac5{5x}-4\ln(5x)=-4(1+\ln(5x))$

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$\dfrac{\mathrm d}{\mathrm dx}(5x)^{-4x}=-4(1+\ln(5x))(5x)^{-4x}$

Question

Which table shows a proportional relationship between x and y? x 1 2 7 8 y 0.5 1 3.5 4 x 2 3 4 5 y 7 9 11 13 x 3 6 8 10 y 12 15 18 20 x 3 7.5 15 20 y 1 2.5 4 6

Solution 1

Answer:

First table.

Step-by-step explanation:

Among the options, the first table is showing a proportional relationship, because each y-value is half of the x-value. The ratio of this proportion is $\frac{1}{2}$ , we can find that by calculating the slope:

$m=\frac{\Delta y}{\Delta x}=\frac{1-0.5}{2-1}=\frac{0.5}{1}=\frac{1}{2}$

Therefore, the right answer is the first table.

Solution 2

The first table shows a proportional relationship.

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Write the equation of a line in point-slope form that has a slope of 1/3 and passes through the point (-6, 0).

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True or false log(x+y)-logy=logx

Solution 1

Log(x + y) - logx = logx

By laws of logarithm, logA - logB = log(A/B)

log(x + y) - logx = log((x +y)/x)

log((x +y)/x) is not equal to log x.

So the statement:

log(x + y) - logx = logx is False.

Hope this helps.

Solution 2

False. That is not how properties of logs works. log(xy)=logx+logy, not log(x+y)=logx+logy.

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Which is shorter 3/6 of a minute or 2/6 of an hour

Solution 1

3/6 of a minute because an hour is much longer

Solution 2

3/6 of a minute which is 30 seconds

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the width of a rectangle is 3 inches less than its length.the perimeter is 130 inches.Whats the dimension of the rectangle

Solution 1

L=w+3
P=2l + 2w
2l= 2w+6
130=4w+6
-6 -6
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Round 1.5/2.5 to the nearest tenth

Solution 1

The Answer is 0.10 I hope this helped

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The radian measure of an angle that is 125 degrees 25'50'' is

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It is 2.19 radians or 180 Degrees

Solution 2

The Angle measurement is 2.19

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the sum of a negative number, ¼ of the negative number, and 7/16 off the negative number = -13½. what is the negative number?

Solution 1

X - the number

$x+\frac{1}{4}x+\frac{7}{16}x=-13 \frac{1}{2} \\
\frac{16}{16}x+\frac{4}{16}x+\frac{7}{16}x=-\frac{27}{2} \\
\frac{27}{16}x=-\frac{27}{2} \\
x=-\frac{27}{2} \times \frac{16}{27} \\
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The number is -8.

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A taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. The rule c =0.20m + 2.00 describes the relationship between the number of miles m and the total cost of the ride c. What is the charge for a 2.7 mile ride?

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c =0.20m + 2.00

Where c is the cost and m = number of miles,

For a 2.7 mile ride, m = 2.7

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I hope this helps.

Solution 2

It should give you 2.54.
First, you have to multiply 2.7 miles times .20 miles. It gives you .54, which you are supposed to add 2.00 to it for every ride.

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