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4 years ago

What is the coefficient of the variable 26=9x

Mathematics

1 answer:

cupoosta [38]4 years ago

7 0

The variable is the letter x
the coefficient is what is multiplied by the variable, and it is 9

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Solve this equation using a common base

GrogVix [38]

Answer:

Step-by-step explanation:

1. 3x - 7 = 5 - x

4x = 12

x = 3

2. 6x + 4 = 2

6x = -2

x = -1/3

6 0

3 years ago

Use the Integral Test to determine whether the series is convergent or divergent

Inga [223]

Answer:

A. $\sum_{n=1}^{\infty}\frac{n}{e^{15n}}$ converges by integral test

Step-by-step explanation:

A. At first we need to verify that the function which the series is related ( $\frac{n}{e^{15n}}$ ) fills the necessary conditions to ensure that the test is effective.

*f(x) must be continuous or differentiable

*f(x) must be positive and decreasing

Let´s verify that $f(x)=\frac{n}{e^{15n}}$ fills these conditions:

*Considering that eˣ≠0 for all x, the function $f(x)=\frac{n}{e^{15n}}$ does not have any discontinuities, so it´s continuous

*Because eˣ is increasing:

if a<b ,then eᵃ<eᵇ

if 0<eᵃ<eᵇ ,then 1/eᵃ > 1/eᵇ

if 1/eᵃ > 1/eᵇ and a<b, then a/eᵃ<b/eᵇ

We conclude that $f(x)=\frac{n}{e^{15n}}$ is decreasing

*Because eˣ is always positive and the sum is going from 1 to ∞, this show that $f(x)=\frac{n}{e^{15n}}$ is positive in [1,∞).

Now we are able to use the integral test in $f(x)=\frac{n}{e^{15n}}$ as follows:

$\sum_{n=1}^{\infty}\frac{n}{e^{15n}}\ converges\ \leftrightarrow\ \int_{1}^{\infty}\frac{x}{e^{15x}}\ dx\ converges$

Let´s proceed to integrate f(x) using integration by parts

$\int_{1}^{\infty}\frac{x}{e^{15x}}\ dx=\int_{1}^{\infty}xe^{-15x}\ dx$

Choose your U and dV like this:

$U=x\ \rightarrow dU=1\\ dV=e^{-15x}\ \rightarrow V=\frac{-e^{-15x}}{15}$

And continue using the formula for integration by parts:

$\int_{1}^{\infty}Udv = UV|_{1}^{\infty} - \int_{1}^{\infty}Vdu$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{-1}{15} \int_{1}^{\infty}e^{-15x}\ dx$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{-1}{15}(\frac{-1}{15e^{15x}})|_{1}^{\infty}$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{1}{225e^{15x}}|_{1}^{\infty}$

Because we are dealing with ∞, we´d rewrite it as a limit that will help us at the end of the integral:

$\int_{1}^{\infty}xe^{-15x}\ dx= \lim_{b \to{\infty}}(\frac{-x}{15e^{15x}}|_{1}^{b}-\frac{1}{225e^{15x}}|_{1}^{b})$

$\int_{1}^{\infty}xe^{-15x}\ dx= \lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}}-(\frac{-1}{15e^{15}}-\frac{1}{225e^{15}})$

$\int_{1}^{\infty}xe^{-15x}\ dx= ( \lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}})+\frac{1}{15e^{15}}(1-\frac{1}{15})$

We only have left to solve the limits, but because b goes to ∞ and it is in an exponential function on the denominator everything goes to 0

$\lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}} = 0$

$\int_{1}^{\infty}xe^{-15x}\ dx= \frac{1}{15e^{15}}(1-\frac{1}{15})$

Showing that the integral converges, it´s the same as showing that the series converges.

By the integral test $\sum_{n=1}^{\infty}\frac{n}{e^{15n}}$ converges

7 0

3 years ago

Which equation represents grants path? A. y=2-4x B. y=4-x/2 C. y=6-x/4 D. y=8-2x

EleoNora [17]

Answer:

Step-by-step explanation:

recall that the point-slope form of a linear equation is given by

y = mx + c

Rearranging so that it is in the same form as the answer choices, we get

y = c + mx

where m is the slope and c is the y-intercept

we note the following observations

1) The line goes from top left to bottom right, this means that the slope is negative, hence m has to be negative. (in our case, all the choices have negative x)

2) The line crosses the y-axis at y = 4, this means the y-intercept is 4 and hence c = 4.

If we look at the choices, only choice B satisfies both observations (that m is negative and c = 4)

6 0

4 years ago

Read 2 more answers

The positive acute angle formed by the _____ side of an angle in standard position and the x-axis is called a reference angle.

Helga [31]

Answer:

option-C

terminal

Step-by-step explanation:

We know that

reference angle is between terminal side and x-axis

so, the other side will be terminal position

so, we can write as

The positive acute angle formed by the terminal side of an angle in standard position and the x-axis is called a reference angle.

So,

option-C

terminal

7 0

4 years ago

7m - 17 = -24 what is m?

aev [14]

Answer:

Move all terms that don't contain

to the right side and solve.

Exact Form:

Decimal Form:

¯¯¯¯¯¯¯¯¯¯¯¯

857142

Mixed Number Form:

Tap to view steps...

3 0

3 years ago