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borishaifa [10]
3 years ago
5

X=y-4 and 2x+4y=10 help me ​

Mathematics
1 answer:
Murljashka [212]3 years ago
6 0

Answer:

Step-by-step explanation:

1. x = y-4

0 = y - 4 -x

4 = y - x

2. 2x+4y = 10

x+4y = 5

x+y = 5/4

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Write the product using exponents. (1/3.(1/3)(1/3) Using exponents, the product is​
Marta_Voda [28]

Answer:

The answer is 1/3 to the power of 3

Step-by-step explanation:

4 0
2 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
How many 1/6 pound servings are in 10 pounds of chicken ? Pls help
Svetlanka [38]

Answer:

60

Step-by-step explanation:

1/6 * 60 = 60/6

60/6 = 10/1 = 10

6 0
3 years ago
HELP ASAP PLZ 39 POINTS<br> Find x, y, u, v
Ad libitum [116K]

Answer:

x = 9; y = 12; u = 24; v = 32

Step-by-step explanation:

The corresponding sides of similar triangles are in the same ratio to each other.

      3/5 = (3 + x)/20     Multiply each side by 20

20×3/5 = 3 + x

       12 = 3 + x             Subtract 3 from each side

        x = 9

=====

      4/5 = (4 + y)/20     Multiply each side by 20

20×4/5 = 4 + y

       16 = 4 + y              Subtract 4 from each side

        y = 12

=====

      3/5 = (3 + x + u)/60     Multiply each side by 60

60×3/5 = 3 + x + u

       36 = 3 + x + u             Insert the value of x

       36 = 3 + 9 + u

       36 = 12 + u                 Subtract 12 from each side

         u = 24

=====

      4/5 = (4 + y + v)/60     Multiply each side by 60

60×4/5 = 4 + y + v

       48 = 4 + y + v             Insert the value of y

       48 = 4 + 12 + v

       48 = 16 + v                 Subtract 16 from each side

         v = 32

x = 9; y = 12; u = 24; v = 32

5 0
3 years ago
Mark recorded the growth of a plant over 8 weeks. The equation y=0.2x+2 represents the height y, in inches, after x weeks.
bezimeni [28]

The statements could be true are:

The height of the plant after week 3 was about 2.6 inches. ⇒ A

The height of the plant after week 9 was about 3.8 inches. ⇒ C

Step-by-step explanation:

Mark recorded the growth of a plant over 8 weeks

The equation y = 0.2x + 2, represents the height y, in inches, after x weeks

From the equation

  • 0.2 represents the rate of increasing of the height of the plant per week
  • 2 represents the initial height of the plant

∵ y represents the height of the plant after x week

∴ x is the number of the weeks

∵ y = 0.2x + 2

∵ x = 3

- Substitute x in the equation by 3

∴ y = 0.2(3) + 2

∴ y = 0.6 + 2

∴ y = 2.6

∴ The height of the plant after 3 weeks is 2.6 inches

∵ x = 9

- substitute x by 9 in the equation

∴ y = 0.2(9) + 2

∴ y = 1.8 + 2

∴ y = 3.8

∴ The height of the plant after 9 weeks is 3.8 inches

The statements could be true are:

The height of the plant after week 3 was about 2.6 inches.

The height of the plant after week 9 was about 3.8 inches.

Learn more:

You can learn more about the linear equations in brainly.com/question/1284310

#LearnwithBrainly

5 0
3 years ago
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