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3 years ago

1/3(33x +15) - 1/3 ( 21x +18) =10

1 answer:

7 0

      ¹/₃(33x + 15) - ¹/₃(21x + 18) = 10
¹/₃(33x) + ¹/₃(15) - ¹/₃(21x) - ¹/₃(18) = 10
   11x + 5 - 7x - 6 = 10
   11x - 7x + 5 - 6 = 10
      4x - 1 = 10
      + 1   + 1
   4x = 11
      4 4
   x = 3³/₄

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PLEASE HELP 30 POINTS Wendell is looking over some data regarding the strength, measured in Pascals (Pa), of some building mater

jarptica [38.1K]

Logarithmic functions and exponential functions are inverse and opposite of one another

The logarithmic function is $y = \log_2(x)$ , and the length at 8 pascals is 3 units

<h3>How to determine the logarithmic function</h3>

The exponential function is given as:

$f(x) = 2^x$

Express f(x) as y

$y = 2^x$

Swap the positions of x and y

$x = 2^y$

Take the logarithm of both sides

$\log(x) = \log(2^y)$

Apply the rule of logarithm

$\log(x) = y\log(2)$

Divide both sides by log(2)

$y = \frac{\log(x)}{\log(2)}$

Apply the change of base rule of logarithm

$y = \log_2(x)$

When the strength is 8 pascals, we have:

$y = \log_2(8)$

Express 8 as 2^3

$y = \log_2(2^3)$

So, we have:

$y =3 \log_2(2)$

Evaluate log 2 base 2

$y =3$

Hence, the logarithmic function is $y = \log_2(x)$ , and the length at 8 pascals is 3 units

Read more about logarithmic and exponential functions at:

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7 0

2 years ago

How do you do this question?

ElenaW [278]

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is $u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x$

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

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3 years ago

24) 28 + 3k < 5(–3 – 8k) -4 -3 -2 -1 0 2 3 4 5 6

ahrayia [7]

Answer:

k < - 1

Step-by-step explanation:

28 + 3k < 5(-3-8k)

28 + 3k < - 15 - 40k

28 + 15 < - 40k - 3k

43 < - 43k

43/- 43 > k (switch signs because 43 is negative)

k < -1

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3 years ago

There are five houses on Philips Road that each use, on average, between 1.61 units and 1.74 units of electricity for 1 to 3 hou

Karo-lina-s [1.5K]

Answer:

C is the correct answer is yes

Step-by-step explanation:

I'm doing this assignment and I got it correct!

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3 years ago

The production department of Celltronics International wants to explore the relationship between the number of employees who ass

Flura [38]

Answer:

(a) Shown below

(b) There is a positive relation between the number of assemblers and production.

Step-by-step explanation:

Let X = number of assemblers and Y = number of units produced in an hour.

(a)

Consider the scatter plot below.

(b)

Based on the scatter plot it can be concluded that there is a positive relationship between the variables X and Y, i.e. as the value of X increases Y also increases.

(c)

The formula to compute the correlation coefficient is:

$r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }$

Compute the correlation coefficient between X and Y as follows:

$r=\frac{n\sum XY-\sum X\sum Y}{\sqrt{[n\sum X^{2}-(\sum X)^{2}][n\sum Y^{2}-(\sum Y)^{2}]}} }=\frac{(5\times430)-(15\times120)}{\sqrt{[(5\times55)-15^{2}][(5\times3450)-120^{2}]}} =0.9272$

Thus, the correlation coefficient is 0.9272.

7 0

3 years ago