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2 years ago

What is the ratio of the two quantities? Warning: different units!

Mathematics

2 answers:

mamaluj [8]2 years ago

4 0

Answer:

2:1

Step-by-step explanation:

Lets start by converting days to hours 5 days is 120 hours so 120:60 but we need to simplify and that would be 2:1

aliya0001 [1]2 years ago

4 0

The answer is 120:60 You have to convert the days to hours since it has to be the same unit or time measurement (1 day = 24 hours) (24 x 5 = 120) so it’s 120:60 and the simple form is 2:1. Hope that helped! ☺️

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Find the indefinite integral using the substitution provided.

Nady [450]

Answer: $7\text{Ln}\left(e^{2x}+10\right)+C$

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation $u = e^{2x}+10$

Apply the derivative and multiply both sides by 7 like so

$u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\$

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

$\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\$

Integrating leads to

$\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\$

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of $\frac{14e^{2x}}{e^{2x}+10}$

4 0

1 year ago

Math - algebra (9th grade) please include work

Naily [24]

Answer:

Step-by-step explanation:

Y) $\frac{x+4}{8}$ = 3

*multiply both sides by 8 - cancels out 8 in denominator*

x + 4 = 24

*subtract 4 from both sides*

x = 20

E) $\frac{x-5}{2}$ = 1

*multiply both sides by 2 - cancels out 2 in denominator*

x - 5 = 2

*add 5 on both sides*

x = 7

N) $\frac{x+2}{4}$ = 2

* multiply both sides by 4 - cancels out 4 in denominator*

x + 2 = 8

*subtract 2 from both sides*

x = 6

3 0

2 years ago

4. Find the value of k. The diagram is not to scale.

shtirl [24]

k=73. All the angles in any triangle must add up to 180.

8 0

2 years ago

Mario is paid a salary of $500 plus 8% of sales. Calculate his total income if his sales total $10,890 in the

Gre4nikov [31]

Answer:

His total income is of $1,371.2.

Step-by-step explanation:

His salary is of $500, plus 8% of his sales.

In this question:

Sales of $10,890. So his salary is given by:

$S = 500 + 0.08*10890 = 500 + 871.2 = 1371.2$

His total income is of $1,371.2.

7 0

2 years ago

Find an equation of the line parallel to x=5y-9 and passing through (2,-4). Express in standard form.

Anon25 [30]

Answer:

x - 5y = 22

Step-by-step explanation:

Step 1: rewrite the equation of the given line in to slope-intercept form by solving for y

x = 5y - 9

-5y = -x - 9 (subtract 5y and x from both sides)

y = x/5 + 9/5 (divide both side by -5)

Step 2: Our line is parallel to this line, so it has the same slope, but a different y-intercept, so set up the equation...

y = x/5 + b

We are given a point (x, y) of (2, -4), so plug that in and solve for b.

-4 = 2/5 + b

-4 - 2/5 = b (subtract 2/5 from both sides to isolate b)

-20/5 - 2/5 = b

-22/5 = b (simplify)

So the equation of our line is y = x/5 - 22/5

Step 3: Standard form is ax + by = c, where a is a positive integer

subtract x/5 from both sides...

-x/5 + y = - 22/5

multiply by -5 so x becomes a positive integer

x - 5y = 22

3 0

2 years ago