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viva [34]
3 years ago
10

A cable is 90 decimeters long. How long is the cable in meters

Mathematics
2 answers:
stealth61 [152]3 years ago
6 0
The answer is 9 meters 
GarryVolchara [31]3 years ago
5 0
9 meters hope i helped
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Indefinite integral need help pleaseeeeeee
tatiyna
Integrate indefinite integral:
I=\int\frac{dx}{e^{2x}+3e^x+2}dx

Solution:
1. use substitution u=e^x 
=>
du=e^xdx
=>
dx=\frac{du}{e^x}
=>
dx=\frac{du}{u}
=>
I=\int\frac{du}{u(u^2+3u+2)}du
=\int\frac{du}{u(u+2)(u+1)}du
2. decompose into partial fractions
\frac{1}{u(u+2)(u+1)}
=\frac{A}{u}+\frac{B}{u+2}+\frac{C}{u+1}
where A=1/2, B=1/2, C=-1
=\frac{1}{2u}+\frac{1}{2(u+2)}-\frac{1}{u+1}
3. Substitute partial fractions and continue
I=\int\frac{du}{2u}+\int\frac{du}{2(u+2)}-\int\frac{du}{u+1}
=\frac{log(u)}{2}+\frac{log(u+2)}{2}-log(u+1)}
4. back-substitute u=e^x
=\frac{log(e^x)}{2}+\frac{log(e^x+2)}{2}-log(e^x+1)}
=\frac{x}{2}+\frac{log(e^x+2)}{2}-log(e^x+1)}

Note: log(x) stands for natural log, and NOT log10(x)

7 0
3 years ago
What is the slope of (3,-20),(5,8)
fomenos
The equation for slope is <u>y² - y
</u>                                        x² - x

So it would be:                <u>8 - (-20)</u>   or    <u>8 + 20
</u>                                          5 - 3               5 - 3 

<u>28</u>
 2

Then, you have to reduce it, divide both by two.
 
 <u>14</u>
  1

Since it is over 1, then it is just the numerator.

Your final is:
<em>Slope = 14</em>                        

4 0
3 years ago
4x-3y=1 and 3y=x-1 use substitution and give an ordered pair
dolphi86 [110]

Answer: below i've attached a file that you view  for ---> 4x-3y=1 and 3y=x-1 using  the  substitution method  (please let me know if you can see it ..you might need to zoom in )

Step-by-step explanation:

8 0
3 years ago
A) What is the equation of the line that passes through the given pair points in slope-intercept form?
lesya [120]

A)

The slope-intercept form:

y=mx+b

m - slope

b - y-intercept

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (2, 5.1) and (-1, -0.5). Substitute:

m=\dfrac{-0.5-5.1}{-1-2}=\dfrac{-5.6}{-3}=\dfrac{5.6}{3}=\dfrac{56}{30}=\dfrac{28}{15}

Therefore we have:

y=\dfrac{28}{15}x+b

Put the coordinates of the point (-1, -0.5) ot the equation:

-0.5=\dfrac{28}{15}(-1)+b

-0.5=-\dfrac{28}{15}+b     <em>multiply both sides by 2</em>

-1=-\dfrac{56}{15}+2b       <em>add \dfrac{56}{15} to both sides</em>

\dfrac{41}{15}=2b            <em>divide both sides by 2</em>

b=\dfrac{41}{30}

Answer: \boxed{y=\dfrac{28}{15}x+\dfrac{41}{30}}

-------------------------------------------------------------------------

B)

We have the points (-2, 3) and (3, -4).

Calculate the slope:

m=\dfrac{-4-3}{3-(-2)}=\dfrac{-7}{5}=-\dfrac{7}{5}

Therefore we have:

y=-\dfrac{7}{5}x+b

Put the coordinates of the point (-2, 3) to the equation of a line:

3=-\dfrac{7}{5}(-2)+b

\dfrac{15}{5}=\dfrac{14}{5}+b              <em>subtract \dfrac{14}{5} from both sides</em>

\dfrac{1}{5}=b\to b=\dfrac{1}{5}

Answer: \boxed{y=-\dfrac{7}{5}x+\dfrac{1}{5}}

7 0
4 years ago
The ratio of cars to residents on a small island is 1:112. There are 2,912 residents on the island. How many cars are there on t
olga2289 [7]

Answer:

26

Step-by-step explanation:

1:112=113

x:2912=y

Divide 2912 and 112

2912/112=26

1 × 26 = 26

3 0
3 years ago
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