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Papessa [141]
3 years ago
13

Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of ca

rs. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together.
Mathematics
1 answer:
Maslowich3 years ago
8 0
If we say there are 100 cars in a lot (It's an arbitrary number. You can use any number you want), Matthew can wash 100 cars in 14 hours or 7.14 cars an hour. Arianna can wash 100 cars in 11 hours or 9.09 cars an hour. Together, in an hour they can wash 7.14 + 9.09 or 16.23 cars. So to wash 100 cars it would take them 100/16.23 = 6.16 or about 6 hours. 
You can do this with variables as well. 
Matthew has a rate of x/14 while Arianna has a rate of x/11. Together their rate is x/14 + x/11= x/y
Divide both sides by x, you would get 1/14 + 1/11 = 1/y
Solve for y which would be around 6 hours. 
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Derivative, by first principle<br><img src="https://tex.z-dn.net/?f=%20%5Ctan%28%20%5Csqrt%7Bx%20%7D%20%29%20" id="TexFormula1"
vampirchik [111]
\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}h

Employ a standard trick used in proving the chain rule:

\dfrac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\cdot\dfrac{\sqrt{x+h}-\sqrt x}h

The limit of a product is the product of limits, i.e. we can write

\displaystyle\left(\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\right)\cdot\left(\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt x}h\right)

The rightmost limit is an exercise in differentiating \sqrt x using the definition, which you probably already know is \dfrac1{2\sqrt x}.

For the leftmost limit, we make a substitution y=\sqrt x. Now, if we make a slight change to x by adding a small number h, this propagates a similar small change in y that we'll call h', so that we can set y+h'=\sqrt{x+h}. Then as h\to0, we see that it's also the case that h'\to0 (since we fix y=\sqrt x). So we can write the remaining limit as

\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan\sqrt x}{\sqrt{x+h}-\sqrt x}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{y+h'-y}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{h'}

which in turn is the derivative of \tan y, another limit you probably already know how to compute. We'd end up with \sec^2y, or \sec^2\sqrt x.

So we find that

\dfrac{\mathrm d\tan\sqrt x}{\mathrm dx}=\dfrac{\sec^2\sqrt x}{2\sqrt x}
7 0
3 years ago
Jean has 1/8 cup of applesauce for her recipe. She needs 5/8 cup more. How much applesauce is needed for the recipe?
Anestetic [448]
2/4 this is a half also known as 1/2 Hope this helps!!!!!!!!!!!!!!!!!!!!!!!!
4 0
3 years ago
CAN SOMEONE HELP ME!!!!!
Ivenika [448]
Area yellow =11 x 6
= 66
red area = 7 x 2
=14
area of yellow
66 - 14 = 52
7 0
3 years ago
HELPPPP PLEASEEEeeeeeee
sergij07 [2.7K]

Answer:

I think it is non proportional

5 0
3 years ago
Read 2 more answers
What is (are) the x- interscepts of the function graphed above
Vilka [71]

Answer:

D. -4, -1, and 5

Step-by-step explanation:

X-intercepts are the values where your graph (function) crosses the x-axis.

So, on this graph-the pink line crosses the x-axis at these values: -4, -1, and 5.

7 0
2 years ago
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