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Ahat [919]
2 years ago
6

A large container holds 14 litres of a solution which is 25% antifreeze, the remainder being water. How many litres of antifreez

e must be added to the container to make a solution which is 30% antifreeze? NOTE: Only put number, DO NOT PUT any units or sentences.
Mathematics
1 answer:
frutty [35]2 years ago
5 0

Answer:

2.8 liters

Step-by-step explanation:

So there are various ways to do this problem, this is just MY preferred way.

Since we are given 1/4th of a total value with 14 liters, we can actually make this 4/4 by multiplying our given value by 4. In this case, 14 liters for 25% becomes 56 liters for 100% antifreeze.

Since we know have a percent of 100%, we can proceed to take 10% increments, all the way up to 30%

10% is 5.6, multiplied by 3 is 16.8

While you might want to put 16.8 instantly, don't forget we are looking for how much is ADDED from 25%, not just how much there is.

In this case, subtract 14 from 16.8 to come out with a grand total of 2.8 liters added.

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barxatty [35]

z=f(x(u,v),y(u,v)),\begin{cases}x(u,v)=2u+v^2\\y(u,v)=3u-v\end{cases}

We're given that f_x(6,1)=3 and f_y(6,1)=-1, and want to find \frac{\partial z}{\partial v}(1,2).

By the chain rule, we have

\dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial v}

and

\dfrac{\partial x}{\partial v}=2v

\dfrac{\partial y}{\partial v}=-1

Then

\dfrac{\partial z}{\partial v}(1,2)=\dfrac{\partial z}{\partial x}(6,1)\dfrac{\partial x}{\partial v}(1,2)+\dfrac{\partial z}{\partial y}(6,1)\dfrac{\partial y}{\partial v}(1,2)

(because the point (x,y)=(6,1) corresponds to (u,v)=(1,2))

\implies\dfrac{\partial z}{\partial v}(1,2)=3\cdot2\cdot2+(-1)\cdot(-1)=\boxed{13}

4 0
3 years ago
Give the slope-intercept form of the equation of the line that is perpendicular to –7x – 8y = 12 and contains P(–3, 1)
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4 0
3 years ago
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Please help Urgent giving brainlist!
notsponge [240]

Answer:

f=-\frac{5}{3}

Step-by-step explanation:

-\frac{3}{4}f=\frac{5}{4}

(4)-\frac{3}{4}f=(4)\frac{5}{4}

-3f=5

\frac{-3f}{-3}=\frac{5}{-3}

f=-\frac{5}{3}

4 0
3 years ago
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55 employees increased by 20 percent<br>please help!​
Rama09 [41]

Answer:

I believe its 66

Step-by-step explanation:

55×20%=11

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4 0
2 years ago
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Please help, thanks!
Mamont248 [21]
((-4x^3)(y^4))^-3
--------------------------
(2xy^4)^-4
16x^4y^16
=------------------------
-64x^9y^12
-16y^4
=------------------------
64x^5
-y
=------------------------
4x^5

So the final answer is:

-y^4
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4x^5

(Btw if "^" is in front of a number, that means it is an exponent, so when your writing this on paper, just write it as a regular exponent without the "^". I had to do that since I'm on a computer.)  

Hopefully this was helpful in some way. 

7 0
3 years ago
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