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Irina18 [472]
2 years ago
12

How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (R

ound to two decimal places if necessary.)
Mathematics
1 answer:
puteri [66]2 years ago
3 0

Answer:

The number of liters of the 45% acid solution = 10 liters

The number of liters of the 70% acid solution is = 40 liters

Step-by-step explanation:

How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)

Let x be the number of liters of the 45% acid solution

The number of liters of the 70% acid solution is y

x + y = 50

x = 50 - y

Also

How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution?

We have:

45% × x + 70% × y = 65% × 50

0.45x + 0.70y = 0.65 × 50

0.45x + 0.70y = 32.5

We substitute x = 50 - y in the equation

0.45(50 - y) + 0.70y = 32.5

= 22.5 - 0.45y + 0.70y = 32.5

= - 0.45y + 0.70y = 32.5 - 22.5

= 0.25y = 10

Divide both sides by 0.25

= y = 10/0.25

y = 40 liters

x = 50 - y

x = 50 - 40

x = 10 liters

Hence,

The number of liters of the 45% acid solution = 10 liters

The number of liters of the 70% acid solution is = 40 liters

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answer:

f(t) = -9.9788169(t -0.76)^2 +57

Step-by-step explanation:

On this question we see that we are given two points on a certain graph that has a maximum point at 57 feet and in 0.76 seconds after it is thrown, we know can say this point is a turning point of a graph of the rock that is thrown as we are told that the function f determines the rocks height above the road (in feet) in terms of the  number of seconds t since the rock was thrown therefore this turning point coordinate can be written as (0.76, 57) as we are told the height represents y and x is represented by time in seconds. We are further given another point on the graph where the height is now 0 feet on the road then at this point its after 3.15 seconds in which the rock is thrown in therefore this coordinate is (3.15,0).

now we know if a rock is thrown it moves in a shape of a parabola which we see this equation is quadratic. Now we will use the turning point equation for a quadratic equation to get a equation for the height which the format is f(x)= a(x-p)^2 +q  , where (p,q) is the turning point. now we substitute the turning point

f(t) = a(t-0.76)^2 + 57, now we will substitute the other point on the graph or on the function that we found which is (3.15, 0) then solve for a.

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f(t) = -9.9788169(t-0.76)^2 +57

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