6. A chemist wishes to make 5 liters of an 7% acid solution by mixing a 10% acid

Mathematics

1 answer:

larisa [96]3 years ago

3 0

Answer:

The chemist will mix 3 liters of the 5% acid solution and 2 liters of the 10% acid solution to get 5 liters of 7% acid solution

Step-by-step explanation:

Here, we are interested in finding the number of liters of each solution the chemist have to make use;

Let the number of liters of the 5% acid solution be x while the number of liters of the 10% acid solution be y

Mathematically;

x + y = 5 •••••••••(i)

Also, let’s work with the percentages now

( x * 5%) + (y * 10%) = (5 * 7%)

0.05x + 0.1y = 0.35 ••••••••(ii)

From i , x = 5-y

Substitute this into ii

0.05(5 -y) + 0.1y = 0.35

0.25 - 0.05y + 0.1y = 0.35

0.25 + 0.05y = 0.35

0.05y = 0.35 -0.25

0.05y = 0.1

y = 0.1/0.05

y = 2

But x + y = 5

x + 2 = 5

x = 5-2

x = 3

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The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is

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The function is graphed as shown below

Part A:

We use the formula $- \frac{b}{2a}$ to find the vertex of the function. A quadratic function of the form of $a x^{2} +bx+c$ and equating this form to the given function $- x^{2} +20x-75$ , we have
$b=20$ and $a=-1$ .

Substituting $a$ and $b$ into the vertex formula, we have
$x=- \frac{20}{2(-1)}=10$ , as shown in the graph

This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos

Part B:

We can find solution to this equation by factorising

$- x^{2} +20x-75=0$
$-( x^{2} -20x+75)=0$
$x^{2} -20x+75=0$
$(x-5)(x-15)=0$
$x=5$ and $x=15$ , as shown in the graph

The two values means that the company makes no profit when they either produce 5 or 15 photos