A=4ℼR2 solve for R SHOW ALL STEPSSSSSSSSSSSSS

Mathematics

1 answer:

GuDViN [60]2 years ago

3 0

Given problem;

A = 4 π R²

To solve for R, we have to make it the subject of the expression.

Since

A = 4 π R² , follow these steps to find R;

Multiply both sides by $\frac{1}{4\pi }$

A x $\frac{1}{4\pi }$ = $\frac{1}{4\pi }$ x 4 π R²

$\frac{A}{4\pi }$ = R²

Then find the square root of both sides

√R² = $\sqrt{\frac{A}{4\pi } }$

R = $\sqrt{\frac{A}{4\pi } }$

The solution is $\sqrt{\frac{A}{4\pi } }$

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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

trasher [3.6K]

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