Answer:
Step-by-step explanation:
Let R be the amount of money Hillel raises is a function of t, the length of his performance in minutes.
We have been given that Hillel raises $15 for each minute of juggling performance. This means that change in amount of money with every minute of juggling performance is 15, so slope of our line will be 15 and money raised in t minutes of performance will be 15t.
His initial appearance raises $500, so 500 will be our y-intercept.
The total money raised by Hillel after t minutes of juggling performance will be: 
.
Since we know that line of an equation in slope-intercept form is: 
, where,
m = slope of line,
b = y-intercept.
We are also given that R is a function of t, so substituting our given values in slope-intercept form of equation we will get our function formula as:
Therefore, the function gives the amount R of money Hillel raises in t minutes of juggling performance.
Im not even sure about this though
Sin 2θ = sin θ
2sin θ cos θ = sin θ
2cos θ = 1
cos θ = 1/2
θ = arccos(1/2) = 60° and 300°
θ = 60° and 300°
Answer:
68%
Step-by-step explanation:
51/75 × 100% = 68%
Answer:
Step-by-step explanation:
We can answer this in two ways: Differentiation and Graphing.
<u>Differentitate:</u>
The first derivative of a function yields a function that provides the slope for any point on the line of the original function. The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.
f(x) = 3(x-1)^2 + 4
f(x) = 3(x-1)(x-1) + 4
f(x) = 3(x^2 - 2x + 1) + 4
f(x) = 3x^2 - 6x + 7
f'(x) = 6x -6
Set this = 0 and find x:
0 = 6x -6
x = 1
The value of y when x=1 in the original equation is:
f(1) = 3(1-1)^2 + 4
y = 4
The vertex is (1,4)
<u>Graph:</u>
You can use DESMOS to plot the function. The result is attached. Look for the vertex and read the coordinates. (1,4) seems to work.
