The vertex will be when the velocity is equal to zero:
df/dx=-12x+24 (using the power rule for differentiation)
df/dx=0 only when:
-12x+24=0 add 12x to both sides
12x=24 divide both sides by 12
x=2, we find the y value to be:
y(2)=-6(2^2)+24*2-20
y(2)=-24+48-20=4
So the vertex is the point (2,4)
And the axis of symmetry is the line x=2
Now if you do not yet do calculus...
The vertex will occur midway between the two zeros.
6x^2-24x+20=0 (using the Quadratic Formula for simplicity)
x=(24±√96)/12
x≈(1.1835, 2.8165)
Now the vertex occurs at the average of the zeros...
x=(1.1835+2.8165)/2=2 (as we saw earlier)
y(2)=4
Vertex is at (2,4) and axis of symmetry is the vertical line x=2
Answer:
c + p = 100
11.50c + 13.00p = 1255
Step-by-step explanation:
The first equation represents the total number of pizzas, and determines how many were cheese or pepperoni,
The second equation represents the total cost of the pizzas, and determines how much each type of pizza contributes to the total cost.
9514 1404 393
Answer:
about 0.299 kg/m³
Step-by-step explanation:
Density is the ratio of mass to volume.
ρ = M/V
ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³
Answer:
Step-by-step explanation:
cos θ=12/16=3/4=0.75
θ=cos^{-1}(0.75)≈41.4°
Mr Sharrone can do 1/3 of the job each hour
<span>the assistant does 1/5 of the job each hour </span>
<span>1(1/3) + H (1/5) = 1 (complete job) </span>
<span>1/3 + 1/5 H = 1 </span>
<span>1/5 H = 1 - 1/3 = 2/3 </span>
<span>H = (2/3) / (1/5) = 10/3 = 3 1/3 hours to complete the job</span>
