Therefore, f(x) = 2x + 3 is your derivative function, and you need to find the original curve. So find the antiderivative using the given conditions...
∫f(x) = ∫2x + 3 dx
F(x) = x^2 + 3x + C
2 = (1)^2 + 3(1) + C
2 = 4 + C
C= -2
Therefore, the curve is F(x) = x^2 + 3x - 2
Proof: The derivative is the slope at every (x, y) point. The derivative of F(x) comes out to be 2x + 3, so we have found the curve. Plug in x = 1, and y = 2, so the conditions have been met.
<span>Hope I helped.</span>
H=-16t² +v(0)t+h(0)
v(0)=192
h=-16t² +192t+h(0)
h(0) should be 0, because the mortar sits on the ground.
h= - 16t²+192t
This function will have maximum because it has minus before x², and parabola is looking down.
h=-(16t²-192t)=-(16t² -2*4t*24+24²)+24²
h=-(4t-24)²+24²
h=-(4t-24)²+576
vertex (24 feet, 576 feet)
24 feet horizontally from the mortar and 576 feet up
Answer:
regular price = $15
Step-by-step explanation:
Represent the regular price by d. Then the discount was 0.20d, and the sale price was (1 - 0.20)d, or 0.80d, which is $12.
Solving for d, we divide both sides by 0.80:
d = regular price = $15
Answer:
$180
Step-by-step explanation:
Well because it is $27 per hour, you can start with the whole hours:
6*27=162
then because you are working with fractions you can find what 1/3 of 27 is:
27* (1/3)=9
this tells us that one-third of an hour is worth 9 dollars but because it is 2/3 then you just add another 9. This means 2/3 of 27 is 18.
Then you just add it all up:
162+18=180
Answer:
50% decrease
Step-by-step explanation:
130-65 = 65
65/130 = 0.5
0.5 x 100 = 50
