Answer:

General Formulas and Concepts:
<u>Calculus</u>
- Derivative Notation
- Definition of a Derivative:

Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = -10x
<u>Step 2: Find Derivative</u>
- Substitute:

- Distribute -10:

- Distribute -1:

- Combine like terms:

- Divide:

- Evaluate:

One rose is 50 cents, so 2 roses cost $1 ( 50 cents x 2).
2 roses per dollar x 20 dollars = 40 total roses sold.
When they sell $20 dollars they make $6, so that means they pay 20-6 = $14 dollars for the 40 roses.
$14 / 40 roses = 0.35 per rose.
She pays 35 cents per rose.
Answer: the speed of the river is 9km/h
Step-by-step explanation:
Let x represent the speed of the river current.
He rides 140 km downstream in a river in the same time it takes to ride 35km upstream. This means that his speed was higher when riding downstream and it was lower when riding upstream.
Assuming he rode in the direction of the river current when coming downstream and rode against the current when going upstream.
time = distance/speed
Manuel has a boat that can move at a speed of 15 km/h
His downstream speed would be
15 + x
time spent coming downstream would be
140/(15 + x)
His downstream speed would be
15 - x
time spent going downstream would be
35/(15 - x)
Since the time is the same, then
140/(15 + x) = 35/(15 - x)
Crossmultiplying
140(15 - x) = 35(15 + x)
2100 - 140x = 525 + 35x
140x + 35x = 2100 - 525
175x = 1575
x = 1575/175
x = 9
Answer:
y=0x+2
Step-by-step explanation:
Integrating
gives

Notice that
forces all terms in the sum to be 0, so that

and hence

making the first option correct.