Remember
for F(x) is the antiderivitive of f(x)
so find the antiderivitive of ((x+1)^2)/x
if we expand we get (x^2+2x+1)/x which simplifies to x+2+(1/x)
the anti-deritivive of x is (1/2)x^2
the antideritiveve of 2 is 2x
the antideritivieve of 1/x is ln|x|
F(x)=(1/2)x^2+2x+ln|x|+C
F(1)=(5/2)+ln1+C
F(2)=6+ln2+C
F(2)-F(1)=6+ln2+C-(5/2+ln1+C)
F(2)-F(1)=(7/2)+ln2
that is the answer
if you want is simplified or expanded it is about 4.1915
This is a combination since the order doesn't matter
C(15, 6) = (15 * 14 * 13 * 12 * 11 * 10)/(6 * 5 * 4 * 3 * 2 * 1)
C(15, 6) = 3603600/720
C(15, 6) = 5005 different combinations of votes
Answer:
x = ± 7
Step-by-step explanation:
Given
(2x - 1)(3x + 2) = x + 292 ← expand left side using FOIL
6x² + x - 2 = x + 292 ( subtract x from both sides )
6x² - 2 = 292 ( add 2 to both sides )
6x² = 294 ( divide both sides by 6 )
x² = 49 ( take the square root of both sides )
x = ± 7
That is x = - 7, x = 7
Answer:
180 miles
Step-by-step explanation:
Going North
<em><u>Formula</u></em>
d = r * t
<em><u>Givens</u></em>
r = 60 mph
t = 5.2 hours
d = ?
<em><u>Solution</u></em>
d = 5.2 * 60 = 312 miles north
Going South
<em><u>Givens</u></em>
r = 55 mph
t = 2.4 hours
<em><u>Solution</u></em>
d = r * t
d = 55 * 2.4
d = 132
Distance from home
Formula: Distance from home = Distance North - Distance South
Distance North = 312 - 132 = 180 miles
(0, 5) is the minimum value.
Find the axis of symmetry by plugging the respective variables into -b/2a
-5/2(0) = 0
There is no b-value in our equation, or rather, the value of b is 0. To see this, y = 2x^2 + 5 can be written as
y = 2x^2 + 0x + 5
We plug 0 into f(x), establishing every x-value as 0.
f(0) = 2(0)^2 + 5
f(0) = 0 + 5
f(0) = 5
5 is now your vertex’s y-value. Plot the two values together.
(0, 5)
We know that this is a minimum because the leading coefficient is positive, meaning the the graph’s parabola will open down.
