Answer:
125/6(In(x-25)) - 5/6(In(x+5))+C
Step-by-step explanation:
∫x2/x1−20x2−125dx
Should be
∫x²/(x²−20x−125)dx
First of all let's factorize the denominator.
x²−20x−125= x²+5x-25x-125
x²−20x−125= x(x+5) -25(x+5)
x²−20x−125= (x-25)(x+5)
∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx
x²/(x²−20x−125) =x²/((x-25)(x+5))
x²/((x-25)(x+5))= a/(x-25) +b/(x+5)
x²/= a(x+5) + b(x-25)
Let x=25
625 = a30
a= 625/30
a= 125/6
Let x= -5
25 = -30b
b= 25/-30
b= -5/6
x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)
∫x²/(x²−20x−125)dx
=∫125/6(x-25) -∫5/6(x+5) Dx
= 125/6(In(x-25)) - 5/6(In(x+5))+C
Answer: 4.2495 feets
Step-by-step explanation:
Given the following :
Rate of change (speed) when rock hits the lake surface = - 3in/s
Distance or depth after 5 seconds :
Distance = rate of change * time
Distance = (- 3 in/s × 5) = - 15 inches
1 inch = 0.0833 feet
15 inches = (-15 * 0.0833) = - 1.2495 feets
Distance between Lisa's hand and lake surface = 3 feets :
Distance between Lisa's hand and rock after 5 seconds :
(3 feets + 1.2495 feets) = 4.2495 feets
Answer:
Step-by-step explanation:
Shobo's age = x years
His mother's age = 6 times of
Shobo's age
= 6x years
Five years from now
________________
Shobo's age = ( x + 5 ) years
According to the problem given,
x + 5 = one by third of his mother's
present age
x + 5 = 6x / 3
x + 5 = 2x
5 = 2x - x
5 = x
Therefore ,
Shobo's present age = x = 5 years
His mother's age = 6x
= 6 × 5
= 30 years
Answer:
the answer should 60°
Step-by-step explanation:
if look at angle pq and rq the measure of the angle is 60° if u were to spin that angle to a u should get the same measurement
The <em><u>correct answers</u></em> are:
The inequality is 75+4t ≥ 400, and they must sell at least 82 tickets.
Explanation:
t is the number of tickets sold. They start out with $75, so that is where our inequality begins. Each ticket is $4; this gives us the expression 4t. Together with the $75 carry over, we have 75+4t.
They must make at least $400 to pay for the dance. This means it must be more than or equal to 400; this gives us 75+4t ≥ 400.
To solve this, first subtract 75 from each side:
75+4t-75 ≥ 400-75
4t ≥ 325
Divide both sides by 4:
4t/4 ≥ 325/4
t ≥ 81.25
We cannot sell a portion of a ticket, so we round. While mathematically this number would "round down," if they only sell 81 tickets, they will not have enough money. Therefore we round up to 82.
