If g(x) = 2x2 + bx + 5 and g(1) = 4, what is the value of g(-1)?

Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio

JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

$\frac{dA}{dt} = kA$

Where k represents the constant of proportionality

$\frac{dA}{dt} = kA$

Multiply both sides by dt/A

$\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}$

$\frac{dA}{A} = k\ dt$

Integrate both sides

$\int\ {\frac{dA}{A} = \int\ {k\ dt}$

$ln\ A = kt + lnC$

Make A, the subject

$A = Ce^{kt}$

$t = 0\ when\ A =1\ million$ i.e. At initial

So, we have:

$A = Ce^{kt}$

$1000000 = Ce^{k*0}$

$1000000 = Ce^{0}$

$1000000 = C*1$

$1000000 = C$

$C =1000000$

Substitute $C =1000000$ in $A = Ce^{kt}$

$A = 1000000e^{kt}$

To solve for k;

$6\ years\ later = 500,000$

i.e.

$t = 6\ A = 500000$

So:

$500000= 1000000e^{k*6}$

Divide both sides by 1000000

$0.5= e^{k*6}$

Take natural logarithm (ln) of both sides

$ln(0.5) = ln(e^{k*6})$

$ln(0.5) = k*6$

Solve for k

$k = \frac{ln(0.5)}{6}$

$k = \frac{-0.693}{6}$

$k = -0.1155$

Recall that:

$\frac{dA}{dt} = kA$

Where

$\frac{dA}{dt}$ = Rate

So, when

$A = 600000$

The rate is:

$\frac{dA}{dt} = -0.1155 * 600000$

$\frac{dA}{dt} = -69300$

Hence, the amount of oil was decreasing at 69300 barrels, yearly

7 0

2 years ago

Find the volume thank you

IgorC [24]

Answer:

the answer is: 27

Step-by-step explanation:

3 x 3 x 3 = 27

4 0

2 years ago

Can someone please help me

harkovskaia [24]

Answer:

E

Step-by-step explanation:

\sqrt 6 is an irrational number, as it cannot be written as the ratio of 2 numbers.

It is also a real number, as it does not include the square root of a negative number.

Therefore, E is the correct option.

3 0

2 years ago

I need help to find the slope of the line the answers are A: 4 B:-1/4 C:-4 D:1/4

dolphi86 [110]

Answer:

-1/4

Step-by-step explanation:

Take two points on the line

(-4,-1) and (0,-2)

Using the slope formula

m = (y2-y1)/(x2-x1)

= ( -2 - -1)/( 0 - -4)

= (-2+1)/ ( 0+4)

-1/4

3 0

2 years ago

Two friends race against each other in 100-meter and 800-meter races. Of the 200 races they ran this year, the wins, losses, and

docker41 [41]

Let makes the table neater. event D= 100m, even E=800m
(Event D) (Event E)
A won the race (Event A) 30 50
B won the race (Event B) 60 25
A and B tied (Event T) 10 25

B did not win the race today. What length of the race was it more likely to have been? The question is asking in what event did the chance of B did not win(lose + ties) is more likely. Then, you need to determine the chance for B did not win in both race.
Chance of B did not win 100-m= 30+10/10=40%
Chance of B did not win 800-m= 50+25/10=75%

The difference would be 75%-40%=35% more likely to lose 800-m race

4 0

3 years ago