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2 years ago

Find the indicated function values for the function below g(x)=9x + 8 g(0) =

Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

6 0

Answer:

$g(0) = 8$

Step-by-step explanation:

The problem gives us the following function:

$g(x) = 9x + 8$

g(0) =

This is the value of g when x = 0. So

$g(x) = 9x + 8$

$g(0) = 9*0 + 8$

$g(0) = 8$

So the answer to this question is:

$g(0) = 8$

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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:

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

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

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

7 0

1 year ago

Two-thirds a number plus 4 is 7

faltersainse [42]

2/3n (put that as a fraction) + 4 = 7

6 0

2 years ago

Solve each proportion t/9=35/6

kotegsom [21]

The answer to the proportion is t=52.5

8 0

2 years ago

??? im lost

Irina-Kira [14]

I’m lost as also sorry I just need some points I’m doing a test rn

8 0

2 years ago

What is the missing constant term in the perfect square that starts with x^2+\dfrac{1}{2}xx

grandymaker [24]

Answer:

1/16

Step-by-step explanation:

Given the expression;

$x^2+\dfrac{1}{2}x$

To find a constant that will make it a perfect square, we will use the square if the half of coefficient of x

Coefficient of x = 1/2

half of Coefficient of x = 1/2*(1/2)

Half of Coefficient of x = 1/4

square of the half of coefficient of x = (1/4)^2

square if the half of coefficient of x = 1/16

hence the constant that will make it a perfect square is 1/16

7 0

2 years ago