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2 years ago

Find S15 for 1 + 1.5 + 2.25 + 3.375 + …

1 answer:

6 0

By keenly investigating the given above, it is observed that the given is a geometric sequence with first term (a1) equals 1 and common ratio (r) is 1.5. The geometric series can be calculated by the equation,

Sn = a1 x (1 - r^n) / (1 - r)

where n is 15.

Substituting the known values,
<span>Sn = 1 x (1 - 1.5^15) / (1 - 1.5) = 873.78778
</span>
Therefore, S15 is approximately equal to 873.79.

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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

2 years ago

What is the slope of the line on the graph?

Bogdan [553]

Answer: 1/2

When looking at a graph, you need to follow the formula rise/run. This means that between two points, you need to find the distance up and down/left and right.

Looking at points (0,2) and (2,3), I see that the second point is 1 point higher. Let’s add that in for rise.

Rise/run

1/run

Now for run. The second point is 2 points to the right of the first one. Let’s add that in.

1/2

This is your answer! Hope this helps comment below for more questions :)

3 0

3 years ago

Read 2 more answers

Help with this please. I’d appreciate if you showed the steps and the answer. Thanks!

olga55 [171]

17^2 because the equation for it is a^2+b^2=c^2 so the longest side (x) is the c so 10 i put as a and 7 i put as b. it will always be squared for pythagorean theorem so the equation will look like 10^2+7^2=17^2 and if it isn’t squared all you have to do is undo the squaring

5 0

2 years ago

Kylie rolls a die. What is the probability that 3 will not appear on the die ?

solniwko [45]

Answer:

if travis tells her to take care of the baby

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

I don’t understand it

Serga [27]

the balloon starts at 158 thats our set number

then it goes up 56 feet a minute, you add that to your height

after that you have the variables h and t you would write it as

h= 56t+ 158

7 0

2 years ago