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2 years ago

Help me find the slope on the line? Thanks in advance.

Mathematics

2 answers:

Ronch [10]2 years ago

6 0

Hoi!

To find the slope of a line, we should first identify two points on the line. Two points I've identified are at (1, 9) and (6, 5).

Now we use the formula y₂ - y₁ / x₂ - x₁ to find the slope.

y₂ = 5
y₁ = 9
x₂ = 6
x₁ = 1

$\frac{5 - 9}{6 - 1} = \frac{-4}{4}$ = -1

The slope is -1. :)

Juliette [100K]2 years ago

5 0

(1, 9) and (11,1)

slope
= (9 - 1)/(1 - 11)
= 8 /-10
= -4/5
= - 0.8

answer
slope = - 0.8

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JulijaS [17]

Answer:

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Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

Required

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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

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Nataly [62]

Answer:

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Step-by-step explanation:

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Answer:

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