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3 years ago

14

Car A leaves a destination at 3 P.M. and travels 60 kph. Car B

1 answer:

Helen [10]3 years ago

8 0

Answer: Car B will catch up with A when the distance travel by the two are equal

Recall Speed = Distance/Time

Distance =Time * Speed

Car A; D=60T1

Car B; D=70T2

Where T1= T2+1

60T1=70T2

60(T2+1)= 70T2

60T2+60=70T2

10T2=60

T2=6hrs

4pm +6hrs

10pm car B catches up with A

Step-by-step explanation:

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AVprozaik [17]

Answer: 63

Step-by-step explanation:

PEMDAS

5 0

3 years ago

How many solutions are there to the following system of equations?

sweet [91]

$4x-8y=0 \\
\underline{-3x+8y=-7} \\
4x-3x=0-7 \\
x=-7 \\ \\
4x-8y=0 \\
4 \times (-7)-8y=0 \\
-28-8y=0 \\
-8y=28 \\
y=\frac{28}{-8} \\
y=-\frac{7}{2} \\ \\
 \left \{ {{x=-7} \atop {y=-\frac{7}{2}}} \right.$

There is one solution to this system of equations. The answer is B.

6 0

3 years ago

Read 2 more answers

Identify the sine function with the given attributes.

Thepotemich [5.8K]

Answer:

<em>Last option </em>

$f(t)=sin(\pi(t -3)) + 4$

Step-by-step explanation:

The general sine function has the following form

$y = Asin(bt-\phi) + k$

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.

$\frac{2\pi}{b}$ is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

$\phi$ phase shift

We know that:

amplitude: 1; period: 2; phase shift: 3; vertical shift: 4

Thus:

$A =1$

$\frac{2\pi}{b}=2$

$b=\pi$

$\phi=3$

$k=4$

Then the function is:

$f(t)=sin(\pi(t -3)) + 4$

The answer is last option

4 0

3 years ago

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

A number is 3 more than 2nd number, the sum of the two numbers is 17. Find the<br> numbers.

Debora [2.8K]

Your numbers are 7 and 10

4 0

3 years ago