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2 years ago

4^2[1/3+4(36÷6)] Show work please.

Mathematics

1 answer:

Vaselesa [24]2 years ago

3 0

Answer:

1168/3 or 389 1/3 as a mixed fraction

Step-by-step explanation:

Simplify the following:

4^2 (4×36/6 + 1/3)

4×36/6 = (4×36)/6:

4^2 ((4×36)/6 + 1/3)

4^2 = 16:

16 ((4×36)/6 + 1/3)

36/6 = (6×6)/6 = 6:

16 (4×6 + 1/3)

4×6 = 24:

16 (24 + 1/3)

Put 1/3 + 24 over the common denominator 3. 1/3 + 24 = 1/3 + (3×24)/3:

16 1/3 + (3×24)/3

3×24 = 72:

16 (1/3 + 72/3)

1/3 + 72/3 = (1 + 72)/3:

16 (1 + 72)/3

1 + 72 = 73:

16×73/3

16×73/3 = (16×73)/3:

(16×73)/3

| | 7 | 3

× | | 1 | 6

| 4 | 3 | 8

| 7 | 3 | 0

1 | 1 | 6 | 8:

Answer: 1168/3

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Let's begin by listing out the information given to us:

8 am

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airplane #2: x = 5000 ft, v = 900ft/min

We must note that the airplanes are moving at a constant speed. The equation for the airplanes is given by:

$\begin{gathered} E=x_1+vt----1 \\ E=x_2+vt----2 \\ where\colon E=elevation,ft;x=InitialElevation,ft; \\ v=velocity,ft\text{/}min;t=time,min \\ x_1=80,870ft,v=-450ft\text{/}min \\ E=80870-450t----1 \\ x_2=5,000ft,v=900ft\text{/}min \\ E=5000+900t----2 \end{gathered}$

We equate equations 1 & 2 to get the time both airlanes will be at the same elevation. We have:

$\begin{gathered} 5000+900t=80870-450t \\ \text{Add 450t to both sides, we have:} \\ 900t+450t+5000=80870-450t+450t \\ 1350t+5000=80870 \\ \text{Subtract 5000 from both sides, we have:} \\ 1350t+5000-5000=80870-5000 \\ 1350t=75870 \\ \text{Divide both sides by 1350, we have:} \\ \frac{1350t}{1350}=\frac{75870}{1350} \\ t=56.2min \\ \\ \text{After }56.2\text{ minutes, both airplanes will be at the same elevation} \end{gathered}$

The elevation at that time (when the elevations of the two airplanes are the same) is given by substituting the value of time into equations 1 & 2. We have:

$\begin{gathered} E_1=80870-450t \\ E_1=80870-450(56.2) \\ E_1=80870-25290 \\ E_1=55580ft \\ \\ E_2=5000+900t \\ E_2=5000+900(56.2) \\ E_2=5000+50580 \\ E_2=55580ft \\ \\ \therefore E_1\equiv E_2=55580ft \end{gathered}$

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4 months ago

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neonofarm [45]

Answer:

Step-by-step explanation:

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2 years ago

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3 years ago

Suppose that y is directly proportional to x, and y = 150 when x = 15. What is the constant of proportionality?

galina1969 [7]

Answer: The required constant of proportionality is 10.

Step-by-step explanation: Given that y is directly proportional to x, and y = 150 when x = 15.

We are to find the constant of proportionality.

According to the given information, we can write

$y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~~~~~~[\textup{where k is the constsnt of propotionality}].$

When y = 150 and x = 15, we get from the above equation that

$y=kx\\\\\Rightarrow 150=k\times15\\\\\Rightarrow k=\dfrac{150}{15}\\\\\Rightarrow k=10.$

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2 years ago

A newspaper is launching a new advertising campaign in order to increase the number of daily subscribers. The newspaper currentl

BARSIC [14]

Answer:

57 days

Step-by-step explanation:

Given that:

t(0) = 26000

Growth rate (S'(t)) = 80t^1/2

Targeted number of subscribers = 49000

Take the integral of the growth rate :

∫80t^1/2dt = [(80t^(1/2 + 1)) / 1/2 + 1] + C

[(80t^(1/2 + 1)) / 1/2 + 1] + C = (80t^3/2) / 3/2 + C

(80t^3/2) * 3/2 + C = (160/3)t^3/2 + C

(160/3)t^3/2 + C

Let C = t(0)

(160/3)t^3/2 + 26000 = 49000

(160/3)t^3/2 = 49000 - 26000

(160/3)t^3/2 = 23000

Multiply both sides by 3/160

t^3/2 = 23000* 3/160

t^3/2 = 69000/160

t^3/2 = 431.25

t^(3/2 * 2/3) = 431.25^2/3

t = 57.080277

t = 57 days (approx.)

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2 years ago