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3 years ago

The function of (x) varies directly with x^2, and f(x)=96 when x=4 what is the value of f(2)

1 answer:

3 0

$\bf \qquad \qquad \textit{direct proportional variation}
\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------$

$\bf \textit{f(x) varies directly with }x^2\qquad f(x)=kx^2
\\\\\\
\textit{we also know that }
\begin{cases}
f(x)=96\\
x=4
\end{cases}\implies 96=k(4)^2\implies 96=16k
\\\\\\
\cfrac{96}{16}=k\implies 6=k\qquad therefore\qquad \boxed{f(x)=6x^2}
\\\\\\
\textit{now, when }\stackrel{f(2)}{x=2}\textit{ what is \underline{f(x)}?}\qquad f(2)=6(2)^2$

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Please give me an approximation of how long it would take to evacuate a population of 91,000 to a destination 21 miles away, usi

RoseWind [281]

Answer:

The time will depend on the number of people who move on each trip from the point of origin to the destination. If done at the maximum speed allowed using 100 vehicles of 50 seats each, the evacuation would be done in 63.68 hours

Step-by-step explanation:

Population = 91,000 ppl

Speed limit = 60 mph

Distance = 21 miles.

1. Assuming that people is evacuated at the max. speed allowed, it means that each trip will take:

T = D/V

D= 21 miles

V = 60 mph:

So;

T = 21 miles / 60mph

T= 0,35 h

2. Asumming that we are going to use an amount of 100 vehicles with 50-seats in each trip for evacuating people, it means that we could evacuate

500 people every 0,35 h ≈ 1,429 ppl/hour (evacuation rate)

To know how long it would take us to evacuate 91,000 people under these conditions, we would have to divide the total amount by the previously calculated evacuation rate

T= 91,000/ 1,429 = 63,68 hours

6 0

3 years ago

Jeanne needed to buy 258 yards of fabric, if the ribbon costs 10¢ per foot, what is the total cost of the ribbon in dollars?

ss7ja [257]

Answer:

Step-by-step explanation:

1 yard is equal to 3 foot

10¢= 1 foot

30¢= 1 yard

30¢ x 258 yards= $77.40

7 0

2 years ago

What is 25% Of 30% Of 400?

marta [7]

Answer:

25% of 30% of 400 = 30

33% decrease in value

Step-by-step explanation:

You can either get 30% of 400 first then 25% of 400 or you can get the total percentage of 400.

Method 1:

30% of 400 = 0.3 of 400 = 0.3 * 400 = 120

25% of 120 = .25 of 120 = .25 * 120 = 30

Method 2:

30% of 25% = 0.3 * 0.25 = 0.075 = 7.5% of 400

7.5% of 400 = 0.075 of 400 = 0.075 * 400 = 30

5.) To find the percentage of the new price, you can build the equation below.

$\frac{new price}{original price} = \frac{percent}{100}$

$\frac{200,000}{300,000} = \frac{x}{100}$

$20,000,000 = 300,000x$

$x = 66.667$

The percentage decrease in price is then 100% of the original price - 66.667% of the original price = 100% - 66.67% = 33.33% = 33% decrease.

3 0

2 years ago

3x^5+6x^3 PRIME b 3x^4(3x + 2) 3(x^5 + x^3) d 3x^3(x^2 + 2x)

Gelneren [198K]

Answer:

Im guessing 33(2+2)

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2 years ago

The function H(t) = −16t2 + 60t + 95 shows the height H(t), in feet, of a projectile after t seconds. A second object moves in t

Dimas [21]

H(t) = -16t² + 60t + 95
g(t) = 20 + 38.7t

h(1) = -16(1²) + 60(1) + 95 = -16 + 60 + 95 = -16 + 155 = 139
h(2) = -16(2²) + 60(2) + 95 = -16(4) + 120 + 95 = -64 + 215 = 151
h(3) = -16(3²) + 60(3) + 95 = -16(9) + 180 + 95 = -144 + 275 = 131
h(4) = -16(4²) + 60(4) + 95 = -16(16) + 240 + 95 = -256 + 335 = 79

g(1) = 20 + 38.7(1) = 20 + 38.7 = 58.7
g(2) = 20 + 38.7(2) = 20 + 77.4 = 97.4
g(3) = 20 + 38.7(3) = 20 + 116.1 = 136.1
g(4) = 20 + 38.7(4) = 20 + 154.8 = 174.8

Between 2 and 3 seconds.
The range of the 1st object is 151 to 131.
The range of the 2nd object is 97.4 to 136.1

h(t) = g(t) ⇒ 131 = 131

It means that the point where the 2 objects are equal is the point where the 1st object is falling down while the 2nd object is still going up.

5 0

3 years ago

Read 2 more answers