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lesya [120]
3 years ago
14

A plane flies at a steady rate of 40 mph while a second plane flies at a steady rate of 100 mph. The planes are 200 miles apart

and fly directly toward each other. In how many hours will they meet?
Mathematics
1 answer:
seraphim [82]3 years ago
7 0

About 2.5 hours or two and a half

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The diameter of a cylindrical construction pipe is 6 ft. If the pipe is 26 ft long, what is its volume?
Mandarinka [93]

Answer:

Step-by-step explanation:

First find the area of the circular base. The diameter is 6, so the radius is 3.

A circle is pi r square, so it is 3.14 x 3^2, = 28.26

Multiply that by the length 28.26 x 26 = 734.76, which rounds to 735 cubic feet.

5 0
2 years ago
A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so
Debora [2.8K]

Let A(t) = amount of salt (in pounds) in the tank at time t (in minutes). Then A(0) = 11.

Salt flows in at a rate

\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}

and flows out at a rate

\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}

which I'll solve with the integrating factor method.

\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95

-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}

\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}

Integrate both sides. By the fundamental theorem of calculus,

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)

\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}

\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}

\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}

After 1 hour = 60 minutes, the tank will contain

A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131

pounds of salt.

7 0
2 years ago
Answer it pls option c
Troyanec [42]

Answer:

x = \frac{1}{4}

Step-by-step explanation:

\frac{x}{2} +\frac{3}{4} =\frac{7}{8}

→ Find the LCM of the denominators (2,4 and 8)

LCM = 8

→ Multiply the whole equation by 8 to get rid of the fractions

4x + 6 = 7

→ Minus 6 from both sides to isolate 4x

4x = 1

→ Divide both sides by 4 to isolate x

x = \frac{1}{4}

5 0
3 years ago
Read 2 more answers
What two numbers multiply to 10 and add to -29 ?
Degger [83]
Xy=10
x+y=29

subtract x from both sides for second equation

y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x=\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}

so
x^2+29x+10=0
a=1
b=29
c=10
x=\frac{-29+/- \sqrt{(-29)^{2}-4(1)(10)} }{2(1)}
x= \frac{-29+/- \sqrt{841-40} }{2}
x= \frac{-29+/- \sqrt{801} }{2}
x= \frac{-29+/- 3\sqrt{89} }{2}

x= \frac{-29- 3\sqrt{89} }{2} or \frac{-29+ 3\sqrt{89} }{2}
those are the 2 numbers
aprox=-28.65 and -0.349


5 0
3 years ago
Read 2 more answers
FREE BRAINLIEST
DedPeter [7]

Answer:

y = 6x -2

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
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