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ratelena [41]
4 years ago
13

A plane flies round-trip to Philadelphia. If flies to Philadelphia at 220 miles per hour and back home with a tailwind at 280 mi

les per hour. If the total trip takes 6.5 hours, how many miles does the plane fly round-trip?
Mathematics
1 answer:
Katena32 [7]3 years ago
6 0
v=\frac{s}{t},\ where\ V-speed,\ s-distance,\ t-time\\v*t=s\\\\
 \left \{ {{v_1*t_1=s} \atop {v_2*t_2=s}} \right.\\\\t_1=6,5-t_2\\\\ \left \{ {{220(6,5-t_2)=s} \atop {280*t_2=s}} \right.  \\\\
220(6,5-t_2)=280*t_2\\
1430-220t_2=280t_2\ \ \ |Add\ 220t_2\\
1430=500t_2\ \ \ |Divide\ by\ 500\\t_2=2,86h\\\\
s=t_2*v_1\\
s=2,86*280=800,8\\
2s=1601,6miles\\\\
Plane\ flew\ 1601,6\ miles\ in\ round\ trip.
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Bill bought 38 1/2 feet of wire fencing to put around his blueberry plants. He cut the wire into several pieces, each one measur
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Step-by-step explanation:

You are given that Bill bought 38 1/2 feet of wire. Convert the mixed fraction into improper fraction.

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You are given that he cut the wire into several pieces, each one measuring 5 1/2 feet. Convert it too to improper fraction.

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What two numbers multiply to 44 and add up to 12?
djverab [1.8K]
This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.      x*y = 44 ..........(a)

Add up to 12.      x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44   

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.       

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.   

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0,  a = 1, b = -12, c = 44 

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a


x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)    

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number.  Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2      or     (12 - √-32 )/ 2   

x = (12 + 4i√2 )/ 2              (12 - 4i√2 )/ 2 

x = 12/2 + (4i√2)/2                12/2 - (4i√2)/2

x = 6 + 2i√2            or         6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2,  y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2,  y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2


x = 6 + 2i√2,  y = 6 - 2i√2

x = 6 - 2i√2,  y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2
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