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Marrrta [24]
3 years ago
10

Simplify (1 − 4i) − (6 + 9i).

Mathematics
1 answer:
ss7ja [257]3 years ago
8 0

Answer: -5-13i

Work Shown:

(1-4i) - (6+9i) = 1-4i-6-9i

(1-4i) - (6+9i) = (1-6) + (-4i-9i)

(1-4i) - (6+9i ) = -5 - 13i

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During the first part of a​ trip, a canoeist travels 96 miles at a certain speed. the canoeist travels 15 miles on the second pa
blondinia [14]
This problem is a problem using 
d = r * t
First part of the trip
d = 96 miles
r = ??
t = ??

Second part of the trip
d = 15 miles
r = r - 5
t = 4 - t

Solve for r first.
96/r + 15/(r - 5) = 4 hours                multiply through by r and r - 5
96(r - 5) + 15r  = 4*(r - 5)(r)             Remove the brackets on the left
96r - 480 + 15r = 4*r*(r - 5)             Collect like terms on the left.
111r - 480 = 4r(r - 5)                        Remove the brackets on the right.
111r - 480 = 4r^2 - 20r                     Bring the left side over to the right side.
0 = 4r^2 - 20r - 111r + 480               Collect like terms.
0 = 4r^2 - 131r + 480

The only way I could do this was to use the quadratic equation.

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}

a = 4

b = - 131

c = 480

\text{x = }\dfrac{ -(-131) \pm \sqrt{(-131)^{2} - 4*4*480 } }{2*4}
\text{x = }\dfrac{ 131 \pm \sqrt{(17161) - 7680 } }{8}
\text{x = }\dfrac{ 131 \pm \sqrt{9481 } }{8}
\text{x = }\dfrac{ 131 \pm 97.37  }{8}

x = (131 + 97.38)/8
x = 28.55
x = (131 - 97.37)/8
x = 4.20

4.2 isn't going to work because the slower speed has to be larger than 5, otherwise you will get a negative speed (as this solution will give), so 4.20 is an extraneous solution.

r = 28.55 for the first  part of the trip and
r = 23.55 for the second part of the trip.

Check.
Let's see if the times add up to 4
d/r = t
96/28.55 = 3.36
15/22.75 = 0.64

The times do = 4, so the rates are correct.

Answers
r1 = 28.55 for the 96 mile trip.
r2 = 23.55 for the 15 mile trip.

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Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inc
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Answer:

A cross-section parallel to the base is a rectangle measuring 15 inches by 8 inches.

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A cross-section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.

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the cross sections that are parallel and perpendicular will have the same measurements as the non-intersected sides. the last one will be a diagonal so the intersected edge is 6 and it creates a right triangle so it must be larger than 15 inches.

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3 years ago
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