quadratic math help asap please?

Question

1. Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

2.The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?


3. A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.

use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex.
1. (3)1/2y2 - 4y - 7(3)1/2 = 0

Answer 1

1) let v be the speed of Steve (in mph) (not the fastest one)
Time of travel (in hours) is: 200/v
when he gone faster, his speed was v+10
then time of travel is 200 /(v+10)
the text says: 200/v = 1 + 200/(v+10)

then v^2+10v-2000=0

2 solutions: v=-50 or v=40
the first is negative, impossible so
v= 40 mph

2) let v be the speed of boat (mph) in still water
the travel upriver have taken 60/ (v-3) and the travel return have taken 60 / (v+3)
The total time is 9 (hours) then:
60/ (v-3) +60 / (v+3) = 9
then 3(3v^2-40v-27)/ [(v+3)(v-3)] =0

2 solutions: v=( 20-sqrt(481) )/3 or v= =( 20+sqrt(481) )/3

only the second is positive
v =( 20+sqrt(481) )/3 ~ 14 mph

Answer 2

a ) there are the two 2, a million, or 0 genuine suggestions for a quadratic equation. if a ingredient is squared, then there is entirely a million answer. if there are 2 aspects, then there are 2 solutions. If the parabola is shifted so as that it would not touch the x-axis, then there is not any genuine answer... b) using the quadratic formula you will discover no rely if the suggestions are genuine or imaginary or complicated... c) factoring, graphing, and the quadratic formula... 12x^2 - 10x - 40 two = 0 6x^2 - 5x -21 = 0 x=[5+/- sqrt (25 - 4(6)(-21))] / (2)(6) x=[5+/- sqrt (25 + 504)] / (12) x=[5+/- sqrt (529)] / (12) x=[5+/- 23]/12 x= 28/12 or -18/12 x = 7/3 or -3/2 2nd approach: (3x-7)(2x+3) = 0 third approach... won't be able to rather demonstrate it...

Answer 3

First one:

1/S - 1(S+10) = 1

Multiple both sides by S(S+10)
10 = S(S+10)

0 = S^2 + 10S - 10

Use the quadratic formula.

Second one:

60/(S+3) + 60/(S-3) = 9.

Proceed as in the first example. You can factor out a factor of 3 early on to help keep things manageable.

Third one:

S^2 + 24 = (S+1)^2 - 25.

That one's not really quadratic. Just expand both sides and it's easy.

For the other one your notation is unreadable. Sorry.