moe_finesse

The answers are provided but i need to know the method

1. If a bus travelled 10kn/h faster, it would take 2 h less time to make a 315 km trip. What is it's speed

ans:35 km/h

2. Over a distance of 120 km, average speed of a train is 40km/h faster than that of a car. If the train covers the distance in 30 mins less time, find its average speed?

ans: 120km/h

3. to save fuel on the 240 km trip to their cottage, the Smith family reduce their usual average speed by 20km/h. This lengthens the journey time by 1 h. what is the slower average speed?

ans: 60 km/h

Finding the tangent line to a circle uses the fact that at any point on a circle the lines containing the center and the tangent lines are perpendicular. Use this method to find an equation of the tangent line to the circle x^2 + y^2 =9 at the point (1, 2sqrt2)

tangent line is y=mx + b

point of tangency is ( -r^2m/b , r^2/b)

answer: sqrt2x + 4y - 9sqrt2 = 0

How do you get the answer?

How do you determine the standard form of a circle when you are not given a radius to work with?

For instance, question 1) center is (2,3) and tangent to the x-axis. I was able to find answer by using the distance formula.

ans: (x-2)^2 + (y-3)^2 = 9.

How do you find determine tangent line is (2,0) what method to find 0?

2) center (-1,3) and tangent to the line y=2. The tangent line touches at (-1,2). The answer came out to (x+1)^2 + (y-3)^2 =1.

My question how did they come to tangent line touching (-1,2). What method did you use to find x= -1?

Please show method. thank you

Find the standard form of equation of circle woth center (-1,3) and tangent to line y=2

ans: (x+2)^2 + (y-3)^2 =1

How did they get radius of 1?

Please show method,

Find the standard form of equation of circle woth center (-1,3) and tangent to line y=2

ans: (x+2)^2 + (y-3)^2 =1

How did they get 1 for radius? I used the distance formula to find radius, but i got radius of 2?

How did they get the answer without a stated radius?

1. center at the origin and containing point (-2,3)

ans: x^2+y^2 =13 (how did they get 13?)

2. center (2,3) and tangent to the x-axis

ans: (x - 2)^2 + (y -3)^2 = 9

3. with endpoints of a diameter at (1,4) and (-3,2)

ans: (x + 1)^2 + (y-3)^2=5

a cereal company finds that the number of people who will buy one of it's products in the first month that it is introduced is linearly correlated to amount of money it spends on advertising. if it spends $40,000 on advertising the 100,000 boxes of cereal will be sold and if it spends $60,000, 200,000 boxes will be sold.

Write an equation that relates amount A spend on advertising to the number of boxes that company aims to sell? (The answer is y=1/5x+ 20,000) HOW DID THEY GET THIS?

The perimeter of a triangle ABC is 57cm. the difference between the shorter sides is 3cm. and the longest side is 9cm shorter than the sum of the shorter sides. what is the length of each side?

x^2 - 3x +4 =0

and

3x^2 + x + 4 =0

ans are = 3/2 +- sqrt 7/2 i and -1/6 +- sqrt 47/6 i

solve for x and express answer in form of a + bi

x^2 - 3x +4 =0

Please show me step by step on how to get the answer. Thanks

1) Find the value of x if 27x3 = 4.8 × 10^−56

answer: x = 1.2 × 10^−19

2) (2.50 × 10^−3) − (3.0 × 10^−1)

answer: 7.5 × 10^−4

The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4ft wide. If the area of the walk is

783 ft^2, determine the dimensions of the pool?

1. The length of rectangular floor is 8 ft greater than its width. If each dimension is increased by 2 ft, the area is increased by 60ft^2. Find the dimensions of the floor.

2. The area of a square exceeds the area of a rectangle by 3 in^2. The width of rectangle is 3 in shorter and the length is 4 in longer than the side of the square. Find the side of square.

A=a^2+2sin0/2

Prove that A is the area of triangle from an octagon which has 8 sides so has 8 triangles within.

1. 2cosx + 2sin2x=0

2. tan^2(2x) = 1/2

You are on a cliff and you throw a rock 60 feet into the air. The rock peaks after 2 seconds and than falls and hits the ground after 3 seconds. What is the height of the cliff?

h(t) = ho + Vi(t) + 2a(t)^2

t= time

ho = height of rock

Vi = velocity

a = acceleration

A colour slide 3 cm high is to be projected on a screen. The light is 7cm behind the slide and 77 cm from the screen. what is the height of the projection?

sin(2t) = 2(cot(t) / 1 + cot^2(t))

Jill has discovered that the number of glasses of juice sold in a day is a function of the sales price. (p=p(x)) where x is the price, in cents, of a glass of juice.

If jill noticed that 75 glasses of lemonade were sold when the price of a glass was .60 cents but only 45 glasses were sold if the price was set to .80 cents. What is the linear function of the sale price, what should p(x) be?

logbase7(343x^2) = 2logbase7(49x)