In order to find how long the the kangaroo's jump was, we are going to find out what the value of x is when y=0, because y=0 represents the kangaroo on the ground.
0 = -0.03(x - 14)2 + 6 Original equation with 0 substituted for y
0.03(x - 14)2 = 6 Add 0.03(x - 14)2 to each side
(x - 14)2 = 200 Divide both sides by 0.03
x - 14 = +/- 10√2 Take the square root of each side
x = 14 +/- 10√2 Add 14 5o each side
Because 10√2 is approximately 14.14, 14 - 10√2 is approximately 0. This makes sense because the kangaroo has not left the ground yet at 0 ft. The correct answer is 14 + 10√2, which is approximately 28.14 ft.
For part a, we want to use the distance that is halfway between the zeroes of the jump. That is the point halfway between 14 - 10√2 and 14 + 10√2. In other words, we need to use the value 10√2 (approx. 14.14) for x and solve for y.
y = -0.03(10√2 - 14)2 + 6 Write original equation with 10√2 substituted for y
y = -0.03(14.14 - 14)2 + 6 (Using approximation)
y = -0.03(0.14)2 + 6 Substitute (14.14 - 14 = 0.14)
y = -0.03(0.0196) + 6 Square 0.14
y = -0.000588 + 6 Multiply -0.03 times 0.0196
y = 5.999412 Add -0.00588 and 6
y = 6 Round
I went through all of the this work to show that the maximum point of the parabola (the highest point in the kangaroo's jump) is actually the point where the value being squared is 0 (14 - 14). The y-value of the vertex is 6. That is also the highest point in the jump.
The answers are:
a. 6 ft
b. 28.14 ft
Margaret traveled 80 miles to the appointment.
Step-by-step explanation:
Given,
Speed while driving for appointment = 80 mph
Speed while coming back = 70 mph
Let,
x be the time taken for the trip
y be the distance covered
Distance = Speed*Time
y = 80x Eqn 1
Time taken in return trip = x+1/7
y = 70(x+1/7)
Eqn 2
Putting value of y from Eqn 1 in Eqn 2
Dividing both sides by 10
x = 1 hour
Putting x = 1 in Eqn 1
Margaret traveled 80 miles to the appointment.
Keywords: linear equation, substitution method
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Answer:
It will take them 15 minutes.
Step-by-step explanation:
1. Since you are given the information that the two typists are typing a certain amount of words in the same time frame (ie. one minute), you can add the two values together to obtain the total number of words the typists would type together in one minute:
95 + 98 = 193 words
2. To calculate how many minutes it would take them to type 2,895 words, you would simply take this total number of words and divide it by the number of words they collectively type in one minute (found in 1.). Thus:
2895/193 = 15
Therefor, it will take them 15 minutes to type 2,895 words.
