Answer:
2.5 seconds.
Step-by-step explanation:
Find the value of t when the height is 28 feet:
-16t^2 + 56t + 4 = 28
-16t^2 + 56t - 24 = 0
-8(2t^2 - 7t + 3) = 0
-8(2t - 1)(t - 3) = 0
t = 0.5, 3 seconds.
So on the upward journey the rock is at 28 feet at 0.5 second after the throw and at 3 seconds it is at 28 feet again while it is falling back.
Therefore the period when it is at least 28 feet above the ground is 3.0 - 0.5 = 2.5 seconds.
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
Answer:
7 Glasses
Step-by-step explanation:
One glass of orange juice needs 1/7 of a bag, she brought 7 bags which all adds up to a full 7 glasses
It states that the ultimate advice is to show how this communicates together
Remember that the angles of a triangle is 180 so:
(7x+8) + (5x+2) + (7x-1) = 180
7x+8+5x+2+7x-1=180
7x+5x+7x=180-8-2+1
19x=171
X= 171/19
X=9
Therefore x=9
