We can create a parabola equation of the trajectory using
the vertex form:
y = a (x – h)^2 + k
The center is at h and k, where h and k are the points at
the maximum height so:
h = 250
k = 120
Therefore:
y = a (x – 250)^2
+ 120
At the initial point, x = 0, y = 0, so we can solve for
a:
0 = a (0 – 250)^2 + 120
0 = a (62,500) + 120
a = -0.00192
So the whole equation is:
y = -0.00192 (x – 250)^2 + 120
So find for y when the golf ball is above the tree, x =
400:
y = -0.00192 (400 - 250)^2 + 120
y = 76.8 ft
So the ball cleared the tree by:
76.8 ft – 60 ft = 16.8 ft
Answer:
16.8 ft
Solving this problem actually requires us the use of the
distance formula of point to a line.
The formula is:
distance = | a x + b y + c | / sqrt (a^2 + b^2)
So we are given the equation:
y = 2 x + 4
rewriting:
<span>y – 2 x – 4 = 0 -->
a = -2, b = 1, c = -4</span>
We are also given the points:
(-4, 11) = (x, y)
Using the distance formula at points (x, y):
distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 +
(1)^2]
distance = 15 / sqrt (5)
distance = 6.7
<span>So the tree is about 6.7 ft away from the zip line.</span>
Answer:
D) 15
Step-by-step explanation:
The sum of the interior angles of a polygon is given by
We have that, the sum of the interior angles of a polygon is
26 right angles. We want to find n, the number of sides.
We substitute into the formula to get:
Divide through by 90
Divide through by 2
Answer:
2 bags of deezznuts and 1 bag of fruit
Step-by-step explanation:
18 bags of nuts
9 bags of fruit
2 bags of nuts mixed with 1 bag of fruit, multiply that by nine and you have no remainder on any of the bags
The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190
Answer: first number is 190
