Answer:
Either a tangent line or a line parallel to the axis of symmetry will do.
A standard high school parabola has a vertical or horizontal axis of symmetry, so a line of the form x=k or y=k is the easiest way
hope it helps you
Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
Answer:
Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.
Step-by-step explanation:
Let the weight of Julie be
Given:
Ted weighs twice as much as Julie
Weight of Ted =
Mike weighs three times as much as Julie.
Weight of Mike =
Together, Ted, Mike, and Julie weigh 210 lbs.
Solving above we get;
Hence Julie weight is 35 lbs.
Weight of Ted =
Hence Ted weight is 70 lbs.
Weight of Mike =
Hence Mike weight is 105 lbs.
Answer:
96
Step-by-step explanation:
The loan duration is for 8 years, a total of 12·8 = 96 monthly payments. The 96th payment is the balloon payment.