Answer:
YES
Step-by-step explanation:
<span>Since
this is an SAT Math Level 2 problem derivatives should not be required
to find the solution. To find "How many more hours of daylight does the
day with max sunlight have than May 1," all you need to understand is
that sin(x) has a maximum value of 1.
The day with max sunlight will occur when sin(2*pi*t/365) = 1, giving the max sunlight to be 35/3 + 7/3 = 14 hours
Evaluating your equation for sunlight when t = 41, May 1 will have about 13.18 hours of sunlight.
The difference is about 0.82 hours of sunlight.
Even though it is unnecessary for this problem, finding the actual max
sunlight day can be done by solving for t when d = 14, of by the use of
calculus. Common min/max problems on the SAT Math Level 2 involve sin
and cos, which both have min values of -1 and max values of 1, and also
polynomial functions with only even powered variables or variable
expressions, which have a min/max when the variable or variable
expression equals 0.
For example, f(x) = (x-2)^4 + 4 will have a min value of 4 when x = 2. Hope this helps</span>
Answer:
one solution
Step-by-step explanation:
-2x - 4 = x - 5
-3x - 4 = -5
-3x = -1
x = 1/3
y = 1/3 - 5
y = 1/3 - 15/3
y = -14/3
(1/3, -14/3)
Answer:
Step-by-step explanation:
We have to first find the vertices of the feasible region before we can determine the max value of P(x, y). We will graph all 4 of those inequalities in a coordinate plane and when we do that we find that the region of feasibility is bordered by the vertices (0, 0), (0, 1), (2, 3), and (5, 0). Filling each x and y value into our function will give us the max value of that function.
Obviously, when we sub in (0, 0). we get that P(x, y) = 0.
When we sub in (0, 1) we get 24(0) + 30(1) = 30.
When we sub in (2, 3) we get 24(2) + 30(3) = 138.
When we sub in (5, 0) we get 24(5) + 30(0) = 120.
Obviously, the vertex of (2, 3) maximized our function for a value of 138.
