Answer:
1) Both 15.
2) 25 and -25.
Step-by-step explanation:
1) Let the 2 numbers be x and 30 - x.
The product = x(30 - x)
f(x) = x(30 - x)
f(x) = 30x - x^2
Finding the derivative:
f'(x) = 30 - 2x
Finding the maximum:
30 - 2x = 0
x = 15.
This gives a maximum f(x) because f"(x) = -2.
So the numbers are 15 and 30 - 15 = 15.
2). If one number is x the other is y.
x - y = 50
y = x - 50
The product =
x(x - 50)
= x^2 - 50x
Finding the derivative:
2x - 50 = 0 for a minimum value.
2x = 50
x = 25.
So the numbers are 25 and 25-50 = -25.
Answer:
Step-by-step explanation:
x²+5x-84
look for the factors of 84 that when you add together it will give +5
look for the factors of 84 that when you multiply together it will give -84
12 and 7
addition, multiplication
-12+7 = -5 -84
-12-7= -19 84
+12-7 = +5 -84 correct
then equate into the =5x and -84
x²+12x-7x-84
then factorize
x(x+12)-7(x+12)
(x-7)(x+12)
<span>The pitch of the roof is one of the two major measures of roof angle, the other being slope. In order to calculate the roof pitch as a fraction, one should divide the rise of the roof by the span, which is defined as the length between the exterior of the top plate of one wall and that of the corresponding wall on the other side of the building.</span>
Answer: 0.0497870 ; 0.87754
Step-by-step explanation:
Given that :
λ = 0.0003
Defining a continuous distribution function :
F(x) = 1 - e^-λx = 1 - e^-0.0003x ; x ≥ 0
a. What proportion of the fans will last at least 10,000 hours?
P(x ≥ 10000) = e^-0.0003(10000) = 0.0497870
b. What proportion of the fans will last at most 7000 hours?
P(x ≥ 7000) = 1 - p(x ≤ 7000) = 1 - e^-0.0003(7000)
1 - 0.12245642825 = 0.87754
we have the equation
Remember that
If an ordered pair is on the graph of the given function, then the ordered pair must satisfy the given function
Verify each option
N 1
(0,1)
x=0, y=1
Is not true, because the log of zero is undefined
N 2
(1,1/2)
x=1, y=1/2
Is not true, because the log of 1 is zero
N 3
(1/2,1)
Is true
therefore
<h2>The answer is (1/2,1)</h2>
