Answer:
(x-8) (x+7)
Step-by-step explanation:
x^2 -x-56
We want to factor this problem.
What two numbers multiply to negative 56 and add to -1
-8 *7 = -56
-8+7 = -1
We can use -8 and 7
(x-8) (x+7)
Check:
FOIL
first: x*x =x^2
outer: 7x
inner:-8x
last: -8*7 = -56
Add this together
x^2 +7x-8x -56 = x^2 -x-56
<h3>Answer:</h3>
<h3>Explanation:</h3>
It can work well to consider the function in parts. Define the following:
... a(x) = (1/2)ln(x^2+3)
... b(x) = x(4x^2-1)^3
Then the derivatives of these are ...
... a'(x) = (1/2)·1/(x^2 +3)·2x = x/(x^2+3)
... b'(x) = (4x^2 -1)^3 + 3x(4x^2 -1)^2·8x = (4x^2 -1)^2·(4x^2 -1 +24x^2)
... = (4x^2 -1)^2·(28x^2 -1)
___
<em>Putting the parts together</em>
f(x) = a(x)/b(x)
f'(x) = (b(x)a'(x) -a(x)b'(x))/b(x)^2 . . . . . rule for quotient of functions
Substituting values, we have
... f'(x) = (x(4x^2 -1)^3·x/(x^2 +3) -(1/2)ln(x^2 +3)·(4x^2 -1)^2·(28x^2 -1)) / (x(4x^2 -1)^3)^2
We can cancel (4x^2 -1)^2 from numerator and denominator. We can also eliminate fractions (1/2, 1/(x^2+3)). Then we have ...
... f'(x) = 2x^2(4x^2 -1) -(x^2 +3)ln(x^2 +3)·(28x^2 -1)/(2x^2·(x^2 +3)(4x^2 -1)^4))
Simplifying a bit, this becomes ...
... f'(x) = (8x^4 -2x^2 -ln(x^2 +3)·(28x^4 +83x^2 -3))/(2x^2·(x^2 +3)(4x^2 -1)^4))
Answer:
Step-by-step explanation:
2×5.20=10.40
3×h=3h
10.40=3h
Substitute the values
-2(-2)^2+4(3)
First evaluate the exponent.
-2(4)+4(3)
Then evaluate multiplication.
-8+4(3)
-8+12
Then add.
Final answer:4
Plane A 520 feet vertical rise 40 feet/min
plane B 3800 feet vertical dip 120 feet per minute.
vertically the speeds are 40 feet / minute & 120 feet /minute.
120 + 40 = 160 feet per minute.
the distance between them = 3800 -520 =3280 feet
t= d/r
3280/160
t = 20.5 minutes. they will be at the same altitude.