Given:
All the edges of a cube are expanding at a rate of 4 in. per second.
To find:
The rate of change in volume when each edge is 10 in. long.
Solution:
Let a be the edge of the cube.
According to the question, we get
We know that, volume of a cube is
Differentiate with respect to t.
Putting the given values, we get
Therefore, the rate of change in volume 1200 cubic inches per second.
F(-4) = 0
Here, we replace x with -4. In doing so, we see that (-4+4) is indeed 0, making this the correct answer.
The next two choices are incorrect since only -4 is a root of f(x), as explained above (a root occurs when the function equals zero when plugging in that “root”).
The last answer is incorrect since plugging in 4 will get f(4)=8.
Xy = -150
x + y = 5
x + y = 5
x - x + y = -x + 5
y = -x + 5
xy = -150
x(-x + 5) = -150
x(-x) + x(5) = -150
-x² + 5x = -150
-x² + 5x + 150 = 0
-1(x²) - 1(-5x) - 1(-150) = 0
-1(x² - 5x - 150) = 0
-1 -1
x² - 5x - 150 = 0
x = -(-5) ± √((-5)² - 4(1)(-150))
2(1)
x = 5 ± √(25 + 600)
2
x = 5 ± √(625)
2
x = 5 ± 25
2
x = 2.5 ± 12.5
x = 2.5 + 12.5 or x = 2.5 - 12.5
x = 15 or x = -10
x + y = 5
15 + y = 5
- 15 - 15
y = -10
(x, y) = (15, -10)
or
x + y = 5
-10 + y = 5
+ 10 + 10
y = 15
(x, y) = (-10, 15)
The two numbers that add up to 5 and multiply to -150 are 15 and -10.
Answer:
1
Step-by-step explanation:
