For this case we have the following function:
<span>w (x) = - 5 (x-8) (x + 4)
</span><span>Rewriting we have:
</span><span>w (x) = - 5 (x ^ 2 + 4x - 8x - 32)
</span><span>w (x) = - 5x ^ 2 - 20x + 40x + 160
</span><span>w (x) = - 5x ^ 2 + 20x + 160
</span><span>Then, deriving we have:
</span><span>w '(x) = - 10x + 20
</span><span>We equal zero and clear x:
</span><span>0 = -10x + 20
</span><span>10x = 20
</span><span>x = 20/10
</span><span>x = 2 seconds
</span><span>Substituting values:
</span><span>w (2) = - 5 (2-8) (2 + 4)
</span><span>w (2) = - 5 (-6) (6)
</span><span>w (2) = 180 meters
</span>Answer:
The maximum height that the stone will reach is:
w (2) = 180 meters
Answer:
(3, 13)
Step-by-step explanation:
The curve decreases from x = 3 to x = 13.
Answer: (3, 13)
Answer:
(-2 , 5)
(-1 , 0)
(1 , -4)
(3 , 0)
(4 , -5)
Step-by-step explanation:
<u>First solve the equation:</u>
x² - 2x - 3
<em><u>Find two numbers with have a sum of -2 and a product of -3.</u></em>
-3 and 1
(x - 3)(x + 1)
Solve for x:
x - 3 = 0
x = 3
x + 1 = 0
x = -1
You know that the graph will cross the x-axis at -1 and 3.
(-1 , 0)
(3 , 0)
You know that the graph is positive.
<u>Complete the square to find the vertex</u>
x² - 2x - 3
(x - 1)² = x² - 2 + 1
x² - 2x - 3 = x² - 2 + 1 - 2 = (x - 1)² - 2
1 = 0
x = 1
Substitute into the original equation:
x² - 2x - 3 =
1² - (2 * 1) - 3 =
1 - 2 - 3 =
-4
(1 , -4)
<em><u>You can input any two numbers within -10 and 10. Such as -2 and 4.</u></em>
x² - 2x - 3 =
-2² - (2 * -2) - 3 =
4- -4- 3 =
5
(-2 , 5)
x² - 2x - 3 =
4² - (2 * 4) - 3 =
16 - 8 - 3 =
-5
(4 , -5)
Answer:
A. ![\sqrt[3]{4}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B4%7D)
= Cube root of 4.
Step-by-step explanation:
We have been given an expression 
. We are asked to find the equivalent expression for our given expression.
Using exponent property ![\sqrt[n]{a^m} =a^{\frac{m}{n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5Em%7D%20%3Da%5E%7B%5Cfrac%7Bm%7D%7Bn%7D)
, we will get,
![2^{\frac{2}{3}}=\sqrt[3]{2^2}](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B2%5E2%7D)
![2^{\frac{2}{3}}=\sqrt[3]{4}](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B4%7D)
Upon looking at our given choices, we can see that option A is the correct choice.
Answer:
0.012
Step-by-step explanation:
