Answer:
x=8
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2 + x^2 = 10^2
36+ x^2 = 100
Subtract 36 from each side
36-36 + x^2 = 100-36
x^2 = 64
Take the square root of each side
sqrt(x^2) = sqrt(64)
x = 8
Answer:
t-shirts: 2790
profit: $12209
Step-by-step explanation:
Given the function:
p(x) = -x³ + 4x² + x
we want to maximize it.
The following criteria must be satisfied at the maximum:
dp/dx = 0
d²p/dx² < 0
dp/dx = -3x² + 8x + 1 = 0
Using quadratic formula:
![x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-4%28a%29%28c%29%7D%7D%7B2%28a%29%7D%20)
![x = \frac{-8 \pm \sqrt{8^2 -4(-3)(1)}}{2(-3)}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-8%20%5Cpm%20%5Csqrt%7B8%5E2%20-4%28-3%29%281%29%7D%7D%7B2%28-3%29%7D%20)
![x = \frac{-8 \pm 8.72}{-6}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-8%20%5Cpm%208.72%7D%7B-6%7D%20)
![x_1 = \frac{-8 + 8.72}{-6}](https://tex.z-dn.net/?f=x_1%20%3D%20%5Cfrac%7B-8%20%2B%208.72%7D%7B-6%7D%20)
![x_1 = -0.12](https://tex.z-dn.net/?f=x_1%20%3D%20-0.12)
![x_2 = \frac{-8 - 8.72}{-6}](https://tex.z-dn.net/?f=x_2%20%3D%20%5Cfrac%7B-8%20-%208.72%7D%7B-6%7D%20)
![x_2 = 2.79](https://tex.z-dn.net/?f=x_2%20%3D%202.79%20)
d²p/dx² = -6x + 8
d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0
d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0
Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.
Replacing into profit equation:
p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209
that is, $12209
It would be 1/3rd because your last number would be 4 in the equation of 12 sandwiches.
Answer:
![\large\boxed{y-5=-4(x-3)}\\\boxed{y-8=\dfrac{1}{2}(x+1)}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7By-5%3D-4%28x-3%29%7D%5C%5C%5Cboxed%7By-8%3D%5Cdfrac%7B1%7D%7B2%7D%28x%2B1%29%7D)
Step-by-step explanation:
The point-slope form of an equation of a line:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
m - slope
![m=-4,\ (3,\ 5)\\\\y-5=-4(x-3)](https://tex.z-dn.net/?f=m%3D-4%2C%5C%20%283%2C%5C%205%29%5C%5C%5C%5Cy-5%3D-4%28x-3%29)
![m=\dfrac{1}{2},\ (-1,\ 8)\\\\y-8=\dfrac{1}{2}(x-(-1))\\\\y-8=\dfrac{1}{2}(x+1)](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B1%7D%7B2%7D%2C%5C%20%28-1%2C%5C%208%29%5C%5C%5C%5Cy-8%3D%5Cdfrac%7B1%7D%7B2%7D%28x-%28-1%29%29%5C%5C%5C%5Cy-8%3D%5Cdfrac%7B1%7D%7B2%7D%28x%2B1%29)
2*2*2 or 2^3 is the prime factorizationi of 8