Answer: 0
Step-by-step explanation:
3 - 3 is 0
6 + 2 is 8
0 x 8 = 0
The idea is to find a linear combination a_1(5, -6) + a_2(-2, -2) = (-6, 2)
It boils down to a system of equations:
Take the augmented matrix:
<span>[<span><span>5<span>−6</span></span><span><span>−2</span><span>−2</span></span><span><span>−6</span>2</span></span>]</span>
Reduced form:
<span>[<span><span>10</span><span>01</span><span><span>−<span>811</span></span><span>1311</span></span></span>]</span>
-(8/11)*(5, -6) + (13/11)*(-2, -2) = (-6, 2)
Answer:
61 cm for each book shelf.
Step-by-step explanation:
First it gives you the width of the boxes so you add them together
132 + 108 + 94 = 334
so 334 cm has already been used out of 456 cm.
Next you will 456 - 334 = 122 cm left over
if they are building 2 book cases you with take what cm's you have left and divide it by 2
122 / 2 = 61
So that means each book case will be 61 cm's wide
Answer:
17) MC(x) = 35 − 12/x²
18) R(x) = -0.05x² + 80x
Step-by-step explanation:
17) The marginal average cost function (MC) is the derivative of the average cost function (AC).
AC(x) = C(x) / x
MC(x) = d/dx AC(x)
First, find the average cost function:
AC(x) = C(x) / x
AC(x) = (5x + 3)(7x + 4) / x
AC(x) = (35x² + 41x + 12) / x
AC(x) = 35x + 41 + 12/x
Now find the marginal average cost function:
MC(x) = d/dx AC(x)
MC(x) = 35 − 12/x²
18) x is the demand, and p(x) is the price at that demand. Assuming the equation is linear, let's use the points to find the slope:
m = (40 − 50) / (800 − 600)
m = -0.05
Use point-slope form to find the equation of the line:
p(x) − 50 = -0.05 (x − 600)
p(x) − 50 = -0.05x + 30
p(x) = -0.05x + 80
The revenue is the product of price and demand:
R(x) = x p(x)
R(x) = x (-0.05x + 80)
R(x) = -0.05x² + 80x
