In order to find the expression that is equivalent to (t*s)(x), use the following steps:
s(x) = x - 7t(x) = 4x^2 - x + 3
(t*s)(x) = t(s(x)) = t(x - 7) = 4(x - 7)^2 - (x - 7) + 3 = 4(x - 7)^2 - x + 7 + 3
The correct result would be 4(x – 7)2 – (x – 7) + 3.
<u>X - Intercept</u>
x + 3y + 2z = 6
x + 3(0) + 2(0) = 6
x + 0 + 0 = 6
x + 0 = 6
<u> - 0 - 0</u>
x = 6
X - Intercept: (6, 0, 0)
<u>Y - Intercept</u>
x + 3y + 2z = 6
0 + 3y + 2(0) = 6
0 + 3y + 0 = 6
0 + 0 + 3y = 6
0 + 3y = 6
<u>- 0 - 0</u>
<u>3y</u> = <u>6</u>
3 3
y = 2
Y - Intercept: (0, 2, 0)
<u>Z - Intercept</u>
x + 3y + 2z = 6
0 + 3(0) 2z = 6
0 + 0 + 2z = 6
0 + 2z = 6
<u>- 0 - 0</u>
<u>2z</u> = <u>6</u>
2 2
z = 3
Z - Intercept: (0, 0, 3)
<u>Volume of the X - Intercept, Y - Intercept, and Z - Intercept</u>
V = ¹/₃(¹/₂lwh)
V = ¹/₃(¹/₂(6)(2)(3))
V = ¹/₃(¹/₂(12)(3))
V = ¹/₃(¹/₂(36))
V = ¹/₃(18)
V = 6 u³
Answer:
150 bikes, $10,500 minimum manufacturing cost
Step-by-step explanation:
5x^2 - 1500x + 123000 is represented by a parabolic graph that opens up. You could easily estimate the x value at which C(x) is at a minimum, as well as the smallest C(x) value.
Or you could do this problem algebraically by finding the vertex of the parabola. The results MUST be the same as before.
-b
The equation of the axis of symmetry of this curve is x = ---------
2a
... which here is x = 1500
--------- = 150 units (150 bikes)
2(5)
Evaluating C(x) (see the problem statement) at x = 150 leads to finding the minimum cost. I like to use synthetic division to evaluate polynomials. Here, the divisor would be 150 and the coefficients of the quadratic would be
5 -1500 123000
Setting up synthetic division, we get:
150 / 5 -1500 123000
750 -112500
--------------------------------------
5 -750 10500
The remainder is $10,500. This is the minimum cost of this manufacturing operation.
Answer:
V= 120
Step-by-step explanation:
due to the formula, V=1/3 * S * H = 1/3 * (9*4) * 10= 1/3*360= 360/3= 120
