Answer:
1 1/4 yards of fabric
Step-by-step explanation:
2 1/2+ 1 3/4=4 1/4
4 1/4 - 3 = 1 1/4
Answer:
a. Narrower
b. Shifts left
c. Opens up
d. Shifts up
Step-by-step explanation:
The original quadratic equation is y = x²
The given quadratic equation is y = 5·(x + 4)² + 7
The given quadratic equation is of the form, f(x) = a·(x - h)² + k
a. A quadratic equation is narrower than the standard form when the coefficient is larger than the coefficient in the original equation
The quadratic coefficient is 5 > 1 in the original, therefore, the quadratic equation is <em>narrower</em>
b. Given that the given quadratic equation has positive 'a', and 'b', and h = -4, therefore, the axis of symmetry <em>shifts left</em>
c. The quadratic coefficient is positive, (a = 5), therefore, the quadratic equation <em>opens down</em>
d. The value of 'k' gives the vertical shift, therefore, the given quadratic equation with k = 7, <em>shifts up.</em>
The point of inflection is calculated by equating the second derivative to zero and determining x from there.
f"(x) = -x²2xsinx² + cosx²(2x) = 0
2xcosx² - 2x³sinx² = 0
2x (cosx² - xsinx²) = 0
2x = 0 ⇒ x = 0
cosx² - xsinx² = 0 ⇒ x = 3.82 (if you use shift+solve in your scientific calculator)
Thus, the function only has 1 point of inflection and it is at x = 0.
2+2+9+0+8+1+2+3+4+5+6+7+8+9 is 66
In order for Andrea to make profit, the value of the C in the given function must not be 0 or less than zero. So, let's find the value of x when C is zero.
C = 0 = 10x - 50
x = 5
Hence, the number of candles sold represented by x must be more than 5 (< 5). Therefore, the domain is (5,+∞). When the value of x is more than 5, the C or the range would be greater than 0. Thus, the range is (0,+∞).
