We are given the following:
- parabola passes to both (1,0) and (0,1)
<span> - slope at x = 1 is 4 from the equation of the tangent line </span>
<span>First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. W</span><span>hen x = 0, y = 1. So, c should be equal to 1. The</span><span> parabola is y = ax^2 + bx + 1 </span>
<span>Now, we can substitute the point (1,0) into the equation,
</span>0 = a(1)^2 + b(1) + 1
<span>0 = a + b + 1
a + b = -1 </span>
<span>The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.</span>
<span>We take the derivative of the equation ,
y = ax^2 + bx + 1</span>
<span>y' = 2ax + b
</span>
<span>x = 1, y' = 2
</span>4 = 2a(1) + b
<span>4 = 2a + b </span>
So, we have two equations and two unknowns,<span> </span>
<span>2a + b = 4 </span>
<span>a + b = -1
</span><span>
Solving simultaneously,
a = 5 </span>
<span>b = -6</span>
<span>Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .</span>
Answer:
2 sqrt(3)
Step-by-step explanation:
Simplify the following:
sqrt(363) - 3 sqrt(27)
sqrt(27) = sqrt(3^3) = 3 sqrt(3):
sqrt(363) - 33 sqrt(3)
sqrt(363) = sqrt(3×11^2) = 11 sqrt(3):
11 sqrt(3) - 3×3 sqrt(3)
-3×3 = -9:
11 sqrt(3) + -9 sqrt(3)
11 sqrt(3) - 9 sqrt(3) = 2 sqrt(3):
Answer: 2 sqrt(3)
Answer:
B. $5.08
Step-by-step explanation:
First find out how much the supermarket pays per dozen of eggs.
$8.00 / 12 dozen cartons per case = $0.66666
It costs the supermarket approximately $0.67 per dozen
Next find out the profit per dozen of eggs sold
$1.09 store price - $0.67 price store pays = $0.42
The supermarket profits about $0.42 per dozen sold
Finally find out the profit per case of eggs
12 dozen cartons * $0.42 profit per carton = $5.04
The supermarket makes about $5.04 per case so the best answer of the choices would be B. $5.08.
Step-by-step explanation:
time ∝ number of door 1
time . ∝ 1/number of people. 2
compare equation 1 and 2
time . ∝ number of door / number of people
put k as constant
time = k number of door / number of people. 3
time =2. people=4 door = 10
putting in equation 3
2 = k (10)/(4)
2×4/10 = k
8/10 =k
4/5 =k
putting in equation 3
time= 4/5 number of door / number of people
now time =5 door= 25 people=?
5=4/5 (5)/ (number of people)
number of people =4/5 ×25/5
number of people= 4
Answer:
hello
Step-by-step explanation:
h-e-l-l-o
