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>
Six more than: 6 + or + 6
twice a number: let n represent the unknown number: 2n
6 + 2n = 16
So, the answer is either c or d
So, solve the equation
Subtract 6 on both sides of the equation
2n=10
Divide by 2 on both sides of the equation
n=5
So, the answer is C
Answer:
15 mph
Step-by-step explanation:
75/5=15
Answer:
He will burn 224 calories.
Step-by-step explanation:
Multiply 8 by 28 to get your answers because he runs 8 times more in 24 minutes.
:))
Answer:
Step-by-step explanation:
a- no u don't need to know
b- 38.7m-3.9m=34.8m
c-3.48+3.9= 38.7
