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:
Volume= 27. 12inches³
Step-by-step explanation:
to solve this question lets write out the parameters given
radius of the cylinder = 1.2 inches
height of the cylinder = 6 inches
volume of the cylinder = ?
<u>solution</u>
the fomular to find the volume of a cylinder is given to be
Volume= πr²h
Volume= 3.14 × ( 1.2)² × 6
Volume= 3.14 × 1.44 × 6
Volume= 27. 12inches³
therefore the volume of the cylinder equals to 27. 12inches³
5 less (-5) than 1/3 of number (n/3) is (=) 2 more than (2+) half of the number (n/2)
-5+n/3=2+n/2
add 5 to both sides
n/3=n/2+7
times 6 both sides
2n=3n+42
minus 2n both sides
0=n+42
minus 42 boh sides
-42=n
the number is -42
the number is 18
The answer is D. all you have to do is solve for y.
