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>
11/12 hours left. 1 2/3 - 3/4 = 11/12. First, find the common denominator (12) . The problem is now 1 8/12 - 9/12. Use the 1 in (1 8/12) to borrow. Multiply the denominator by 1 (12) and add that to the numerator. The question is now 20/12 - 9/12. I assume that you can finish it off from there.
Answer:
49/83 = m
Step-by-step explanation:
49=83m
Divide each side by 83
49/83 = 83m/83
49/83 = m
Answer:
Angle of elevation from Kim to the satellite launch = 6.654°
Step-by-step explanation:
The distance from Kim to the satellite launch
= 6 miles
Height of the satellite launch
= 0.7 miles
Angle of elevation from Kim to the satellite launch = b
Tan b = height of satellite/distance from Kim
Tan b= 0.7/6
Tan b= 0.1166667
b = tan^-1 (0.1166667)
b= 6.654°
Angle of elevation from Kim to the satellite launch = 6.654°
