Graph r=2-4sin(theta)
1 answer:
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Answer:
The graph with B(2,-3) i.e) y= x goes through the point M(-10,15).
Step-by-step explanation:
Consider M(-10,15) and given that equation is y = kx.
Now, substitute M(-10,15) in the equation
⇒ 15 = k × -10
⇒ k = =
⇒ y = x
Now, check with the given points B(2,-3) and B( , -2)
1) B(2,-3)
y = x
⇒(-3) = × 2
⇒ -3 = -3 ⇒ LHS = RHS
⇒ B(2,-3) is the required point.
2) for b( , -2)
LHS ≠ RHS.
So,The graph with B(2,-3) i.e) y= x goes through the point M(-10,15).
General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as .
Comparing the function f(x)=ax^{2} +bx+c with the given function , we get
,
and
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds
The maximum height is found by substituting in the function as below:
Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts.