Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Al released his balloon from the 1010-yard line, and it landed at the 1616-yard line. If the ball reached a height of 2727 yards, what equation represents the path of his toss?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Mean, variance, and standard deviation of binomial distributionsright chevron icon

Full solution

Q. Al released his balloon from the 1010-yard line, and it landed at the 1616-yard line. If the ball reached a height of 2727 yards, what equation represents the path of his toss?
  1. Identify Parabolic Path: To find the equation that represents the path of Al's balloon toss, we need to determine the type of path it would take. Since the balloon is being released and lands at a different point, we can assume it follows a parabolic path, similar to the path of a projectile. We will use the vertex form of a parabolic equation, which is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
  2. Determine Vertex Coordinates: The vertex of the parabola is the highest point of the toss. Since the balloon reached a height of 2727 yards, this is the kk value in our vertex form equation. We need to find the hh value, which is the xx-coordinate of the vertex. The balloon was released from the 1010-yard line and landed at the 1616-yard line, so the vertex is halfway between these two points. The midpoint is (10+16)/2=13(10 + 16) / 2 = 13 yards.
  3. Substitute Vertex into Equation: Now that we have the vertex (h,k)=(13,27)(h, k) = (13, 27), we can substitute these values into the vertex form equation to get y=a(x−13)2+27y = a(x - 13)^2 + 27. However, we still need to find the value of aa, which determines the shape of the parabola.
  4. Find Value of aa: To find the value of aa, we need another point on the parabola. We know that the balloon started at the 1010-yard line, which is 33 yards away from the vertex horizontally. Since the balloon starts at ground level, the yy-coordinate at this point is 00. So, we have the point (10,0)(10, 0) to use in our equation.
  5. Use Additional Point for aa: Substitute the point (10,0)(10, 0) into the equation y=a(x−13)2+27y = a(x - 13)^2 + 27 to solve for aa. This gives us 0=a(10−13)2+270 = a(10 - 13)^2 + 27. Simplifying, we get 0=a(3)2+270 = a(3)^2 + 27, which is 0=9a+270 = 9a + 27.
  6. Solve for a: To solve for a, we subtract 2727 from both sides of the equation, which gives us −27=9a-27 = 9a. Then, we divide both sides by 99 to get a=−27/9a = -27 / 9, which simplifies to a=−3a = -3.
  7. Write Final Equation: Now that we have the value of aa, we can write the final equation of the parabola. The equation representing the path of Al's balloon toss is y=−3(x−13)2+27y = -3(x - 13)^2 + 27.

More problems from Mean, variance, and standard deviation of binomial distributions

Question
A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well. \newlineIf the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?\newlineWrite your answer as a decimal rounded to the nearest thousandth.
Get tutor helpright-arrow

Posted 7 months ago

Question
There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____
Get tutor helpright-arrow

Posted 9 months ago

Question
There are two different raffles you can enter.\newlineIn raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are 1,0001,000 in the raffle, each costing `$11`.\newlineRaffle B is for a `$370` prize. Out of 125125 tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.\newlineWhich raffle is a better deal?\newlineChoices:\newline[A]Raffle A\text{[A]Raffle A}\newline[B]Raffle B\text{[B]Raffle B}
Get tutor helpright-arrow

Posted 8 months ago

Question
XX is a normally distributed random variable with mean 4949 and standard deviation 2525.\newlineWhat is the probability that XX is between 2424 and 7474??\newlineUse the 0.68−0.95−0.9970.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.\newline____
Get tutor helpright-arrow

Posted 9 months ago

Question
XX is a normally distributed random variable with mean 6565 and standard deviation 88.\newlineWhat is the probability that XX is between 6262 and 6868??\newlineWrite your answer as a decimal rounded to the nearest thousandth.\newline____
Get tutor helpright-arrow

Posted 9 months ago

Question
Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4343 and standard deviation 33, the bottom 30%30\% of the values are those less than ______.
Get tutor helpright-arrow

Posted 9 months ago

Question
Y Y is the number of desserts available in a randomly chosen restaurant.\newlineIs the random variable Y Y discrete or continuous?\newlineChoices:\newline[A]discrete \text{[A]discrete} \newline[B]continuous \text{[B]continuous}
Get tutor helpright-arrow

Posted 9 months ago

Question
Which of the following functions are continuous for all real numbers?\newlineg(x)=ln⁡(x) g(x)=\ln (x) \newlinef(x)=1x f(x)=\frac{1}{x} \newlineChoose 11 answer:\newline(A) g g only\newline(B) f f only\newline(C) Both g g and f f \newlineD Neither g g nor f f
Get tutor helpright-arrow

Posted 9 months ago

Question
Which of the following functions are continuous at x=−1 x=-1 ?\newlineg(x)=sin⁡(x+1) g(x)=\sin (x+1) \newlinef(x)=1x−1 f(x)=\frac{1}{x-1} \newlineChoose 11 answer:\newline(A) g g only\newline(B) f f only\newline(C) Both g g and f f \newline(D) Neither g g nor f f
Get tutor helpright-arrow

Posted 8 months ago

Question
Let g g be a continuous function on the closed interval [−1,4] [-1,4] , where g(−1)=−4 g(-1)=-4 and g(4)=1 g(4)=1 .\newlineWhich of the following is guaranteed by the Intermediate Value Theorem?\newlineChoose 11 answer:\newline(A) g(c)=−3 g(c)=-3 for at least one c c between −1-1 and 44\newline(B) g(c)=3 g(c)=3 for at least one c c between −4-4 and 11\newline(C) g(c)=−3 g(c)=-3 for at least one c c between −4-4 and 11\newline(D) g(c)=3 g(c)=3 for at least one c c between −1-1 and 44
Get tutor helpright-arrow

Posted 8 months ago

View all (16)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant