The tabulated values of height, h , when the basketball is thrown upward with the initial velocity 79 feet per second, and complete the table given below such that the height as a function of time is represented as h t = − 16 t 2 + 79 t + 5 , t 0 1 2 3 4 5 h Also, from the above table, determine whether the basketball reaches the height of 110 feet or not.
The tabulated values of height, h , when the basketball is thrown upward with the initial velocity 79 feet per second, and complete the table given below such that the height as a function of time is represented as h t = − 16 t 2 + 79 t + 5 , t 0 1 2 3 4 5 h Also, from the above table, determine whether the basketball reaches the height of 110 feet or not.
Solution Summary: The author explains how to calculate the height as a function of time when the basketball is thrown upward with the initial velocity 79 feet per second.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Chapter 4.2, Problem 78E
( a)
To determine
To calculate:The tabulated values of height, h, when the basketball is thrown upward with the initial velocity 79 feet per second, and complete the table given below such that the height as a function of time is represented as ht=−16t2+79t+5,
t012345h
Also, from the above table, determine whether the basketball reaches the height of 110 feet or not.
( b)
To determine
Whether the ball reaches the height of 110 feet or not, when height, as a function of time, is represented as ht=−16t2+79t+5 for 0≤t≤5.
( c)
To determine
To graph:The function ht=−16t2+48t, and determine graphically whether the ball reaches the height of 110 feet or not.
( d)
To determine
The comparison between the results obtained in part a,b and c, when the height with respect to time function is given as ht=−16t2+79t+5 for 0≤t≤5.
The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f(θ) = 2sinθ + √2.Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function?Part C: A toddler is jumping on another pogo stick whose length of its spring can be represented by the function g(θ) = 1 cos^2θ + √2. At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.Student AStep 1:1/Cos x * 1/sin x = cot x + tan xStep 2: 1/cos x sin x = cot x + tan xStep 3: (cos^2 x + sin^2 x)/cos x sin x = cot x + tan xStep 4: cos^2 x/cos x sin x + sin^2x/cos x sin x= cot x + tan xStep 5: cos x/sin x + sin x/cos x = cot x + tan xStep 6: cot x + tan x = cot x + tan xStudent BStep 1: sec x csc x = cos x/ sin xStep 2: sec x csc x = cos^2x/cos x sin x + sin^2x/cos x sin xStep 3: sec x csc x = cos^2x + sin^2x/cos x sin xStep 4: sec x csc x = 1/cos x sin xStep 5: sec x csc x = (1/cos x), (1/sin x)Step 6: sec x csc x = sec x csc xPart A: Did either student verify the identity properly? Explain why or why not. Part B: Name two identities that were used in Student A's verification and the steps they appear in.
Let sinθ = 2√2/5 and π/2 < θ < πPart A: Determine the exact value of cos 2θ.Part B: Determine the exact value of sin(θ/2)
Chapter 4 Solutions
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