The tabulated values of height, h , when the ball from the ground level is kicked upwards with the initial velocity of 48 feet per second such that, the height as a function of time is represented as h t = − 16 t 2 + 48 t for 0 ≤ t ≤ 3 , t 0 0.5 1 1.5 2 2.5 3 h and determine whether the ball reaches the height of 64 feet or not as given below.
The tabulated values of height, h , when the ball from the ground level is kicked upwards with the initial velocity of 48 feet per second such that, the height as a function of time is represented as h t = − 16 t 2 + 48 t for 0 ≤ t ≤ 3 , t 0 0.5 1 1.5 2 2.5 3 h and determine whether the ball reaches the height of 64 feet or not as given below.
Solution Summary: The author calculates the tabulated values of height, h, when the ball from the ground level is kicked upwards with the initial velocity of 48feet 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 77E
( a)
To determine
To calculate:The tabulated values of height, h, when the ball from the ground level is kicked upwards with the initial velocity of 48 feet per second such that, the height as a function of time is represented as ht=−16t2+48t for 0≤t≤3,
t00.511.522.53h
and determine whether the ball reaches the height of 64 feet or not as given below.
( b)
To determine
Whether the ball reaches a height of 64 feet or not when the height as a function of time is represented as ht=−16t2+48t for 0≤t≤3, algebraically.
( c)
To determine
To graph:The provided function ht=−16t2+48t, and determine graphically whether the ball reaches the height of 64 feet or not.
( d)
To determine
The comparison between the results obtained in part a,b and c for the ball to reach a height of 64 feet, when the height with respect to time function is given as ht=−16t2+48t for 0≤t≤3.
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
WebAssign Printed Access Card for Larson's Trigonometry, 10th Edition, Single-Term
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