A baseball is hit and its height is given by h = 29.4t – 4. 9t^2, where h is the
height of the ball in metres and t is time in seconds. Determine the maximum height
of the baseball.
Answers
Answer:
44.1m
Step-by-step explanation:
we are given a quadratic function which represents the height and time of a baseball
[tex] \displaystyle h = 29.4t - 4.9 {t}^{2} [/tex]
we want to figure out maximum height of
the baseball
since the given function is a quadratic function so we have a parabola
which means figuring out the maximum height is the same thing as figuring out the maximum y coordinate (vertex)
to do so we can use some special formulas
recall that,
[tex] \displaystyle \rm t= \frac{ - b}{ 2a} [/tex]
[tex]\displaystyle H_{\text{max}}=f(t)[/tex]
notice that, our given function is not in standard form i.e
[tex] \displaystyle f(x) = a {x}^{2} + bx + c[/tex]
let's make it so
[tex] \displaystyle h = - 4.9 {t}^{2} + 29.4t[/tex]
therefore we got
our a is -4.9 and b is 29.4
so substitute:
[tex] \displaystyle\rm t= \frac{ -( 29.4)}{ 2 \cdot - 4.9} [/tex]
remove parentheses and change its sign:
[tex] \displaystyle\rm t= \frac{ -29.4}{ 2 \cdot - 4.9} [/tex]
simplify multiplication:
[tex] \displaystyle\rm t= \frac{ -29.4}{ - 9.8} [/tex]
simplify division:
[tex] \displaystyle \: t = 3[/tex]
so we have figured out the time when the baseball will reach the maximum height
now we have to figure out the height
to do so
substitute the got value of time to our given function
[tex]\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot {3}^2[/tex]
simplify square:
[tex]\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot 9[/tex]
simplify mutilation:
[tex]\displaystyle H_{\text{max}}=88.2-44.1[/tex]
simplify substraction:
[tex]\displaystyle H_{\text{max}}=44.1[/tex]
hence,
the maximum height of the baseball is 44.1 metres
Answer:
Solution given:
height
h=29.4t – 4.9t²
differentiating each term with respect to time (t)
[tex] \frac{d'(h)}{d(t)} [/tex]=[tex] \frac{d(29.4t – 4.9t²)}{d(t)} [/tex]
[tex] \frac{d'(h)}{d'(t)} [/tex]=29.4-9.8t
again second derivative
[tex] \frac{d''(h)}{d"(t)} [/tex]=-9.8
for maximum, minimum
first derivative =0
29.4-9.8t=0
t=[tex] \frac{29.4}{9.8} [/tex]=3
So it attains maximum height at t=3
so
maximum height=29.4×3-4.9×3² =44.1meters
So.
maximum height of the basketball is 44.1meters
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Answers
Answer:
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Step-by-step explanation:
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According to given statements;
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Cost of one notebook is 1.40 and one pen is1.40andonepenis0.90
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Answers
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Step-by-step explanation:
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The fractional part of the guest ate roast beef is 77/159.
What is a fraction?
A fraction is a part of a whole number, and a way to split up a number into equal parts. The number on the top is called the numerator, and the number on the bottom is called the denominator.
For the given situation,
Number of chicken dinners served by the national committee = 159
Number of roast beef dinners served by the national committee = 77
The fractional part of the guest ate roast beef is given as 77 in the numerator and 159 in the denominator,
⇒ [tex]\frac{77}{159}[/tex]
Hence we can conclude that the fractional part of the guest ate roast beef is 77/159.
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