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KengaRu [80]
11 months ago
10

A softball player throws a ball into the air with an initial velocity of 32 feet per second. The ball is released at a height of

5 feet. The function h(t) = -16t^{2}+32t+5 models the height h (in feet) of the ball as a function of the time t (in seconds) after it is thrown. Use the equation to find the time that the ball is in the air if the player lets the ball drop
Mathematics
1 answer:
Flura [38]11 months ago
6 0

The time that the ball is in the air if the player lets the ball drop is 2.145 sec

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

-16t²+32t+5

by comparing this equation to the standard form of the quadratic equation we get

a=-16 b=32 c=5

the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:

the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)

t = -32/2×-16

t=1sec

by putting h(t) to zero and determining the time (t) when the ball hits the ground:

-16t²+32t+5=0

-16(t²+2t+5/16)=0

t²-2t-5/16=0

(t)²-2×1×t+(1)²-5/16=1

(t-1)²=21/16

t-1=√21/√16

t=1+4.58/4

t=1+1.145

t=2.245sec

Learn more about quadratic equations here:

brainly.com/question/1214333

#SPJ1

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Maksim231197 [3]

Answer:

x = tan⁻¹(⅘)

Step-by-step explanation:

We can solve for x by using trigonometric ratios (sin, cos, and tan)

We need to apply the appropriate ratio that uses the two sides 8 and 10 from the perspective of x. See attached image for information about ratios. (Source: Math is Fun)

The tangent ratio is opposite divided by adjacent. It will relate x to the two sides. So we would write

tan(x) = ⁸⁄₁₀

Then we simplify and move the tan to the other side by multiplying both sides by the inverse of tan (since you cannot divide by tan)

tan(x) = ⅘

x = tan⁻¹(⅘)

Then we can use a calculator to evaluate x

If you want to find y, now that you have two angles of the triangle, you can find the sum of 90 + x and subtract that from 180 (since all angles of a triangle add up to 180) to find y.

6 0
3 years ago
The solution set of 4x-(x+7)=2(x+3)​
maria [59]

Step-by-step explanation:

<h3><u>To</u><u> </u><u>Solve</u><u>:</u><u>-</u></h3>

\\ \tt{:}\leadsto 4x-(x+7)=2(x+3)

<h3><u>SOL</u><u>UTION</u><u>:</u><u>-</u></h3>

\\ \tt{:}\leadsto 4x-(x+7)=2(x+3)

\\ \tt{:}\leadsto 4x-x-7=2x+6

\\ \tt{:}\leadsto 3x-7=2x+6

\\ \tt{:}\leadsto 3x-2x=6+7

\\ \tt{:}\leadsto x=13

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HELPPPP THIS IS 7TH GRADE MATH AND IM CONFUSEDDDD
irga5000 [103]

Answer:

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Step-by-step explanation:

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2 years ago
Sal was tired of waiting for Amir to show up at their meeting place, so he started running at an average speed of 4.5 mph withou
sergiy2304 [10]
A=-.25+6.7t, s=.75+4.5t  when Amir catches up a=s so:

-.25+6.7t=.75+4.5t  add .25 to both sides

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2.2t=1  divide both sides by 2.2

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t≈0.45 hr (to nearest hundredth)
4 0
2 years ago
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