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elena55 [62]
2 years ago
8

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function

h = −16t2 + 36t + 5. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
Mathematics
1 answer:
elixir [45]2 years ago
7 0
This can be solved in two ways: With heavy tools or with just algebra. 
What is your level? Have you studied calculus? 

With pure algebra: 
We need to find the maximum of the function <span>h = −16t^2 + 36t + 5
Lets take out -1 for simplicity: 
</span><span>h = −(16t2 - 36t - 5) 
For now lets just work with this: </span>16t^2 - 36t - 5
16t^2=(4t)^2 
(4t-x)^2= 16t^2-2*4xt+x^2
we have -36t so x should be 4.5 as 2*4*4.5=36

Lets see what we have now:
16t^2 - 36t - 5= (4t-4.5)^2 is this true? No but close
(4t-4.5)^2= 16t^2- 2*4*4.5t +4.5^2= 16t^2-36t+20.25

16t^2 - 36t - 5   and 16t^2-36t+20.25 nearl the same just take away 25.25 from the right hand side

Getting long, just stay with me: 
16t^2 - 36t - 5= (4t-4.5)^2 - 25.25

h= -{(4t-4.5)^2 -25.25}
h=-(4t-4.5)^2 + 25.25

We want to find the maximum of this function. -(4t-4.5)^2 this bit is always negative or 0, so it maximum is when it is 0. Solve: 4t-4.5=0
t=1,125
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TiliK225 [7]

Answer:

Sabemos que:

MH(x, y) = \frac{2xy}{x+y}

y tenemos que:

MH (a,4) = \frac{2*a*4}{a+4} = \frac{8*a}{a+4} = 6

Con esto podemos encontrar el valor de a:

8*a/(a+ 4) = 6

8*a = 6*(a + 4) = 6*a + 24

8a - 6a = 24

2a = 24

a = 24/2 = 12.

Tambien sabemos que:

MH(8,b) = \frac{2*8*b}{8+b} =\frac{16*b}{8+b} = 12

Y de ahí podemos despejar b:

(16*b)/(b + 8) = 12

16*b = 12*(b + 8) = 12b + 96

16b - 12b = 96

4b = 96

b = 96/4 = 24

Entonces tenemos a = 12 y b = 24, y el MH de a y b es:

MH(12,24) = 2*12*24/(12 + 24) = 24*24/36 = 16

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2 years ago
Whats 1797.26 rounded to the nearest 100
yanalaym [24]

Answer:1797.3


Step-by-step explanation:


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Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people c
Alex17521 [72]

Answer:

a)X=3300

b)Y=7770

Step-by-step explanation:

From the question we are told that:

Number Teachers T=6

Number Student S=12

Number in committee n=5

a) Generally the equation for exactly 3 students on the committee is mathematically given by

X=^{S}C_3*^{T}C_3

X=^{12}C_3*^{6}C_3

X=3300

b) Generally the equation for at least one teacher and at least one student on the committee is mathematically given by

Total Ways-(no of ways of selection no teacher or student)

Where total Ways

T=^{(6+12)}C_5

T=8568

Therefore

Y=8568-^{6}C_0*^{12}C_5+^{12}C_0*^{6}C_5

Y=8568-798

Y=7770

8 0
2 years ago
Question 1(Multiple Choice Worth 1 points)
tester [92]

The correct answer is d15

7 0
2 years ago
At a particular restaurant, each mini hotdog has 80 calories and each pizza roll has 50 calories. A combination meal with mini h
cestrela7 [59]

There are 15 mini hotdogs and 5 mini pizza rolls in the combination meal.

Step-by-step explanation:

Given,

Calories in each hotdog = 80 calories

Calories in each mini pizza = 50 calories

Combined meal = 20

Combined calories = 1450 calories

Let,

x represent the number of hot dogs.

y represent the number of mini pizzas.

According to given statement;

x+y=20     Eqn 1

80x+50y=1450    Eqn 2

Multiplying Eqn 1 by 80

80(x+y=20)\\80x+80y=1600\ \ \ Eqn\ 3

Subtracting Eqn 2 from Eqn 3

(80x+80y)-(80x+50y)=1600-1450\\80x+80y-80x-50y=150\\30y=150

Dividing both sides by 30

\frac{30y}{30}=\frac{150}{30}\\y=5

Putting y=5 in Eqn 1

x+5=20\\x=20-5\\x=15

There are 15 mini hotdogs and 5 mini pizza rolls in the combination meal.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/10546617
  • brainly.com/question/10552347

#LearnwithBrainly

7 0
2 years ago
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