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ivanzaharov [21]
3 years ago
14

A = 1/3 find the value of expression 6a + 4​

Mathematics
1 answer:
allochka39001 [22]3 years ago
5 0

Answer:

6

Step-by-step explanation:

1/3 times 6 = 2

2 +  6 = 6

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Kesha threw her baton up in the air from the marching band platform during practice. The equation h(t) = −16t² + 54t + 40 gives
lapo4ka [179]

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

                           h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

                         h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

                         h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

                        v ( t ) = dh / dt

                        v ( t )= d ( −16t² + 54t + 40 ) / dt

                        v ( t )= -2*(16)*t + 54

                        v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

                        v ( 0 ) = vi = -32*( 0 ) + 54

                        v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

                     h ( t ) = 0

                     0 = −16t² + 54t + 40

                     0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

                     

                    t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t =  \frac{27 + 37}{16} \\\\t = 4

Answer: The time taken for the baton to hit the ground is t = 4 mins

3 0
3 years ago
What is the y-intercept of function f?<br> A. 1<br><br> B. -1<br><br> C. -2<br><br> D. 5
shtirl [24]

Answer:

1

Step-by-step explanation:

The y intercept is when x =0

We need to use the second equation

-x+1  since -2 < 0 <3

0+1

The y intercept is 1

5 0
3 years ago
Determine A:B:C, if A:B= 2:3 and B:C =4: 5​
cestrela7 [59]
I’m confused what we are suppose to do
6 0
3 years ago
Convert into mixed fraction 48 by 8
Rasek [7]

Answer:

48÷8 = 6

Therefore the answer is 6/1 or just 6

4 0
3 years ago
rya uses 4 gallons of gas to drive 120 miles on the highway if she gets that same gas mileage how many miles can she drive on 1
hoa [83]
Divide 120 by 4 and your answer will be: Rya can drive 30 miles on 1 gallons of gas.
5 0
3 years ago
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