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Yuki888 [10]
3 years ago
14

The equation y 4.9t 2 3.5t 2.4 relates the height y in meters to the elapsed time t in seconds for a ball thrown downward at 3.5

meters per second from a height of 2.4 meters from the ground In how many seconds will the ball hit the ground Express your answer as a decimal rounded to the nearest hundredth
Mathematics
1 answer:
tamaranim1 [39]3 years ago
3 0

Answer:

t \approx 0.43\,s

Step-by-step explanation:

The vertical displacement function is y(t) = -4.9\cdot t^{2}-3.5\cdot t + 2.4, where y(t) is measured in meters and t in seconds. Ball hits the ground when y(t) = 0. That is:

-4.9\cdot t^{2}-3.5\cdot t + 2.4 = 0

Whose roots can be found by using the General Formula for Second-Order Polynomials:

t_{1,2} = \frac{3.5\pm \sqrt{(-3.5)^{2}-4\cdot (-4.9)\cdot (2.4)} }{2\cdot (-4.9)}

Solutions of this polynomial are:

t_{1} \approx 0.43\,s,t_{2} \approx -1.14\,s

Only the first root is physically consistent.

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Aaron bought a set of plastic ice cubes with a mixture of water and air inside.
LekaFEV [45]

Answer:

Volume of water and air is 3,000 mm³

Step-by-step explanation:

Given:

Length of base = 15 mm

Width of base = 20 mm

Height of figure = 30 mm

Find:

Volume of water and air is inside each of the plastic ice cubes.

Computation:

Height of each rectangular pyramid = Height of figure / 2

Height of each rectangular pyramid = 30 / 2

Height of each rectangular pyramid = 15 mm

Volume of each rectangular pyramid = lbh / 3

Volume of each rectangular pyramid = [15 × 20 × 15] / 3

Volume of each rectangular pyramid = [4,500] / 3

Volume of each rectangular pyramid = 1,500 mm³

Volume of water and air is inside each of the plastic ice cubes = 2 × Volume of each rectangular pyramid

Volume of water and air is inside each of the plastic ice cubes = 2 × 1,500

Volume of water and air is inside each of the plastic ice cubes = 3,000 mm³

6 0
3 years ago
The taxi fare in a city is as follows: For the first kilometer, the
Ksju [112]

Answer:

The linear equation is y = 6 x + 9

The graph is attached down

Step-by-step explanation:

The given information:

The cost of 1st km is 9 Rs

The cost of every kilometer after the first is 6 Rs

x represents the number of km

y represents the total cost of x km

The form of the linear equation is

y = m x + b, where

  • m is the slope of the line (rate of change)
  • b is the y-intercept (initial value)

From the given information above

m = 6 Rs/km

b = 9 Rs

Substitute them in the form of the equation

y = 6 x + 9

The graph:

3 0
3 years ago
Tim Hortons is hiring and offers $200 every week plus $5 per hour. McDonalds offers $300 every week plus $2 per hour. State the
Ray Of Light [21]

Answer:

Assuming you want better payment each week, any number of hours above 33.333 or 33 hours and 20 minutes per week

Step-by-step explanation:

There are several ways we could do this.  We could say we want to have Tim Hortons be the better employer on the first week, or after so many weeks by adjusting the hours.  I am going to assume we are saying we want it to be a better employer on the first week, so the profit will be the amount made every week plus the money made per hour times the number of hours.

Let's say number of hours is H

So Tim Hortons winds up as 200 + 5H for one week and  Mcdonalds will be 300 + 2H.

If you set the two expressions equal to each other you will find where they intersect, which means at that number of hours they will give the same amount of money while any amount before one of the companies will give more and after that many hours the other will.  Let's go ahead and solve.

200 + 5H = 300 + 2H

3H = 100

H = 100/3

So H is about 33.333.  let's check.

200 + 5(33.333) = 366.665 which rounds to 366.67 dollars

300 + 2(33.333) = 366.666 which also rounds to 366.67 dollars

So at 33.333 hours both give 366.67 dollars.  Let's look at a value below it, say 32.

200 + 5(32) = 360

300 + 2(32) = 364

So you can see here Tim Hortons  pays less.  Now we will try 34 as a value above 33.333

200 + 5(32) = 370

300 + 2(32) = 368

Here Mcdonalds pays less.  This was to show that values below 33.333 make Tim Hortonspay less and values above 33.333 make Mcdonalds pay less.  In other words any value above 33.333 hours will have Tim Hortons be the better employer.  And this is per week

I want to repeat, you can expand this to be multiple weeks and see which of the two becomes better in that epriod of time.  This was, I think, the simplest way to answer though.  

So the conditions where Tim Horton pays more isif you work more than 33.333 hours per week.  This will make them pay more every single week.  

7 0
2 years ago
If someone could help it would be great :)
malfutka [58]

Answer:

2.2

Step-by-step explanation:

<u>  -6-5  </u> = -11/-5=2.2

-9-(-4)

3 0
3 years ago
Karen spent a total of $15.45 on a trip to the movies. She spent $5.00 on a daily bus pass, and $3.95 on movie snacks. How much
Vikentia [17]

Answer:

The answer is 24.4

Step-by-step explanation:

If you add 15.45, 5.00 and 3.95 you get 24.4

3 0
2 years ago
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