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andrew-mc [135]
3 years ago
14

The function f(t) =16t 2 + 248 models the height f(t) in feet of a stone t seconds after it is dropped from the edge of a vertic

al cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.
a. 0.25 seconds
Selected:b. 3.94 secondsThis answer is incorrect.
c. 5.57 seconds
d. 7.87 seconds
Mathematics
1 answer:
Hatshy [7]3 years ago
7 0

Answer:

The time it takes for the stone to reach the ground is 3.94 s. This answer is correct.

Step-by-step explanation:

I believe there's a mistake in the equation shown, the acceleration (number that multiplies t²) should be negative, since the stone is falling, therefore I'll answer assuming it's -16 instead of 16, otherwise there would be no real solution to the equation.

In order to calculate how long it'll take for the stone to hit the ground we must make f(t) = 0 and find the time "t" that makes the equation valid, so we have:

f(t) = -16t² + 248 = 0

-16t² = -248

t² = -248/(-16) = 15.5

t = sqrt(15.5) = 3.94

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A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and clarinets cost $99. If total s
vodomira [7]
Answer: 16

Solution:

1) Use letters to identify the variables:

Number of trumpets: t
Number of clarinets: c

2) Translate each statement into algebraic (mathematical) language.

2.1) Sold a total of 27 used trumpets and clarinets

=> t + c = 27

2.2) Trumpets cost $149 and clarinets cost $99

Total cost of the trumpets: 149t
Total cost of clarinets: 99c

Total cost = 149t + 99c

2.3) Total sales were $3223

=> 149t + 99c = 3223.

3) State the system of equations:

Equation (1) t + c = 27
Equation (2) 149t + 99c = 3223

4) Solve the system of equations:

4.1) Multiply equation 1 by 149:

=> 149t + 149c = 4023

4.2) Subtract the equation (2) from the equation obtained in 4.1

=> 149c - 99c = 4023 - 3223

=> 50c = 800

=> c = 800 / 50 = 16

5) Verify the solution:

From equation (1) t = 27 - 16 = 11

Total cost = 149*11 + 99*16 = 3223

Now you have a verified answer: they sold 16 clarinets
7 0
3 years ago
For what values of b the relation R:{(b^2, 5), (5b, 6)} is not a function?
xenn [34]

Answer:

B=5,0.

Step-by-step explanation:

It's not that hard. It's just that it might throw you off a bit with the R and the other things. Functions if you don't remember are where the coordinates don't have the same x and y. So since the y1 and y2 are different then to make it not a function, you have to make x1 and x2. To make it that b would have to be = to 5 and 0.

6 0
3 years ago
Using a standard six-sided die, janice rolled either a 2 or a 5on the last 6 rolls of the die. what is the probability of janice
Vedmedyk [2.9K]

Answer:

1/3

Step-by-step explanation:

probability = favorable outcomes/total possible outcomes

There are two favorable outcomes, 2 and 5.

There are 6 total possible outcomes.

Make your fraction.

2/6

reduce

1/3

8 0
2 years ago
On a recent trip to the convenience store, you picked up 4 gallons of milk, 6 bottles of water and 5 snack size bags of chips. Y
cricket20 [7]

Answer:

Cost of a snack size bag of chips = $0.8

Cost of a water bottle = $1.6

Cost of a gallon of milk = $3.4

Step-by-step explanation:

Let the cost of water bottle = $a

Cost of 1 gallon milk = $b

and cost of 1 bag of chips = $c

So, cost of 4 gallons of milk, 6 bottles of water and 5 bags of chips = $(4b + 6a + 5c)

4b + 6a + 5c = 27.2 -----(1)

Cost of one water bottle = 2 × cost of one bag of chips

a = 2c -----(2)

A gallon of milk = cost of water bottle + $1.80

b = a + 1.8

From equation (2)

b = 2c + 1.8 -----(3)

Now we substitute these values from equations (2) and (3) in equation (1)

4(2c + 1.8) + 6(2c) + 5c = 27.2

8c + 7.2 + 12c + 5c = 27.2

25c = 27.2 - 7.2

c = \frac{20}{25}

c = $0.8

From equation (2)

a = 2×0.8

a = $1.6

From equation (3)

b = 2(0.8) + 1.8

b = 1.6 + 1.8

b = $3.4

Therefore, cost of a snack size bag of chips = $0.8

Cost of a water bottle = $1.6

Cost of a gallon of milk = $3.4

5 0
3 years ago
Evans dog weighs 63 pounds. Oxanas dog weighs 9 pounds. How much more does evan’s dog weigh than oxanas dog?
natima [27]

Answer:54pounds

Step-by-step explanation:63-9=54

7 0
2 years ago
Read 2 more answers
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