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sveticcg [70]
2 years ago
9

The height (in ft) of an object over time(in seconds) is modeled by the function h(t)=-6t^2+23t+7. How high is the object after

3 seconds?
Mathematics
1 answer:
riadik2000 [5.3K]2 years ago
5 0

About 4.1 seconds. How long was the ball in the air? We are told that t represents time in seconds since the ball was thrown, so it started to be 'in the air' at t = 0 To answer the question, then, we need to know the time when it stopped being in the air. We are told that the ball hit the ground. So that's what happened when it stopped being airborne. We need to relate that event to the mathematics we're working with. What can we say about h , the height of the ball when the ball hits the ground? Answer: The height will be 0 when the ball stops being in the air. Now translate this back to the mathematics: The ball is in the air from t = 0 until the time t when h = 0 . Find the time t that makes h = 0 . That means: solve: − 5 t 2 + 20 t + 2 = 0 We can solve this by solving: 5 t 2 − 20 t − 2 = 0 (Either multiply both sides of the equation by − 1 , or add 5 x 2 − 20 x and − 2 to both sides and then re-write it the other way around) That's a quadratic equation, so try to factor first. But don't spend too much time trying to factor, because not every quadratic is easily factorable and that's OK, because we still have the quadratic formula if we need it. We do need it. t = − ( − 20 ) ± √ ( − 20 ) 2 − 4 ( 5 ) ( − 2 ) 2 ( 5 ) = 20 ± √ 440 10 = 20 ± √ 4 ( 110 ) 10 = 20 ± 2 √ 110 10 = 2 ( 10 ± √ 110 ) 2 ( 5 ) = 10 ± √ 110 5 We can see that 10 < √ 110 < 11 . In fact ( 10 + 1 2 ) 2 = 10 2 + 10 + 1 4 = 110.25 Using 10.25 as an approximation for √ 110 , we get : for the solution t = 10 − √ 110 5 we'll get a negative t . That doesn't make sense. The other solution gives t ≈ 10 + 10.25 5 = 20.5 5 = 4.1 seconds. So the ball was in the air from t = 0 until about t = 4.1 . The elapsed time is the difference, 4.1 seconds.

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Need some help please would really be greatful
Gnesinka [82]

Answer:

x = 100°

Step-by-step explanation:

Actually the drawing is very inaccurate, so it is a regular pentagon, otherwise x would be 60° and none of the answers would fit.

The formula for finding the sum of all angles in a polygon is:

(n-2) * 180°

n is the number of sides

Here n = 5, so the sum of all angles is (5-2) * 180° = 540°

x + 2x + 86 + 92 + 62 = 540

3x = 300

x = 100

6 0
3 years ago
A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. How
anyanavicka [17]

Answer: 60 gallons of the 20% solution and 120 gallons of the 50% solution should be mixed.

Step-by-step explanation:

Let x represent the number of gallons of 20% solution that should be mixed.

Let y represent the number of gallons of 50% solution that should be mixed.

A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. This means that

0.2x + 0.5y = 0.4×180

0.2x + 0.5y = 72- - - - - - - - - - - -1

Since the total number of gallons is 180, it means that

x + y = 180

Substituting x = 180 - y into equation 1, it becomes

0.2(180 - y) + 0.5y = 72

36 - 0.2y + 0.5y = 72

- 0.2y + 0.5y = 72 - 36

0.3y = 36

y = 36/0.3

y = 120

x = 180 - y = 180 - 120

x = 60

4 0
3 years ago
Please help me find the area and perimeter of this composite figure.
pentagon [3]

Answer:

the area is 26 the perimetier is 52

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
10
Mrrafil [7]

Answer:

£510

Step-by-step explanation:

Simple interest = (principal × rate × time) / 100

Principal = £1700

Rate = 10%

Time = 3 years

Simple interest = (principal × rate × time) / 100

= (1700 × 10 × 3) / 100

= 51,000/100

= 510

Simple interest = £510

7 0
3 years ago
How to solve this problem 7/20 =
wlad13 [49]
7/20=2.857142857142857 divide 20 by 7
4 0
3 years ago
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