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Liono4ka [1.6K]
3 years ago
7

When an object is thrown upwards with a speed of 64 ft/sec, its height above the ground is given by the function h(t)=−16t2+64t

, where t is the time in seconds after it has been thrown. At what time will the object reach its highest point?
Mathematics
1 answer:
Svet_ta [14]3 years ago
3 0

Answer:

The object will reach its highest point 0.5 seconds after it has been thrown.

Step-by-step explanation:

The object reaches its maximum height when velocity is equal to zero, the velocity is the derivative of function height. That is:

v(t) = \frac{d}{dt}h(t) (1)

Where v(t) is the velocity of the object at time t, in feet per seconds.

If we know that h(t) =-16\cdot t^{2}+64\cdot t and v(t) = 0\,\frac{ft}{s}, then the time when object reaches its highest point is:

v(t) = -32\cdot t+64

-32\cdot t + 64 = 0

t = 0.5\,s

The object will reach its highest point 0.5 seconds after it has been thrown.

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Mekhanik [1.2K]

Answer/Step-by-step Explanation:

Given:

a = no. of DVDs

b = no. of CDs

Total cost ($) for DVDs and CDs = 2.5a + 2b

a. The cost for 1 DVD = 2.5(a) = 2.5(1) = $2.5

The cost for 1 CD = 2(b) = 2(1) = $2

b. Total cost for 4 DVDs and 4 CDs:

Substitute a = 4, and b = 4 into the equation.

2.5(4) + 2(4)

10 + 8 = 18

Total cost for 4 DVDs and 4 CDs = $18

c. To find out if $20 would be enough to buy 6 DVDs and 3 CDs, substitute a = 6, and b = 3 into the equation. Solve for the total cost to see if it equals $20 or is less than $20. If it's greater than $20, then it won't be enough.

2.5(6) + 2(3)

15 + 6 = 21

6 DVDs and 3 CDs cost more than $20, therefore, $20 is not enough.

5 0
3 years ago
22-(x+8)=9x-6 helppp
viktelen [127]
The answer is x=2 :3333
3 0
3 years ago
At a fast food​ restaurant, 10 cheeseburgers​ w/onion and 5 orders of french fries contain 6900 calories. 5 cheeseburgers​ w/oni
Leona [35]

Write the equations,

10 c + 5 f = 6900

5c + 3f = 3660

Double,

10c + 6f = 7320

Subtract,

f = 7320 - 6900 = 420

10 c = 6900 - 5f = 6900 - 2100 = 4800

c = 480

Answer: Cheeseburger 480 calories, fries 420 calories

Check:

10 (480) + 5 (420) = 4800 + 2100 = 6900 good

5(480) + 3(420) = 2400 + 1260 = 3660 good

5 0
3 years ago
Rating Frequency Present Frequency Excellent 18 _______Very Good 25 _______Good 4 _______Fair 1 2Poor 2 4 Total 50 100What do th
nata0808 [166]

Answer:

a) Rating Frequency Percent Frequency

Excellent 18 ___36%____Very Good 25 ___50%____Good 4 ___8%____Fair 1   2% Poor 2  4%  Total 50 100 What do these summaries indicate about the overall customer satisfaction with the Delta flight? ____94%______ % customers are satisfied with the Delta Flight Et either a good, very good, or excellent rating. Only ____6%_______% of customers rated the Delta flight Fair or Poor.

b. The online survey questionnaire enabled respondents to explain any aspect of the flight that Failed to meet expectations. Would this be helpful information to a manager looking for ways to improve the overall customer satisfaction on Delta flights? Explain.

Allowing survey respondents to explain their 5-point scale responses would provide helpful information to managers looking for ways to improve customer satisfaction on Delta flights. The ____6______% respondents indicating that the flight failed to meet expectations would have the opportunity to provide detailed information about their expectations.

Step-by-step explanation:

a) Data and Calculations:

                  Rating Frequency     Percent Frequency

Excellent                18                       ____36%___

Very Good            25                       ____50%___

Good                       4                       ____  8%___

Fair                          1                        ____  2%___

Poor                        2                       _____4% __

Total                     50                               100%

b) Percentage Frequencies are obtained as follows:

Excellent = 18/50 * 100 = 36%

Very Good = 25/50 * 100 = 50%

Good = 4/50 * 100 = 8%

Fair = 1/50 * 100 = 2%

Poor = 2/50 * 100 = 4%

c) Good, very good, and excellent = 47/50 * 100 = 94%

d) Fair or Poor rating = 3/50 * 100 = 6%

 

e) Moreover, dissatisfied customers can be sources of great information on the performance of a good or service.  Though, with only 6% of customers giving a dissatisfaction rating with the Delta flights, it is still important to dive deep to unearth the reasons for their dissatisfaction as this may provide valuable information to improve the services.  Usually, this class of customers is the most sincere in most cases, unless their dissatisfaction can be proved to be attitudinal on their own part.

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G evaluate lim h → 0 (1 + h)9 − 1 h . hint: this limit represents the derivative of a function f at a given point
Bond [772]
\displaystyle\lim_{h\to0}\frac{(1+h)^9-1}h

Write 1=1^9, and recall that for a differentiable function f(x), the derivative at a point x=a is given by

f'(a)=\displaystyle\lim_{h\to0}\frac{f(a+h)-f(a)}h

which would suggest that for this limit, f(x)=x^9 and a=1. We have f'(x)=9x^8, and so the value of the limit would be 9(1)^8=9.
7 0
3 years ago
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