Water coming out from a fountain is modeled by the function: f(x)=−x2+6x+6
Where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 2 to x = 5 represent?

a.The water travels an average distance of 4 feet from 2 seconds to 5 seconds.

b.The water travels an average distance of 1 foot from 2 seconds to 5 seconds.

c.The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.

d. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Answers

Answer 1

Answer: Average rate of change from x = 2 to x = 5 is (f(5) - f(2))/(5 - 2) = ((-(5)^2+6(5)+6) - (-(2)^2+6(2)+6))/3 = ((-25+30+6) - (-4+12+6))/3 = (11 - 14)/3 = -3/3 = -1

Therefore, the water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Answer 2

Answer: Average speed = change in position / change in time.
m = (f( b ) - f ( a )) / ( b - a )
a = 2, b = 5
f ( a ) = f ( 2 ) = - 4 + 12 + 6 = 14
f ( b ) = f ( 5 ) = - 25 + 30 + 6 = 11
m = (11-14) / (5-2) = -3/3 = -1
Answer: D ) The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

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College BoardThe number of hours of daylight, d, in Hartsville can be modeled by d = (35/3) + (7/3) (sin((2π/365)t)), where t is the number of days after March 21. The day with the greatest number of hours of daylight has how many more daylight hours than May 1? (March and May have 31 days each. April and June have 30 days each.)
A. 0.8 hr
B. 1.5 hr
C. 2.3 hr
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Answers

Sincethis is an SAT Math Level 2 problem derivatives should not be requiredto find the solution. To find "How many more hours of daylight does theday with max sunlight have than May 1," all you need to understand isthat sin(x) has a maximum value of 1.

The day with max sunlight will occur when sin(2*pi*t/365) = 1, giving the max sunlight to be 35/3 + 7/3 = 14 hours

Evaluating your equation for sunlight when t = 41, May 1 will have about 13.18 hours of sunlight.

The difference is about 0.82 hours of sunlight.

Even though it is unnecessary for this problem, finding the actual maxsunlight day can be done by solving for t when d = 14, of by the use ofcalculus. Common min/max problems on the SAT Math Level 2 involve sinand cos, which both have min values of -1 and max values of 1, and alsopolynomial functions with only even powered variables or variableexpressions, which have a min/max when the variable or variableexpression equals 0.

For example, f(x) = (x-2)^4 + 4 will have a min value of 4 when x = 2. Hope this helps

Final answer:

In Hartsville, the summer solstice has about 1.5 hours more daylight than May 1.

Explanation:

The problem requires calculating the difference in daylight hours between the day with the longest day (also known as the summer solstice) and May 1. The summer solstice is typically around June 21, which is 92 days after March 21. We can find the number of daylight hours on this day by substituting t = 92 into the formula: d = (35/3) + (7/3) (sin((2π/365)*92)). This equals about 16.2 hours.

Next, we find the number of daylight hours on May 1, which is 41 days after March 21, by substituting t = 41 into the formula: d = (35/3) + (7/3)(sin((2π/365)*41)), which equals approximately 14.7 hours.

Then, we find the difference between the two by subtracting the daylight hours on May 1 from the daylight hours on the summer solstice: 16.2 - 14.7 = 1.5 hours. Therefore, the summer solstice has 1.5 hours more daylight than May 1.

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(2x^+3x-4)+(x²-x-2) help me please!

Answers

you would want to make it into an addition problem that looks like this:
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___________
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--------------
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Answers

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Answers

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