Answer:
The average speed is 
Step-by-step explanation:
we know that
To find out the average speed divide the distance by the time
Let
s -----> average speed
d -----> the distance in feet
t ----> the time in minutes
we have
substitute
Simplify
Answer:
.
Step-by-step explanation:
The given series is,
When we substitute 
, we get the first term, which is 
This implies that,
.
The common ratio is
The finite geometric sum is given by the formula,
.
Since there are 9 terms, we find the sum of the first nine terms by putting 
in to the formula to get,
.
.
.
.
.
.
.
The correct answer is B
Answer:
48
Step-by-step explanation:
Wrong : right
1 :12
Multiply by 4 because she gets 4 problems wrong
1*4 : 4*12
4 :48
If she gets 4 problems wrong, she gets 48 problems right
The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
