3/4x-1/4x+14=3 how do I get the answer
1 answer:
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Answer:
The formula is
The 14th term is 40, in other words,
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Explanation:
The given sequence is 1, 4, 7, 10, ...
Subtract each adjacent term:
- 4-1 = 3
- 7-4 = 3
- 10-7 = 3
This shows that each term is increasing by 3. This is the common difference, so d = 3.
The first term is
The nth term of the arithmetic sequence is...
As a check, let's plug in say n = 3 to find that:
The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.
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We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.
The 14th term is 40.
You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.
Answer:
a) 51 feet
b) 3.5 seconds
Step-by-step explanation:
The y-coordinate of the vertex of the given parabola is what we are looking for.
We first need to find the t-coordinate of the vertex.
The t-coordinate can be found using -b/(2a).
We need to compare
-16t^2+56t+2
to
at^2+bt+c
to identify a,b, and c.
a=-16
b=56
c=2
We are ready to compute -b/(2a).
-b/(2a)=-56/(2*-16)=-56/-32=7/4.
The vertex occurs at t=7/4.
To find y, we use y=2+56t-16t^2
y=2+56(7/4)-16(7/4)^2
y=51
So the maximum height is 51 feet.
Part b)
Hitting ground means the height between the ball and the ground is 0.
So we need to replace h(t) with 0.
0=2+56t-16t^2
I'm going to use quadratic formula.
a=-16
b=56
c=2
The quadratic formula is:
Computing the thing inside the square root and the thing in the denominator using my handy dandy calculator:
.
I'm going to compute both
and
using my handy dandy calculator:
while the other one is
The negative value doesn't make sense for our problem so the answer is approximately 3.5 seconds.