Answer:
the runner’s pulse will be 70 beats per minute in 7.9 minutes
Step-by-step explanation:
Graph the function using a graphing utility.
Graph is attached below.
P(t) is beats per minute
Given P(t) is 70, so we plug in 70 for P(t) and solve for t
Divide both sides by 145
Now take ln on both sides
Divide both sides by -0.092
So t≈7.91564
Round to nearest tenth t= 7.9
We can verify it from second graph
It’s 120 because 10 times 3 times 4 = 120
Answer:
Step-by-step explanation:
The formula for determining the sum of the first n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
n represents the number of terms in the arithmetic sequence.
d represents the common difference of the terms in the arithmetic sequence.
a represents the first term of the arithmetic sequence.
If a = 5, the expression for the sum of the first 12 terms is
S12 = 12/2[2 × 5 + (12 - 1)d]
S12 = 6[10 + 11d]
S12 = 60 + 66d
Also, the expression for the sum of the first 3 terms is
S3 = 3/2[2 × 5 + (3 - 1)d]
S3 = 1.5[10 + 2d]
S3 = 15 + 3d
The sum of the first 12 terms is equal to ten times the sum of the first 3 terms. Therefore,
60 + 66d = 10(15 + 3d)
60 + 66d = 150 + 30d
66d + 30d = 150 - 60
36d = 90
d = 90/36
d = 2.5
For S20,
S20 = 20/2[2 × 5 + (20 - 1)2.5]
S20 = 10[10 + 47.5)
S20 = 10 × 57.5 = 575
