After first week pond will be:
10 + 10* 0.03 = 10*(1.03) feet deep
after second week it will be:
10*(1.03) + 10*(1.03)*0.03 = 10*(1.03)^2
from this we can conclude that after x week its will be:
10*(1.03)^x
Note that when second week starts our starting pond is already greater by 3%. every week we add 3% of prevous weeks size of pond
for x = 8 we get
f(x) = 10*(1.03)^8 = 12.66 or rounded 13 feet
Answer is D.
Answer:
a2=12 (the second term of the sequence is 12)
Step-by-step explanation:
a5=324
If the term to term rule is multiply by any number, we deal with geometrical sequence
The formula you should use is an= a1*r^(n-1) where n is the number of the term which we know. In our case we know
a5, so use 5 instead of n
Then you have a5=a1*r^4 where r is the number 3 (because each next term is greater than previous in 3 times)
a5=324
324= a1*3^4
324=a1*81
a1=4 (We find the first term of sequence, because having it you can easily search for every term )
Return to the formula an= a1*r^n-1
Now search for the second term using 2 instead of n in the formula
a2= a1*r^1
a2=a1*r, a1=4, r=3
a2=4*3=12
Answer:
65.4°
Step-by-step explanation:
According to question
The equation is
Cos(x)=5/12
x=acos(5/12)
x=65.4°
Answer:
Frank
Step-by-step explanation:
First let's start by calculating the speed of each runner.
Let's use feet per second
Frank's speed is already given in feet per second: 14 feet/second
We are given that Jake runs 382 feet in 38 seconds. To bring this down to feet/second we need to divide both numbers by 38.
382/38=10.05 feet/second (about)
We are given that Will runs 1 mile in 394 seconds. 1 mile is equivalent to 5280 feet. Now we divide both numbers by 394 to bring it down to feet/second.
5280/394=13.401 feet/second (about)
We are given that Ron runs 555 feet in 1 minute. 1 minute is equivalent to 60 seconds. Now we divide both numbers by 60 to bring it down to feet/second.
555/60=9.25 feet/second
After comparing all the speeds, we can conclude that Frank runs the fastest
Answer:
n = -7
Step-by-step explanation:
Solve for n:
-3 n - 5 = 16
Hint: | Isolate terms with n to the left-hand side.
Add 5 to both sides:
(5 - 5) - 3 n = 5 + 16
Hint: | Look for the difference of two identical terms.
5 - 5 = 0:
-3 n = 16 + 5
Hint: | Evaluate 16 + 5.
16 + 5 = 21:
-3 n = 21
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -3 n = 21 by -3:
(-3 n)/(-3) = 21/(-3)
Hint: | Any nonzero number divided by itself is one.
(-3)/(-3) = 1:
n = 21/(-3)
Hint: | Reduce 21/(-3) to lowest terms. Start by finding the GCD of 21 and -3.
The gcd of 21 and -3 is 3, so 21/(-3) = (3×7)/(3 (-1)) = 3/3×7/(-1) = 7/(-1):
n = 7/(-1)
Hint: | Simplify the sign of 7/(-1).
Multiply numerator and denominator of 7/(-1) by -1:
Answer: n = -7
