Answer:
d + n = 147
0.10d + 0.05n = 11.65
d = 86, n = 61
Step-by-step explanation:
Let
Number of dimes = d
Number of nickels = n
Total coins = 147
Total value = $11.65
d + n = 147 (1)
0.10d + 0.05n = 11.65 (2)
From (1)
d = 147 - n
Substitute d = 147 - n into
0.10d + 0.05n = 11.65
0.10(147 - n) + 0.05n = 11.65
14.7 - 0.10n + 0.05n = 11.65
- 0.10n + 0.05n = 11.65 - 14.7
-0.05n = -3.05
n = -3.05 / -0.05
= 61
n = 61
Substitute n = 61 into
d + n = 147
d + 61 = 147
d = 147 - 61
d = 86
A recursive sequence is a sequence of numbers whose values are determined by the numbers that come before them in the sequence.
We’re given a sequence whose (n + 1)-th term f(n + 1) depends on the value of the n-th term f(n), specified by the recursive rule
f(n + 1) = -4 f(n) + 3
We’re also given the 1st term in the sequence, f(1) = 1. Using this value and the recursive rule, we can find the next term f(2). (Just replace n with 1.)
f(1 + 1) = -4 f(1) + 3
f(2) = -4 • 1 + 3
f(2) = -1
We do the same thing to find the next term f(3) :
f(2 + 1) = -4 f(2) + 3
f(3) = -4 • (-1) + 3
f(3) = 7
One more time to find the next term f(4) :
f(3 + 1) = -4 f(3) + 3
f(4) = -4 • 7 + 3
f(4) = -25
What do we know about these angles? Immediately, you might notice that (4y-8)° and (16x-4)° share a line. The same is true of (16x-4)° and (14x+4)°. Any straight line forms what's called a <em>straight angle</em>, which measures 180°, so we know that, since they add up to form a straight angle, (14x+4)° and (16x-4)° must add up to 180°. We can use that fact to set up an equation to solve for x:
(14x+4)+(16x-4)=180
After you solve for x, you should look to solve for y. How can we figure out what y is? If you're familiar with the vertical angle theorem, you'll know that all vertical angles (angles that are directly across from each other diagonally) are equal. So we know that 14x+4=4y-8. You can use the value of x you solved for before to solve this one fairly easily, and then you'll have both values.
Answer:
37.68 units³
Step-by-step explanation:
To calculate the volume of a cone, the formula is:
V = π x r² x ( h / 3 )
Simply input the corresponding numbers into the equation:
V = π x ( 2 )² x ( 9 / 3 )
V = π x 4 x ( 3 )
V = π x 12
V = 3.14 x 12
V = 37.68 units³
If we use 3.14 for pi, the answer comes out to 37.68 units³
