Solve for n and graph the solution.
1 answer:
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Answer:
a)
b)
When d = 3
n = (3+2)/4 = 5/4 inches
When d= 6
n = (6+2)/4 = 2 inches
When d = 10
n = (10+2)/4 = 3 inches
Step-by-step explanation:
<u>Complete Question:</u>
<em>The penny size of a nail indicates the length of the nail. The penny size d is given by the literal equation d=4n−2, where n is the length (in inches) of the nail.</em>
<em>a) Solve equation for n</em>
<em>b) Use part (a) to find length of nails with the following penny sizes: 3, 6, 10.</em>
<u>Solution:</u>
<u />
a)
We use algebra and take 2 to the other side and divide to solve for n. Shown below:
So,
n = (d+2)/4
b)
Since we have to find length of nails, we plug in 3, 6, and 10 respectively into d of the formula we found in part (a).
When d = 3
n = (3+2)/4 = 5/4 inches
When d= 6
n = (6+2)/4 = 2 inches
When d = 10
n = (10+2)/4 = 3 inches
When solving logarithmic/natural log equations, the strategy is to get ln (x) alone on one side, and all the stuff on the other side. Then exponentiate both sides to get to x.
2 ln (x + 3) = 0
ln (x + 3) = 0
At this point, we can't isolate anymore or use logarithm properties to separate this further. But we have ln (something), and we can exponentiate.
x+3 = 1 <--This come from the fact the ln (x) and are inverse functions that undo each other. This is why exponentiating works.
x = -2
So x = -2 is our solution.