Answer:
T is 13.9 years to the nearest 10th of a year
Step-by-step explanation:
In this question, we are to calculate the number of years at which someone who invests a particular amount will have a particular amount based on compound interest.
To calculate the number of years, what we do is to use the compound interest formula.
Mathematically,
A = P(1+ r/n) ^nt
Where A is the final amount after compounding all interests which is $19,200 according to the question
P is the initial amount invested which is $10,000 according to the question
r is the rate which is 4.75% according to the question = 4.75/100 = 0.0475
n is the number of times per year in which interest is compounded. This is 2 as interest is compounded semi-annually
t= ?
we plug these values;
19200 = 10,000(1+0.0475/2)^2t
divide through by 10,000
1.92 = (1+0.02375)^2t
1.92 = (1.02375)^2t
We find the log of both sides
log 1.92 = log [(1.02375)^2t)
log 1.92 = 2tlog 1.02375
2t = log 1.92/log 1.02375
2t = 27.79
t = 27.79/2
t = 13.89 years
The question asks to give answer to the nearest tenth of a year and thus t = 13.9 years
The translation that flips sides
Answer:
Step-by-step explanation:
You need to use synthetic division to do all of these. The thing to remember with these is that when you start off with a certain degree polyomial, what you get on the bottom line after the division is called the depressed polynomial (NOT because it has to math all summer!) because it is a degree lesser than what you started.
a. 3I 1 3 -34 48
I'm going to do this one in its entirety so you get the idea of how to do it, then you'll be able to do it on your own.
First step is to bring down the first number after the bold line, 1.
3I 1 3 -34 48
_____________
1
then multiply it by the 3 and put it up under the 3. Add those together:
3I 1 3 -34 48
3
----------------------------
1 6
Now I'm going to multiply the 6 by the 3 after the bold line and add:
3I 1 3 -34 48
3 18
_________________
1 6 -16
Same process, I'm going to multiply the -16 by the 3 after the bold line and add:
3I 1 3 -34 48
3 18 -48
___________________
1 6 -16 0
That last zero tells me that x-3 is a factor of that polynomial, AND that the depressed polynomial is one degree lesser and those numbers there under that line represent the leading coefficients of the depressed polynomial:

Factoring that depressed polynomial will give you the remaining zeros. Because this was originally a third degree polynomial, there are 3 zeros as solutions. Factoring that depressed polynomial gives you the remaining zeros of x = -8 and x = 2
I am assuming that since you are doing synthetic division that you have already learned the quadratic formula. You could use that or just "regular" factoring would do the trick on all of them.
Do the remaining problems like that one; all of them come out to a 0 as the last "number" under the line.
You got this!
If AB is 6 and AC is 4. Look at how BC it longer than AC but shorter than AB. The number in between would be 5 so the answer is 5cm.