Answers
$$
R=\$ 610, r=6.5 \%, t=25, k=12
$$
.
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For number three We need to solve for V. And so when you get the V squared alone, so we're gonna take this, are and we're going to cross multiply to move it over to the other side. So a R is equal to B squared. And whenever you need to get rid of a square, you square root both sides. And so our final answer is going to be V Sorry.
That's a V V is equal to remember. Square radically to a plus or a minus square root of eight has are..
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So in the given question we are told to find are if we have the if we have the expression or condition that five P. R. Is equal to two raised to six P. R minus one. So it is not too raised to six, it is two times two times six P.
R. P. Of six P. R minus one. And what we can use this we can use the formula NPR which is equal total N factorial divided by n minus R.
Factorial. And using this formula we can write then five factorial divided by five minus R. Factorial. This equal to two times six factorial divided by six minus r minus one factorial which would be six minus R plus one. Factory in And from this we can right five factorial divided by five minus R.
Factorial is then equal to we can write six factorial as six times five factorial. And we can write six minus R plus one factorial as seven minus R. Factorial. And we can write seven minus our factory last seven minus r times six minus r times five minus R. Praetorian.
So from this attraction we can cancel off the common terms. And what is left is that seven minus R times six minus R is equal to 12. Now, when we expand this, what we would have is they would have 40 to minus seven ar minus six R plus R squared is equal to 12. Or we can write our square minus 13 are plus 40 to minus 12 is 30. This is equal to zero.
So in the next step, what we can do is we can write our square minus 30 minus 10. Ar minus three R plus 30 is equal to zero, which we can fact arise as our times ar minus 10 minus three times are minus 10 is equal to zero. And from this weekend, right? The value of our as either equal to and or it can be equal to three. So this is the value of our for the first expression that is given to us. Now when we take the second expression that isn't the question which has given us five P r is equal to six P r minus one.
Then using the same formula, we can write five factorial divided by five minus R. Factorial is equal to six factorial divided by six minus r minus one factorial. Which we can write us six minus R plus one factorial. Right? And similarly over here we can write five factorial divided by five minus R. Factorial is equal to six times five factorial divided by seven minus r times six minus r times five minus art Equatoria.
Now, when we cancel the common tools from each other options, what will be left is seven minus r times six minus R is equal to six. And from this weekend right, 40 to minus 13 R plus r square is equal to six. And we can write our square minus 13 are plus 40 to minus six est plus 36 is equal to zero. And from this what we can like this, we can write we can find the roots of the situation, right? So finding the root of this situation can be done by start tracing the situation as toros and we can write this as hard times ar minus. Made minus four times ar minus nine equal to zero.
Now minus nine is a common factor. So what we would have as ar minus nine times ar minus port is equal to zero from which we can write the values of art that satisfies this condition are nine and four. So this is the required answer. Right? So in both cases we can just look at the expression that is given over here. We've got the values of our a smile and for right.
So nine and four is fine to be placed over here. We can't have a negative number in this place. That is what we need to check. So then what we would have is when we take five P. R.
If r is nine then what we would have is five up during the weighted by five minus nine factorial, which is actually a negative number which is wrong, right? The factory of a negative number is not defined. So then what we can do is we can say that the values that we found from the values that we found our cannot be equal. Dude the value nine, but as having a value which is equal to four. And similarly, we should check the first question also where we got the possible values of our as 10 and three. So when we take and and place it over here, what would happen is you will have five ft 10 which would evaluate the five factorial divided by five minus 10 factorial, which gives us a negative five factorial over here, which would be not defined.
So then we can say that the value of our in this case would be not equal to 10, but it would be equal to three. So this is how we find find the values of R. And very funny if they are actually possible. So I hope you understood the method. Thank you..
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