25.
If the area of a circle is 100 cm2, find the
diameter.

The answer is 2(√(100)/√(π)) cm.

Step-by-step explanation:

Since the area of a circle is π(r)^2, you can write an algebraic equation to find the radius:

π(r)^2 = 100

Simplify this by dividing both sides by π:

r^2 = 100/π

Then take the square root of both sides:

r = ±(√(100)/√(π))

Since radius can't be negative, the ± (plus-or-minus) becomes a plus.

r = √(100)/√(π)

Now, since the radius is half the diameter, you can write another algebraic expression:

2r=d

If you know algebra, you can solve solve the rest from here.

Plug in √(100)/√(π) for r:

2(√(100)/√(π)) = d

Bam, you're done.

(not using the equation feature because I don't really know how yet. Will edit later)

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for