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uysha [10]
3 years ago
13

Write the following using index notation2 x 9 x 9 x 9 x 2 x 9​

Mathematics
1 answer:
taurus [48]3 years ago
4 0
9^4 not totally sure tho
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A cylinder with a 2 centimeter diameter is drilled through the triangular prism shown on the left find the volume of the prism
saw5 [17]

Answer:

The volume of a prism on its own = 248.5cm^3

The volume of a cylinder  = 87.92cm^3

Step-by-step explanation:

The volume does not change for the prism as the hole was drilled.

We can show the drilled space with v(l) and (p) for prism V

v(l) 248.5p - 87.92p + 87.92p

= 248.5p

3 0
3 years ago
A swimsuit is in sale for 45.50. if the sales price is discounted 5%from the orginal price. what was the original price. round t
AnnyKZ [126]
The answer is 42.80 , 2.28 is what they saved and i got the .80 cents because i rounded up from .78
8 0
3 years ago
What is a quick and easy way to remember explicit and recursive formulas?
Oliga [24]
I always found derivation to be helpful in remembering. Since this question is tagged as at the middle school level, I assume you've only learned about arithmetic and geometric sequences.

First, remember what these names mean. An arithmetic sequence is a sequence in which consecutive terms are increased by a fixed amount; in other words, it is an additive sequence. If a_n is the nth term in the sequence, then the next term a_{n+1} is a fixed constant (the common difference d) added to the previous term. As a recursive formula, that's

a_{n+1}=a_n+d

This is the part that's probably easier for you to remember. The explicit formula is easily derived from this definition. Since a_{n+1}=a_n+d, this means that a_n=a_{n-1}+d, so you plug this into the recursive formula and end up with 

a_{n+1}=(a_{n-1}+d)+d=a_{n-1}+2d

You can continue in this pattern, since every term in the sequence follows this rule:

a_{n+1}=a_{n-1}+2d
a_{n+1}=(a_{n-2}+d)+2d
a_{n+1}=a_{n-2}+3d
a_{n+1}=(a_{n-3}+d)+3d
a_{n+1}=a_{n-3}+4d

and so on. You start to notice a pattern: the subscript of the earlier term in the sequence (on the right side) and the coefficient of the common difference always add up to n+1. You have, for example, (n-2)+3=n+1 in the third equation above.

Continuing this pattern, you can write the formula in terms of a known number in the sequence, typically the first one a_1. In order for the pattern mentioned above to hold, you would end up with

a_{n+1}=a_1+nd

or, shifting the index by one so that the formula gives the nth term explicitly,

a_n=a_1+(n-1)d

Now, geometric sequences behave similarly, but instead of changing additively, the terms of the sequence are scaled or changed multiplicatively. In other words, there is some fixed common ratio r between terms that scales the next term in the sequence relative to the previous one. As a recursive formula,

a_{n+1}=ra_n

Well, since a_n is just the term after a_{n-1} scaled by r, you can write

a_{n+1}=r(ra_{n-1})=r^2a_{n-1}

Doing this again and again, you'll see a similar pattern emerge:

a_{n+1}=r^2a_{n-1}
a_{n+1}=r^2(ra_{n-2})
a_{n+1}=r^3a_{n-2}
a_{n+1}=r^3(ra_{n-3})
a_{n+1}=r^4a_{n-3}

and so on. Notice that the subscript and the exponent of the common ratio both add up to n+1. For instance, in the third equation, 3+(n-2)=n+1. Extrapolating from this, you can write the explicit rule in terms of the first number in the sequence:

a_{n+1}=r^na_1

or, to give the formula for a_n explicitly,

a_n=r^{n-1}a_1
6 0
3 years ago
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 5. If there were 4
kow [346]

Answer:

1551 Yes voters

Step-by-step explanation:

Yes : No

3 : 5

total = 4136

add up both no and yes :3+5 =8

8 will be the total ratio of voters

Yes

3/8 × 4136

= 0.375 × 4136

= 1551 Yes Votes

6 0
2 years ago
64 video game ; 25% discount
oksano4ka [1.4K]
64 divided by 4 is 16. The answer is 16 I believe!

Edit: I realized you were asking for the cost. That would be 48. 64 - 16 = 48.
8 0
3 years ago
Read 2 more answers
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