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zepelin [54]
3 years ago
14

A triangle has a base of 52/3 in. and a height of 3 in. what is the area of the triangle

Mathematics
1 answer:
marusya05 [52]3 years ago
6 0
52/3. *. 3. *. 1/2 = 156/6 = 26
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dexar [7]

\huge\boxed{x=25}

The mistake is in Step 1. The solver should have also squared 9 when squaring the other side of the equation.

<h3>Correctly solving</h3>

\begin{aligned}\sqrt{3x+6}&=9\\(\sqrt{3x+6})^2&=9^2\\3x+6&=81\\3x+6-6&=81-6\\3x&=75\\\frac{3x}{3}&=\frac{75}{3}\\x&=25\end{aligned}

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Mama had several notebooks. If she give 13 notebooks to each of her children, she will have 8 left. If she give 15 notebooks to
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Help. Not good at word problems
earnstyle [38]

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Option A

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3 years ago
Find a recurrence relation for the amount of money in a savings account after n years if the interest rate is 6 percent and $50
Korvikt [17]

Answer:

a_n = a_{n-1} (1.06) + 50

Step-by-step explanation:

Suppose, a_0 is initial amount in the saving account,

Here, the annual interest rate is 6% and additional amount in each year is $ 50,

So, the amount after one year,

a_1 = a_0 + 6\%\text{ of }a_0 + 50 = a_0 + 0.06a_0 + 50 = a_0(1.06) + 50

Amount after 2 years,

a_2 = a_1 + 6\%\text{ of }a_1 + 50 = a_1(1.06) + 50

Amount after 3 years,

a_3 = a_2 + 6\%\text{ of }a_2 + 50 = a_2(1.06) + 50

................................., so on....

Hence, by following the pattern,

The amount after n years,

a_n = a_{n-1} (1.06) + 50

Which is the required recurrence relation for the amount of money in a savings account

3 0
3 years ago
The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i
kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.


Recall the formula for the sum of consecutive positive integers,

\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2

Now,

1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224

numbers, and their sum is

\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of 1+9\times2=19.

So, the sum of the first 1234 terms in the sequence is 2419.

8 0
2 years ago
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