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2 years ago

Sally begins hiking at an elevation of 224 feet. Then, she descends 131 feet

Mathematics

1 answer:

Tatiana [17]2 years ago

6 0

Answer:

-3 feets

Step-by-step explanation:

Given the following :

Starting point = 224 feets

Then descends 131 feets

Then climbs 67 feets higher than her current position

Then descends 163 feets

Addition sentence to describe the situation :

224feets + (-131)feets + 67feets + (-163)feets

Negative (-) points represents descent

224feets - 131feets + 67feets - 163feets = - 3feets

This means Sally is - 3 feets below her initial position.

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2 years ago

in a AP the first term is 8,nth term is 33 and sum to first n terms is 123.Find n and common difference

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I believe there is no such AP...

Recursively, this sequence is supposed to be given by

$\begin{cases}a_1=8\\a_k=a_{k-1}+d&\text{for }k>1\end{cases}$

so that

$a_k=a_{k-1}+d=a_{k-2}+2d=\cdots=a_1+(k-1)d$

$a_n=a_1+(n-1)d$

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$n$ has to be an integer, which means there are 4 possible cases.

Case 1: $n-1=1$ and $d=21$ . But

$\displaystyle\sum_{k=1}^2(8+21(k-1))=37\neq123$

Case 2: $n-1=21$ and $d=1$ . But

$\displaystyle\sum_{k=1}^{22}(8+1(k-1))=407\neq123$

Case 3: $n-1=3$ and $d=7$ . But

$\displaystyle\sum_{k=1}^4(8+7(k-1))=74\neq123$

Case 4: $n-1=7$ and $d=3$ . But

$\displaystyle\sum_{k=1}^8(8+3(k-1))=148\neq123$

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2 years ago