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3 years ago

Use compatible numbers to find two estimates that the quotient is between. 1,754 divided 9

Mathematics

2 answers:

lutik1710 [3]3 years ago

6 0

Answer: Between 194 and 195

Step-by-step explanation: Compatible numbers are numbers in pairs that by mental exercise one can easily add, subtract, multiply, or divide. This is applied usually in estimation to approximate a calculation. Here, you replace actual numbers with compatible numbers (easy to estimate pairs).

Two numbers with close quotients with 1754 on dividing by 9 are by estimation 194 and 195. To check, on multiplying these figures by 9 you get 1746 and 1755 respectively. 1755 is actually very close to the required result, therefore 195 is a better estimate than 194 if we were to pick just one. So 194 and 195 fits perfectly

andre [41]3 years ago

4 0

In between 194, and 195, but closer to 195

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Answer:

Part A

$f(n)=52-12(n-1)$

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

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Part C

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Part D:

$h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right$

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

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Explicit Formula

To write an explicit formula is to write it as function.

$f(n)=52-12(n-1)$

Recursive Formula

To write it as recursive formula, is to write it as recurrence given to some restrictions:

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

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Part C

$(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\$

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$d=\frac{2}{4}$

Explicit Formula:

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)$

Recursive Formula

$g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.$

Part D

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Explicit formula

$h(n)=1.1+0.4(n-1)\\$

Recursive Formula

$h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.$

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