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3 years ago

5

How can you show that two objects are proportional with an equation

1 answer:

Andreas93 [3]3 years ago

8 0

You can show that (y) is proportional to (x) by writing:

This would mean that:

Whereby (k) would be the constant of proportionality.

This value can be an element of a real number.

k∈R

What are real numbers?

Integers, rational numbers and irrational numbers.

Example of a graph which would show that 2 objects are proportional:

y=2x

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Ice cream cones cost $2.80. How many ice cream cones can be bought with $42?

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15 ice cream cones can be bought with $42

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Square root of 6 (3- square root of 3)

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Step-by-step explanation:

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3 years ago

Tell whether this sequence is arithmetic. If it is identify the common difference. 19,8,-3,-14

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3 years ago

State whether each sequence is arithmetic and justify your answer. If the sequence is arithmetic, write a recursive and an expli

nasty-shy [4]

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

$(2,4,8,16,32)\: \:$ Geometric Sequence

Part C

1/4,3/4,5/4,7/4,9/4

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

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

$(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12$

<u>Explicit Formula</u>

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

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

<u>Recursive Formula</u>

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

$(2,4,8,16,32)\: \:$

Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24

Part C

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

Arithmetic Sequence, difference

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

<u>Explicit Formula:</u>

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

<u>Recursive Formula</u>

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

Part D

(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4

<u>Explicit formula</u>

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

<u>Recursive Formula</u>

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

6 0

3 years ago

Vhich expression is equivalent to 16^3

LenKa [72]

Answer:16×16×16

Step-by-step explanaution:

16 ^3 so that means you need to but 16 3 times

6 0

3 years ago