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2 years ago

) Which object's liquid volume is best measured in milliliters? Bathtub, Milk carton, big spoon or small fish tank

Mathematics

1 answer:

Mariulka [41]2 years ago

8 0

Answer:

big spoon

Step-by-step explanation:

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Solve the following recurrence relation: <br> <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

4 0

2 years ago

Please someone help me...

laiz [17]

Step-by-step explanation:

First factor out the negative sign from the expression and reorder the terms

That's

$\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \cot(6A) - \cot(2A) }$

<u>Using trigonometric </u><u>identities</u>

That's

<u>Rewrite the expression</u>

That's

$\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \frac{1}{ \tan(6A) } } - \frac{1}{ \frac{1}{ \tan(2A) } }$

We have

<u>Rewrite the second fraction</u>

That's

Since they have the same denominator we can write the fraction as

$- \frac{1 + \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) }$

Using the identity

<u>Rewrite the expression</u>

We have

<u>Using the trigonometric identity</u>

<u>Rewrite the expression</u>

That's

Which is

<u>Using the trigonometric identity</u>

Rewrite the expression

That's

<u>Simplify the expression using symmetry of trigonometric functions</u>

That's

<u>Remove the parenthesis </u>

We have the final answer as

As proven

Hope this helps you

6 0

3 years ago

Read 2 more answers

Check all the answers to represent the same level of precision. A-0.59 B-100.6 C-98.42<br> D-1.045

sp2606 [1]

A) 0.59 uses 2 sig figs
B) 100.6 uses 4 sig figs (the zeros in this case are significant)
C) 98.42 uses 4 sig figs
D) 1.045 uses 4 sig figs (the zero is between other sig figs so it's significant)

Every choice but choice A has 4 sig figs. So the answers are B, C, and D

5 0

2 years ago

Find the distance between these two points (-6, -5) and (2, 0)

Charra [1.4K]

Answer:

$\sqrt{89}$

Step-by-step explanation:

Use Distance Formula

$\sqrt{(x_{2}-x_{1} )^{2} + (y_{2}-y_{1} )^{2} }$

Substitute

$\sqrt{(-5-0)^{2}+(2+6)^{2} }$

Simplify

$\sqrt{(-5)^{2}+(8)^{2} }$

Simplify

$\sqrt{25+64}$

Add

$\sqrt{89}$

3 0

3 years ago

What is the value of x?<br><br>A.) -9<br>B.) -10<br>C.) 10<br>D.) -12

Dennis_Churaev [7]

Answer:

A.) -9

Step-by-step explanation:

it is observed that triangles ABL and KML are similar triangles

hence the following ratios are valid:

LA / LK = LB/LM = AB/KM

we can see that LA/LK = LB/LM = 1/2

hence the above ratio becomes

1/2 = AB/KM (rearranging)

KM = 2AB

We are given that KM = (x + 21) and AB = (x + 15)

hence

KM = 2AB

(x + 21) = 2 (x + 15)

x + 21 = 2x + 30

x - 2x = 30 - 21

-x = 9

x = -9

6 0

3 years ago