What is the pattern in the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21,

A cone is placed inside a cylinder. The cone has half the radius of the cylinder, but the height of each figure is the same. The

Yuliya22 [10]

Here is the answer: 3/4 (pi r^2 h)

5 0

3 years ago

Read 2 more answers

Please answerrrrr Thank you!!!!!!!!!!!!

dlinn [17]

The correct answers are:

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" (x − 13) ° = 53 ° " ;

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" x = 66 " ;

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" m∠2 = 55° " ;

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" m∠1 = 55° " .

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Step-by-step explanation:

Note: The following "given values/answers" within the attached image:

Specifically:

(x − 13)° = 72° ; and;

x = 85° ;

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are: "incorrect"—and are "arbitrarily assigned values"

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The values and expressions given in the attached image, however, are correct/do make sense; and we can use such data to solve the problem.

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Let's start by finding the measure of ∠2 ; that is: " m∠2 " :

To find m∠2:

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Note that: both: "∠2 " ; and the angle that measures "175" with the attached image:

→ both form a straight line—that is;

→ they are "supplementary angles" ;

→ which means they add up to "180° " ;

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So: To solve for: "m∠2" :

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→ m∠2 = 180 − (125) = 55° ,

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Now; to solve for: " m∠1 " :

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Note that ∠1 and ∠2 are vertical angles: which means that they have equal measurements;

{since: vertical angles are congruent; which means that vertical angles are equal.} ;

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→ As such, m∠1 = m∠2 = 55 °.

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Now, take either ∠1 or ∠2 ; (each has the same "measurement"—"55° " ;

And combine with angle with the given measurement of 72° ;

And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;

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All three of these angles form a straight line—that is;

→ they are "supplementary angles" ;

→ which means they add up to "180° " ;

So, 55° + 72° + (x − 13)° = 180° ;

Let us solve for "x" ; and for "(x − 13)" ;

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55 + 72 = 127 ;

→ 127 + (x − 13) = 180 ;

Now, subtract "127" from each side of the equation:

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→ 127 + (x − 13) − 127 = 180 − 127 ;

to get:

" (x − 13) = 53 " ; → which is one of our answers;

Now, to solve for "x" ; we add "13" to Each Side of the equation;

to isolate "x" on one side of the equation; & to solve for "x" :

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x − 13 + 13 = 53 + 13 ;

to get:

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x = 66 ;

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So: The correct answers are:

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" (x − 13) ° = 53 ° " ;

→ Double check by substituting our value of "66" for "x" :

" (66 − 13) =? 53 ? Yes! ;

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" x = 66 " ;

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" m∠2 = 55° " ;

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" m∠1 = 55° " .

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Hope these answers—and explanations—are helpful!

Best wishes!

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3 0

3 years ago

HOMEWORK HELP NEED IT FAST PLEASE!

Lunna [17]

I hope this helps you

6 0

3 years ago

Read 2 more answers

The recursive function LaTeX: f\left(0\right)=1,\:f\left(n\right)=f\left(n-1\right)+2nf ( 0 ) = 1 , f ( n ) = f ( n − 1 ) + 2 n

m_a_m_a [10]

Question:

The recursive function $f(0) = 1$ , $f(n) = f(n-1) + 2n$ represents the nth term of a sequence. Determine the explicit function

Answer:

$f(n) = n^2 + n+1$

Step-by-step explanation:

Given

$f(0) = 1$

$f(n) = f(n-1) + 2n$

Required

Write an explicit formula

Let n = 1

$f(1) = f(1-1) + 2*1$

$f(1) = f(0) + 2$

$f(1) = 1 + 2 = 3$

Let n = 2

$f(2) = f(2-1) + 2*2$

$f(2) = f(1) + 4$

$f(2) = 3 + 4 = 7$

Let n =3

$f(3)=f(3-1) + 2 * 3$

$f(3)=f(2) + 6$

$f(3)=7+ 6 = 13$

Let n = 4

$f(4) = f(4 - 1) + 2 * 4$

$f(4) = f(3) + 8$

$f(4) = 13+ 8 = 21$

So, we have:

$f(1) = 3= 1 + 2 * 1=1+0*1*2*1$

$f(2) = 7= 3 + 2 * 2=1+1*2+2*2$

$f(3) = 13= 7 + 2 * 3= 1+2*3+2*3$

$f(4) = 21 = 13 + 2 * 4= 1+3*4 +2 *4$

Following the above pattern:

$f(n) = 1 + (n - 1) * n + 2 * n$

$f(n) = 1 + n(n - 1) + 2n$

Open bracket

$f(n) = 1 + n^2 - n + 2n$

$f(n) = 1 + n^2 + n$

$f(n) = n^2 + n+1$

3 0

2 years ago

The quotient is 45 1/4 what is the divisor

vredina [299]

1. Well if the quotient is 45 ¼, the divisor will depends on the dividend.
Since the dividend is not given, there it would be hard for us to tell what is the divisor.
Because we only have the quotient, there are a lot of answers then if the dividend is not given.
it can be that the divisor is 2 and the dividend is 90 ½ to be able to get 45 ¼ as an answer.
it’s hard to tell without identifying the dividend.

4 0

4 years ago