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3 years ago

PLSSSS HELPPP MEEEEEE

Mathematics

1 answer:

labwork [276]3 years ago

5 0

Circumference of the smaller circle, using $C = \pi d$ , is approximately equal to 18.85 (I used the high floating point precision approximation of pi my calculator has in memory, then rounded to 2 decimal points.)

Using the formula $S = 0.2L$ , which in English says "the smaller circle's circumference is equal to 20% of the larger circle's", we can substitute the known value S: $18.85 = 0.2L$ and solve for L: $\frac{18.5}{0.2} = L, L = 92.5$ .

So the larger circle has a circumference approximately equal to 92.5 units.

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Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

Let

$P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}$

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

$P(1):\ 1 = \dfrac{1\cdot 2}{2}=1$

So, the base case is ok. Now, we need to assume $P(n)$ and prove $P(n+1)$ .

$P(n+1)$ states that

$P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}$

Since we're assuming $P(n)$ , we can substitute the sum of the first n terms with their expression:

$\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}$

Which terminates the proof, since we showed that

$P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}$

as required

4 0

3 years ago

2x1/8 trying get help it’s hard for me I have difficulty doing these problems

dmitriy555 [2]

Answer:

1/4

2 x 1/8 is also 1/8 + 1/8 and that is then 2/8 and after that when you simplify you get 1/4.

7 0

3 years ago

A prism _____ has two congruent, parallel bases. always sometimes never

Hunter-Best [27]

Answer :

A prism __always___ has two congruent, parallel bases.

always

sometimes

never

5 0

3 years ago

Read 2 more answers

a. For what values of x does f (x )equals 3 x plus 3 sine x have a horizontal tangent line? b. For what values of x does f (x )

laila [671]

Answer:

(a)Therefore the value of x= $\pi$

(b) Therefore the value of x $=\frac{\pi}{2}$

Step-by-step explanation:

Horizontal tangent line: The first order derivative of a function gives the slope of the tangent of the function. The slope of horizontal line is zero.If the slope of tangent line is zero then the tangent line is called horizontal tangent line.

(a)

Given function is,

$f(x)= 3x+3sin x$

Differential with respect to x

$f'(x)=3+3cos x$

For horizontal tangent line, f'(x)=0

3+ 3 cos x= 0

⇒3 cos x=-3

⇒cos x=-1

⇒x = 180° $=\pi$

Therefore the value of x= $\pi$

(b)

Given that, the slope is 3.

Then,f'(x)=3

3+ 3 cos x= 3

⇒3 cos x= 3-3

⇒cos x=0

⇒x = 90° $=\frac{\pi}{2}$

Therefore the value of x $=\frac{\pi}{2}$

5 0

3 years ago

What does the expression 12f + 24 represent? Answers:

PSYCHO15rus [73]

24 more than 12 times a number

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3 years ago

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