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3 years ago

Approximate the value of 13√ to the nearest tenths place. Plot the approximation on the number line.

Mathematics

2 answers:

Shtirlitz [24]3 years ago

5 0

3.60
It is a pretty simple question, I hope this helps

aalyn [17]3 years ago

4 0

The square root of 13 rounded to the nearest tenth is 3.6, so you would plot this somewhere in between 3 and 4 on a number line.

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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

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3 years ago

Please help What is the value of x? A:12 B:15 C: 6 D: 30

pickupchik [31]

Answer: A, 12

Step-by-step explanation:

The line in the middle is a midsegment, making the two triangles similar by a ratio of two. So, dividing 60 by five will give you twelve

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3 years ago

If the diameter of an entire coconut is 5 inches, and the coconut meat is 1 inch thick, then there is room for approximately (bl

svetoff [14.1K]

The answer is 14.137 cubic inches.

For this case, the radius of whole coconut is 2.5 inches (which is 5 inches / 2).
You have to subtract the thickness of the coconut from this radius for you to get the volume of the space for coconut milk.

new radius = 2.5 - 1 = 1.5 inches

Volume = (4/3)(pi)(r^3)
= (4/3)(pi)(1.5^3)
= 14.137 cubic inches

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3 years ago

Writer and solve a real-word promblem involving the multiplication of a fraction and a whole number whose is between 10and15

pickupchik [31]

Give me an operation like the one you are talki ng about and I can solve it

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3 years ago

Translate into an algebraic expressions: 120 is increased by d% and increased by 25% . What is the result ?

anastassius [24]

Answer:

The result is 150 + 1.5d

Step-by-step explanation:

We want to translate the wordings into algebraic expression.

Firstly, we increase 120 by d%

d% = d/100

So increasing 120 by d % means;

120 + (d/100 * 120)

= 120 + 1.2d

Then increase this by 25%

= (120 + 1.2d) + 25/100(120 + 1.2d)

= 120 + 1.2d + (120+1.2d)/4

= 120 + 1.2d + 30 + 0.3d

= 120 + 30 + 1.2d + 0.3d

= 150 + 1.5d

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3 years ago