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3 years ago

Summation notation help!!!!

Mathematics

1 answer:

solniwko [45]3 years ago

4 0

3 is always on the numerator. It is not effected by a power. The answer has to be something that leaves the numerator alone. That means that B is not correct.

The answer is going to be something that makes the denominator 1 when n = 1. That's going to be the answer to the question, because the first term in the sequence is just 3. The denominator must be 1. (not zero).

D is not the answer, because 3/5^1 = 3/5, so D is wrong.

A is not going to get us anywhere either. 3/5^(1 + 1) = 3/5^2 = 3/25 which is not the first term.

The only choice we have left is C. It must be the answer. 3/5^(1 - 1) = 3/5^0 = 3/1 = 3. There's your answer. Note anything raised to the zero power = 1.

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The area of two similar triangles are 50dm^2 and 32dm^2. The sum of their perimeters is 117dm. What us the perimeters of each of

Kay [80]

Answer:

Perimeter of one triangle is 65 dm

Perimeter of other triangle is 52 dm

Step-by-step explanation:

Please remember the concept

If sides are in the ratio of a:b

Then the area in the ratio of $a^{2} :b^{2}$

It is given sum of their perimeter is 117.

Let the small triangle has perimeter as x.

So, perimeter of big triangle is 117-x.

So, we can set up equation as

$\frac{50}{32} =\frac{x^{2} }{(117-x)^{2} }$

Cross multiply

50(117-x)^2 =32x^2

Expand the left side

50 $(13689 -234x+x^{2} )$ = $32x^{2}$

Distribute the left side

684450-11700x+ $50x^{2}$ = $32x^{2}$

Subtract both sides $32x^{2}$ and rewrite it $18x^{2} -11700x+684450=0$

Solve this quadratic for x.

Divide both sides of the equation by 18 to simplify.

$x^{2}$ -650 x+38025=0

Now, if possible let's factor

Find two integers whose multiplication is 38025 but adds to -650.

-65 and -585 works.

So, we can rewrite it as

(x -65)(x-585) =0

Solve them using zero product property

x=65, x=585

So, x=65 works here.

So, perimeter of one triangle is 65 dm

Perimeter of other triangle is 117-65= 52 dm

5 0

3 years ago

Compound interest earns interest on both the principal and the interest already earned.

kow [346]

Answer:

Step-by-step explanation:

Pretty sure its true but im a little iffy

5 0

3 years ago

240 is 240% of what number?

dybincka [34]

240 is 240% of 576
240% x 240 = x
(240 x 240) divide by 100
57,600 divide by 100 = 576 x = 576

5 0

4 years ago

Read 2 more answers

The quotient of w and 5 is at least 25

const2013 [10]

I think the answer is 5 because 25 divided by 5=5

8 0

3 years ago

Read 2 more answers

Simplify this equation Thanks a lot!!!

den301095 [7]

Answer:

-1

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

$\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}$

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

$\bf\implies a^m \times b^m = (ab)^m$

Using this property , we have ,

$\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}$

This can be written as ,

$\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}$

Simplifying using ( a+b)(a-b) = a² - b² ,

$\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1}$

Subtracting the numbers inside the brackets ,

$\rm\implies (-1)^{2n - 1 }$

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the power is odd .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

$\rm\implies\boxed{\quad \red{ -1 }\quad }$

Hence the required answer is (-1) .

4 0

3 years ago