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inn [45]
4 years ago
15

Sydney was asked whether the following equation is an identity: (2x^2-18)(x+3)(x-3)=2x^4-36x^2+162

Mathematics
2 answers:
weqwewe [10]4 years ago
4 0

Answer:

Any value of x x makes the equation true. All real numbers Interval Notation: ( − ∞ , ∞ ) .

Hatshy [7]4 years ago
4 0

Answer:

Yes it is.

See below.

Step-by-step explanation:

(2x^2-18)(x+3)(x-3)

= (2x^2 - 18(x^2 - 9)

= 2x^4 - 18x^2 - 18x^2 + 162

= 2x^4 - 36x^2 + 162.

The left side transforms to the right side so it is an identity.

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Answer:

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Step-by-step explanation

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3 years ago
Answer the question with explanation;​
PSYCHO15rus [73]

Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0

Therefore, by the series divergence test, the series \sum_{n=1}^\infty\frac{n^2}{(n+1)^2} diverges.

EDIT: To VectorFundament120, if (x_n)_{n\in\mathbb N} is a sequence, both \lim x_n and \lim_{n\to\infty}x_n are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.

7 0
3 years ago
Read 2 more answers
E<img src="https://tex.z-dn.net/?f=e%5E%7Bx%7D%20-%20e%5E%7B-2%7D%20%3D-2" id="TexFormula1" title="e^{x} - e^{-2} =-2" alt="e^{x
pav-90 [236]

$e\cdot e^x -e^{-2}=-2$

$\implies e^{x+1}=e^{-2}-2$

note that RHS is negative. (because e with negative exponent is less than 1)

and LHS is always positive.

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3 0
3 years ago
At the market, 8 apples cost $4dollar. How much do 9 apples cost?
Lorico [155]

Answer: $4.50 for 9 apples

Step-by-step explanation: To find out how much it is for 1 apple, we need to find the unit price of 1 apple which is the cost per apple.

Since we know that it costs $4 for 8 apples, to find the cost for 1 apple, we need to divide 8 into $4 or 4 divided by 8 which is 0.5 of 50 cents per apple.

Since we know that it costs 50 cents per apple, to find the cost for 9 apples, we will need to multiply .50 by 9.

(.50) (9) = 4.50

Therefore, it will cost $4.50 for 9 apples.

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d1i1m1o1n [39]

Answer:

see below

Step-by-step explanation:

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