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lukranit [14]
3 years ago
10

The farther an integer is from 0, the ______ its absolute value.

Mathematics
2 answers:
Mashutka [201]3 years ago
8 0
bigger it's absolute value since absolute value is how far it is away from zero. Hope this helps.
Citrus2011 [14]3 years ago
5 0
I think it's higher because as far as the integer gets, the higher its absolute value gets. So, put higher in the blank.

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There are 104 coins in a bottle.
fredd [130]

Answer:

its easy solve it with calculator

Step-by-step explanation:

8 0
3 years ago
Cos4theta+cos2theta/ cos4theta-cos2theta= _____
vovangra [49]

\bf \textit{Sum to Product Identities} \\\\ cos(\alpha)+cos(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ cos(\alpha)-cos(\beta)=-2sin\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \cfrac{cos(4\theta )+cos(2\theta )}{cos(4\theta )-cos(2\theta )}\implies \cfrac{2cos\left( \frac{4\theta +2\theta }{2} \right)cos\left( \frac{4\theta -2\theta }{2} \right)}{-2sin\left( \frac{4\theta +2\theta }{2} \right)sin\left( \frac{4\theta -2\theta }{2} \right)} \implies \cfrac{cos\left( \frac{6\theta }{2} \right)cos\left( \frac{2\theta }{2} \right)}{-sin\left( \frac{6\theta }{2} \right)sin\left( \frac{2\theta }{2} \right)}

\bf \cfrac{cos(3\theta )cos(\theta )}{-sin(3\theta )sin(\theta )}\implies -\cfrac{cos(3\theta )}{sin(3\theta )}\cdot \cfrac{cos(\theta )}{sin(\theta )}\implies -cot(3\theta )cot(\theta )

8 0
3 years ago
Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$
horrorfan [7]

Answer:

A +B+C+D  = 3 is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

A+B+C+D = ? if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under \sqrt (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \   (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, A +B+C+D = 5+6-10+2 = \bold3

5 0
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Allushta [10]

Answer:

hope you can understand

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Find the greatest common factor of 48 and 36.
tatiyna

Answer:

One, two, six, four, twelve are some greatest common factors.

Step-by-step explanation:

5 0
3 years ago
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