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Veseljchak [2.6K]
3 years ago
14

What are the coordinates of the vertices of a rectangle with an perimeter of 12 units and an area of 5 sq. units.

Mathematics
2 answers:
ale4655 [162]3 years ago
3 0
I believe it is 12 minus 3
statuscvo [17]3 years ago
3 0

ion but u wanna wut I think? I think its a rectangle on a coordinate line

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How many math problems can i complete in 12 mins?
Tatiana [17]

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Step-by-step explanation:

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Evaluate the limit as x approaches 0 of (1 - x^(sin(x)))/(x*log(x))
e-lub [12.9K]
sin~ x \approx x ~ ~\sf{as}~~ x \rightarrow 0

We can replace sin x with x anywhere in the limit as long as x approaches 0.

Also,

\large  \lim_{ x \to 0  } ~  x^x = 1

I will make the assumption that <span>log(x)=ln(x)</span><span>.

The limit result can be proven if the base of </span><span>log(x)</span><span> is 10. 
</span>
\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x  \log x }  \\~\\  \large = \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{ \log( x^x)  }   \\~\\  \large = \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x)  }  ~~ \normalsize{\text{ substituting x for sin x } } \\~\\   \large  = \frac{\lim_{x \to 0^{+}} (1) - \lim_{x \to 0^{+}} \left( x^{x}\right) }{ \log(  \lim_{x \to 0^{+}}x^x)  } = \frac{1-1}{\log(1)}   = \frac{0}{0}

We get the indeterminate form 0/0, so we have to use <span>Lhopitals rule 

</span>\large \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x)  } =_{LH} \lim_{x \to 0^{+}} \frac{0 -x^x( 1 + \log (x)) }{1 + \log (x)  }   \\ = \large \lim_{x \to 0^{+}} (-x^x) = \large - \lim_{x \to 0^{+}} (x^x) = -1
<span>
Therefore,

</span>\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x  \log x }  =\boxed{ -1}<span>
</span>
3 0
3 years ago
How many three-digit numbers can be formed under each condition?
Leokris [45]

Answer:

(a) 900

(b) 648

(c) 180

(d) 600

Step-by-step explanation:

If there are no restrictions, there are 10 possible values for each digit of a three-digit number.

(a) The leading digit cannot be zero

There are 9 options for the first digit and 10 for the remaining digits.

n=9*10*10 = 900

(b) The leading digit cannot be zero and no repetition of digits is allowed.

n=9*9*8=648

(c) The leading digit cannot be zero and the number must be a multiple of 5.

If a number is a multiple of five, it must end in 0 or 5

n=9*10*2=180

(d) The number is at least 400.

If the number is at least 400, the first digit can only be 4, 5, 6, 7, 8 or 9. There are no restrictions for the remaining digits.

n=6*10*10=600

8 0
3 years ago
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