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Ask QuestionPosted by Harinder Kaur 6 years, 6 months ago
- 2 answers
Sia ? 6 years, 6 months ago
An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8.
Posted by Kńîghť Đėvìł 6 years, 6 months ago
- 2 answers
Sia ? 6 years, 6 months ago
Let the units digit of the two-digit number be x.
Then, the tens digit of the two-digit number = 9 – x
[{tex}\because {/tex} Sum of the digits of the two-digit number 9]
∴ Original number = 10(9 – x) + x
= 90 – 10x + x
= 90 – 9x
When we interchange the digits, then
Units digit = 9 – x
and, tens digit
∴ Resulting number = 10x + (9 – x)
= 9x + 9
According to the question,
(9x + 9) = (90 – 9x) + 27
∴ 9x + 9x = 90 + 27 – 9. . . . [Transposing – 9x to L.H.S. and 9 to R.H.S.]
∴ 18x = 108
∴ {tex}x = \frac{{108}}{{18}}{/tex} . . . . [Dividing both sides by 18]
∴ x = 6
∴ 9 – x = 9 – 6 = 3 hence, the required two–digit number is 36.
Verification
3 + 6 = 9
63 = 36 + 27 hence, result verified.
Posted by Prabh Fateh 6 years, 6 months ago
- 1 answers
Sia ? 6 years, 6 months ago
According to the question, {tex}f ( x ) = 1 - | x + 2 |{/tex}
We can see that {tex}f(x){/tex}( x ) is defined for all x {tex}\in{/tex} R.
{tex}\therefore{/tex} Domain of f = R
As we know, {tex}0 \leq | x + 2 | < \infty{/tex}for all {tex}x \in R{/tex}
{tex}\Rightarrow - \infty < - | x + 2 | \leq 0{/tex} for all {tex}x \in R{/tex}
{tex}\Rightarrow - \infty < 1 - | x + 2 | \leq 1{/tex} for all {tex}x \in R.{/tex}
{tex}\Rightarrow - \infty < f ( x ) \leq 1{/tex} for all {tex}x \in R \Rightarrow f ( x ) \in ( - \infty , 1 ]{/tex}
{tex}\therefore{/tex} Range of {tex}f = ( - \infty , 1 ]{/tex}
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All doublets are (1,1) (2,2) (3,3) (4,4) (5,5) (6,6)
doubles of even no. : 2, 2 4, 4 6, 6
Probability of doublet of even number: 3 / 6
= 1/ 2
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Sia ? 6 years, 6 months ago
An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8.
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