Please answer this correctly without making mistakes

Mathematics

2 answers:

AnnZ [28]3 years ago

7 0

Answer:

10.99 inches

Step-by-step explanation:

7*2=14

diameter=14

circumference=diameter*pi

14*3.14=43.96

quarter circle

43.96/4=10.99

10.99 inches

AfilCa [17]3 years ago

6 0

Answer:

the quarter circle's perimeter = 24.99 inch

Step-by-step explanation:

1. Calculate circumference of a complete circle.

2. Divide by 4 and you have the quarter part. (This is the same as multiplying by 0.25).

3. Just like a pie chart, there are 2 sides from the center to the left and right side edge of the quarter circle. Both are equal to the radius r.

4. Add the numbers found in step 2 and step 3 and you will have found the quarter circle's perimeter.

Given: use 3.14 for pi and r = 7 inch

1. Circumference = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * 7 ) = 10.99 inch

3 Since r = 7 and we have to sides.

So you just add 2 * 7 = 14 inch

4. Add 10.99 + 14 = 24.99 inch

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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:

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