All categories

3 years ago

2/5- square root of 3 simplify

Mathematics

1 answer:

mel-nik [20]3 years ago

8 0

Answer:

(5 + √3)/11

Step-by-step explanation:

2/(5 - √3) =
2(5 + √3)/(5 - √3)(5 + √3) = multiply by conjugate of the denominator
2(5 + √3)/(25 - 3) = simplify
(5 + √3)/11 answer

You might be interested in

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side

lorasvet [3.4K]

Answer:

Step-by-step explanation:

cot x sec⁴ x = cot x+2 tan x +tan³x

L.H.S = cot x sec⁴x

=cot x (sec²x)²

=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]

= cot x(1+ 2 tan²x +tan⁴x)

=cot x+ 2 cot x tan²x+cot x tan⁴x

=cot x +2 tan x + tan³x [ ∵cot x tan x $=\frac{ \textrm{tan x }}{\textrm{tan x}}$ =1]

=R.H.S

(sin x)(tan x cos x - cot x cos x)=1-2 cos²x

L.H.S =(sin x)(tan x cos x - cot x cos x)

= sin x tan x cos x - sin x cot x cos x

$=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}$

= sin²x -cos²x

=1-cos²x-cos²x

=1-2 cos²x

=R.H.S

1+ sec²x sin²x =sec²x

L.H.S =1+ sec²x sin²x

= $1+\frac{{sin^2x}}{cos^2x}$ [ $\textrm{sec x}=\frac{1}{\textrm{cos x}}$ ]

=1+tan²x $[\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]$

=sec²x

=R.H.S

$\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}$

L.H.S= $\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}$

$=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}$

$=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}$

$=\frac{\textrm{2sin x}}{sin^2 x}$

= 2 csc x

= R.H.S

-tan²x + sec²x=1

L.H.S=-tan²x + sec²x

= sec²x-tan²x

= $\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}$

$=\frac{1- sin^2x}{cos^2x}$

$=\frac{cos^2x}{cos^2x}$

8 0

4 years ago

Using the Pythagorean Theorem, find the distance between the points.

Paha777 [63]

Answer:

(5,7,8.6)

Step-by-step explanation:

Create a line on each the x axis and the y axis which intersects at a right triangle. The x axis line is 7 squares and the y axis is 5 squares. Now you can use the Pythagorean theorem.

a^2+b^2=c^2

7^2+5^2=c^2

49+25=c^2

74=c^2

8.6=c

4 0

3 years ago

The surface area for a rectangular prism with a square base is SA=2s2+4sh. What is the surface area if s=3 and h=5?

Zigmanuir [339]

Answer:

The surface area is 78 unit square.

Step-by-step explanation:

Given : The surface area for a rectangular prism with a square base is $SA=2s^2+4sh$ .

To find : What is the surface area if s=3 and h=5?

Solution :

The surface area for a rectangular prism with a square base is $SA=2s^2+4sh$

Substitute, s=3 and h=5

$SA=2(3)^2+4(3)(5)$

$SA=2\times 9+4\times 15$

$SA=18+60$

$SA=78$

Therefore, The surface area is 78 unit square.

7 0

3 years ago

The cubic crystal company has a new crystal cube they want to sell. The packaging manager insists that the cubes be arranged to

Nat2105 [25]

Answer:

Following are the responses to the given question:

Step-by-step explanation:

$height \ \ \ \ \ \ \ Width \ \ \ \ \ \ \ Length\\\\$

$1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 12\\\\ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6\\\\ 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4\\\\2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\$

7 0

3 years ago

Read 2 more answers

Evaluate if x =3 and y = -2: x squared + 2 y A. 5 B. 10 C. 2 D. 3

Luden [163]

Of you have 3 squared you get 9 then 2 times -2 is -4. then you add them 9=-4 which would be ...A: 5

5 0

4 years ago

Read 2 more answers