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3 years ago

Here you go the brainless

Mathematics

1 answer:

sattari [20]3 years ago

6 0

When you see questions with dirrerent scales, find the scale factor first.

Scale factor
= A ÷ A’ = 12 ÷ 4 = 3

Larger flag perimeter = 3 × 16 = 48 units

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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn

mash [69]

Let $a=\tan A$ and $b=\sin A$ . Then

$m^2-n^2=(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab$

$\implies m^2-n^2=4\tan A\sin A$

and

$mn=(a+b)(a-b)=a^2-b^2$

$\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}$

The expression under the square root can be rewritten as

$\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)$

Recall that

$\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A$

so that

$\tan^2A-\sin^2A=\sin^2A\tan^2A$

and assuming $\sin A>0$ and $\tan A>0$ , we end up with

$4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A$

so that

$m^2-n^2=4\sqrt{mn}$

as required.

5 0

2 years ago

Graph a line with a slope of -2/5 that contains the point (-3, 5)

ValentinkaMS [17]

Picture so I am able to solve problem please

8 0

3 years ago

If the radius is 18 cm and the angle at centre of circle is 120° then the

PolarNik [594]

The area of a sector is 339.336 cm²

The area of a sector is defined to be as the region of space bounded by a boundary from the center of the circle.

It can be determined by using the formula:

$\mathbf{A = \dfrac{\theta }{360}\times \pi r^2 }$

Given that;

Radius r = 18 cm
Angle θ = 120°

Then. the area of the sector can be calculated as:

$\mathbf{A = \dfrac{120}{360}\times \pi (18)^2 }$

$\mathbf{A = \dfrac{1}{3}\times 3.142 \times 324 }$

A = 339.336 cm²

Learn more about the area of a sector here:

brainly.com/question/7512468?referrer=searchResults

4 0

2 years ago

What is the result of converting 81 inches to feet remember there are 12 inches in a foot?

AlekseyPX

81 inches converted to feet is 6.75 feet

7 0

3 years ago

Read 2 more answers

If sin(A+B)=1/2 & sin(A-B)=1/3 find sin(2A)

timofeeve [1]

Answer:

sin(2A) = (2√2 + √3) / 6

Step-by-step explanation:

2A = (A+B) + (A−B)

sin(2A) = sin((A+B) + (A−B))

Angle sum formula:

sin(2A) = sin(A+B) cos(A−B) + sin(A−B) cos(A+B)

sin(2A) = 1/2 cos(A−B) + 1/3 cos(A+B)

Pythagorean identity:

sin(2A) = 1/2 √[1 − sin²(A−B)] + 1/3 √[1 − sin²(A+B)]

sin(2A) = 1/2 √(1 − 1/9) + 1/3 √(1 − 1/4)

sin(2A) = 1/2 √(8/9) + 1/3 √(3/4)

sin(2A) = 1/3 √2 + 1/6 √3

sin(2A) = (2√2 + √3) / 6

6 0

2 years ago