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3 years ago

How many different triangles can you make if you are given these three measurements for angles?

Mathematics

1 answer:

Elena L [17]3 years ago

6 0

Answer:

Infinite triangles

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

In this problem with these three measurements for angles i can make infinite different similar triangles

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\int\limits^0_\pi {x*sin^{m} (x)} \, dx

Ket [755]

Let

$I(m) = \displaystyle \int_0^\pi x\sin^m(x)\,\mathrm dx$

Integrate by parts, taking

u = x ==> du = dx

dv = sinᵐ (x) dx ==> v = ∫ sinᵐ (x) dx

so that

$I(m) = \displaystyle uv\bigg|_{x=0}^{x=\pi} - \int_0^\pi v\,\mathrm du = -\int_0^\pi \sin^m(x)\,\mathrm dx$

There is a well-known power reduction formula for this integral. If you want to derive it for yourself, consider the cases where m is even or where m is odd.

If m is even, then m = 2k for some integer k, and we have

$\sin^m(x) = \sin^{2k}(x) = \left(\sin^2(x)\right)^k = \left(\dfrac{1-\cos(2x)}2\right)^k$

Expand the binomial, then use the half-angle identity

$\cos^2(x)=\dfrac{1+\cos(2x)}2$

as needed. The resulting integral can get messy for large m (or k).

If m is odd, then m = 2k + 1 for some integer k, and so

$\sin^m(x) = \sin(x)\sin^{2k}(x) = \sin(x)\left(\sin^2(x)\right)^k = \sin(x)\left(1-\cos^2(x)\right)^k$

and then substitute u = cos(x) and du = -sin(x) dx, so that

$I(2k+1) = \displaystyle -\int_0^\pi\sin(x)\left(1-\cos^2(x)\right)^k = \int_1^{-1}(1-u^2)^k\,\mathrm du = -\int_{-1}^1(1-u^2)^k\,\mathrm du$

Expand the binomial, and so on.

8 0

3 years ago

Find the distance between j(4,-5) and h(3,3)

Savatey [412]

Jh=√((4-3)²+(-5-3)²)

8 0

3 years ago

PLZZZZZZ HELPPPPPPPP

nikitadnepr [17]

Answer:

1/2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Please help

Schach [20]

Answer:

Hence, option: B is correct (11.02 seconds)

Step-by-step explanation:

Spencer hits a tennis ball past his opponent. The height of the tennis ball, in feet, is modeled by the equation h(t) = –0.075t2 + 0.6t + 2.5, where t is the time since the tennis ball was hit, measured in seconds.

Now we are asked:

How long does it take for the ball to reach the ground?

i.e. we have to find the value of t such that height is zero i.e. h(t)=0.

$-0.075t2+0.6t+2.5=0$