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3 years ago

The picture shows a triangular island: Which expression shows the value of c?

Mathematics

1 answer:

xenn [34]3 years ago

8 0

Answer:

c = b/cos 45

Step-by-step explanation:

SOHCAHTOA

We use Cos
Cos 45 = b/c
c = b/cos 45

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Rasek [7]

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

$I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx$

Replace $x \to x^{\frac1\phi} = x^{\phi-1}$ :

$I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

Split the integral at x = 1. For the integral over [1, ∞), substitute $x \to \frac1x$ :

$\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

The integrals involving tan⁻¹ disappear, and we're left with

$I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}$

8 0

2 years ago

The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. find the diameter of the base of the cylinder

White raven [17]

Answer:

2 cm

Step-by-step explanation:

h = 14 cm

Curved surface area of a right circular cylinder = 88 cm²

2πrh = 88

$2 * \frac{22}{7}*r*14=88\\\\r = \frac{88*7}{2*22*14}\\\\ r =1 \\\\r = 1 cm$

Diameter = 2 * r = 2 * 1 = 2 cm

6 0

3 years ago

The path of a football can be modelled by the equation, h=-10d2+120d , where h represents the height, in metres, of the football

Marta_Voda [28]

Answer:

12 m

Step-by-step explanation:

The path of a football has been modeled by the equation:

$h= -10d^2+120d$

where h represents the height and d represents the horizontal distance.

When the ball lands, it means that its height is back at 0 metres. This means that we have to find horizontal distance, d, when height, h, is 0.

=> $0= -10d^2+120d$

$=> 10d^2 - 120d = 0$

$d(10d - 120) = 0$

∴ d = 0 m

and

10d - 120 = 0

=> d = 120 / 10 = 12 m

There are two solutions for d when h = 0 m.

The first solution (d = 0 m) is a case where the ball has not been thrown at all. This means the ball has not moved away from the football player and it is still on the ground.

The second solution is the answer to our problem (d = 12 m). The ball lands at a horizontal distance of 12 m

3 0

3 years ago

A triangle has sides 42, 4x, and 2x−6. What is the possible range of x? <br><br>? < x < ?

natulia [17]

Answer:

$8\ units< x < 18\ units$