$\int \! 70 - 6 \csc(\theta) \cot(\theta) \ \mathrm{d}\theta = \int \! 70 - 6 \cdot \frac{1}{\sin(\theta)} \cdot \frac{\cos(\theta)}{\sin(\theta)} \ \mathrm{d}\theta = \int \! 70 \ \mathrm{d}\theta - \int \! \frac{6 \cos(\theta)}{\sin^2(\theta)} \ \mathrm{d}\theta = 70 \theta + \frac{6}{\sin(\theta)} + C, \ C \in \mathbb{R}.$

8 0

3 years ago

Cellus

Solnce55 [7]

Answer:

Step-by-step explanation:

Corresponding angles have the same matching corner.

<6 has the same matching corner as <2. <6 and <2 are congruent.

Therefore, it can be concluded that <6 corresponds to <2.

6 0

3 years ago

A sphere and a cube have equal surface areas. The length of one edge of the cube is 1.11 meters. What is the radius of the spher

Nady [450]

Answer:

0.767 m

Step-by-step explanation:

The area of a cube of edge length s is given by ...

A = 6s^2

The area of a sphere of radius r is given by ...

A = 4πr^2

When these two are equal, we have ...

6s^2 = 4πr^2

r^2 = 6s^2/(4π)

r = s·√(3/(2π)) ≈ s·0.690988

The radius of the sphere is about ...

r ≈ 0.690899×1.11 m

r ≈ 0.767 m . . . . approximate sphere radius

3 0

4 years ago

How many vertices does a cube have

PolarNik [594]

A cube has 8
A square has 4

4 0

3 years ago

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