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A sphere has a diameter of 22 units what is the radius and volume

lilavasa [31]

Answer:

Step-by-step explanation:

11

7 0

2 years ago

What is the domain of validity for csctheta =start fraction 1 over sine theta end fraction? (1 point) all real numbers all real

dem82 [27]

We know the following relationship:

$csc(\theta)=\frac{1}{sin(\theta)}$

The domain of a function are the inputs of the function, that is, a function $f$ is a relation that assigns to each element $x$ in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function $csc(\theta)$ we can write its domain as follows:

1. Domain of validity for $csc(\theta)$ :

$D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0$

When:

$sin(\theta)=0$ ?

when:

$\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi$

where k is an integer either positive or negative. That is:

$sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...$

To match this with the choices above, the answer is:

"All real numbers except multiples of $\pi$ "


2. which identity is not used in the proof of the identity $1+cot^{2}(\theta)=csc^{2}(\theta)$ :

This identity can proved as follows:

$sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)$

The identity that is not used is as established in the statement above:

"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

 $\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)$

4 0

2 years ago

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Find the dimensions of a deck which will have railings on only three sides. There is 28 m of railing available and the deck must

Roman55 [17]

Answer:

The largest possible area of the deck is 87.11 m² with dimensions;

Width = 9.33 m

Breadth = 9.33 m

Step-by-step explanation:

The area of a given dimension increases as the dimension covers more equidistant dimension from the center, which gives the quadrilateral with largest dimension being that of a square

Given that the railings will be placed on three sides only and the third side will cornered or left open, such that the given length of railing can be shared into three rather than four to increase the area

The length of the given railing = 28 m

The sides of the formed square area by sharing the railing into three while the fourth side is left open are then equal to 28/3 each

The area of a square of side s = s²

The largest possible area of the deck = (28/3)² = 784/9 = 87.11 m² with dimensions;

Width = 28/3 m = 9.33 m

Breadth = 28/3 m = 9.33 m.

5 0

2 years ago

If w= the weight of trout. Which algebraic expression represents the phrase below?

konstantin123 [22]

Product means multiplication.

Given w= weight of a trout.

So, we need to convert "product of 16 and weight of trout: w " into an algebraic expression.

So, product of 16 and w can be written as 16*w or simply 16w.

Hence, B is the correct choice.

8 0

2 years ago

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Write a real world problem that can be represented by the equation 3/4c=21

Black_prince [1.1K]

Answer: Real world problem is "A student have c toffee he distribute $\frac{3}{4}$ th part of those toffees to his friends. He gave total 21 toffees to his friend".