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3 years ago

What is the domain of validity for csc theta =

1 answer:

4 0

For the three basic trig identities (sin, cos, tan) there are three more which act as their reciprocals (csc, sec, and cot respectively)

A reciprocal of x can be represented as 1/x.
Therefore, cscӨ can also be represented as the reciprocal of sinӨ...1/sinӨ.

In that case, our answer should always be true so long as we put in a real number for theta, because that's the domain of sinӨ, right? However, we also have to satisfy the domain of cscӨ, and the limitations become extremely obvious when you look at this reciprocal identity equation...sinӨ cannot be zero because it is impposible to divide by zero! Looking at the unit circle, any multiple of π will make sinӨ = 0, so there's your answer.
D. All real numbers except multiples of pi

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Alison knits 1/10 of scarf in 4/5 of an hour. what fraction of a scarf can alison knit in 1 hour? and how do u solve it?

pav-90 [236]

For this case we can make the following rule of three:
1/10 scarf ------> 4/5 hour
x ------------------> 1 hour
Clearing the value of x we have:
x = (1 / (4/5)) * (1/10)
Rewriting we have:
x = (5/4) * (1/10)
x = 5/40
x = 1/8
Answer:
A fraction of a scarf that alison can knit in 1 hour is:
x = 1/8

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3 years ago

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A can do a piece of work in 4 hours and B can do it in 6 hours. How much time would they take working together to finish the wor

Kipish [7]

Answer:

2.4 hours

Step-by-step explanation:

Let total work = X

Rate of work done = X ÷ time

Rate of A = X/4

Rate of B = X/6

If they work together, rate is the sum of their individual rates, i.e.

X/4 + X/6

= (3X + 2X)/12 (taking LCM)

=5X/12

Rate = X/time

5X/12 = X/time

time = X÷(5X/12)

time = X × 12/(5X)

time = 2.4 hours

Shortcut:

Product of individual times/sum of individual times

= (4×6)/(4+6)

=24/10

=2.4 hours

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3 years ago

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Find the missing length triangle a=4,b=?,c=11

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Answer:

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3 years ago

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The sum of 3 consecutive even numbers is 66. write an equation and solve to find the smallest even number.

Alekssandra [29.7K]

X+(x+2)+(x+4)= 66
3x+6=66
3x=60
x=20

20,22, and 24. so 20 is the answer

6 0

3 years ago

Describe the graph of y=3/4x-12 as compared to the graph of y=1/x

Eddi Din [679]

Answer:

Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.

Step-by-step explanation:

We are asked to describe the transformation of function $y=\frac{3}{4x-12}$ as compared to the graph of $y=\frac{1}{x}$ .

We can write our transformed function as:

$y=\frac{3}{4(x-3)}$

$y=\frac{3}{4}*\frac{1}{(x-3)}$

Now let us compare our transformed function with parent function.

Let us see rules of transformation.

$f(x-a)\rightarrow\text{Graph shifted to the right by a units}$ ,

$f(x+a)\rightarrow\text{Graph shifted to the left by a units}$ ,

Scaling of a function: $a*f(x)$

If a>1 , so function is stretched vertically.

If 0<a<1 , so function is compressed vertically.

As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.

As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.

Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.

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3 years ago