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1 year ago

Perform the indicated operations and simplify the result so there are no quotients.

Mathematics

1 answer:

posledela1 year ago

5 0

Given an expression:

$\csc \theta(\sin \theta+\cos \theta)$

We have to simplify the given expression.

$\begin{gathered} \csc \theta(\sin \theta+\cos \theta)=\csc \theta\sin \theta+\csc \theta\cos \theta \\ =\frac{1}{\sin\theta}\cdot\sin \theta+\frac{1}{\sin\theta}\cdot\cos \theta \\ =1+\frac{\cos \theta}{\sin \theta} \\ =1+\cot \theta \end{gathered}$

Thus, the answer is 1 + cot theta.

You might be interested in

What is the slope of this line?

jeyben [28]

9514 1404 393

Answer:

1/4

Step-by-step explanation:

The slope can be found using the slope formula with the two left-most marked points:

m = (y2 -y1)/(x2 -x1)

m = (6 -5)/(0 -(-4)) = 1/4

The slope of the line is 1/4.

6 0

3 years ago

2 of the dozen eggs in a cartoon are cracked about what percent of the carton is not cracked

pychu [463]

well, a carton has a dozen, namely 12 or the 100%, two were cracked.

if we know 12 is the 100%, what is 2 off of it in percentage?

$\bf \begin{array}{ccll}
amount&\%\\
\cline{1-2}
12&100\\
2&x
\end{array}\implies \cfrac{12}{2}=\cfrac{100}{x}\implies x=\cfrac{2\cdot 100}{12}\implies x=16.\overline{66}$

4 0

3 years ago

Read 2 more answers

A hollow metal sphere has 6 cm inner and 8cm outer radii. The surface charge densities on the exterior surface is +100 nC/m2 and

natulia [17]

Answer:

<h2>Outer Electric Field is 11250 N/C.</h2><h2>Inner Electric Field is -10000 N/C.</h2>

Step-by-step explanation:

First of all, we need to read carefully and analyse the problem. As you can see, is an electrical subject, and it's given surface charge densities and radius.

So, to calculate electric fields, we need to find the proper equation to do so: $E=k\frac{q}{r^{2} }$ ; as you can see, first we need to find the charges.

We can find all charges using the surface charge densities, because it has the next relation: $p=\frac{q}{A}$ ; which indicates that charge density is the amount of charge per area. But, there's a problem, we don't have areas, so we have to calculate them first with this relation: $S=4\pi r^{2}$ ; which gives us the surface of a sphere.

The inner surface: $Si=4\pi (0.06m)^{2} = 0.04 m^{2}$

The outer surface: $S=4\pi (0.08m)^{2}=0.08m^{2}$

Now we can calculate the charges,

Inner charge: $Qi=pA=(-100\frac{nC}{m^{2} } )(0.04m^{2} )=-4nC$

Outer charge: $Qo=pA=100\frac{nC}{m^{2} } )(0.08m^{2} )=8nC$

Then, we are able to calculate both fields:

Inner field: $Ei=k\frac{Qi}{r^{2} }=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{-4x10^{-9} }{0.06m^{2} }=-10000\frac{N}{C}$

Outer field: $Eo=k\frac{Qo}{r^{2} }=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{8x10^{-9} }{0.08m^{2} }=11250\frac{N}{C}$

The directions that field have is opposite each other, the inner one has an inside direction, and the outer electric field has an outside direction.

3 0

3 years ago

A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One

vodka [1.7K]

Answer:

Step-by-step explanation:

x is the number of students

(x+5) is the number of students and chaperons

$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have

2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)

The inequality "90 greater-than 2.50 (x + 5) "

90 > 2.50(x+5) is an error becase it excludes the possibility that <u>the trip can cost exact $90</u> so we need not just greater than > , yet greater and equal than ≥ sign

90 ≥ 2.50(x+5)

7 0

2 years ago

Use the figure to find the measure of angle 1. *

QveST [7]

Answer: angle 1 = 110 degrees

This is because angle 1 and the red 110 degree angle are corresponding angles.

They correspond to one another due to the fact they are both in the southwest corner of each 4-corner angle configuration (which is the result of crossing two lines)

Corresponding angles are congruent only when we have parallel lines like this.

6 0

3 years ago