Prove that:-




[tex] \sqrt{ \frac{1 + cos30 {}^{ \circ} }{1 - cos {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]

Answers

Answer 1

Answer:

[tex] \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} }[/tex]

[tex]LHS = \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{1 + \frac{ \sqrt{3} }{2} }{1 - \frac{ \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{2 - \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{(2 + \sqrt{3} {)}^{2} }{4 - 3} } }[/tex]

[tex] \displaystyle{2 + \sqrt{3} }[/tex]

[tex]RHS = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]

[tex] = 2 + \sqrt{3} [/tex]

[tex] \rm\therefore{LHS=RHS,proved. }[/tex]


Related Questions

f(x) = x^1/2 is continuous for all x but not differentiable at x=0. is it True or False?

Answers

Answer:

it's true because the x=0 and that why it must be true FX may be the some I would say it's true

Solve for x: ___ degrees.

Answers

Answer:

63

Step-by-step explanation:

This is a cyclic quadrilateral, meaning that its opposite angles are supplementary. So, x=180-117=63.

There are 150 boys and girls playing in the soccer tournament.50 of the students are wearing red.what percent of the of players are wearing red.

Answers

Answer:

1/3 or 33%

Step-by-step explanation:

You can first do: 50/150

Which is 5/15 simplified

And do the quick math:

1/3 or 33%

What is the answer? Please simplify!

Answers

Answer:

2/125 or 0.016

Step-by-step explanation:

0.1= 1/10

1/10^3 × 2^-4

2 × 1/5^3

2 × 1/125

2/125

How many different ways can 6 different positions be filled by 12 applicants?

Answers

Answer:665280

Step-by-step explanation:

12•11•10•9•8•7=665280

PLEASE HELP!!! I JUST NEED A STEP-BY-STEP!!!!!!

HINT: integrate with respect to y first (it is an easier approach)
∫∫5x sec^2(xy) dA; R={(x,y): 0 ≤ x ≤ π/6 , 0 ≤ y ≤ 2

[Answer] -5/2 ln(1/2)

Answers

Answer:

Step-by-step explanation:

[tex]=5\displaystyle\int_{0}^{\pi/6}dx\displaystyle\int_{0}^{2}x\sec^2(xy)dy\\=5\displaystyle\int_{0}^{\pi/6}dx\displaystyle\int_{0}^{2}\sec^2(xy)d(xy)\\=5\displaystyle\int_{0}^{\pi/6}dx\tan(xy)|_{y=0}^{y=2}[/tex]

[tex]=5\displaystyle\int_{0}^{\pi/6}\tan(2x)dx\\=-\frac{5}{2}\ln\cos(2x)|_{0}^{\pi/6}\\=-\frac{5}{2}[\ln\cos(\pi/3) - \ln\cos(0)]\\[/tex]

[tex]=-\frac{5}{2}\ln{\frac{1}{2}[/tex]

Help Picture below problem 17

Answers

Answer:

139°

Step-by-step explanation:

18°+23°+?= 180°{sum of angles on a triangle}

41°+?° = 180°

?° =180-41=139°

is -2^3b^3 + 15c^3/8 z^3 a monomial, binomial, trinomial, or other polynomial.

Answers

It is trinomial because all have power 3

Answer: binomial

Step-by-step explanation: it has 2 terms

Which expressions are equivalent to 4b

Choose all answers that apply:


b + 2(b + 2b)


3b + b


2(2b)


2(b + 2b) - 4b
ANSWER ASAPP PLSSSSSSSSSSSSSSSSSSSSSSSSSSs

Answers

[tex]3b+b=4b\\\\2(2b)=4b\\\\[/tex]

need help with this question please

Answers

Answer:

your answer is correct

Step-by-step explanation:

The following refers to a purchase of a machine by a company on January 1, 2021:

Salvage Value: $7,500

Life: 6 years

Desired Rate of Return 4%

Interest Compounded: semi-annually

Maximum amount the company can pay $32,348



What is the semi-annual net cash flow the company must achieve in order for the purchase to be made?

Answers

The semi-annual net cash flow that the company must achieve in order for the purchase to be made is $5041.

How to calculate the cash flow?

Maximum amount that can be invested = $32348.

Less: Present value of salvage value = $5927

Present value of cash inflow = $32348 - $5927 = $26421.

Net cash flow will be:

= $26421 / PV factor

= $26421/5.242

= $5041

In conclusion, the correct option is $5041.

Learn more about cash flow on:

https://brainly.com/question/735261

If 14 is added to a number, the result is 40 less than twice the number. Find the number.

Answers

Answer:

Asher should be 61

Step-by-step explanation:

In circle O. AD and BE are diameters. The measure of arc AB is 55° and the measure of arc CD is 25° B с F D E What is the measure of BC ? 090 O 110 O 100 O 80​

Answers

Answer:

100°

Step-by-step explanation:

the total of all angles around O on one side of AD is 180° (as that would represent a half-circle).

and the sum of the arc angles AB + BC + CD covers the whole 180°.

so, we have

180 = 55 + BC + 25

180 = 80 + BC

BC = 100°

A suit is on sale for 72% off. The sale price is $263.20.
What is the regular price?

Answers

Answer:

940

Step-by-step explanation:

To find the original price of something that been discount do the following:

Subtract the discount from 100 to get the percentage of the original price.Multiply the final price by 100.Divide by the percentage in Step One.

Or we can do the following:

We shall consider the original price as x; hence the discount can be considered as (x−263.20). We can write the equation:

x · 72/100=x - 263.20

x · 18/25 = x - 263.20

Multiply both sides by 25

18x = 25(x - 263.20)

Open the brackets.

18x = 25x-6580

Add 6580 to each side.

6580 +18x = 25x

Subtract 18x from each side.

6580 = 7x

Subtract 7x from each side.

x = 940

Check Answer:

940 * 72% = 676.80

940 - 676.80=263.20

Hence, the regular price is 940.

~lenvy~

Step-by-step explanation:

The sale price ( The marked price ) :- $263.20

Discount :- 72%

Discount :- marked 100 ,Discount 72 ,Seliing ( Regular ) 28

Regular price :- 263.20 × 28 / 100

$ 73.69

I did half the answer but what is e= ?​

Answers

Answer:

See below.

Step-by-step explanation:

e=12c+6

e=12(1)+6

e=12+6

e=18

e=12(2)+6

e=24+6

e=30

e=12(3)+6

e=36+6

e=42

e=12(4)+6

e=48+6

e=54

-hope it helps

Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.

Answers

Answer:

The answer should be 3 :)

Step-by-step explanation:

Pick a point on f(x) and count up until you hit the g(x) point :)

When i did this, i got 3 :)

Have an amazing day!!

Please rate and mark brainliest!!

I THINK ITS C BUT PLSS TELL ME IF IM RIGHT


Use a number line to find the value of:

eight tenths plus one eighth equals

A. eight tenths
B. one tenth
C. nine tenths
D. seven tenths

Answers

Answer:

it is .925 which is very close to 9/10 so C would be correct

Step-by-step explanation:

Answer:

0.925 so I would pick option C.

Help? Anything can help I’m in a rush

Answers

Answer: A vertical line from (-5 , 4 ) to (5 , 4)

Step-by-step explanation: The y axis is the vertical  one. Go up 4 and draw a line connecting all the points with 4 in the coordinates.

Hope that helps :)

Answer:

Step-by-step explanation:

go up 4 lines on the y-axis then draw a straight line from left to right on y=4

I don't know if you can see the picture, but I drew a line on the picture you provided...

Please 5 stars if correct!!!

I hope this helps

When using synthetic division you must switch the signs in the divisor

Correct answer:

True

False


















b a dddddddies hmuuuuuuuuuuuu XD

Answers

True, you switch the sign when you write the divisor so that you can add

Consider the expression 1.1(1.3)x+4Which of the following is an equivalent expression?

Answers

Answer:

the equivalent expression is 1.1(1.3)^4 ×(1.3)^x

Answer:

d

Step-by-step explanation:

i took the test

Which phrase best describes the relationship indicated by the scatter plot? A. Constant correlation B. negative correlation C. Positive correlation D. no correlation

Answers

B. negative correlation

Answer:the largest angle has a measure of _____degrees.

Answers

Answer:

depends mostly it'll b 180 degress

Step-by-step explanation:

You need to buy insulation to cover the inside of a shipping container. The container is a rectangular prism that is 15 feet long, 8 feet wide, and 7 feet high. How much insulation do you need to buy if you want to insulate all the inside surfaces of the shipping container except the floor?

Answers

Answer:

  442 ft²

Step-by-step explanation:

The amount of insulation needed is the amount that covers the area of the side walls and the ceiling. The area of the side walls is the product of the perimeter and height. The area of the ceiling is the product of length and width.

__

Lateral area = Ph = 2(L+W)h = 2(15 ft +8 ft)(7 ft) = 322 ft²

Ceiling area = LW = (15 ft)(8 ft) = 120 ft²

__

Insulation needed = lateral area + ceiling area = 322 ft² +120 ft²

Insulation needed = 442 ft²

Which is the equation of the line with slope 3 that contains point (-1,5)?


y-1 = 3(x + 5)
y - 1 = 3(x - 5)
y - 5= 3(x - 1)
y - 5= 3(x + 1)

Answers

the answer is y-5=3(x+1)

Answer:

D

[tex]y-5=3(x+1)[/tex]

Step-by-step explanation:

We can see that the question is asking for the Point-Slope Form;

[tex]y-y_{1} =m(x-x_{1})[/tex]

The points go into the equation for [tex]y_{1}[/tex] and [tex]x_{1}[/tex]

[tex]y-5=m[x-(-1)][/tex]

M would be the slope;

[tex]y-5=3[x-(-1)][/tex]

Which basically is:

[tex]y-5=3(x+1)[/tex]

A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.


Box-and-whisker plot ranging from 34 to 58 with ticks at increments of one half. Plot defined by points at 35, 37, 41, 49, 55


How many employees took a break that lasted between 37 and 41 minutes?


Select from the drop-down menu to correctly complete the statement.


About (blank) employees took a break that lasted between 37 and 41 minutes.

Answers

Answer:

90

Step-by-step explanation:

37 and 41 is only in the 25% percentile.  

360 X .25 = 90

Plus, I took the K12 test and got it right.

The number of employees took a break that lasted between 37 and 41 minutes is 60.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We know that;

There are 360 employees in total and that they are evenly distributed along this plot. Therefore, we can divide 360 by the width of this plot to find how many employees are represented by one unit on this plot. The width of this plot is 58 - 34 = 24 units.

So, 360 / 24 = 15

This means that for every unit on this plot, there are 15 employees who took a break with that duration.

Now we can multiply this number by the width of the box to find how many employees took a break between 37 and 41 minutes. The width of the box is 41 - 37 = 4 units. So,

15 * 4 = 60

This means that there are 60 employees who took a break that lasted between 37 and 41 minutes.

Therefore, by the unitary method the answer will be 60 employees

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ3

the product of two consecutive odd number is 143 find those two odd numbers show ll workings

Answers

Answer:

11,13

11×13=143

Step-by-step explanation:

please mark me as brainlest

Answer choices:

y = x
y = 1/4x - 2
y = -x + 7/4
y = 7/4x - 2

Answers

Answer:

all in all it's y=x

Step-by-step explanation:

A (4,1); B (0,-2)

G=delta y

--------

delta x

1-(-2)

-------

4-0

3/4=G

3/4=y-1/x-4

4 (y-1)=3 (x-4)

4y-4=3x-12

4y=3x+4-12

y=3/4x-3


Someone pls

.
A
A
A
A
A
A
S

Answers

Answer:

7

Step-by-step explanation:

Degree of a polynomial is a variable's highest exponent

In this expression the degree is 7

Answer:

7

Step-by-step explanation:

If you used

P.E.M.D.A.S

Brainly please I worked so hard for this answer

What is the mean absolute deviation of the following set
of data?
9
2
9
9
5
4.
9
1
4
10

Answers

Answer:

  3

Step-by-step explanation:

You want the mean absolute deviation of the set of numbers ...

  {9, 2, 9, 9, 5, 4, 9, 1, 4, 10}

MAD

The mean of this 10-number set of data is 6.2. The mean absolute deviation (MAD) is found by subtracting that from the members of the dataset, taking the absolute values of the result, and finding the means of those.

The attachment shows those calculations.

The MAD of this set of data is 3.

__

Additional comment

The period (decimal point) in the column of numbers suggests this is a 6-number dataset, and the last 4 numbers are answer choices. If that is the case, none of those answer choices is correct. That is why we assumed that this problem has a 10-number dataset.

When you're calculating this by hand, you only need to consider the values for which the deviation is negative. The MAD is twice their total absolute value, divided by the number of numbers in the dataset. Here, that is 2(4.2+2.2+5.2+2.2+1.2)/10 = 3. (Numbers 2, 5, 4, 1, 4 are less than the mean of 6.2.)

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Sam buys a tent priced at $50 if the sales tax is 5% how much tax will Sam pay

Answers

tax will be = 50 x 5% = $2.5

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