Very quickly: since tan(30°) = 1/√3,
(1 + tan(30°)) / (1 - tan(30°)) = (1 + 1/√3) / (1 - 1/√3)
… = (√3 + 1) / (√3 - 1)
… = (√3 + 1)² / ((√3)² - 1²)
… = ((√3)² + 2√3 + 1²) / (3 - 1)
… = (3 + 2√3 + 1) / 2
… = (4 + 2√3) / 2
… = 2 + √3
On the other side, we have sin(30°) = 1/2 and sin(60°) = √3/2, so
(1 + sin(60°)) / (1 - sin(30°)) = (1 + √3/2) / (1 - 1/2)
… = (1 + √3/2) / (1/2)
… = 2 (1 + √3/2)
… = 2 + √3
and we're done, both sides are equal.
We can also prove this algebraically:
Force the denominator on the left side into a difference of squares:
(1 + tan(30°)) / (1 - tan(30°)) × (1 + tan(30°)) / (1 + tan(30°))
… = (1 + tan(30°))² / (1 - tan²(30°))
Expand the numerator:
… = (1 + 2 tan(30°) + tan²(30°)) / (1 - tan²(30°))
Recall that 1 + tan²(x) = sec²(x) :
… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°))
Since sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x), multiply through every term by cos²(30°) :
… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°)) × cos²(30°) / cos²(30°)
… = (1 + 2 sin(30°) cos(30°)) / (cos²(30°) - sin²(30°))
Recall that sin(2x) = 2 sin(x) cos(x) and cos(2x) = cos²(x) - sin²(x) :
… = (1 + sin(2×30°)) / cos(2×30°)
… = (1 + sin(60°)) / cos(60°)
Finally, recall that cos(90° - x) = sin(x), so cos(60°) = sin(30°) = 1/2, and we can write 1/2 = 1 - 1/2, so
… = (1 + sin(60°)) / (1 - sin(30°))
as required.
Jason sells his radio for 20% profit.if he bought it for 290$,what did he sell it for?
Answer:
$348
Step-by-step explanation:
original value times 1+ percent increase
290 * (1+.20)
290 * 1.20 = 348
Jason sold his radio for $348
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Answer:
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Answer:
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___________________________________________________________
Please help as soon as possible
Answer:
c= 12.19
Step-by-step explanation:
Let's solve for c.
5.3(4x−2.3)=21.2x+c
Step 1: Flip the equation.
c+21.2x=21.2x−12.19
Step 2: Add -21.2x to both sides.
c+21.2x+−21.2x=21.2x−12.19+−21.2x
c=−12.19
Answer:
c=−12.19
What is the image point of (-8, -1) after a translation left 3 units
and up 4 units?
If the mean of 6 10 12 x 16 18 is 15 find the value of x
Answer:
x=28
Step-by-step explanation:
I am assuming the mean is arithmetic mean. So we first add up the numbers:
6+10+12+18+16+x
=22+10+30+x
=22+40+x
=62+x
Then since there's 6 numbers in total, we have an equation:
[tex]\frac{62+x}{6}=15\\62+x=90\\x=28[/tex]
The answer is 28!
Have a nice day! :)
There are 320 students in a school. The ratio of the number of boys to the number of girls is 3:2. When some new boys and girls are admitted, the number of boys increases by 8 and the ratio of number of boys and girls changes to 4:3. Find how many new girls are admitted.
The area of the trapezoid is 40 square units. A trapezoid is shown. The lengths of the bases are 6 and 10, and the height of the altitude is h. What is the height of the trapezoid? Group of answer choices 10 units 12 units 5 units 3 units
Answer:
5 units or B
Step-by-step explanation:
Answer:
It is 5 units
Step-by-step explanation:
PLEASE HELP!! PERCENTS (:
Answer:
7 is the answer
Explanation:
because if you use a calculator, by doing 10% of 70 which equals to 7 which that is the answer.
Answer:
B: $63
Step-by-step explanation:
You can make an equation: 70(10%)
Which can be simplified into 70(0.1)
70×0.1=7
Since it was discounted, you subtract
$70 - $7 = $63
Tucker worked 5.5 hours on Saturday. He earns $7.20 per hour.
How much did he earn on Saturday?
Answer:
$39.6
Step-by-step explanation:
5.5 times 7.20 = $39.6
Nevaeh opened a savings account and deposited the money she received for her birthday. If she did not deposit any additional funds or make any withdrawals, her balance can be calculated using the functie
(0)
= 1,250(1.045)', where t represents the number of years since the initial deposit was made. What does 1, 250 represent in context?
Answer:
the initial amount of money deposited
Step-by-step explanation:
A birch tree is 9 feet tall and grows at a rate of 2 feet per year. The table shows the height h (in feet) of a willow tree after x years.
Answer:
No linear relationship between x and y
Step-by-step explanation:
change in y is constant, change in x is increasing not a constant. constant means it remains the same doesnt change.
What is the answer to number 2?
Answer:
5⁴
Step-by-step explanation:
→ Remember when dividing indices, minus them from each other
5⁶ ÷ 5² = 5 ⁶ ⁻ ² = 5⁴
(0,2), (3,3), (8,7), (2,2), (3,9)
Domain :
Range:
Answer:
Domain: ( 0, 3, 8, 2 )
Range : (2, 3, 7, 9)
Step-by-step explanation:
28.In the year 2006, the number of malaria patients admitted in the hospital of a state was 4375. Every year this number decreases by 8%. Find the number of patients in the year 2008?
Answer:number of patients in the year 2008 =3,703 Patients.
Step-by-step explanation:
Number of malaria patients admitted in the hospital of a state in 2006= 4375.
Number of malaria patients admitted in the hospital of a state in 2007 if there was Decrease by 8% in 2007
= 8% x 4375 =350
4375-350=4,025 patients
Number of malaria patients admitted in the hospital of a state in 2008 since there was Decrease by 8% in 2008
8% x 4,025.= 322
4,025-322=3,703 Patients.
12 is 15% of what number?
Answer:
80
Step-by-step explanation:
Go to go ogle
9/10 x 3 1/3 simplest form
Answer:
9/10x3 1/3 =3 or 10/3x9/10 =3
Step-by-step explanation:
You are helping your family run a store and decide to mark up the items you are selling for a profit by 35%. An item you want to sell in the store cost $4.38 from the warehouse. If you apply the 35% mark up, what will be the sale price of the item in your store. (Round to the nearest cent)
Answer: $6
Step-by-step explanation:
Cost of item = $4.38
Mark up percent = 35%
Sakes price will be the addition of the cost price and the mark up price. This will be;
= $4.38 + (35% × $4.38)
= $4.38 + (0.35 × $4.38)
= $4.38 + $1.533
= $5.913
= $6 approximately
A car was valued at $30,000 in the year 2009. By 2013, the car value had depreciated to $14,000. If the
car's value continues to drop by the same percentage, what will it be worth in 2020? Round to the
nearest dollar
Morgan pays $25 in monthly fees for her baseball team's uniforms and field rental. What kind of expense is the fee she pays? I don't know what the answer is
Answer:
Miscellaneous Expenses
Step-by-step explanation:
Given that Miscellaneous Expenses are a type of expense that defines the non-major expenditures which cannot be categorized as any of the manufacturing, selling, and administrative costs.
And according to Internal Revenue Service, expenses that do not conform to one of their tax categories are considered Miscellaneous Expenses, for example, clothing, and rent payments are a form of Miscellaneous Expenses.
4. Which of these is equal to sin(70°)?
a. cos(1109)
c. cos(20°)
b. cos(160)
d. cos(709)
help please and thank youuu
Answer:
16 = Y
Step-by-step explanation:
A jar contains 660 beans. Of them, 440 are kidney beans and the rest are cranberry
beans. What is the ratio of kidney beans to all beans?
Answer:
Step-by-step explanation:
kidney beans : all beans
440:660 (simplify by dividing each by gcf which is 2^2(5)11=220)
2:3
Answer:
440:660 OR Simplified 2:3
Step-by-step explanation:
You already had the two numbers for the ratio, they added the cranberry beans in the sentence like that to confuse you and draw you away from the real answer. All you needed to do was arrange the numbers into a ratio, and simplify.
These problems are meant to to be confusing, so to stay away from the confusing parts, just reread them and you'll get it correct 24/7!
Hope you get this right.
A cylinder has diameter of 6 cm and a volume of 36 pi cm 3 . Find it's height and radius in centimeters
Answer:
Radius is 3
Height is 4
Step-by-step explanation:
First you'll have to find the radius
6/2=3
Then, use the formula Base (PI*radius squared)* height
To find the base, you'll have to use the radius, 3, times it by itself, 3, and get 9.
3*3=9
Then, multiply 9 by 3.14, first three digits of pi, and get 28.26
9*3.14=28.26
28.26=base
Now, you'll have to find the height
Since you know what the volume is 36 pi 3
36*3.14=113.04 <--volume without pi
Then, divide 113.04 (volume) by 28.26 (base) and get 4 (height)
113.04/28.26=4
That's why the radius is 3 and the height is 4
Answer:
r=3
h=4
Step-by-step explanation:
Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
correspondence or alliance
Answer:
B
Step-by-step explanation:
what is the value of x.
Answer:
x=47
Step-by-step explanation:
180-121=59
180-(59+74)=47
Answer:
x = 47
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
121° is an exterior angle of the triangle, then
x + 74 = 121 ( subtract 74 from both sides )
x = 47
I NEED HELP WITH MATH CAN ANYONE HELP!!!
Answer:
ummmmmmmmmm I can try c:
Answer:
YES MAM , WHAT SEEMS TO BE THE PROBLEM < BECAUSE I DONT SEE ONE
Step-by-step explanation:
Plz help Me and thank you
Find the area of the composite shape below.
Answer: 1106.13 (2 decimal places)
Step-by-step explanation:
To work out the area of this composite shape you would have to put the two semi circles together to form a circle and work out the area of the circle (they have provided the radius which is 11in), then work out the area of the rectangle separately.
The formula for the area of a circle is πr^2 (pi x radius squared).
So when you put the numbers in the formula the area is πx11^2=380.1327111
Then to work out the area of the rectangle you would do base x height.
The height of the rectangle is the same as the diameter of the circle (the diameter is double the radius of a circle) which is 22in.
To find the area of the rectangle you do 22x33=726
So then to find the area of the whole shape you would have to add the area of the circle and the rectangle together.
726+380.1327111=1106.13 (2 decimal places).
Pls help me figure it out! (6th grade math)
Answer:
The answer to your question would be 18.
Step-by-Step explanation:
simplify, 3^4/9
3^4 divided by 3^2 = 3(^4-^2) = 3^2
9*2 = 18
I hope this helps! Have a great day! :]
You bought 3.5 pounds of turkey that costs $5.50 per pound. How much did you spend ?
Answer:
5.50 per pond
3.5 pound
3.5 × 5.50
$19.25