if sin (α+β) = 1, sin (α-β) = 1/2 then tan (α+2β) tan(2α+β) = a. 1 b.-1 c.0 d. none

Answers

Answer 1

Answer: $\alpha;\ \beta\in(0^o;\ 90^o)\n\nsin(\alpha+\beta)=1\to sin(\alpha+\beta)=sin90^o\to\alpha+\beta=90^o\n\nsin(\alpha-\beta)=(1)/(2)\to sin(\alpha-\beta)=sin30^o\to\alpha-\beta=30^o\n\n +\left\{\begin{array}{ccc}\alpha+\beta=90^o\n\alpha-\beta=30^o\end{array}\right\n---------\n.\ \ \ \ \ \ \ 2\alpha=120^o\ \ \ /:2\n.\ \ \ \ \ \ \ \ \ \alpha=60^o\n\n60^o+\beta=90^o\ \ \ /-60^o\n\beta=90^o-60^o\n\beta=30^o$

$tan(\alpha+2\beta)\cdot tan(2\alpha+\beta)\n\n=tan(60^o+2\cdot30^o)\cdot tan(2\cdot60^o+30^o)\n\n=tan120^o\cdot tan150^o=tan(180^o-60^o)\cdot tan(180^o-30^o)\n\n=-tan60^0\cdot(-tan30^o)=-\sqrt3\cdot(-(\sqrt3)/(3))=(3)/(3)=1\n\n\nAnswer:A$

Related Questions

If 5 is increased to 8 , the increase is what percent of the original number?
Two planes leave an airport at noon. If the eastbound plane flies at 560 mph and the westbound plane flies at 500 mph, at what time will they be 2,000 miles apart? Round your answer to the nearest minute.
Find the value of the variable and YZ if Y is between X and Z XY=6b, YZ=8b, XZ=175
The regular price of an item is $65. The item is on sale with a discount of $8.What is the discount rate
What is the basic unit of weight in the metric system

write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 40 to 56

Answers

Answer:

5/7

Step-by-step explanation:

A common factor of 8 can be canceled from numerator and denominator.

40/56 = (5·8)/(7·8) = (5/7)·(8/8) = (5/7)·1 = 5/7

_____

Since you know your multiplication tables, you know that 40 and 56 are both multiples of 8.

If you don't know your multiplication tables, you can find the greatest common divisor (GCD) of the two numbers and divide each by that. The GCD can be found using Euclid's algorithm. For that, you divide the larger by the smaller and use the remainder as the new smaller number. The original smaller number is now the larger number. For these numbers, that looks like ...

56 ÷ 40 = 1 r 16

40 ÷ 16 = 2 r 8

16 ÷ 8 = 2 r 0 . . . . . the zero remainder signals that the divisor (8) is the GCD

Now, your fraction is ...

(40/8) / (56/8) = 5/7

Answer:

5/7

Step-by-step explanation:

40/56 both divided by 8 and that is how to get your answer because you can not simplify further

County X has a population density of 250 people per square mile. The totalpopulation of the county is 150,000. Which geometric model could be the shape of
county X?
A a parallelogram with a base of 25 miles and a height of 25 miles
B a rectangle that is 15 miles long and 45 miles wide
C a right triangle with a leg that is 30 miles long and a hypotenuse that is
50 miles long
D a trapezoid with base lengths of 10 miles and 30 miles and a height of
25 miles

Answers

Answer:

Option C. is the correct option.

Step-by-step explanation:

County X has a population density of 250 people per square mile.

Total population of the county is 150000.

Total area which represents the population = $\frac{\text{Total population}}{\text{Population density}}$ = $(150000)/(250)=600$ square mile.

So geometric model which has the same area as 600 square miles will be the answer.

A). Area of a parallelogram = Base × height

= 25×25

= 625 square miles

which is not equal to 600 square miles so it's not the correct option.

B). Area of a rectangle = Length×width

= 15×45 = 675 square miles ≠ 600 square miles

Therefore, not the correct option.

C). Area of a right triangle = $(1)/(2)(Base)(height)$

Since length of hypotenuse is given so we will find the length of height.

Height = √[(Hypotenuse)²- (Base)²] = $\sqrt{50^(2)-30^(2)}$

= $√(2500-900)$

= $√(1600)$

= 40 miles

So area of the right triangle = $(1)/(2)(40)(30)$

= $(1200)/(2)$

= 600 square miles

Which matches the area of County X, so it's a correct option.

D). area of trapezoid = $(1)/(2)[(base1 + base2)](height)$

= $(1)/(2)(10+30)(25)$

= $(1)/(2)(40)(25)$

= 20×25

= 500 square miles ≠ 600 miles

Therefore, this option is not correct.

C. with a 150,000 person population at 250 persons per square mile the country would be 600 square miles. The last leg would equal 40 miles and therefore making the area equal 600 square miles.

Admission to a baseball game is $4.50 for general admission and $6.00 for reserved seats. The receipts were $4210.50 for 845 paid admissions. how many of each ticket were sold?

Answers

Let's solve this problem using a system of equations. Let's assume the number of general admission tickets sold is represented by 'x' and the number of reserved seats sold is represented by 'y'.

We know that the total number of paid admissions is 845, so we can write the equation:

x + y = 845 (Equation 1)

We also know that the total receipts from ticket sales is $4210.50. Since the price for general admission is $4.50 and the price for reserved seats is $6.00, we can write the equation:

4.50x + 6.00y = 4210.50 (Equation 2)

Now, we can solve this system of equations to find the values of 'x' and 'y'.

From Equation 1, we can rewrite it as:

x = 845 - y

Substituting this value of 'x' into Equation 2, we get:

4.50(845 - y) + 6.00y = 4210.50

Expanding and simplifying:

3802.50 - 4.50y + 6.00y = 4210.50

Combine like terms:

1.50y = 408.00

Divide both sides by 1.50:

y = 272

Substituting this value of 'y' back into Equation 1, we can solve for 'x':

x + 272 = 845

x = 573

Therefore, 573 general admission tickets and 272 reserved seats were sold.

Find the value of x.
The polygons are similar, but not necessarily drawn to scale.

Answers

Answer:

$x=10 units$

Step-by-step explanation:

Given: The polygons ABCD and JKLM are similar.

To find: The value of x.

Solution: Since, the given polygons are similar, therefore using the similarity condition, we have

$(AD)/(JM)=(CD)/(LM)$

Substituting the given values, we get

$(12)/(40)=(3)/(x)$

On cross multiplying, we get

$(3*40)/(12)=x$

$x=10 units$

Therefore, the value of x is 10 units.

$(12)/(40) = (3)/(x)$

Cross multiply:
$12x = 3 * 40$

Evaluate RHS:
$12x = 120$

Divide both sides by 12:
$x = 10$

Answer this and EXPLAIN why and HOW you got your answer!

SHOW YOUR WORK.......

Answers

You will need to set up your table of values for each person.

Let x represent the months, and y for the amount of money.

For Carissa: For Louann:
x = y x = y
-- -- -- --
0 $250     0 $1230
1 $330    1 $1170
2 $410 2 $1110
3 $490     3 $1050
4 $570 4 $990
5 $650   5 $930
6 $730   6 $870
7 $810 7 $810

You could also do the equation:
80x + 250 = -60x + 1250
where you will get x=7.
Then substitute 7 to the x's in the equation which will give you $810 for each.

The answer is: It will take 7 months. Then, they will both have $810 in their accounts.

This exercise is trying to get you to write an equation
that describes what's going on.

Carissa has $250 today, and she adds $80 to it each month.
In 'm' months from now, she'll have 80m more than $250.

C (for Carissa) = 250 + 80m

Louann has $1230 today, and she takes out $60 each month.
In 'm' months from now, she'll have 60m less than $1230.

   L (for Louann) = 1230 - 60m

Carissa has less money today, but it's growing $80 every month.
Louann has more money today, but it's losing $60 every month.
Eventually, they'll both have the same amount.
The question is: When and how much ?

Well, when they both have the same amount, then C = L .

   250 + 80m = 1230 - 60m

That's the end of the hard part of this problem ... writing
the equation. The rest is easy, and I'm sure you'd have
no trouble solving it. But since I'm on a roll, and I'm
going to take your 5 points, I might as well keep going:

   250 + 80m = 1230 - 60m

Subtract 250 from each side: 80m = 980 - 60m

Add 60m to each side: 140m = 980

Divide each side by 140 : m = 7

This is telling us that after 7 months, Carissa and Louann will both
have the same amount of money in their accounts.

The problem also asks us how much that is. So let's find the
amount for both of them, just to check our work and make sure
they're both the same:

Carissa: 250 today + (7 months x $80/month) = 250+560 = $810 .

Louann: 1230 today - (7 months x $60/month) = 1230-420 = $810

   yay !

What is multiplication properties. Example a number line that goes from 0-27. Using numbers 6,7,8 and 9.

Answers

They are the commutative, associative, multiplicative identity and distributive properties.

Commutative property: For example 6 * 7 = 7 * 6;

Associative Property: For example (7 * 8) * 9 = 7 * (8 * 9);

Multiplicative Identity Property: For example 6 * 1 = 6 or, 1 * 6 = 6;

Distributive property: For example 6 * ( 7 + 8) = 6 * 7 + 6 * 8 or, ( 7 + 8) * 6 = 7 * 6 + 8 * 6.

Other Questions

Multiply. 3√2⋅2√8⋅√3⋅√6 explanation would be lit

Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?-5-1/2 = -3 -10-2/2 = -4 1+5/2 = 3 2+10/2 = 4

A bag of marbles contains 16 blue, 8 green, 9 red, 12 yellow and 5 black marbles. What is the probability of drawing a green marble?

Kylie measured a swimming pool and made a scale drawing. She used the scale 1 inch = 1 foot. What is the scale factor of the drawing?Simplify your answer and write it as a fraction.