Trigonometric equations

5sinx = 3sinx + square root of 2

Answer:

13

Step-by-step explanation:

the sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]

where a is the first term and r the common ratio

here a = 6 , r = [tex]\frac{12}{6}[/tex] = 2 and [tex]S_{n}[/tex] = 49146 , then

[tex]\frac{6(2^{n}-1) }{2-1}[/tex] = 49146

6([tex]2^{n}[/tex] - 1) = 49146 ( divide both sides by 6 )

[tex]2^{n}[/tex] - 1 = 8191 ( add 1 to both sides )

[tex]2^{n}[/tex] = 8192 ( take log of both sides )

log [tex]2^{n}[/tex] = log 8192 , that is

n log 2 = log 8192 ( divide both sides by log 2 )

n = [tex]\frac{log8192}{log2}[/tex] = 13

[tex]\red{ \underline { \boxed{ \sf{Common \: Ratio,r = \frac{any\:observed\:term}{previous\:term}}}}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf Common \: Ratio,r = \frac{12}{6} [/tex]

[tex]\quad \boxed{\sf {Common \:Ratio,r = 2 }}[/tex]

Now,

[tex]\green{ \underline { \boxed{ \sf{Sum\: of \: G.P. \: to\: n\:term,S_n = \frac{a(r^n-1)}{r-1}}}}}[/tex]

where

Putting Values -

[tex]\begin{gathered}\\\implies\quad \sf 49146 = \frac{6(2^n-1)}{2-1} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf \frac{\cancel{49146}}{\cancel{6}} = \frac{2^n-1}{1} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 8191= \frac{2^n-1}{1} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n-1 =8191 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n =8191+1 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n =8192 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n =2^{13}\quad(8192= 2^{13}) \\\end{gathered} [/tex]

Comparing powers on both sides-

[tex]\begin{gathered}\\\implies\quad \boxed{\sf{ n = 13}}\\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, to get a sum of 49146 , 13 terms of this G.P. should be taken.

Answer:

solution 1= 40ml

solution 2= 160ml

Step-by-step explanation:

%alcohol= amount of alcohol/total solutionx100

0.52x200=104ml of alcohol present

0.2x L=0.2Lml of alcohol in solution one

0.6 x M=0.6Mml of alcohol in solution two

1st equation

0.2L+0.6M=104ml alcohol

times 10 to get whole

2L+6M=1040ml

2nd

same for this equation

10L+10M=2000ml

10L+10M=2000

2L+6M=1040

elimination method

=20L+20M=4000

-

=20L+60M=10400

-40M=-6400

M=160ml

2L+6 (160)=1040

2L=1040-960

2L=80

L=40ml

Answer:

3 1/5 = 16 / 5

1 1/2 = 3 / 2

16 / 5 * 3 / 2 = 48 / 10 = 24 / 5

The correct answer is 24 / 5 = 4 4 /5

(You can check on your calculator)

Answer:

8w² -8w +2

Step-by-step explanation:

(2w-1)(4w-2)

= 8w² -4w -4w + 2

= 8w² -8w +2

Answer:

A leprechaun (Irish: leipreachán/luchorpán) is a diminutive supernatural being in Irish folklore, classed by some as a type of solitary fairy. They are usually depicted as little bearded men, wearing a coat and hat, who partake in mischief. In later times, they have been depicted as shoe-makers who have a hidden pot of gold at the end of the rainbow.

Answer:

Step-by-step explanation:

Answer:

z = 58

Step-by-step explanation:

Since SU is a midsegment of QRT, the length of SU is one-half the length of RQ.

[tex] \frac{1}{2} (z - 40) = z - 49[/tex]

[tex]z - 40 = 2z - 98[/tex]

[tex]z = 58[/tex]

Answer:

Step-by-step explanation:

you will read the directions 2x before solving the problem then solve the problem

Answer:

624

Step-by-step explanation:

Hello!

This equation is written in Point-Slope Form (y-y₁=m(x-x₁)

Where

y₁=y-coordinate of the point

m=slope

x₁=x-coordinate of the point

In this case, the slope is

[tex]\boxed{\boxed{\bold{\frac{1}{2}}}}[/tex]

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

Answer:

C) 1/2

Step-by-step explanation:

woof woof

Answer:

The answer would be A.

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

Billy has 55 stamps and his brother Tommy has 73. Add 73 and 55 together. 55+73=128

Answer:

well i wrote it in paper nothing to explain it's ez

f(x) = x² + 3x - 2

f(-2) = (-2)² + 3*(2) - 2 = 4 - 6 - 2 = - 4

[tex]|-16-x|=0\\\\\implies -16-x = 0\\\\\implies x = -16[/tex]

Answer:

cos4(x)+2cos2(x)sin2(x)+sin4(x)

Step-by-step explanation:

Answer:

895.05

Step-by-step explanation:

5% of 663 is 33.15, so times 33.15 by the 7 months and the answer to that is 232.05 then add that to the current battier life.

The answer is 895.05

Answer:

d

Step-by-step explanation:

area=length ×width

156=13×w

w=156/13=?

P=2(l+w)

P=2(13+w)

[tex] \cos(60) = \frac{12}{x} \\ [/tex]

[tex] \frac{1}{2} = \frac{12}{x} \\ [/tex]

[tex]x = 24[/tex]

_____________________________________________

[tex] \sin(60) = \frac{y}{x} \\ [/tex]

[tex] \frac{ \sqrt{3} }{2} = \frac{y}{24} \\ [/tex]

[tex]y = 12 \sqrt{3} [/tex]

Answer: 1/6

Step-by-step explanation: There are 4 primes. So the probability for the first draw is 4/9. Since the card is not replaced, the second probability is 3/8. 3/8 * 4/9 is 12/72, which simplifies into 1/6.

Answer:

Fraction answer (about):
1 1/4

Decimal answer (about):
1.24

Step-by-step explanation:

7 2/3 - 6 3/7 =
1.2380952381

1.2380952381 = about 1.24

The difference between 7 2/3 and 6 3/7 = 1.24
1.24 in fraction form is about 1 1/4

Have a great rest of your day
#TheWizzer

Answer:26/21

Step-by-step explanation:

Answer:

82 ft²

Step-by-step explanation:

Answer:

b.

Step-by-step explanation: its 50 shares the to straiges you should use is multiplying or adding i used both bt its b.

Answer:

▲ Base and height. This is the basic volume equation of a triangular prism: Volume = 0.5 * Base * Height * Length. ...

◣ Right triangle. Probably the most popular type of prism! ...

▲ 3 sides. Volume = 0.25 * √( (a+b+c) * (-a+b+c) * (a-b+c) * (a+b-c) ) * Length.

Step-by-step explanation:

Answer:

14*2

Step-by-step explanation:

8 x {22 x [15 + (14 x 2)]}

With multiple parentheses work from the inside out

The inner most parentheses are

14*2

Answer:

Point A

Step-by-step explanation:

It can be seen from the image that the chosen value for N is greater than zero but less than 1, i.e,

[tex]0 < n < 1[/tex]

The square of such numbers will always result values less than N since they're decimals with zeroes on the whole number parts.

Hence, the value for N squared will be in the region of Point A.

Answer:

4

Step-by-step explanation:

3x = 5:

x = 1 ⅔

5x + 7 = 3

5x = 3- 7

5x = -4

x = -⅘

4x = 9x

9x - 4x = 0

5x = 0

x = 0 / 5

x = 0

x = x - 2:

x -x = -2

0 = -2?

Answer:

4

Step-by-step explanation:

Its because x=x-2 =-2 subtract x from both sides and you get 0 so theres no solution and you get -2

Answer:

You're answer is D.18b

Hey there!

The product of a number and 18 means you multiply that number times 18; the result is called the product.

When we multiply a number times a variable, we always write the number before the variable.

For example, we multiply 4 times d, and the result is 4d.

Let's check the options and see if we can spot something like "5a"

The first option:  we multiply 18 times the difference of b and 18.

The second option: we add 18 and b

The third option: we divide 18 by b

The fourth option: we multiply 18 times b (That's the right option! We did it  :)

Hence, the answer is

[tex]\boxed{\boxed{\bold{18b}}}[/tex]

Hope everything is clear.

Let me know if you have any other questions; if so, please comment.

#LearningDoesn'tEnd

#LearningIsFun

[tex]\rule{200}{2}[/tex]

Let x be the original price of the object.

After the 40% discount, the price of the object now becomes;

x-0.4x=0.6x

0.6x is our new price after the first discount.

Now if we want to find the price after the second discount, (5%)

That would come off to be;

0.6x-0.6(0.05)x=0.6x-0.03x=0.57x

Our last price is 0.57x

If you notice, there was a 43% discount in total, as it goes to 57% of its original price.

This is very non intuitive for some people, as they may think there will be a 45% discount.

Answer:

Step-by-step explanation: 1.587401052

Answer:

8

Step-by-step explanation:

this means

[tex] \sqrt{ {4}^{3} } [/tex]

4³ = 4×4×4 = 64

the square root of 64 is 8.