Answers
As we know an identity that ;
[tex]{\boxed{\bf{\cos{(2\theta)}=2\cos^{2}(\theta)-1}}}[/tex]Setting, [tex]{\bf{{\theta}=\footnotesize \dfrac{\pi}{8}}}[/tex] will give us ;
[tex]{:\implies \quad \sf \cos \left(2\times \dfrac{\pi}{8}\right)=2\cos^{2}\left(\dfrac{\pi}{8}\right)-1}[/tex]
[tex]{:\implies \quad \sf 2\cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1}{\sqrt{2}}+1}[/tex]
[tex]{:\implies \quad \sf 2\cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{2\sqrt{2}}}[/tex]
Rationalizing the denominator of RHS, will yield ;
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{1+\sqrt{2}}{2\sqrt{2}}\times \dfrac{2\sqrt{2}}{2\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{2\sqrt{2}+4}{8}}[/tex]
[tex]{:\implies \quad \sf \cos^{2}\left(\dfrac{\pi}{8}\right)=\dfrac{2\sqrt{2}+4}{8}}[/tex]
[tex]{:\implies \quad \sf \cos \left(\dfrac{\pi}{8}\right)=\pm \sqrt{\dfrac{2\sqrt{2}+4}{8}}}[/tex]
Now, as we know that ;
[tex]{\boxed{\bf{\sin (2\theta)=2\sin (\theta)\cos (\theta)}}}[/tex]Now, setting the same [tex]{\bf{{\theta}=\footnotesize \dfrac{\pi}{8}}}[/tex]
[tex]{:\implies \quad \sf 2\sin \left(\dfrac{\pi}{8}\right)\cos \left(\dfrac{\pi}{8}\right)=\sin \left(2\times \dfrac{\pi}{8}\right)}[/tex]
[tex]{:\implies \quad \sf 2\sin \left(\dfrac{\pi}{8}\right)\cos \left(\dfrac{\pi}{8}\right)=\dfrac{1}{\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)\left(\pm \sqrt{\dfrac{2\sqrt{2}+4}{8}}\right)=\dfrac{1}{2\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)=\dfrac{\sqrt{8}}{2\sqrt{2}(\pm \sqrt{2\sqrt{2}+4})}}[/tex]
[tex]{:\implies \quad \sf \sin \left(\dfrac{\pi}{8}\right)=\pm \dfrac{1}{\sqrt{2\sqrt{2}+4}}}[/tex]
This is the required answer
Related Questions
Please help me with this , I hope it's easier.
Answers
Hi! I hope you're enjoying your day!
Let's add the following polynomials.
How to add them? Just combine like terms. :)
[tex]\bold{2x^2-10x+1 ~and~x^2+15x-8}[/tex]
[tex]\bold{2x^2+x^2-10x+15x+1-8}[/tex]
Hence, the answer is
[tex]\boxed{\boxed{\bold{3x^2+5x-7}}}[/tex]
[tex]\rule{250}{2}[/tex]
[tex]\bold{2x^3-3x^2+5\;and\;5x^2-3x^3+7}}}\\[/tex]
Combine Like terms:
[tex]\bold{2x^3-3x^3-3x^2+5x^2+5+7}[/tex]
Hence, the answer is
[tex]\boxed{\boxed{\bold{-x^3+2x^2+12}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
Evaluate
x(y+3)
_____
(3+y)z
for x = 12, y = 1, and z = 6
A.5
B.6
C.8
D.2
Answers
Answer:
12(1+3)
6(3+1)
12(4)
6(4)
48
24
answer = 2
If x – 4y = 6 is a true equation, what would be the value of – 4y + x?
Answers
Answer:
6
Step-by-step explanation:
it's basically the same equation just different arrangement
riders must be 48 inches tall to get on a new ride at an amusement park. there are 12 inches in 1 foot. some amusement parks use meters for the minimum height of riders. about how many meters are equivalent to 48 inches?
Answers
Answer: Around 1.2 meters
Step-by-step explanation:
12——4
24——8
36——12
48——
What number complete the sequence
Answers
Answer:
I think it's 16
Step-by-step explanation:
your adding 4
Reason: every time you add 12 on the left you add 4 on the right
What is the answer to
Solve n/4 -8 =-6
Answers
1. Find a markdown of 1/9 on $450?
2. 15 is what percent of 60?
3. 124% of 10 represents a certain number. What is that number?
Answers
Step-by-step explanation:
1. 1/9 of 450
of is multiply
1/9 × 450
= ???
2. 15/60 = decimal number
change number to percentage = ???
I dont know what 3 is
put answers to 1 and 2 in comments i will mark if u don't understand comment
please mark brainiest
Kelsey had 8 entries in her science journal. Last week, she wrote x more entries. How many entries are in her science journal now?
Answers
Answer:
Kelsey has 8 plus more entries
8 + x
Identify the quadratic function(s). (Select all that apply). y(y + 4) - y = 6 (3x + 2) + (6x - 1) = 0 4b(b) = 0 3a - 7 = 2(7a - 3)
Answers
Answer:
[A] y(y + 4) - y = 6
[C] 4 b (b)=0
Step-by-step explanation:
First let know what is a quadratic functions(s):
A function is called Quadratic if it consist of only one variable, maximum of three terms, and highest degree of the variable in that Polynomial is 2.
Now let's go through the answer choices:
[A]
y *(y+4) - y =6
y² + 4 y - y -6=0
y²+3 y -6=0
Thus, This is Quadratic Function.
[B]
3 x +2 + 6 x -1=0
9 x-1=0
Thus, This is not Quadratic Function
[C]
4 b*(b)=0
4 b²=0
Thus, This is Quadratic Function.
[D]
3 a- 7 =2 * (7 a-3)
3 a - 7=14 a - 6
3 a - 14 a = 7 -6
-11 a =1
Thus, This is not a Quadratic Function.
Hence, [A] and [C] are quadratic functions.
[RevyBreeze]
1. A room is 5 m by 3m. What is the area of the room?
Answers
Answer:
15m2 is the answer my friend.....
Answer:
Step-by-step explanation:
All you would do is multiply the length and the width, so you would multiply 5m by 3m and get 15m as your answer.
Which of the following statements are true about the equation below?
22 - 61 + 2 = 0
The solutions are = -3 17
The extreme value is at the point (3,-7).
o o o o o
The graph of the quadratic equation has a maximum value.
The graph of the quadratic equation has a minimum value.
The solutions are = 3 + 17
The extreme value is at the point (7,-3).
Answers
Answer:
Option 1, 2, 5 are the correct answer.
Lily invested $60,000 in an account paying an interest rate of 6 1 2 6 2 1 % compounded continuously. Lydia invested $60,000 in an account paying an interest rate of 6 1 8 6 8 1 % compounded monthly. To the nearest hundredth of a year, how much longer would it take for Lydia's money to triple than for Lily's money to triple?
Answers
Using interest equations, it is found that it will take 1.08 year more for Lydia's money to triple than for Lily's.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.What is the amount in continuous compounding?It is given by:
[tex]A(t) = Pe^{rt}[/tex]
For Lily, the parameters are as follows: r = 0.065, with continuous compounding. The time to triple is t for which A(t) = 3P, hence:
[tex]A(t) = Pe^{rt}[/tex]
[tex]3P = Pe^{0.065t}[/tex]
[tex]e^{0.065t} = 3[/tex]
[tex]\ln{e^{0.065t}} = \ln{3}[/tex]
[tex]0.065t = \ln{3}[/tex]
[tex]t = \frac{\ln{3}}{0.065}[/tex]
[tex]t = 16.90[/tex].
For Lydia, using compound interest, the parameters are: r = 0.06125, n = 12, hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]3P = P\left(1 + \frac{0.06125}{12}\right)^{12t}[/tex]
[tex](1.00510416667)^{12t} = 3[/tex]
[tex]\log{(1.00510416667)^{12t}} = \log{3}[/tex]
[tex]12t\log{(1.00510416667)} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{12\log{(1.00510416667)}}[/tex]
[tex]t = 17.98[/tex]
17.98 - 16.9 = 1.08, hence, it will take 1.08 year more for Lydia's money to triple than for Lily's.
More can be learned about interest equations at https://brainly.com/question/25781328
Find the interest on a $6000 loan at 4% for 5 years.
Answers
Answer:
6000/1+0.04 power of 5
= 32,269.44
How do I solve 5/9x+ 6=10?
Answers
Answer:
x = 36/5, 7 1/5, or 7.2 (all same, just in different form)
Step-by-step explanation:
Step 1: Subtract 6 from both sides.
[tex]\frac{5}{9}x+6-6=10-6[/tex] [tex]\frac{5}{9}x=4[/tex]Step 2: Multiply both sides by 9/5.
[tex]\frac{5}{9}x*\frac{9}{5} =4*\frac{9}{5}[/tex] x = 36/5, 7 1/5, or 7.2Have a lovely rest of your day/night, and good luck with your assignments! ♡
Please help with this:) 20 points!
Answers
Step-by-step explanation:
Here,
[tex]\angle{ADB}[/tex] = [tex]\angle{BDC}[/tex]
⇒4x-23° = 3x-5°
⇒4x-3x=(-5°)+23°
⇒x=18°
.°. x = 18°
Answer:
x = 18°
Step-by-step explanation:
Consider a Poisson distribution with a mean of two occurrences per time period. a. Which of the following is the appropriate Poisson probability function for one time period? 1 2 3 - Select your answer - b. What is the expected number of occurrences in three time periods? c. Select the appropriate Poisson probability function to determine the probability of occurrences in three time periods. 1 2 3 - Select your answer - d. Compute the probability of two occurrences in one time period (to 4 decimals). e. Compute the probability of six occurrences in three time periods (to 4 decimals). f. Compute the probability of five occurrences in two time periods (to 4 decimals)
Answers
Answer:
F(k) = 2k e-2 / k!
Mean =µ = 2 x 3 = 6
f(k) = 6k e-6 / k!
F(2) = 22 e-2 / 2!
= 0.2707
F(6) = 66 e-6 / 6!
= 0.1606
f(5) = 45 e-4 / 5!
= 0.1563
Step-by-step explanation:
Solution:
Given:
Mean = µ = 2 per time period
Poisson probability:
F(k) = µk e-µ / k!
(a) Poisson probability for one time period.
Put µ = 2 in formula, we get:
F(k) = 2k e-2 / k!
(b) Expected number of occurrence in three time period.
Mean of one time period is multiply with number of time period.
Mean =µ = 2 x 3 = 6
(c) Probability of occurrence in three time period.
Put the value of µ = 6 in the given formula, we get:
f(k) = 6k e-6 / k!
(d) Probability of two occurrences in one time period.
Put k = 2 in given formula:
F(2) = 22 e-2 / 2!
= 0.2707
(e) Probability of six occurrences in three time period.
Put k = 6, in given formula, we get:
F(6) = 66 e-6 / 6!
= 0.1606
(f) Probability of five occurrences in two time period.
Mean of one time period is multiply by the number of time periods.
µ = 2 x 2 = 4
put k = 5 and µ = 4 in formula, we get:
f(5) = 45 e-4 / 5!
= 0.1563
One of the legs of a right triangle measures 4 cm and the other leg measures 4 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answers
Answer:
4[tex]\sqrt{2\\[/tex] or 5.7
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
4[tex]\sqrt{2\\[/tex] or 5.7
what is 333333,3333333333,000 x 2,000,000,000,000,000,000
Answers
Answer:
[tex]6666666666666666000000000000000000000[/tex]
Answer:
66666666666666666666666666666666
Step-by-step explanation:
Algebraically, an ordered pair is a solution to a system of two linear inequalities if and only if it __________.
A.
makes both the top and bottom inequalities false
B.
makes the top inequality true and the bottom inequality false
C.
makes the top inequality false and the bottom inequality true
D.
makes both the top and bottom inequalities true
Answers
Answer:
D. Makes both the top and bottom inequalities true
Step-by-step explanation:
System of linear inequalities
Consider these two inequalities:
2x+3y > 20
3x-2y > 5
The solution of the system consists of all the ordered pairs (x,y) that satisfy both inequalities. The ordered pair (3,5) makes the first inequality true because
2*3+3*5=21 and it's effectively greater than 20.
But that pair makes the second inequality false, since
3*3-2*5=-1 is not greater than 5.
Thus, the pair (3,5) is not part of the solution.
If we test the pair (6,2), we'll check both inequalities are true, thus (6,2) is part of the solution.
Thus, the correct answer to the question is
D. Makes both the top and bottom inequalities true
what is the answer to 15x+6y
Answers
Answer:
x = -0.4y
Step-by-step explanation:
Simplifying
15x + 6y = 0
Solving
15x + 6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6y' to each side of the equation.
15x + 6y + -6y = 0 + -6y
Combine like terms: 6y + -6y = 0
15x + 0 = 0 + -6y
15x = 0 + -6y
Remove the zero:
15x = -6y
Divide each side by '15'.
x = -0.4y
What is the answer to 5+{2×[(5−1)+6]}÷4 with no frations
Answers
Answer:
15.5
Step-by-step explanation:
5+2x5-1+6/4=15.5
using a calculator this answer is correct.
find the rate of change from the equation y=-7/8x+3
Answers
Answer:
-7/8
Step-by-step explanation:
rate of change is the same as slope so -7/8
Answer:
-7/8Step-by-step explanation:
find the rate of change from the equation:
y = -7/8x + 3
use the formula: y = mx + b
where:
y = how far up the line goes
m = slope
x = how far along
b = Y-intercept
so the rate of change is the same as the slope
therefore, the slope = -7/8
I need HELP please solve the blank space. It says that it isn’t 100 so I need HELP!!
Answers
yeah 5 is 5% of 100 i dunno bro
if anything try .25
sorry
Which of the following is a correct interpretation of the expression -4- (-7)?
Choose 1 answer:
А
The number that is 4 to the left of - 7 on the number line
B
The number that is 4 to the right of - 7 on the number line
The number that is 7 to the left of -4 on the number line
D
The number that is 7 to the right of -4 on the number line
Answers
Answer:
D the number 7 to the right of -4 on the number line
Bill has a bag of 24 marbles. 6 are blue, 12 are red, 3 are black and 3
are green. What are the percentages of each colour?
Answers
Answer:
25%, 50%, 12.5%,12.5%
Step-by-step explanation:
6/24
3/24
12/24
3/24
Write the equation of the line that passes through the points (3,5) and
(-5,0). Put your answer in fully reduced point-slope form, unless it is a
vertical or horizontal line.
Answers
Answer:
5/8
Step-by-step explanation:
solution
x1,y1= 3 , 5
x2,y2= -5,0
slope= y2-y1÷x2-x1
can someone answer these questions?
Answers
Answer:
The first question I got 1056.25
Step-by-step explanation:
What is the scale factor of the reduction?
GIVEING BRAINLY 3
Answers
Scale factor
[tex]\\ \rm\rightarrowtail k=\dfrac{y}{x}[/tex]
[tex]\\ \rm\rightarrowtail k=\dfrac{0.5}{2.5}[/tex]
[tex]\\ \rm\rightarrowtail k=\dfrac{1}{5}[/tex]
Which Box-and-Whisker Plot below correctly illustrates the data shown below? {22, 24, 24, 25, 26, 26, 27, 28, 28, 30} A. B. C. D.
Answers
b i your answer i know it
Step-by-step explanation:
The 3rd Box-and-Whisker Plot correctly depicts the data given.
What is a expression? What is a mathematical equation? What is a box and whisker plot?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles.We have the Box-and-Whisker Plots for the data -
{22, 24, 24, 25, 26, 26, 27, 28, 28, 30} shown in the image.
We can identify the boxplot by the median calculation easily. We can find the median of the given data set as -
[M] = (26 + 26)/2 = (2 x 26)/2 = 26
Therefore, the 3rd Box-and-Whisker Plot correctly depicts the data given.
To solve more questions on Box-and-Whisker Plots, visit the link below
https://brainly.com/question/26963285
#SPJ2
‼️‼️3) Brad was going to make
$53.85 a day for 5 days in his
new job. He figured that he
would make about $350.00. Is
this a reasonable answer?
Explain why or why not.‼️