Answers
Answer:
see explanation
Step-by-step explanation:
Using the identity
cos²A - sin²B = cos(A + B) . cos(A - B)
Here A = [tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] , B = [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex]
Consider the left side
cos²([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] ) - sin²( [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex] )
= cos([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] + [tex]\frac{\pi }{8}[/tex] - [tex]\frac{A}{2}[/tex] ) × cos([tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] - [tex]\frac{\pi }{8}[/tex] + [tex]\frac{A}{2}[/tex] )
= cos ([tex]\frac{\pi }{4}[/tex] ) × cos ( A)
= [tex]\frac{1}{\sqrt{2} }[/tex] cosA
= right side , thus proven
Related Questions
hasil dari 64^5/6 + 27^2/3 - 81^3/4 adalah
tolong bantuannya kakak kakak
Answers
Answer:
14
Step-by-step explanation:
Given the indicinal expression 64^5/6 + 27^2/3 - 81^3/4
According to indices;
[tex]a^{m/n} = (\sqrt[n]{a}) ^m[/tex]
Applying this to the question
[tex]64^{5/6} \\= (\sqrt[6]{64}) ^5\\= 2^5= 32[/tex]
Similarly
[tex]27^{2/3}\\= (\sqrt[3]{27}) ^2\\= 3^2\\= 9\\[/tex]
Also;
[tex]81^{3/4}\\= (\sqrt[4]{81}) ^3\\= 3^3\\= 27[/tex]
Substitute inti the original equation
64^5/6 + 27^2/3 - 81^3/4
= 32 + 9- 27
= 41 - 27
= 14
Hence the required answer is 14
The Johnson family pays 1,783 per month for rent. If the cost of their rent remains the same, how much will they pay for rent over 15 years?
Answers
Answer:
1 year= 12 months
1 months rent=1783
1783x12=21396
15 years = 180 months
the equation would be
1783x180=320940
or
21396x15= 320940
help asap pls, thank u
Answers
Answer:
1243.4 [tex]cm^{3}[/tex]
Step-by-step explanation:
if the endpoints of a circles are at (-5, 6) and (3, -7), what is the length of the radius rounded to the nearest tenth?
Answers
Answer:
7.632169 units
Step-by-step explanation:
7.6 is radius Step-by-step explanation:
y+8 can be translated as "the
of a number and elght."
quotient
product
difference
sum
Answers
hope this helped
I hope you get an a
Nieves y Ana juegan tres partidas partidas. Nieves tenía 10 cromos y Ana 80. En la primera partida ganó Nieves y elevó sus cromos al cuadrado, en la segunda perdió el cubo de 3, y en la tercera perdió el cuadrado de 4. ¿Cuántos cromos les quedan a Ana y a Nieves?¿Quién ha ganado?
Answers
Answer:
A Nieves le quedan 57 cromos y a Ana 33.
Nieves ha ganado 47 cromos
Step-by-step explanation:
Para la primera partida, el cuadrado de los cromos de Nieves es de 100.
El cubo de 3 es 27. Nieves queda con 100-27 = 73 cromos
El cuadrado de 4 es 16. Nieves queda con 73-16 = 57 cromos
A Nieves le quedan 57 cromos
A Ana 90-57 = 33 cromos
Así, Nieves ha ganado 57-10 = 47 cromos
Consider the function f(x)=x^2
What effect does adding 2 to the input have on the graph of the function?
(a) shifts the graph right 2
(b) shifts the graph up 2
(c) shifts the graph down 2
(d) compresses the graph horizontally by 2
(e) stretches the graph vertically by 2
(f) shifts the graph left 2
Answers
Answer:
b
Step-by-step explanation:
if the 2 is like this (x+2) it would move to the left but if its like this x+2 it would move up
Solve for x.
9 - 3x = 1 + x
Answers
Answer:
x=2
Step-by-step explanation:
9
−
3
=
1
+
{\color{#c92786}{9-3x}}=1+x
9−3x=1+x
−
3
+
9
=
1
+
Answer:
2
Step-by-step explanation:
9-3x=1+x
9-3x-x=1
9-4x=1
4x=9-1
4x=8
x=8/4
x=2
OH LORD THIS IS A NIGHTMARE FOR ME
Answers
Answer:
∠1 = 150°
Step-by-step explanation:
supplementary angle to angle 1 = 180° - 100° - 50° = 30°
∠1 = 180° - 30° = 150°
Let f (x) = -1/2(x + 2)+ 5
-3 to x=1?
What is the average rate of change for the quadratic function from x=-3 to x=1
Answers
Answer:
Rate of change = -1
Step-by-step explanation:
Given:
f(x) = -½(x + 2)² + 5
Required:
Average rate of change from x = -3 to x = 1
Solution:
Rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
Where,
a = -3,
f(a) = f(-3) = -½(-3 + 2)² + 5 = -½(-1)² + 5 = 4.5
b = 1,
f(b) = f(1) = -½(1 + 2)² + 5 = -½(9) + 5 = 0.5
Plug in the values into the formula:
Rate of change = [tex] \frac{0.5 - 4.5}{1 - (-3)} [/tex]
Rate of change = [tex] \frac{-4}{4} [/tex]
Rate of change = -1
can someone help?? i’ll mark brainlist
Answers
Answer:
G. y = -[tex]\frac{1}{9}[/tex](x - 2)² -3
Step-by-step explanation:
There's this website called Desmos it has graphing calculators that will help you on these type of questions. This is not a random website so please trust me.
Math
Can anyone help me with this question? I can’t find the answer for the ? Box
The question(s) are :
-4 - ? = -7
? - (-3) = 5
Answers
All we need to do is get the ? by itself in both equations.
-4 - ? = - 7
-? = -7 + 4
-? = -3
? = 3
? - ( -3) = 5
? + 3 = 5
? = 5 - 3
? = 2
Answer:
First ?: 3
Second ?: 2
Step-by-step explanation:
Do the inverse operation of what is shown to get the answer.
First ?:
-4 - ? = -7
-7 + 4 = -?
-3 = -?
3 = ?
Second ?:
? + 3 = 5 (Two negatives in a row make a positive.)
5 - 3 = ?
2 = ?
I hope this helps! \(★ω★)/
Please help me! This may be easy for some of you..
Answers
Answer:
9) 5
10) 5x+2
11) -1
12) -x+6
Sarah surveyed 100 people. She asked each person two
Sarah made the following two-way table to display information about the responces
of the people Sarah surveyed who listen to jazz, what is the probability that a randomly
selected person also plays a musical instrument?
Answers
There are 90 girls and 60 boys in sixth grade at a middle school. Of these students, 9 girls and 3 boys write left-handed. What percentage of the sixth graders write left-handed.
10%
8%
5%
15%
Answers
Answer:
8% of the kids are left-handed. I used 12/150 to yield 0.08 which equals 8%
David puts 0 . 40.4 liters of solution in each of 55 beakers.
How much solution is there in total?
Answers
Answer:
2 liters
Step-by-step explanation:
There are 5 beakers in total, in which David adds 0.4 liters into each of them. To solve, multiply 5 with 0.4: 5 x 0.4 = 2.0 2.0 or 2 liters is your answer.
Answer: 2 liters
Step-by-step explanation: There are 5 beakers in total, in which David adds 0.4 liters into each of them. To solve, multiply 5 with 0.4: 5 x 0.4 = 2.0
2.0 or 2 liters is your answer.
Which of the following is true? A) −16=−16 B) −29>24 C) −47<−43 D) −70<−77
Answers
Answer:
A and C are true.
Step-by-step explanation:
-16 = -16 that's just a given, they are the same number. And -47 is less than -43, since -43 would be a higher number considering it's in the negatives.
If x = 4, y = 3, z = -5, then evaluate: z - z + x - y
Answers
Answer:
The answer is 1
Step-by-step explanation:
z-z+x-y
(-5)-(-5)+(4)-(3)
-5+5+4-3
4-3
1
Solve for c when,
[tex]7c = 28[/tex]
Answers
Answer:
c = 4
Step-by-step explanation:
hope this helps
Calculate the interest
Answers
Answer:
120$
Step-by-step explanation:
as we know the formula to calculate i is (ptr)/100
so i =(1000×6×2)/100
=(12000)/100
=120$
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answers
The factors need to add up to 49x
They need to multiply to -56
thanks for help have nice day
Answers
Answer: 6. d
7. b
8. d
9. c
Step-by-step explanation:
What angle pair is pictured?
1)Alternate lantern angles
2)corresponding angles
3)same-side interior angles
4)Alternate exterior angles
Answers
Step-by-step explanation:
Alternate and corresponding angles.
Answer:
corresponding angles
Step-by-step explanation:
it has six points
it is a corresponding angles
Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4547 patients treated with the drug, 114 developed the adverse reaction of nausea. Construct a 99% confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion p.
Answers
Answer:
The best point estimate of the population proportion p is 0.0251.
The 99% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In clinical trials, among 4547 patients treated with the drug, 114 developed the adverse reaction of nausea.
This means that [tex]n = 4547, \pi = \frac{114}{4547} = 0.0251[/tex]
The best point estimate of the population proportion p is 0.0251.
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0251 - 2.575\sqrt{\frac{0.0251*0.9749}{4547}} = 0.0191[/tex]
The upper limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.0251 + 2.575\sqrt{\frac{0.0251*0.9749}{4547}} = 0.0311[/tex]
The 99% confidence interval for the proportion of adverse reactions is (0.0191, 0.0311).
Plot the vertices (–4, –4), (–2, 1), and (5, 1).
To form a parallelogram, plot the last vertex at point
✔ (3, –4)
.
The area of the parallelogram is
✔ 35
square units.
Answers
Answer:
✔ (3, –4)
✔ 35
Step-by-step explanation:
What type of triangle is a 45/45/90 triangle?
Answers
Answer:
An isosceles triangle.
Step-by-step explanation:
Answer:
right isosceles
Step-by-step explanation:
Alice has 15 times as many crayons as Bryan. Write an equation to find the total number of crayons that Alice has.
Answers
Answer:
a = 15b
Step-by-step explanation:
It's given in the question that Alice has 15 times as many crayons as Bryan.
Let the number of crayons with Bryan = b
And the number of crayons with Alice = a
Therefore, equation representing the number of crayons with Alice will be,
a = 15b
What is the slope represented in the table ?
Answers
Answer:
slope:2
Step-by-step explanation:
Slope is rise/run, or change in y/change in x.
With that being said, we only need two points to solve this.
Let's take the points (0,7) and (1,9)
The formula for finding the slope from two points is m=(y2-y1)/(x2-x1).
M is the slope.
y2 would be the y-value of the second point,9. y1 would be the y-value of the first point, 7.
x2 would be the x-value of the second point, 1. x1 would be the x-value of the first point, 0.
Plugging those values in to the formula, we get m=(9-7)/(1-0)
Simplifying, we get m=2/1, which is m=2.
2. 5x2 + 16x - 84 = 0
Helppp please
Answers
Answer:
the x would equal 25 as 5x2 is 10 + 16x25 - 84 is 0.
Step-by-step explanation:
Answer:
2.8, –6
Step-by-step explanation:
The equation is already instandard form. Use the quadraticformula.5x2+16x−84=0x=−b±b2−4ac√2aSubstitute 5 for a, 16 for b,and −84 for c. Solve to getx=2. 8 or x=− 6.
PLS HELP I PROMISE ILL GIVE U BRAINLEST
Answers
5:15pm was the start time.