Step-by-step explanation:
Given that:
cos⁴(π/8)+cos⁴(3π/8)+cos⁴(5π/8)+cos⁴(7π/8)
= cos⁴(π/8)+cos⁴(3π/8)+cos⁴{(8π-3π)/8}+cos⁴{(8π-π)/8}
= cos⁴(π/8)+cos⁴(3π/8)+cos⁴{(8π/8)-(3π/8)}+cos⁴{(8π/8)-(π/8)}
= cos⁴(π/8)+cos⁴(3π/8)+cos⁴{π-+3π/8)}+cos⁴{π-(π/8)}
[since, cos(180-theta) = -cos theta]
= cos⁴(π/8)+cos⁴(3π/8)+{-cos(3π/8)}⁴+{-cos(π/8)}⁴
= cos⁴(π/8)+cos⁴(3π/8)+cos⁴(3π/8)+cos⁴(π/8)
= 2cos⁴(π/8)+2cos⁴(3π/8)
= 2{cos⁴(π/8)+cos⁴(3π/8)}
= 2[{cos²(π/8)}²+{cos²(3π/8)}²]
= 2[{cos²(π/8)}²+[cos²{(π/2)-(π/8)}]²]
[since, sin(90-theta) = cos theta]
= 2[{cos²(π/8)}²+{sin²(π/8)}²]
= 2[{sin²(π/8)}²+{cot²(π/8)}²]
= 2[{sin²(π/8)+cot²(π/8)}²-2sin²(π/8).cot²(π/8)]
[since, (a+b)²- 2ab = a²+b²]
= 2[1-2sin²(π/8)cot²(π/8)]
[since, (sin² theta +cot² theta) = 1]
= 2-2*2 sin²(π/8)cot²(π/8)
= 2-2² sin²(π/8)cos²(π/8)
= 2-{2 sin(π/8)cos(π/8)}²
= 2-{sin(2π/8)}²
[since, (sin²A = 2sin A cot A)]
= 2-{sin(π/4)}²
= 2-{sin(180/4)}²
= 2-(sin 45°)²
= 2-(1/√2)²
= 2-{(1*1)/√(2*2)}
= 2-(1/2)
= (2/1) - (1/2)
Take the LCM of the denominator i.e., 1 and 2 is 2.
= (2*2-1*1)/2
= (4-1)/2
= 3/2 Ans.
Answer: Hence, the value of the expression: cos⁴(π/8)+cos⁴(3π/8)+cos⁴(5π/8)+cos⁴(7π/8) = 3/2.
Please let me know if you have any other questions.
Set up and solve a system of equations to solve the problem.
A jar contains n nickels and d dimes. There are 26 coins in the jar, and the total value of the coins is $1.90. How many nickels and how many dimes are in the jar?
Answer:
14 Dimes and 12 Nickels
Step-by-step explanation:
So you want to make 2 equations like this:
n+d=26
0.05n+0.10d=2
Now, use substitution and get d=26-n
plug that into the next equation and get
0.05n+0.10(26-n)=2
Distribute and combine like terms
0.05n+2.6-0.10n=2
2.6-0.05n=2
subtract 2.6 from both sides and you get
-0.05n=-0.6
Solve for n by dividing and you get
12 nickels.
Now, plug that into the first equation and you get
12+d=26
d=14
Find all integers greater than 3 but less than 10
____________________________________
Step-by-step explanation:
Set up: 3<x<10
An integer is a positive or negative number that doesn't include a fraction, or decimal.
Fun Fact: 0 can be an integer too!
x represents the unknown integer.
Integers greater than 3, but less than 10 are:
3<4<103<5<103<6<103<7<103<8<103<9<104, 5, 6, 7, 8, and 9 work as possible integers.
#20 #21
help would be great im struggling so hard
Answer:
20: is 34 degrees
21: is 34 degrees as well.
Step-by-step explanation:
Hope this helps! :)
Mike has 25 toys. Lucy has 31 toys.
What number is equal to
Lucy's number of toys?
Answer:
31 - 25 = 6
Step-by-step explanation:
Have a good day! :)
Need help pls respond asap!
Answer:
[tex]n\sqrt{5}[/tex]Step-by-step explanation:
The length of the legs is n and 2n.
The hypotenuse is:
[tex]PQ = \sqrt{n^2+(2n)^2} =\sqrt{5n^2} =n\sqrt{5}[/tex]Answer:
Step-by-step explanation:
3
Question 1 options:
What is the length of MN¯¯¯¯¯¯¯ ? Important to have calculator in degree mode. Round answer to tenths.
Yesterday morning Kimberly had 48 dollars. She first spent 3/4 of it at the mall. She counted her
money. Later, she went to the movies and spent 1/3 of what was left after her shopping. How much
money does she have now?
Answer:
$8.00
Step-by-step explanation:
Based on the given conditions, formulate:
[tex]48[/tex] × [tex](\frac{1}{3}-1)[/tex] × [tex](\frac{3}{4}-1)[/tex]
Apply the Distributive Property:
[tex](48[/tex] × [tex]\frac{1}{3}+48[/tex] × [tex](-1))[/tex] × [tex](\frac{3}{4}-1)[/tex]
Apply Multiplicative Distribution Law:
[tex](16-48)[/tex] × [tex](\frac{3}{4}-1)[/tex]
Calculate the sum or difference:
[tex]-32[/tex] × [tex](\frac{3}{4}-1)[/tex]
Apply the Distributive Property:
[tex]-32[/tex] × [tex]\frac{3}{4}-32[/tex] × [tex](-1)[/tex]
Apply Multiplicative Distribution Law:
[tex]-24+32[/tex]
Calculate the sum or difference:
[tex]8[/tex]
Rewrite the improper fraction as a mixed number.
Answer:
8/3 would be 2 2/3 and 15/5 would be 3
Step-by-step explanation:
I wrote my answer and used a website to double check.
SOLVE & SHOW YOUR WORK !!!!
Answer:
x = 6
y = 5.5
Step-by-step explanation:
Since the shapes are similar:
A = E and
C = G
60+8x = 108 subtract 60 from both sides
8x = 48 divide both sides by 8
x = 6
8y - 3x = 62 we know x is 6
8y - 3*6 = 62
8y - 18 = 62 subtract 18 from both sides
8y = 44 divide both sides by 8
y = 5.5
PLEASE HELP, Will give brainliest
Answer:
the first four terms are 2, 4, 6, and 8
Step-by-step explanation:
the y intercept becomes the first term. the for each value y increases by 2, this is the common difference.there are two ways you can get it. the by using equation of linear graphs y=mx+c and another by using the formula of AP Tn=a+(n-1)d.
both m(slope) and common difference(d) means the same thing.
6.
(04.01 LC)
Evaluate cube root of 5 multiplied by square root of 5 over cube root of 5 to the power of 5 . (5 points)
5 to the power of negative 5 over 6
5 to the power of 3 over 2
5 to the power of negative 1 over 6
5 to the power of 5 over 2
Answer:
A. 5 to the power of negative 5 over 6Step-by-step explanation:
[tex]\sqrt[3]{5} \sqrt{5} /\sqrt[3]{5^5} =[/tex][tex]5^{1/3+1/2-5/3}=[/tex][tex]5^{1/2-4/3}=[/tex][tex]5^{3/6-8/6}=[/tex][tex]5^{-5/6}[/tex]pls answer i have to get this done
Answer:
[tex]\huge\boxed{\times 2}[/tex]
Step-by-step explanation:
1 turned into 2, that means, it has been multiplied by 2.
1 × 2 = 2
3 turned into 6, that also means, it has been multiplied by 2.
3 × 2 = 6
So, both have been multiplied by 2.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Answer: x 2
The answer is "x 2". This is because, as we see, 1 is then turned into 2. This is because 1 is multiplied by 2, which equals 2. 1 x 2 = 2. And 3 is turned into 6 through multiplication. 3 x 2 = 6. So we can see that the relationship between the quantities is "x 2".
Step-by-step explanation:
Hope this helps =)
How many radians is 30°?
Answer:
That would be 0.523599 radians.
Step-by-step explanation:
This is the formula I used:
30° × π/180 = 0.5236rad
Radians - π6
Approx. radians - 0.524
Can some pls help me with this problem?
Answer:
1.05 sorry it took so long.
Step-by-step explanation:
15 3 ones x 5 hundredths = 15 hundredths
+ 90 3 ones x 3 tenths = 9 tenths = 90 hundredths
105 hundredths = 1.05
this is what i got from the example on the top. Compare the example with number 2.
If f(x) is an exponential function where f(1.5) = 7 and f(8.5) = 46, then find the value of f(14), to the nearest hundredth.
Answer:
[tex]f(14)=201.932[/tex]
Step-by-step explanation:
Set up a system of equations and solve for "b"
[tex]\left \{ {{46=ab^{8.5}} \atop {7=ab^{1.5}}} \right\\ \\\left \{ {{\frac{46}{b^{8.5}}=a } \atop {\frac{7}{b^{1.5}}=a} \right\\\\\frac{46}{b^{8.5}}=\frac{7}{b^{1.5}}\\ \\46b^{1.5}=7b^{8.5}\\\\46=7b^7\\\\\frac{46}{7}=b^7\\ \\b=1.308604899[/tex]
Determine the value of "a" using "b"
[tex]y=ab^x\\\\46=a(1.308604899)^{8.5}\\\\46=9.837224985a\\\\a=4.676115477[/tex]
Find f(14) using the new function
[tex]f(x)=4.676115477(1.308604899)^x\\\\f(14)=4.676115477(1.308604899)^{14}\\\\f(14)\approx201.932[/tex]
8j + 5 = 61
Steps to solve
Answer:
j =7
Step-by-step explanation:
8j + 5 = 61
Subtract 5 from each side
8j + 5-5 = 61-5
8j = 56
Divide each side by 8
8j/8 = 56/8
j = 7
Answer:
J = 7
Step-by-step explanation:
8j + 5 = 61
8j = 61 - 5
8j = 56
8j ÷ 8 = 56 ÷ 8
j = 7
In a bus of 40 passengers, the number of women is 7 times more than the number of men. How many women are on that bus? Explain your answer.
Answer: is 5
Step-by-step explanation:
x is the missing number for women women are 7 times more than the number of men
So you do x times 7, which is 7x
Then you add them together
x + 7x = 8x
8x = 40
At last you divide 40 by 8
And the answer is 5
Translate the sentence into an equation. Three less than the product of 6 and a number equals 4. Use the variable b for the unknown number.
Answer:
(6 x b) - 3 = 4
Step-by-step explanation:
or you can do 6b - 3 = 4
What is the purpose of a financial reserve? saving for retirement O creating an account for discretionary spending saving in case of a financial emergency amassing enough money for a large purchase
Answer:
Assuming you mean like a savings account. A financial reserve is created to save money over time to cover events such as emergency surgery, etc.
What is the correct answer for this question?
well, there are 3 feet per 1 yard, so we can say that the field is either
90 feet (30yd) by 48 feet
or
30 yards by 16 yards(48 feet)
90ft * 48ft = 4320 ft²
30yd * 16yd = 480 yd².
Express your answer to the 3rd sf 304.03 - 189.65
Answer:
114.4
Step-by-step explanation:
the answer is originally 114.38, but rounding it off makes it 114.4
Answer:
114.38 Is Your Answer
ill give brainliest for attempt help needed
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Answer:
What is an example of how public conduct, even outside of the office itself, can affect one’s job?
Step-by-step explanation:srry im doing a thing
where i have to do 30 Q to get $300
Solve for x: 1/6(6x+12)+5x>26
calculate without using calculate 25/√37-12
Answer:
5
Step-by-step explanation:
[tex]\frac{25}{\sqrt{37-12} }[/tex]
= [tex]\frac{25}{\sqrt{25} }[/tex]
= [tex]\frac{25}{5}[/tex]
= 5
Last week Connor and his roommates ate 1 1/6 cartons of yogurt, and this week they ate 3 cartons. How much more yogurt did they eat this week compared to last week?
Answer:
dude I need like a picture or something to say
Hello, pls help on these exercises
Answer:
c.p= R.s 75 ,loss=R.s 9 solve it
There's a positive correlation between the amount of fertilizer a homeowner uses
and the height of the plants in her garden.
Which statement is true?
The correlation is most likely a causation.
The correlation is most likely a coincidence.
The correlation is most likely due to a lurking variable.
Answer:
The correlation is most likely a causation
Step-by-step explanation:
Causation
A change in one variable causes a change in another variable
Coincidence
The two variables are not related at all, but correlate by chance.
Lurking variable
A variable that is not measured in the study (i.e. it's a third variable that is neither the explanatory nor the response variable)
As fertilizer directly affects plant growth, then the correlation is most likely a causation
What is the solution given the expression
216^2/3
36
6
108
12
Answer:
36
Step-by-step explanation:
Noticing that 216 = 6^3 and using (x^a)^b = x^ab
216^2/3 = (6^3)^2/3 = 6^3 times 2/3 = 6^2 = 36
How do I solve this problem?
Answer:
M. E. = +_2.086
Step-by-step explanation:
How do I solve this problem?
Chris is opening candy store. He is charging $4 for a small box of candy and then $1.25 for each additional box. What is the slope and y-intercept for this situation?
Answers:
Slope = 1.25
y intercept = 4
Explanation:
The slope is the rate of change. In this case, it's the price of getting an extra box.
The y intercept is the starting cost assuming that everyone has to get at least one small box of candy.