Answers
Step-by-step explanation:
cos 20° cos 40° cos 60° cos 80°
Simplify cos 60° to ½.
½ cos 20° cos 40° cos 80°
We can use double angle formula, sin(2θ) = 2 sin θ cos θ. Multiply and divide by 2 sin 20°.
½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)
½ (sin 40° cos 40° cos 80°) / (2 sin 20°)
Multiply and divide by 2 and use double angle formula again.
½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)
½ (sin 80° cos 80°) / (4 sin 20°)
Multiply and divide by 2 and use double angle formula again.
½ (2 sin 80° cos 80°) / (8 sin 20°)
½ (sin 160°) / (8 sin 20°)
Use phase shift identity sin θ = sin(180−θ).
½ (sin 20°) / (8 sin 20°)
1/16
In this case we have the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = 1 / 16, and are asked to prove that this equation is true. Let's start by using the property 'cos(s)cos(t) = cos(s + t) + cos(s - t) / 2.' Taking the bit 'cos(20°)(cos(40°)' we know that s should = 20°, and t should = 40°.
[tex]\mathrm{Using\:the\:following\:identity}:\quad \cos \left(s\right)\cos \left(t\right)=\frac{\cos \left(s+t\right)+\cos \left(s-t\right)}{2},[/tex]
[tex]\cos \left(20^{\circ \:}\right)\cos \left(40^{\circ \:}\right)=\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\\[/tex]
[tex]\mathrm{Substituting\:the\:value\:back}:\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]
This expression is indeed not simplified, but remember that we can use the identities 'cos(- 20°) = cos(20°)' and 'cos(60°) = 1 / 2.' Let's substitute one step and a time.
[tex]\cos \left(-20^{\circ \:}\right)=\cos \left(20^{\circ \:}\right): \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
[tex]\cos \left(60^{\circ \:}\right)=\frac{1}{2}:\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
[tex]\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\cos \left(80^{\circ \:}\right)\left(1+2\cos \left(20^{\circ \:}\right)\right)}{8}[/tex]
Now that we have this 'simplified expression,' if we take the numerator as a whole in decimal form, it will = 0.5. Respectively 0.5 / 8 = 1 / 2 / 8 = 1 / 16. Hence our equation is true.
[tex]\cos \left(80^{\circ \:\:}\right)\left(1+2\cos \left(20^{\circ \:\:}\right)\right) = 0.5,\\0.5 / 8 = (1 / 2) / 8 = 1 / 16[/tex]
Related Questions
Solve for y.
6 = -2/9v
Answers
Answer:
: 1: Exact form : v = - 1/27
: 2 : Decimal form : v = -0.037037037037037037037037...
Step-by-step explanation: Multiply the equation to remove your variable (v) from the denominator.
I hope this helps you out.
I need help again help me pllsssssss
Answers
Answer: you end up at (2,2)
Step-by-step explanation:
Answer:
2,2
Step-by-step explanation:
go down to the bottom right corner (5,-5)
move over left 3 boxes
and then up 7 boxes
hope this helps :P
K - 8 = -7 What is K?
Answers
Answer:
1
Step-by-step explanation:
To find the answer of a negative and a positive, you subtract and then keep the symbol of the bigger number. So in the equation 1-8 you subtract 1 from 8, then keep the symbol of the 8 (which is a negative) since it is the bigger number. 1 minus 8 is 7, and the symbol is negative, so the answer is -7. This makes K=1.
if bob simsim went to the cinema and brought 200g of popcorn and he ate 100g of popcorn how many grams of popcorn does he have left?
Answers
Answer:
He has 100 g left.
Step-by-step explanation:
We start with 200 g, then bob eats 100 g, 200-100=100 grams!
Brett and Max are diving. Brett is 34 feet below the surface and Max is 25 feet below the surface. How many feet above Brett isMax?
Answers
Answer:
Max is 9 ft above Brett
Step-by-step explanation:
Brett is 34 feet below the surface = -34
Max is 25 feet below the surface = -25
Subtract the heights
-25 - -34
-25 +34
9
Max is 9 ft above Brett
Fatima has 2 gallons of milk she wants to pour all milk into glasses which each hold 1 cup (1/16 gallon). how many cups can she fill
Answers
Answer:
32 cups
Step-by-step explanation:
1 cup= 1/16 gallon
? cup= 2 gallon ( crisscross)
⇒[tex]\frac{2*1}{\frac{1}{16} }\\ \frac{2}{\frac{1}{16}} \\2*16=32 cups[/tex]
how to do this question plz answer me step by step plzz
Answers
Answer:
Adult's ticket is 7, child's ticket is 2
Step-by-step explanation:
Let adult's ticket be "x" and child's ticket be "y"
So, for family 1, the equation would be: 2x+3y=20
And, for family 2, the equation would be: 1x+4y=15
Use the substitution method in the second equation to know what x in terms of y is:
x + 4y = 15 (substact 4y from both sides)
x= 15 - 4y
Plugin y into the first equation:
2(15-4y)+3y=20 (distribute)
30-8y+3y=20 (simplify)
30-5y = 20 (get y by itself)
-5y = -10 (divide by -5)
y = 2
Now that you know the value of y (child's ticket), figure out x by plugging in 2 into any of the equations (I chose the second):
1x+4(2) = 15 (simplify)
x + 8 = 15 (subtract 8)
x = 7
Answer:
price of adult ticket=7 £
price of childrens' ticket =2 £
Step-by-step explanation:
let x be price for adult and y price for for children
family 1 : 2x+3y=20
family 2: x+4y=15
solve by eliminating : multiply equation 2 by (2) to eliminate x
2x+3y=20
2x+8y=30
subtract the two equations:
2x+3y-2x-8y=20-30
-5y=-10
y=-10/-5
y=2( the price for children)
x+4y=15
x+4(2)=15
x=15-8
x=7 ( the price for adults)
check : 2x+3y=20
2(7)+3(2)=14+6=20
15. Apply Mathematics (1)(A) Suppose you have a box with a 4 X 4-in.
square base and variable height h. The surface area of this box is a
function of its height. Write a function to represent the surface area.
Evaluate the function for h=6.5 in.
Answers
Answer:
Step-by-step explanation:
Formula for calculating the surface area of the box S = 2(LW+LH+WH) where
L is the length of the box
W is the width of the box
H is the height of the box
If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;
S = 2(4(4)+4H + 4H)
S = 2(16+8H)
S = 32+16H
Hence, The function that represents the surface area of this box as a
function of its height is S = 32+16H where H is the height of the box
Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;
S = 32+16H
S = 32+16(6.5)
S = 32+106
S = 138in²
Hence the total surface area of the box is 138in²
6(n - 2) - 8 = 22 + 4(2-n)
Answers
Answer:
5
Step-by-step explanation:
6n -12 -8=22+8-4n
6n-20=30-4n
6n=50 -4n
10n = 50
5
The 14 digits of a credit card are written in the boxes shown.If the sum of any three consecutive digits is 20, what is the
value of A?
Answers
Answer:
9
Step-by-step explanation:
Working backwards, the blank box between the 7 and 4 at the end must be 9 in order for the three digits to equal 20. Then we see the pattern of 947 repeated. The whole number would be 94794794794794. That way, any three consecutive numbers would be 20. The number in the box marked a would be 9.
Victoria and her friends are going on a road trip that is 632.64 miles long. If they have 32.3 miles until their destination, how far have they already traveled? Answer in decimal form.
Answers
can someone help me graph this.
Answers
Answer:
Use a graphing calc.
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
For the third equation, m = 2
y = 2x + b
3 = 3(2) + b
3 = 6 + b
b = -3
y = 2x - 3
Sherry brings two containers of cookies to a party. Each container contains 6 cookies. Sally shows up with a dozen cookies. Sandy arrives with 2 cookies and 10 donuts. How many cookies will Harry need to bring if the total cookie count is 4 dozen
Answers
Answer:
22 cookies
Step-by-step explanation:
A dozen items means 12 number of items.
Number of cookies brought by Sherry = No. of containers multiplied by number of cookies in one container
= 2 [tex]\times[/tex] 6 = 12
Number of cookies brought by Sally = A dozen cookies = 12
Number of cookies brought by Sandy = 2
Number of cookies brought by Sherry, Sally and Sandy together = 12 + 12+2 = 26
Total number of cookies to be brought = 4 dozen = 48 cookies
Number of cookies to be brought by Harry = Total number of cookies to be brought - Number of cookies brought by Sherry, Sally and Sandy together
48 - 26 = 22 cookies
Find the product of 10n5 and 6n2
Answers
[tex]10 \times 10 \times 10 \times 10 \times 10 = 2000[/tex]
[tex]6 \times 6 = 36[/tex]
= 2036n
Is x^4+3x^3-x+7 in standard form
Answers
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
The standard form of a polynomial has the exponents decreasing left to right. Here, the exponents are 4, 3, 1, 0, so are decreasing left to right. The expression is in standard form.
Order the following expressions by their values from least to greatest.
Answers
Answer:
-2, b, a+c
Step-by-step explanation:
Answer:
All you have to do is switch A + C and B around. (basically if you wrote it out, it would look like this: -2, B, A + C.)
4x + 6 - 11 help needed
Answers
Answer:
4x-5Step-by-step explanation:
[tex]4x+6-11\\\\\mathrm{Add/Subtract\:the\:numbers:}\:6-11=-5\\=4x-5[/tex]
Your hotel sells four types of rooms: double queen beds for $140/night; king bed for $160/night; junior suite for $220, and full business suites for $285. If there are 200, 150, 100, and 50 of each, respectively, what is your average price per room?
Answers
Answer:
$176.50
Step-by-step explanation:
Take each room type and multiply the number of rooms by the price of the room. Add the total for prices and add the total for the number of rooms. Divide the total prices by the total number of rooms.
Type of room Number Cost Total
Double queen 140 $200.00 $28,000.00
King 160 $150.00 $24,000.00
Junior Suite 220 $100.00 $22,000.00
Full business 285 $50.00 $14,250.00
$500.00 $88,250.00
Average cos per room $176.50
[tex]6\sqrt{7-11}\sqrt{7+2}\sqrt{7}[/tex]
Answers
Answer:
[tex]=36\sqrt{7}i[/tex]
Step-by-step explanation:
sqrt of 7-11=2i
simplify to [tex]6\cdot \:2\sqrt{9}\sqrt{7}i[/tex]
then sqrt of 9=3
then we simplify again to [tex]=36\sqrt{7}i[/tex]
hope this helps and if you don't mind please consider giving me brainliest
A certain shade of lavender is created by adding 5 cups of purple paint to 8 cups of white paint. a. How many cups of purple paint should be added to 1 cup of white paint? Cups of white paint Cups of purple paint 1 8 b. What is the constant of proportionality?
Answers
Answer:
a. [tex]\frac{5}8[/tex] cups of purple paints required.
b. [tex]\frac{5}8[/tex]
Step-by-step explanation:
Given that
Number of purple paints required with 8 cups of white paint = 5
To find:
a. Number of cups of purple paint needed to be added to 1 cup of white paint ?
b. Constant of proportionality.
Solution:
Answer a. We can use unitary method here to find the number of cups of purple paint that are to be added to 1 cup of white paint.
Let us use the given statement:
8 cups of white paint require = 5 cups of purple paint
Let us divide both sides by 8:
1 cup of white paint require = [tex]\frac{5}8[/tex] cups of purple paint
Answer b.
Constant of proportionality is nothing but the ratio of two numbers which are present in a proportion.
Here, the ratio between number of cups of purple paint and number of cups of white paint is:
5:8 or [tex]\frac{5}8[/tex].
so, the answer is: [tex]\frac{5}8[/tex]
What is -5 5/8+ 3 1/2
Answers
Round 24.772 to each value listed below
Nearest tens:
Nearest tenths:
Nearest whole:
Nearest hundredths
Answers
Answer:
Nearest tens: 20
Nearest tenths: 24.8
Nearest whole: 25
Nearest hundredths: 24.77
Answer:
Nearest tens: 20 ⇔ the ones digit is 4, no rounding up
Nearest tenths: 24.8 ⇔ the hundredths is 7, need to round up
Nearest whole: 25 ⇔ the tenths digits is 7, need to round up
Nearest hundredths: 24.77 ⇔ the thousandths digit is 2, no rounding up
Hope this helps!! :)
Please let me know if you have any question
5+11n=13n help with this one too..
Answers
Answer:
n = 2.5
Step-by-step explanation:
We need to isolate n by first moving it to one side.
11n = 13n - 5
11n - 13n = -5
-2n = -5
n = -5/-2
n = 2.5
If you would like more help with math or other subjects for FREE, check out growthinyouth.org.
Answer:
n = 5/2
Step-by-step explanation:
5 + 11n = 13n
5 = 13n - 11n
5 = 2n
n = 5/2
Check:
5 + 11*5/2 = 13*5/2
10/2 + 55/2 = 65/2
Help ASAP, Brainliest to whoever answers!
Answers
Answer:
these are the ten numbers :
0 8 2 6 9 2 0 8 0 0
3+g=a/3h
what does a equal
Answers
Answer:
a = 3gh+9hStep-by-step explanation:
[tex]3+g = \frac{a}{3h} \\\\Cross\:Multiply\\\\3h(3+g) = a\\9h +3gh = a\\\\a = 3gh+9h[/tex]
Evaluate 1/3m−1−1/2n when m=21 and n=12
Answers
Answer:
[tex]0[/tex]
Step-by-step explanation:
[tex] \frac{1}{3}m - 1 - \frac{1}{2}n = \frac{1}{3}(21) - 1 - \frac{1}{2}(12) = 7 - 1 - 6 = 6 - 6 = 0[/tex]
Answer:
0
Step-by-step explanation:
1/3m - 1 - 1/2n
= 1/3(21) -1 1/2(12)
= 7 - 1 - 6
= 0
Round off to three significant digits: 4.53619
Answers
Answer:
4.54
Step-by-step explanation:
The 4th digit (6) is greater than 4, so the 3rd digit (3) is increased by 1 before you drop the remaining digits:
4.54
The Venn diagram represents different categories of real numbers. Which category on the Venn diagram is represented by 4π? A) Irrational Numbers B) Integers C) Natural Numbers D) Rational Numbers
Answers
Answer:
Irrational Number
Step-by-step explanation:
The Venn diagram is not attached; However, the question can still be answered
Given
[tex]Number = 4\pi[/tex]
Required
What category of number is the given number
[tex]Number = 4\pi[/tex]
Substitute [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex]
[tex]Number = 4 * \frac{22}{7}[/tex]
[tex]Number = \frac{4 *22}{7}[/tex]
[tex]Number = \frac{88}{7}[/tex]
[tex]Number = 12.5714285714......[/tex]
Notice that there's .... at the end of the number;
This implies that, the decimal number still extends
Numbers like 12.5714285714...... are categorized as irrational numbers because it can't be changed back to a fraction
Answer:
A. irrational number
Step-by-step explanation:
I took the test
5 pizzes are shared equally between 10 people. What fraction of a pizza does each person receive?
Answers
Answer:
1/2
Step-by-step explanation:
f(x) = 5x + 12. Find f−1(x)
Answers
Answer:
(x-12)/5
Step-by-step explanation: