Answers
Step-by-step explanation:
8 cos 80° cos 140° cos 160°
4 (2 cos 80° cos 140°) cos 160°
4 cos 160° (2 cos 80° cos 140°)
Use product to sum formula.
4 cos 160° (cos 60° + cos 220°)
4 cos 160° (½ + cos 220°)
2 cos 160° + 4 cos 220° cos 160°
2 cos 160° + 2 (2 cos 220° cos 160°)
Use product to sum formula again.
2 cos 160° + 2 (cos 60° + cos 380°)
2 cos 160° + 2 (½ + cos 380°)
2 cos 160° + 1 + 2 cos 380°
2 cos 160° + 1 + 2 cos 20°
Use shift identity cos(180 − θ) = -cos θ.
-2 cos 20° + 1 + 2 cos 20°
1
Our question that we have at hand here is 8(cos 80°)(cos 140°)(cos 160°). We need to convert that into 'decimal form' to prove that it equals 1. However decimal form doesn't generally give us a decimal, in this case.
Let's start by using the identity cos(s)cos(t) = cos(s + t) + cos(s - t) / 2. In this case we are looking particularly at the expression (cos 80°)(cos 140°), where s = 80, and t = 140.
[tex]\cos \left(80^{\circ \:}\right)\cos \left(140^{\circ \:}\right)=\frac{\cos \left(80^{\circ \:}+140^{\circ \:}\right)+\cos \left(80^{\circ \:}-140^{\circ \:}\right)}{2}[/tex]
[tex]=8\cdot \frac{\cos \left(80^{\circ \:}+140^{\circ \:}\right)+\cos \left(80^{\circ \:}-140^{\circ \:}\right)}{2}\cos \left(160^{\circ \:}\right)[/tex]
[tex]= 4\cos \left(160^{\circ \:}\right)\left(\cos \left(220^{\circ \:}\right)+\cos \left(-60^{\circ \:}\right)\right)[/tex]
To further simplify this expression, we know that cos(- 60°) = cos(60°). This may not seem like a very effective step, but we can apply a few trivial identities here. Remember that cos(60°) = 1 / 2,
[tex]4\cos \left(160^{\circ \:}\right)\left(\cos \left(220^{\circ \:}\right)+\frac{1}{2}\right)[/tex]
[tex]= 4(0.25)\\= 1[/tex]
And hence we proved that 8(cos 80°)(cos 140°)(cos 160°) in decimal form, = 1.
Related Questions
which best describes how to solve the equation below 64x = 37
Answers
Answer: Division
Step-by-step explanation: divide both sides by 64
PLZ ANSWER ASAP Select all the true statements. Line segment from -6 to 6. Point A is at -2, point b is at 1 and point c is at 6 The length of AB is -3. AB + BC = AC AB + AC = BC d(B, C) = BC = |6 - 1| The length of BC is 6.
Answers
Answer:65
Step-by-step explanation:
hgjvmd
How do I find f(2) if f(x)=2x-1
Answers
I hope this helps you
let's write 2 for x
f(2)=2.2-1
f(2)=4-1
f(2)=3
0=2x-1
-2x=-1
X= 1/2
Help please thank youu <3
Answers
Answer:
4. 10m+50=200
Step-by-step explanation:
10m meaning hes getting 10 each month that's why the m is there and on too he is getting another 50 which is why you would need to add 50 and obviously a total of 200 is at the end
Answer:
4) 10m+50 = 200
Step-by-step explanation:
As here "m" denotes "month" , Maxs save $10 a month so it is - 10m .
$50 for grandma and he need to save $200.
So we get the equation :
10m+50=200
What is (0.83)4 rounded to the nearest hundredth?
Answers
Answer:
3
Step-by-step explanation:
Make y the subject of the following: 7(y-3)=4(3-y) no spamming
Answers
Answer:
y = 3Step-by-step explanation:
7(y - 3) = 4(3-y)
7y - 21 = 12 - 4y
+4y +4y
11y - 21 = 12
+21 +21
11y = 33
÷11 ÷11
y = 3
∠A and ∠B are complementary angles. If the measure of ∠A is 42°, find the measure of ∠B.
Answers
Answer:
∠B = 48°Step-by-step explanation:
Since ∠A and ∠B are complementary angles their angles sum up to 90°.
In order to find ∠B add both ∠A and ∠B and equate them to 90° and solve for ∠B
That's
∠A + ∠B = 90
42 + ∠B = 90
∠B = 90 - 42
We have the final answer as
∠B = 48°Hope this helps you
Answer:
∠B = 48°
Step-by-step explanation:
A Complementary angles are total of 90°
If the measure of ∠A is 42°, find the measure of ∠B:
∠A + ∠B = 90°
42° + ∠B = 90°
∠B = 90° - 42°
∠B = 48°
The speed(S) of a car varies partly directly as its mass(M) and partly directly as the quantity (Q) of fuel in it. When the speed is 80km/hr, the mass is 220kg and the quantity of fuel is 30litres, when the speed is 60km/hr, the mass is 300kg and the quantity of fuel is 40 litres. Find the volume of fuel if the speed is 100km/hr and the mass 250kg
Answers
Answer:
S varies partly directly as M and Q.
S=C.
S=KMQ+C.
For the first one...
speed=80,m=220,Q=30.
80=K20×30+C.
80=600K+C......(I).equation one.
For the second one....
speed=60,m=300,Q=40.
60=K300×40+C.
60=12000K+C.....(ii). equation two.
Minus eqtn(I) from eqtn(ii).
80=600K+C.
- 60=12000K+C.
K=0.01754~0.018.
Substitute K=0.018 into eqtn(I).
80=600K+C
80=600×0.018+C.
80=10.8+C.
C=80-10.8=69.2.
The relation is S=0.018MQ+69.2
when speed is 100 and mass is 250 find the volume.
100=0.018×250×Q+69.2.
100=4.5Q+69.2.
4.5Q=100-69.2
4.5Q=30.8.
Q=30.8/4.5.
Q=6.8~7litres.
easy 10 points and brainliest!
Answers
Answer:
x must be 0
Step-by-step explanation:
because if there is any point that is on the y axis that would mean that it would be dirrectly on the line and that would be the equivslent of x = 0
Answer:
x = 0
Step-by-step explanation:
If the point (x,y) is on the y-axis, that means the x coordinate is 0. The point can travel vertically anywhere on the axis, but not left or right of the axis.
Cheers.
What is the area of the wreck site?
Answers
Answer:
where is the photo?
Step-by-step explanation:
Where is the photo, I need you to give me more details so i can officially answer your question, thank you :)
calculate the mid points of the line segments below using the midpoint formula given two endpoints (9,7) (-8, 10)
Answers
Answer: (0.5, 8.5)
Step-by-step explanation: (9+-8/2) is 1/2 and (7 + 10/ 2) is 8.5. After plugging it into the equation, I checked with a graphing site.
2. It takes 6 eggs to make 2 loaves of banana bread. How many eggs are needed to make 1 loaf of
bread?
Answers
Answer:
3
Step-by-step explanation:
Answer:3
Step-by-step explanation: because half of 6 eggs are need to make 2 loaves so split that in half and you have 3
Please help! (Question in picture)
Answers
The answer is C. You just simplify all of the terms.
I think it is C but i'm not entirely sure sorry if its wrong gotta go
1. Simplify 2(1 - 10x) - 2(6x - 4)
Answers
Julie has a jewlery box shaped like a cube. The volume of the jewlery box is v cubic inches. Write an
expression that represents the edge length of Julie's jewlery box, in inches.
Answers
Answer: ∛v
Step-by-step explanation:
Since we know volume is measured height x width x length, we know the equation we'd use here would be:
___ x ___ x ___ = v in³
If this was area, we would have ___ x ___ = v in², and it would be easy to find each blank. You would just find the square root of "v", making your answer √v.
When you have 3 things multiplied by each other (that are exactly the same, which is the situation here since this is a cube), you will want to find ∛x (if x is our unknown variable). This means that we are finding ONE-THIRD of the number ... sort of. So if x was equal to 8, then ∛x = 2, because 2 x 2 x 2 = 8.
In our situation here, x = v, and since we don't know the actual number, we will keep it as a square root, so the answer to your question is ∛v.
I really hope I was able to explain easy enough, feel free to ask anything else!
determine the prime factors of 84 in tree map
Answers
Step-by-step explanation:
I hope i got it right...
What’s the sum of the number m and the number after it?
Answers
Answer:
wat number put the value there
The required sum of the number m and the number after it 2m + 1.
Given that,
To determine the sum of the number m and the number after it.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Let the number m and the number after m is m+1
Now the sum = m + m + 1
= 2m + 1
Thus, the required sum of the number m and the number after it 2m + 1.
Learn more about arithmetic here:
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A square piece of cheese covers 8 square inches of a plate. What is the approximate length of one side of the piece of cheese? (Approximate to the nearest hundredth inch.) (4 points)
Answers
Greetings from Brasil...
According to the statement, we can conclude that 1 square (of cheese) has 8in²
The area of a square is given by the expression:
A = S²
where S is the side of the square - just what we want to know
So:
A = S²
8 = S²
√8 = S
S ≈ 2.83inWhats the answer? 8(2 ÷ 2) = 2(8 ÷ 2) A. 6=6 B. 4=4 C. 8=8
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 = 8}}}}}[/tex]
Option C is the correct option
Step-by-step explanation:
[tex] \sf{8(2 \div 2) = 2(8 \div 2)}[/tex]
Left hand side ( L.H.S )
⇒[tex] \sf{8(2 \div 2)}[/tex]
Divide 2 by 2
⇒[tex] \sf{8 \times 1}[/tex]
Multiply the numbers : 8 and 1
⇒[tex] \sf{8}[/tex]
Again, Right hand side ( R.H.S )
[tex] \sf{2(8 \div 2)}[/tex]
Divide 8 by 2
⇒[tex] \sf{2 \times 4}[/tex]
Multiply the numbers : 2 and 4
⇒[tex] \sf{8} [/tex]
∴ 8 = 8
Hope I helped!
Best regards!!
given the expotential function f(x) = 4(3)^x find f(0) and f(1)
Answers
Answer:
4 and 12
Step-by-step explanation:
Given
f(x) = 4[tex](3)^{x}[/tex] , then
f(0) = 4[tex](3)^{0}[/tex] = 4 × 1 = 4 [ [tex]a^{0}[/tex] = 1 ]
f(1) = 4[tex](3)^{1}[/tex] = 4 × 3 = 12
Given the diagram above, m∠Z is:
Answers
Answer:
z = 120º
Step-by-step explanation:
t + 2t + t + 2t = 360º
60 + 2(60) + 60 + 2(60) = 360
t = 60
2t = z
z = 120º
This is all based on the fact there there are 360º in a quadrilateral.
Please helpppp meeee
Answers
Answer:
AB=62, BC=61, AC=57, PR=75, PQ=52.5, QR=52.5
Step-by-step explanation:
-9x+10y = -18
3x- y =6
Elimination
Answers
Explanation:
-9x + 10y = -18
3x - y = 6
————————
-9x + 10y = -18
10(3x - y = 6)
————————
-9x + 10y = -18
30x - 10y = 60
————————-
21x = 42
x = 42/21
x = 2
Find y:
3x - y = 6
3(2) - y = 6
6 - y = 6
-y = 6 - 6
-y = 0
y = 0
Step-by-step explanation:
Hey, there!!
To solve this type of equation it is very easy from elimination method,
Firsty, you try to search if there is opposite sign of same variables or not in both equation. Then find their LCM to make easy to cancel.And thirdly add or subtract the terms to get value of one variable. Then substitute the value of one variable to get value of another variable.Here, the given equation are,
-9x+10y = -18..........(i)
3x-y = 6....................(ii)
Let's take LCM to solve for x.
To solve for "x" we must cancel "y".
LCM= 10 { lcm of 1 and 10 is 1}
So, let's multiply equation (ii) by 10 and add them.
Then,
-9x + 10y = -18
30x - 10y = 60
21x = 42 { as +10y and -10y gets cancelled}
[tex]x = \frac{42}{21} [/tex]
Therefore, x= 2.
Substituting the value of x in equation (i)
-9x + 10y = -18
-9 × 2 +10y = -18
-18 + 10y = -18
or, 10y = -18 +18
Therefore, y= 0.
So, the value of x is 2 and y is 0.
Hope it helps...
ALGEBRA 1: HELP ME PLEASE 20POINTS
When a value for x is put into the machine, a value for y comes out. That output then becomes the input for another machine. An example is shown at the bottom.
What is the output from the second function machine? Explain.
Answers
Here you go queen/king hope this helps!
Inverse Function f(x)= 5 -1/3x
Answers
Answer:
f(x)⁻¹ = -3x + 15
Step-by-step explanation:
y = -1/3x + 5
x = -1/3y + 5
x - 5 = -1/3y
(x - 5)(-3) = y
-3x + 15 = y
someone help me please
Answers
Answer:
-x^2 + 2x + 1
Step-by-step explanation:
Standard form of a polynomial is Ax^2 + Bx + C. (Highest degree to lowest degree)
-x^2 + 2x + 1.
Li uses 8.4 grams of sugar every day in her tea. Sue uses 12.6 grams of sugar every day in her coffee. If Li’s sugar canister contains 128 grams of sugar and Sue’s canister contains 191 grams, in how many days will Li and Sue have the same amount of sugar in their canisters?
Answers
Answer:
They will have the same amount of sugar in their canisters in 15 days
Step-by-step explanation:
Here in this question, we are concerned with knowing the number of days in which the amount of sugar in both canisters will be the same.
Since we do not know the number of days it will take, we have to represent it using a variable.
Let the number of days be x days
Now, we are told Li uses 8.4 g per day.
So in x days, the amount user will be 8.4 * x = 8.4x g
Thus, the amount of sugar remaining in her canister after x days will be 128 - 8.4x
For Sue, she uses 12.6 grams each day. So in x days, the amount of sugar used will be 12.6 * x = 12.6x g
So the amount of sugar left in her canister will be 191-12.6x
Since on the xth day , the amount of sugar remaining is same, we can equate the amount of sugar remaining in both canisters. That would be;
128-8.4x =191-12.6x
Collect like terms;
12.6x-8.4x = 191-128
4.2x = 63
x = 63/4.2
x = 15 days
helppppp
Simplify (93 - √25+? 42
÷ 8)2
** show all of your steps using order of operation
Answers
Answer:
186.5 + 2x
Step-by-step explanation:
First, radify 25. Luckily it's a perfect square so it will be 5.
Second, divide within the parentheses. You're expression should look like this.
(93-5+x+42/8)2
Divide 42/8. The decimal form would be 5.25, while the fraction should be 5 1/4.
Third, solve within the parentheses from left to right. Right now you're expression should look like this:
(93-5+x+5.25)2
Add all like terms
93-5+5.25=93.25
Fourth, multiply. Right now the expression should look like this:
(93.25 + x) 2
186.5 + 2x
Translate this sentence into an equation.
The sum of 14 and Vidya's score is 43.
Use the variable v to represent Vidya's score.
Answers
The equation shows the sum of 14 and Vidya’s score (v), which equals 43.
The sum of 14 and Vidya's score (v) can be translated into an equation as follows: 14 + v = 43
Let's represent Vidya's score using the variable "v."
In this equation, "v" represents Vidya's score, and the left-hand side of the equation represents the sum of 14 and Vidya's score. The right-hand side represents the value 43, which is the total sum according to the given statement.
To know more about equation:
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Simplify each expression 7(9k + 6m)
Answers
Answer:
The correct answer is 63k + 42m.
Step-by-step explanation:
To solve this problem, we must remember how to use the distributive property. The distributive property tells us that if we have a coefficient outside of the parentheses (in this case, 7), we can multiply each term inside the parentheses by this coefficient and add the products together. This is modeled below:
7(9k + 6m)
(7*9k) + (7 * 6m)
63k + 42m
Therefore, the correct answer is 63k + 42m.
Hope this helps!
Explanation: you take 7 and multiple it by 9k and that equals 63k and then you take 7 again and multiply it by 6m and that equals 42m