You can find the angles using the unit circle. You can also find the angle using algebra.
I want to show you the algebra way.
Since cos(x) = cos(2•pi - x), this leads to two equations.
The two equations are as follows:
cos (x) = -1/2...the given problem.
We also have cos (2•pi - x) = -1/2.
To isolate x for both trigonometric equations, use the inverse trig function idea.
Equation 1
arccos(cos x) = arccos (-1/2)
x = 2•pi/3
Equation 2
arccos(cos (2•pi - x)) = arccos (-1/2).
Note: 2•pi - x = 2•pi/3. We are not done with this equation. We must isolate x. In other words, like any other equation, solving for x is needed.
When we subtract 2•pi from both sides, the answer for x in the second equation is 4•pi/3.
As you know, 2•pi/3 and 4•pi/3 lie between 0 and 2•pi on the unit circle.
Answer: 2•pi/3, 4•pi/3
I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $20per foot, and the fencing for the east and west sides costs $10 per foot. If I have a budget of $200 for the project, what are the dimensions of the garden with the largest area I can enclose? HINT [See Example 2.]
ft (smaller value) ? ft (larger value)
ft2
Answer:
Length = [tex]5\ \text{ft}[/tex]
Breadth = [tex]5\ \text{ft}[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the length of the garden
and [tex]y[/tex] be the width of the garden
From the details of the cost in the question we get
[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]
Now area of the garden is
[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]
Differentiating with respect to x we get
[tex]\dfrac{dA}{dx}=10-2x[/tex]
Equating with 0
[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]
Double derivative of the area is
[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]
So, area is maximum at [tex]x=5[/tex]
[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]
So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].
Samir usually drink 3 cups of coffee in the morning how many liters of coffee does he drink round
Answer:
0.709765 liters
Step-by-step explanation:
Question 2 options: A consumer advocate group selects a random sample of 205 snack foods and finds that 174 of them contain more fat grams than what is indicated in the snack's nutritional information. Create a 90% confidence interval for the population proportion for snack foods that contain more fat grams that what is indicated in the snack's nutritional information.
Answer:
156 snack foods.
Step-by-step explanation:
205 - 174 = 31
To find 90% of 174, multiply 174 by 0.90.
174 x 0.90 = 156
The answer is 156 snack foods.
evaluate 103 × 97 without directly multiplying
Answer:
9991
Step-by-step explanation:
103 × 97
(100 +3) (50+47)
get two number which you can add to get the value in the question
n then expand
100(50+47) +3(50+47)
5000+4700+150+141
9991
HELP I GIVE BRAINLIEST
Answer:
The answer is 15/19
Step-by-step explanation:
Both 60 and 76 are divisible by 4:
60/4 = 15 and 76/4 = 19
Final answer; 15/19
Is 4/10 closer to 0, 1, 1/2
Answer:
1/2
Step-by-step explanation:
Divide the denominator in half
10/2 = 5
4 is close to 5 so 4/10 is close to 1/2
Answer:
4/10 is closer to 1/2.
Think of a pie. There are 10 slices total, but only 4 slices remain, because I ate them all! Do you think that 4 out of 10 slices would be closer to a whole pie or half a pie? It would be closer half a pie.
Further explanation:
If you were to round the number 44 to the closest ten, it would be 40. If you were to round 47 to he nearest ten, it would be 50. If you were to round 45 to the nearest ten, it would also be 50. I hope this helps!
Half (1/2) is the answer.
Pizza time: A local pizza parlor is offering a half-price deal on any pizza with one topping. There are nine toppings from which to choose. In addition, there are three different choices for the size of the pizza, and two choices for the type of crust. In how many ways can a pizza be ordered?
Answer:
You can order pizza in 56 ways.
Step-by-step explanation:
A pizza can be ordered in 56 ways
Step-by-step explanation:
From the information that the problem gives to us, we have that:
For each topping, there are four different choices for the size of the pizza.
For each size of pizza, there are two possible choices of crust.
There are seven toppings for us to choose.
So
4*2*7 = 56
A pizza can be ordered in 56 ways
Which ordered pair would form a proportional relationship with the point graphed below?
(10.-20)
(-30, 20)
(-10,5)
(35, -20
Do you guys know this.
Answer:
0.77
Step-by-step explanation:
You solve the inner first, then move to the outer.
Plug in x = 20 for g(x) = [tex]\frac{2x+2}{x-6}[/tex]. It should give you [tex]\frac{42}{14}[/tex], which simplifies to 3.
You then need to solve f(x) with the given value from g(x), which is 3.
Plug in x = 3 for the equation [tex]\sqrt{0.4x^2-x}[/tex], and you should get [tex]\sqrt{0.6}[/tex].
The answer is roughly 0.77.
Olivia does chores every Saturday morning. She spends 1/3 of her time cleaning her room. Of the remaining 2/3 of her time, she spends 6/7 of it cleaning the kitchen. How much of Olivia's total time does she spend cleaning the kitchen?]
Answer:
she spends 9 hours
Step-by-step explanation:
Geometry please help!!!!!!!?
Answer:
It is same as the length of YX =8 inches so the length of VW=8 inches
HURRY!! At the snack bar, hot dogs cost $4 each and bottled water costs $2 each:
Answer: (2,1) (1,3)
Step-by-step explanation: Assume that the number of hot dogs is X and the number of water bottles is y.
What number divided by−3 gives 12 as the result?
Answer:
-36
Step-by-step explanation:
x / (-3) = 12
x = 12*(-3)
x = -36
A radius of 8.5m what is the area
Answer:
22/7 * 8.5 * 8.5 = answer
Answer:
Step-by-step explanation:
A = π r² ≈ 3.14 × (8.5)² = 226.865 m²
For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 500 with a standard deviation of 100. Assume that the SAT scores are normally distributed. What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
b) between 450 and 675?
Answer:
The probability that a randomly selected high school senior's score on mathematics part of SAT will be
(a) more than 675 is 0.0401
(b)between 450 and 675 is 0.6514
Step-by-step explanation:
Mean of Sat =[tex]\mu = 500[/tex]
Standard deviation = [tex]\sigma = 100[/tex]
We will use z score over here
What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
P(X>675)
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]
Z=1.75
P(X>675)=1-P(X<675)=1-0.9599=0.0401
b)between 450 and 675?
P(450<X<675)
At x = 675
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]
Z=1.75
At x = 450
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{450-500}{100}[/tex]
Z=-0.5
P(450<X<675)=0.9599-0.3085=0.6514
Hence the probability that a randomly selected high school senior's score on mathematics part of SAT will be
(a) more than 675 is 0.0401
(b)between 450 and 675 is 0.6514
5+3*3x-2 let x=2 i need help please
Answer:
21
Step-by-step explanation:
archilles ordered a pizza with 16 slices every hour he ate half of the remaining slice
Answer:
so there is 8 slice left
Step-by-step explanation:
WHICH NUMBER MEANS THE SAME AS 2,000,000 + 70,000,000 + 6,000,000 +
300,000 + 40,000 + 2,000 + 100 +10 +7 ANSWER
78,342,117
Step-by-step explanation:
Just add! And yeah have a good day ^-^
Answer:im assuming we add them
Step-by-step explanation:
78342117
Rewrite −x−6 with a positive exponent. Assume x is not equal to zero.
On a map , 1 inch represents 10 feet . How many inches would represent 35 feet .
Answer:
3 and a half inches or 3.50 inches
Step-by-step explanation:
if ten feet is 1 inch 30 feet would be 3 inches, 5 feet would make a half a inch since 10 feets divided by 2 is 5. one inch divided by 2 is 0.50 inches (or a half)
there for the answer is 3 and a half inches
2. What is the place value of the 5 in 3562?
Answer:
Hundreds Place
Step-by-step explanation:
The 5 is in the hundreds place.
Hope this helps :D
3 is the thousands place
5 is the hundreds place
6 is the tens place
2 is the ones place
You tell me the answer.
if 8 identical items together weigh 30 kg, how much does each one weigh?
Answer:
each weighs 3.75 minimum
Answer:
Each item weighs 3.75 kg, or 3 and 3/4 kg.
Step-by-step explanation:
divide the total weight by the total amount of items. 30/8=3.75
hope this helped! :)
find the slope and the y-intercept of 7x = 2y-4
Answer:
Slope: [tex]\frac{7}{2}[/tex]
Y-intercept: (0, 2)
Step-by-step explanation:
7x = 2y - 4
-2y = -7x - 4
y = [tex]\frac{-7}{-2}[/tex] x - [tex]\frac{4}{-2}[/tex]
y = [tex]\frac{7}{2}[/tex] x + 2
The slope is always the coefficient of x and the y-intercept is always the constant. It looks like (0, constant) when written in y-int form.
Answer:
slope (m) is 7/2 (aka 3.5) and y-int is (0,2)
Step-by-step explanation:
I don't really have an explanation, basically rearrange the problem so that to y is on the left but it would be 2y so divide the right side by two. I an explain further in depth if needed
y-4=-x+7 in standard form.
Answer:
Step-by-step explanation:
x + y = 11
Dorian posted two online videos on the same day. The total number of views for Video A after t days can be modeled by the equation v = 12t. The total number of views for Video B after t days is shown by the graph. Which statement is true?
Answer: C The rate of change for the function for video a is constant but the rate of change for video b is not constant
Step-by-step explanation:
Margaret is making strawberry milkshakes for the kids party. The recipe calls for 1/3 of a cup of strawberry syrup to make 8 milkshakes. How many cups of Strawberry syrup are needed to make 48 milkshakes?
A.) 3
B.)2
C.)16
D.) 8
Answer:
B. The answer is 2 cups.
Solve the formula 5x + 2y = 19 for y
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[tex]5x + 2y = 19[/tex]
Subtract sides 5x
[tex] - 5x + 5x + 2y = - 5x + 19[/tex]
[tex]2y = - 5x + 19[/tex]
Divide sides by 2
[tex] \frac{2y}{2} = \frac{ - 5x + 19}{2} \\ [/tex]
[tex]y = \frac{ - 5x}{2} + \frac{19}{2} \\ [/tex]
[tex]y = - \frac{5}{2} x + \frac{19}{2} \\ [/tex]
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The solution of the equation 5x + 2y = 19 for the value of y is y = (-5 / 2)x + ( 19 / 2).
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given expression is 5x + 2y = 19. The value of y will be calculated as:-
5x + 2y = 19
2y = 19 - 5x
y = ( 19 / 2 ) - ( 5x / 2 )
Therefore, the solution of the equation 5x + 2y = 19 for the value of y is y = (-5 / 2)x + ( 19 / 2).
To know more about an expression follow
https://brainly.com/question/723406
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A recipe uses 150g butter, 500g sugar, and 100g currants to make 18 small cakes?
a. how many of each ingredient will be needed to make 6 dozen cakes
b. how many whole cakes could be made with 1kg of butter
Answer:
a. The following will be needed to make 6 dozen cakes:
Number of grams of butter needed = 600g
Number of grams of sugar needed = 2,000g
Number of grams of currants needed = 400g
b. The number whole that cakes could be made with 1kg of butter is still 18 whole cakes.
Step-by-step explanation:
a. how many of each ingredient will be needed to make 6 dozen cakes
This can be calculated as follows:
One dozen = 12
Number of small cakes in 6 dozen cakes = 6 * 12 = 72 small cakes
Number of 18 small cakes that can be obtained from 72 small cakes = 72 / 18 = 4
Therefore, we multiply each ingredient by 4 to obtain the number oof each ingredient that will be needed to make 6 dozen cakes as follows:
Number of grams of butter needed = 150 * 4 = 600g
Number of grams of sugar needed = 500 * 4 = 2,000g
Number of grams of currants needed = 100 * 4 = 400g
b. how many whole cakes could be made with 1kg of butter
Ordinary in terms of measurement, we have:
1kg = 1,000g
Since it is not indicated in the question that additional grams of other ingredients are made available, only 150g butter will be used out of the 1,000g butter made available together with already available 500g sugar and 100g currants to make just 18 cakes. This implies that no additional whole cakes will be made to add to the current 18 small cakes that is being made. Additional whole cakes would only be made when additional grants of sugar and currants are made available.
Therefore, the number whole that cakes could be made with 1kg of butter is still 18 small cakes.
A garden is in the shape of a rectangle 90 m by 60 m.
Flowers are grown in 40% of the garden.
The rest of the garden is grass.
Work out the area of the garden that is grass.
Answer:
3240 sq meters
Step-by-step explanation:
Area of garden = 90*60= 5400 square meters.
Flowers grown on = 40%
So, grass grown on = (100 -40)% = 60%
60% of 5400 = 0.6*5400 = 3,240.
So, the area of the garden that is grass = 3,240 square meters
Sierra, an Event Planner for Hilton, has group medical insurance with an annual premium of $8,245. Her employer pays 74%. If she is paid semi monthly, a) what is her portion of the annual premium? b) her medical insurance deduction per pay period?
9514 1404 393
Answer:
$2,143.70$89.32Step-by-step explanation:
If 74% is paid by Hilton, then Sierra pays 26% of $8245 per year. Her annual share is ...
0.26 × $8245 = $2143.70 . . . Sierra's share
__
Then the deduction in each of her 24 pay periods is ...
$2143.70/24 = $89.32 . . . per pay period