Sum of the maximum and minimum values of y=2cos^2 x + 3sin^2 x + 5
Answers
To begin with, we can simplify y using the Pythagorean identity:
y = 2 cos²(x) + 3 sin²(x) + 5
y = 2 (cos²(x) + sin²(x)) + sin²(x) + 5
y = 2 + sin²(x) + 5
y = sin²(x) + 7
Next, we can further rewrite this using the half angle identity for sine:
y = (1 - cos(2x))/2 + 7
y = 15/2 - 1/2 cos(2x)
Now, since cos(x) is bounded between -1 and 1, we have
max(y) = 15/2 - 1/2×(-1) = 15/2 + 1/2 = 8
and
min(y) = 15/2 - 1/2×1 = 15/2 - 1/2 = 7
Then the sum of the maximum and minimum is 8 + 7 = 15.
Related Questions
glassdoor four players pick a real number from [0,1]. the players with the middle two numbers are paired together, while the players with the two extreme numbers are paired together. the pair with a lower sum has to each pay the difference to the pair with a higher sum. if you are allowed to choose your number (while everyone else draws uniformly at random), which number should you choose?
Answers
The expected value of the sum of the two extreme numbers is 1/2.
Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
The optimal strategy for you would be to choose the number 0.5, as it maximizes the probability that your pair will have the highest sum, and minimizes the probability that your pair will have the lowest sum.
This is because if all players choose a number uniformly at random, the expected value of the lowest and highest numbers will be 0 and 1 respectively, and the expected value of the middle two numbers will be 0.5. Therefore, by choosing 0.5, you have the best chance of having the highest sum, which means you will have to pay the least amount of money.
Therefore, the expected value of the sum of the two extreme numbers is 1/2.
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chegg what is the average gpa for an individual who scored 500 on both the sat critical reading and sat math sections? find the 95% confidence interval for this average.
Answers
To determine the average GPA for an individual who scored 500 on both the SAT Critical Reading and SAT Math sections, we would need more information as the SAT scores alone do not provide a direct measure of GPA
To calculate the 95% confidence interval for the average GPA, we would need a sample of individuals who scored 500 on both SAT sections, along with their corresponding GPAs. With this data, we can compute the sample mean GPA and the standard error of the mean.
The 95% confidence interval represents the range within which we can be 95% confident that the true population average GPA lies. It is calculated as the sample mean plus or minus the margin of error. The margin of error is determined by the standard error of the mean and the critical value corresponding to a 95% confidence level.
The formula for the 95% confidence interval is:
CI = sample mean ± (critical value * standard error)
The critical value is obtained from a t-distribution table based on the sample size and desired confidence level. The standard error is calculated by dividing the sample standard deviation by the square root of the sample size.
By plugging in the appropriate values into the formula, we can compute the 95% confidence interval for the average GPA of individuals who scored 500 on both SAT sections, assuming we have the necessary data.
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If Nelson needs $5500 in 17 years, how much does he need to invest if the interest will be compounded continuously at an interest rate of 4.64%
Answers
The amount Nelson needs to invest if he wants $5500 in 17 years is $2543.91
What is an equation?An equation is an expression that shows how numbers and variables are related to each other.
A compound interest is in the form:
A = P(1 + r/100)ⁿ
Where P is the principal, A is the final amount, r is the rate and n is the number of years.
Given that A = $5500, r = 4.64%, t = 17, hence:
5500 = P(1 + 4.64/100)¹⁷
5500 = P(1.0464)¹⁷
P = $2543.91
The amount he needs to invest is $2543.91
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What are the miller indices for the plane shown in the unit cell?
A negative index is indicated with a minus sign (-) in front of (rather than over) the index number.
Answers
The Miller indices for the plane shown in the unit cell are (1,1,0).
The Miller indices are a set of integers used to describe the orientation of a crystal plane in a crystal lattice. The indices are calculated as the reciprocal of the fractional coordinates of the normal to the plane with respect to the lattice vectors.
The indices are expressed in a reduced form, with the greatest common divisor of the indices being 1. In this case, the plane has a normal that intersects the x and y axes of the unit cell at equal distances, hence the indices (1,1,0), which indicate that the plane is inclined towards the z-axis.
The minus sign is not needed as the Miller indices only describe the orientation of the plane and not its handedness.
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The following information, taken from records in the Circle Restaurant, provides the results of butcher tests on 10 legs of veal, Canada Grade A1, purchased over the last several weeks from George's Meats, Inc. Veal legs are purchased to produce 150 -gram portions of veal cutlets. The restaurant paid $850.41 for the 10 legs, which weighed a total of 112.93 kilograms as purchased. a. Given the preceding information, complete butcher test calculations to determine standard cost of the 150 gram portion. b. Find the cost of the standard 150 gram portion at each of the following dealer prices: 1. $7.79/kg. 2. $8.10/kg 3. $8.50/kg. c. Find the cost of each of the following: 1. A 175 gram portion, if dealer price is $7.79/kg 2. A 125 gram portion, if dealer price is $8.10/kg 3. A 125 gram portion, if dealer price is $8.55/kg d. The owner of the Circle Restaurant wants portion cost for veal cutlet to be $2.65, regardless of variations in dealer price. Determine the correct portion size if 1. Dealer price is $7.80/kg 2. Dealer price is $8.20/kg e. Develop a chart showing the costs 130 gram, 155 gram, and 180 gram portions at dealer prices per kilogram of $8.00,$8.10, and so on in $0.10 increments up to $9.00 per kilogram. f. How many kilograms of veal leg (as purchased) will be needed to prepare and serve 150 gram portions to 250 people? g. Given the weight of the average leg of veal, as determined in the butcher test, how many legs should the steward order to prepare and serve 150 gram portions to 250 people? h. Records show that the Circle Restaurant used 48 legs of veal last month. How many standard 175 gram portions should have been produced from these 48 legs? i. The restaurant has a banquet for 500 people scheduled for tonight, and the manager has promised to serve veal cutlet as the entrée. The steward neglected to order veal legs for this specific party, but there are 25 legs of veal in the house and veal cutlet is not on the regular dining room menu for tonight. Using these 25 legs of veal for the party, what size portion should be prepared so that all 500 people can be served?
Answers
a) cost of the 150 gram portion is $1.1343. b)cost of each of the following: $1.1685, $1.215, $1.275. c)cost of each of the following: $1.363, $1.0125, 1.06875 d) the correct portion size are: 0.3397 kg, 0.3232 kg f)To serve 150-gram portions to 250 people, we need to calculate the total weight of veal needed is 37.5 kg g)Number of legs is 3 h) 3 portions of 175 gram portions should have been produced from these 48 legs i)
a)To determine the standard cost of the 150-gram portion, we need to calculate the cost per kilogram of veal.
Total cost of 10 legs = $850.41
Total weight of 10 legs = 112.93 kg
Cost per kilogram = Total cost / Total weight = $850.41 / 112.93 kg = $7.5265 per kg. Cost of 150g = $1.1343
b. 1. Cost of the standard 150-gram portion at a dealer price of $7.79/kg:
Cost of 150 grams = 150 g * $7.79/kg = $1.1685
Cost of the standard 150-gram portion at a dealer price of $8.10/kg:
Cost of 150 grams = 150 g * $8.10/kg = $1.215
Cost of the standard 150-gram portion at a dealer price of $8.50/kg:
Cost of 150 grams = 150 g * $8.50/kg = $1.275
c. 1. Cost of a 175-gram portion at a dealer price of $7.79/kg:
Cost of 175 grams = 175 g * $7.79/kg = $1.363
Cost of a 125-gram portion at a dealer price of $8.10/kg:
Cost of 125 grams = 125 g * $8.10/kg = $1.0125
Cost of a 125-gram portion at a dealer price of $8.55/kg:
Cost of 125 grams = 125 g * $8.55/kg = $1.06875
d. 1. To determine the portion size at a dealer price of $7.80/kg with a desired portion cost of $2.65:
Portion size = Portion cost / Dealer price per kilogram = $2.65 / $7.80/kg = 0.3397 kg (or 339.7 grams)
To determine the portion size at a dealer price of $8.20/kg with a desired portion cost of $2.65:
Portion size = Portion cost / Dealer price per kilogram = $2.65 / $8.20/kg = 0.3232 kg (or 323.2 grams)
e. Here is a chart showing the costs of 130-gram, 155-gram, and 180-gram portions at dealer prices per kilogram ranging from $8.00 to $9.00 in $0.10 increments.
f. To serve 150-gram portions to 250 people, we need to calculate the total weight of veal needed.
Weight per portion = 150 g
Total weight needed = Weight per portion * Number of portions = 150 g * 250 = 37,500 grams = 37.5 kg
g. Given the weight of the average leg of veal, we can determine the number of legs required to serve 150-gram portions to 250 people.
Weight per portion = 150 g
Number of portions = 250
Total weight required = Weight per portion * Number of portions
Number of legs required = Total weight required / Average weight of a leg = 3
h. To determine the number of standard 175-gram portions that should have been produced from 48 legs, we need to calculate the total weight of veal available.
Total weight of veal = Average weight of a leg * Number of legs
Number of portions = Total weight of veal / Weight per portion = 3.089
i. To serve 500 people using 25 legs of veal, we need to calculate the portion size.
Number of portions = Number of people / Number of legs
Portion size = Total weight of veal / Number of portions / 1000 (to convert grams to kilograms)
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A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
A. 14 and 1 over 7 in2
B. 23 and 4 over 7 in2
C. 47 and 1 over 7 in2
D. 84 and 6 over 7 in2
Answers
Answer:
D. 84 and 6 over 7 in2
Step-by-step explanation:
The surface area of the cylindrical mini muffin can be calculated as follows:
Surface area = 2πr^2 + 2πrh
where r is the radius of the circular base and h is the height of the cylinder.
Given that the diameter of the mini muffin is 2 inches, the radius can be calculated as 1 inch (since radius = diameter / 2).
So, r = 1 inch and h = 1 and 1/4 inches.
Substituting these values into the surface area formula, we get:
Surface area = 2 x (22/7) x 1^2 + 2 x (22/7) x 1 x (5/4)
= (44/7) + (55/7)
= 99/7
≈ 14.14 square inches
Therefore, the surface area of 1 mini muffin is approximately 14.14 square inches.
To wrap 6 mini muffins, we need to multiply the surface area of 1 mini muffin by 6:
Surface area of 6 mini muffins = 6 x 14.14
≈ 84.84 square inches
Rounding off to one decimal place, the minimum amount of paper needed to wrap 6 mini muffins is approximately 84.8 square inches, which is closest to option D, 84 and 6/7 in^2.
draw a coordinate plane and find points A(-2;0) B(1;4) C(-5;-1) D(5;0) E(0;0)
pls help me
20 points
Answers
System analysts define an object's attributes during the systems design process. true or false?
Answers
The statement "System analysts define an object's attributes during the systems design process" is true because defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.
In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.
For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.
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Can someone help please?
Answers
Answer:
2.48
Step-by-step explanation:
Find the value of x . Write your answer in simplest form.
Answers
BRAINLIEST ANSWER!! I need help ASAP!
Answers
Answer:
n = -9.5
Step-by-step explanation:
6n + 15 = -42
6n = -57
n = -9.5
an inlet pipe on a swimming pool can be used to fill the pool in 26 hours. the drain pipe can be used to empty the pool in 30 hours. if the pool is 25 filled and then the inlet pipe and drain pipe are opened, how many more hours would it take to fill the pool? round your answer to two decimal places, if needed.
Answers
The total time required to fill the pool completely as per the inlet and drain pipe capacity is given by 146.25 hours.
Let's assume that the capacity of the pool is 1 unit .
The inlet pipe can fill the pool at a rate of 1/26 units per hour.
The drain pipe can empty it at a rate of 1/30 units per hour.
When both pipes are open,
The net rate of filling is the difference between the rate of filling and the rate of emptying,
Net rate = Rate of filling - Rate of emptying
⇒Net rate = 1/26 - 1/30
⇒Net rate = (30 -26 )/780
⇒Net rate = (4)/780
⇒Net rate = 1/195 units per hour
Since the pool is already 25% filled.
This implies,
It still needs to be filled by another 0.75 units.
The time required to fill the pool by 0.75 units at a net rate of 1/195 units per hour can be found using the formula,
Time = Amount of filling needed / Net rate
⇒Time = 0.75 / (1/195)
⇒Time = 146.25 hours
Therefore, the total time taken to fill the pool completely would take another 146.25 hours.
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help me
pleaseeee
i need help
Answers
Answer:
4:2:3
Step-by-step explanation:
First you need to divide each number by a common factor like 2.
1. 16:8:12
Divide all numbers by two
8:4:6
Divide by two again
4:2:3
Since, you cannot simplify all of them again, the asnwer is
4:2:3
Answer:
4:2:3
Step-by-step explanation:
Blue : Green : Red
16 : 8 : 12
4 : 2 : 3
*Spam answers will not be tolerated*
Use the attachment to solve.
Cave (Use the integer alphabet chart to solve.)
Ex: A is -13
Answers
Step-by-step explanation:
C = -11
A = -13
V = 9
E = -9
If you are adding them: -24
Hope this helps!
Find the measure of each arc in circle C.
Answers
The measure of the arc PN, arc QN, arc RP, arc RM, arc RZ, and arc RPN will be 65°, 128°, 125°, 120°, 55°, and 215°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
The measure of the arc MZ is given as,
arc MZ + arc MN = 90
arc MZ + 25 = 90°
arc MZ = 65°
The measure of the arc QN is given as,
arc QN = 38° + 90°
arc QN = 128°
The measure of the arc RP is given as,
arc PR = 87° + 38°
arc PR = 125°
The measure of the arc RZ is given as,
arc RZ + 87° + 38° + 90° + 25° + 65° = 360°
arc PR = 55°
The measure of the arc RM is given as,
arc RM = 55° + 65°
arc RM = 120°
The measure of the arc RPN is given as,
arc RPN = 87° + 38° + 90°
arc RPN = 215°
The measure of the arc PN, arc QN, arc RP, arc RM, arc RZ, and arc RPN will be 65°, 128°, 125°, 120°, 55°, and 215°, respectively.
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The parallelogram is rotated 90° anticlockwise about point G
Which of the points A , B , C and D is the image of point R ?
Answers
Answer:
C
Step-by-step explanation:
Let's say that point G is the origin, (0,0). Then, the coordinates of point R would be (-3, -5). Rotating the point 90° counter-clockwise would result in the final coordinates being (5, -3), therefore the answer is C.
Please help me I'm so stress out
.· Find the perimeter of a parallelogram with the following measurements
: a = 8, b = 5, h = 4
Answers
Answer:
The answer is 26
Step-by-step explanation:
Its right just do it
3t(t+2)-3t² for t = 19
Answers
Answer: 114.
Step-by-step explanation:
\(3t(t+2)-3t^2=\\3t*t+3t*2-3t^2=\\3t^2+6t-3t^2=\\6t.\\t=19\\6*19=\\114.\)
The value of the expression 3t(t+2) - 3t² for t = 19 is 114.
Here, we have to evaluate the expression 3t(t+2) - 3t² for t = 19, follow these steps:
Substitute t with 19 in the expression.
3(19)(19 + 2) - 3(19)²
Perform the operations inside the parentheses.
3(19)(21) - 3(361)
Perform the multiplications.
3 * 19 * 21 - 3 * 361
Perform the remaining operations.
1197 - 1083
Finally, calculate the result.
1197 - 1083 = 114
So, the value of the expression 3t(t+2) - 3t² for t = 19 is 114.
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if f (x) =3(x+3)^2 - 10 then calcutlate f (2)
pls answer todayyy i need help
Answers
Answer:
x
=
−
8
−
√
13
3
,
−
8
+
√
13
3
I dont know why the answer is spacing out like this
for the demand function, q=-5p 1200, determine the price p, that maximizes revenue
Answers
The price that maximizes revenue is p = 120.
The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.
Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:
R = p × q
R = p × (-5p + 1200)
To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.
dR/dp = -10p + 1200 = 0
Solving this equation for p:
-10p + 1200 = 0
-10p = -1200
p = -1200 / -10
p = 120
Therefore, the price that maximizes revenue is p = 120.
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what is the x intercept
Answers
Answer:
The answer is B
declare the variables
set up the equation:
The difference in ages between Joe and his older brother Sam is five years. The sum of
their ages is 35. How old is each brother?
Answers
Find the solution of the equation.
b – 12 = –8
A 4
B 20
C -4
D -20
Answers
Help Me Please
I need to do this for school
Answers
Answer:
He worked for 3 hours.
Step-by-step explanation:
you can solve this by muiltipling the amount of hours by the kilograms done in an hour.
Answer:
3 hours
I hope its right
A chemist is observing a solution temperature over a four-hour period that starts at -12. 4c. In the four hours, the temperature rises 5. 7c and drops 8. 1c. What is the temperature of the solution after four hours ?
Answers
After four hours, the solution's temperature will be negative at 14.8 °C.
What does the expression mean?The result of the calculation that the mathematical model depicts is the expression's result when the necessary parameters and natural laws are given values.
Given Data
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To solve the equation properly and accurately, this rule is applied.
A chemist is monitoring the temperature of a solution during a four-hour period that begins at -12.4°C. The temperature increases by 5.7°C throughout the four hours and decreases by 8.1°C.
Afterward, the phrase will be
-12.4 + 5.7 - 8.1
If we condense the phrase, we have
-14.8°C
After four hours, the solution's temperature will be negative.
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A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer ?
Answers
Answer: Its B i just took the test
Step-by-step explanation:
the formula for finding the surface area of a cylinder is sa = πr2 πrh . truefalse unlimited attempts remain
Answers
The statement ''the formula for finding the surface area of a cylinder is sa = πr2 πrh.'' is false because the formula for finding the surface area of a cylinder is given by: SA = 2πrh + 2πr^2 , where SA represents the surface area, r is the radius of the base, and h is the height of the cylinder.
The first term, 2πrh, represents the area of the curved surface of the cylinder (the lateral surface area), which is a rectangle that wraps around the cylinder. It is calculated by multiplying the height of the cylinder by the circumference of the base.
The second term, 2πr^2, represents the areas of the two circular bases of the cylinder.
By adding these two terms together, we obtain the total surface area of the cylinder.
Therefore, the correct formula for finding the surface area of a cylinder is SA = 2πrh + 2πr^2.
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Julie needs to cut 4 pieces of yam, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the
length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the
total length of all of the yarn that she ends up cutting, y is the graph of the equation continuous or discrete?
Answers
Answer:
She has to cut another piece = 7.75 inches
Total length = 4x + 7.75
This is what y represent, so
y = 4x + 7.75
The graph of the equation is continuous
find a polar equation of the form r=f(θ), where r>0, for the curve represented by the cartesian equation x2 y2=9.
Answers
The polar equation of the curve represented by the Cartesian equation \(x^2\) + \(y^2\) = 9 can be expressed as r = 3. This means that the distance from the origin (r) is always equal to 3, regardless of the angle (θ).
In Cartesian coordinates, the equation \(x^2\) + \(y^2\) = 9 represents a circle centered at the origin with a radius of 3. To express this equation in polar form, we need to convert it to the polar coordinates (r, θ), where r represents the distance from the origin and θ represents the angle.
In polar coordinates, x = rcos(θ) and y = rsin(θ). Substituting these expressions into the Cartesian equation, we get:
\((rcos(θ))^2\) + \((rsin(θ))^2\) = 9
Expanding and simplifying, we have:
\(r^2\)\(cos^2\)(θ) + \(r^2\)\(sin^2\)(θ) = 9
Since \(cos^2\)(θ) + \(sin^2\)(θ) = 1, the equation simplifies to:
\(r^2\) = 9
Taking the square root of both sides, we obtain:
r = ±√9
Since r is always positive in polar coordinates, we take the positive square root, which gives:
r = 3
Therefore, the polar equation for the given curve is r = 3. This means that for any angle θ, the distance from the origin is always 3 units, forming a circle of radius 3 centered at the origin.
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Michael is making a scale drawing of a rectangular room using a scale of 1 inch equals 1.5 feet. He wants to use paper that has a width of 8.5 inches and length of 11 inches.
Will a room that is 12 feet by 15 feet fit on a single sheet of the paper?
HINT: Write and solve a proportion comparing the scale of 1 inch to 1.5 feet equal to how many inches to 12 feet. Then solve for how many inches. Do the same step for the other dimension of 15 feet.
REMEMBER: Your paper is 8.5 inches by 11 inches. Each dimension of the room must be less than both 8.5 inches and 11 inches.
A
Yes
B
No
PLEASE ANSWER ASAP. I REALLY NEED HELP LIKE FR FR
Answers
From the statements, the expression is 1 inch/2.2 ft = x/16 ft
How to determine the expression?
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We can use ratios to solve
Changing 11/5 into a decimal
1 inch x
-------------- = -----------
2.2 ft 16 ft
Using cross products
16 = 2.2 x
Divide each side by 2.2
16/2.2 = x
7.2727 =x Since this is less than 8.5 inches Yes
1 inch x
-------------- = -----------
2.2 ft 15 ft
Using cross products
15 = 2.2x
Dividing each side by 2.2
6.8 =x
Yes
1 inch x
-------------- = -----------
2.2 ft 20 ft
Using cross products
20 = 2.2x
9.09 =x
If this is the 11.5 inch side (15 ft is 6.8 inches which is less than 8.5 inches)
yes
1 inch x
-------------- = -----------
2.2 ft 12 ft
12 = 2.2x
5.4 inches yes since 16 is 6.8 inches
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