Find the absolute maximum and minimum values of f on the set
d. f(x, y) = 9 + xy − x − 2y, d is the closed triangular region with vertices (1, 0), (5, 0), and (1, 4)
For the function f(x, y) = 9 + xy - x - 2y in the triangular region, the maximum value is 9 at point (1,0), and the minimum value is 1 at point (1,4). The critical point does not lie within the triangle region.
Explanation:To find the absolute maximum and minimum values of the multivariate function f(x, y) = 9 + xy − x − 2y on the triangular region with vertices (1, 0), (5, 0), and (1, 4), we first locate the critical points within the region by solving the system of first order partial derivative equations.
∂f/∂x = y - 1 = 0, which means y = 1∂f/∂y = x - 2 = 0, which means x = 2
Notice that (2,1) is not in the triangle region, so there's no critical point in the interior of the triangle. The maximum and minimum must occur somewhere on the boundary, i.e., the lines connecting (1, 0), (5, 0), and (1, 4).
After using these points in the function, we get the following:
F(1,0) = 9F(5,0) = 4F(1,4) = 1
The maximum value is 9 when (x,y) are (1,0) and the minimum value is 1 when (x,y) are (1,4).
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Suppose P(E) = 0.3. Find P(not E). Suppose P(not E) = 65%. Find P(E).
What is the relationship between E and not E?
If the width of a rectangle is 3in less than the length, and the perimeter of the rectangle is 14in, find the length and width of the rectangle.
One half of some number
Kendra bought a magazine for $3 and four paperback books for $5 each the expression 3 + 4 x 5 represents the total cost in dollars of her purchases what are the terms in this expression
What is f(x)=8x2+4x written in vertex form
Answer:
Vertex form:
[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]
Step-by-step explanation:
Given: [tex]f(x)=8x^2+4x[/tex]
We need to write in vertex form.
Vertex form:
[tex]y=a(x-h)^2+k[/tex]
vertex: (h,k)
[tex]f(x)=8x^2+4x[/tex]
Step 1: Take out 8 common from each term
[tex]f(x)=8(x^2+\frac{1}{2}x)[/tex]
Step 2: Add and subtract square of half of coefficient of x
[tex]f(x)=8(x^2+\frac{1}{2}x+\frac{1}{16}-\frac{1}{16})[/tex]
Step 3: Factor the term inside parentheses
[tex]f(x)=8(x^2+2\cdot \frac{1}{4}\cdot x+(\frac{1}{4})^2)-8\cdot \frac{1}{16})[/tex]
[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex] [tex]\because (a^2+2ab+b^2)=(a+b)^2[/tex]
Hence, The vertex form of f(x)
[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]
Hattie jumps rope 57 times in 3 minutes. If Hattie jumps at a constant speed, how many times does she jump per minute?
Answer: Hattie Can jump 57 times in 3 minutes so therefore she jumps 19 times per minute. Because if do 57/3 it would give you 19.
Hope this helped!
What's the radius of a circle with an area of 64 square feet?
Answer:
4.51
Step-by-step explanation:
if a/4 = b/7, what is the value of a-b/b ?
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.
Answer:
The outfielder must throw the ball 125 feet to return it to the pitcher.
Step-by-step explanation:
It is given that On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder.
Now, applying the law of cosines,
[tex]a^2=b^2+c^2-2bccosA[/tex],
Putting b=43, c=162 and A=27°, we have
[tex]a^2=(43)^2+(162)^2-2(43)(162)cos27^{\circ}[/tex]
[tex]a^2=1849+26244-12413.4[/tex]
[tex]a^2=15679.6[/tex]
[tex]a=125.21[/tex]
[tex]a[/tex]≈[tex]125 feet[/tex]
Thus, the outfielder must throw the ball 125 feet to return it to the pitcher.
Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.
Determine the values of n for which f(x)=x^2 has an inverse that is a function. Assume that n is a whole number.
Of the computer games Lynne owns, 5-12 are sport games and 3-12 are educational. What fraction of the games are either sport games or educational games?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
We have that:
Lynne owns 12 games.
Of those
5 are sports games
3 are educational
What fraction of the games are either sport games or educational games?
[tex]f = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}[/tex]
In the casino game roulette players bet on which of 38 equally likely outcomes will occur on a single spin of the wheel. The probability of the ball landing on black is 18/38. If you bet $100 on black, which of the following is the best choice for your expected value?
a)-$5.26
b)+$5.26
c)+$52.63
d)-$52.63
e)0.00
Answer is a) -$5.26, just not sure how to achieve that. I know it's asking to find the mean (mu).
B) the first marble is replaced, and another marble is chosen at random. if you're told the marble has the number 6 on it, what is the probability the marble is blue?
The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, is 4 out of 7.
Explanation:The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, can be found using conditional probability.
The probability of drawing a blue marble on the first draw is 4 out of 7 (4 blue marbles out of a total of 7 marbles). Since the first marble was replaced, the probability of drawing a blue marble on the second draw is still 4 out of 7. Therefore, the probability that the marble is blue on the second draw, given that the first marble had the number 6 on it, is also 4 out of 7.
What integer is equivalent to 9 3/2
Which ordered pair is identified by the letter "G" on this coordinate grid?
A cell phone plan includes 450 anytime minutes for $35 per month, plus $18.85 for a cell phone and $25 for a one-time activation fee. let x represent the number of months of service. write an equation in the form y equals mx plus
b. find the ordered pair associated with the equation for xequals9. if you sign a 1-yr contract, how much will this cell phone package cost?
The cost of the cell phone plan over x months is represented by the equation y = 35x + 43.85. For 9 months, the total cost is $359.85, and for a 1-year contract, the total annual cost is $463.85.
The total monthly cost of the cell phone plan for x months of service can be represented by the linear equation y = 35x + 18.85 + 25. Here, y represents the total cost, x represents the number of months, 35 is the cost per month, 18.85 is the cost of the cell phone, and 25 is the one-time activation fee. The equation simplifies to y = 35x + 43.85, since the cost of the phone and the activation fee is a one-time charge, independent of the number of months.
For x = 9 months of service, the ordered pair is (9, y), where y = 35(9) + 43.85. Therefore, the ordered pair associated with x = 9 is (9, 359.85).
If you sign a 1-year contract, which is 12 months, you will pay y = 35(12) + 43.85, which results in a total cost of $463.85 for the year.
Dylan made his credit card payment at noon on the payment due date. According to Consumer Protection Law, how much time does the bank have to credit the payment to his account?
Answer:
Step-by-step explanation:
The transaction time is 24 hours or one business day.
Dylan made his credit card payment at noon on the payment due date. According to Consumer Protection Law, how much time does the bank have to credit the payment to his account? So, it is the same day/date or within 24 hours.
Final answer:
Banks are typically required to credit card payments to the customer's account by the end of the business day on which the payment was made, according to Consumer Protection Law. This ensures consumers are not unfairly charged late fees if payments are made on the due date.
Explanation:
The question concerns the timeframe within which a bank is required to credit a payment to a customer's account, according to Consumer Protection Law. If Dylan made his credit card payment at noon on the payment due date, the bank is typically required to credit the payment to his account by the end of that business day.
This requirement ensures that consumers are not unfairly penalized with late fees if they make their payment on the due date. It's essential for consumers to understand the specific policies of their credit card issuer and the relevant consumer protection laws to avoid any unnecessary charges. Timely payments are crucial for maintaining good credit health and avoiding additional fees.
Jaclyn sells candles that are in the shape of cones. She makes a green candle that has a radius of 2.5 inches and a height of 9 inches. She sells each candle at a price of $0.25 per cubic inch of wax. Which statements about the green candle are true? Check all that apply. Use 3.14 for pie.
The volume of the green candle is about 23.55 in.(cubed)
The volume of the green candle is about 58.88 in. (cubed)
The diameter of the green candle is 5 in.
The diameter of the green candle is 1.25 in.
The base area of the green candle is about 19.63 in. (squared)
The base area of the green candle is about 7.85 in. (squared)
The price of one green candle is about $5.89.
The price of one green candle is about $14.72.
Answer:
2,3,5,8
Step-by-step explanation:
edge 22
From a group of 10 candidates, a committee of 4 people is selected. In how many different ways can the committee be selected?
Identify the percent of change as increase or decrease then find the percent of change round to the nearest tenth of a percent (if necessary)
1. 6 yards to 36 yards
2. 6 hits to 3 hits
3. 120 meals to 52 meals
4. 35 words to 115 words
The area of a triangular block is 25 square inches. If the base of the triangle is twice the height, how long are the base and the height of the triangle?
Suppose a cake was cut into 8 equal size pieces and 6 people ate all the pieces. Explain how they could have divided the pieces so that everyone ate the same amount of cake
4 minus the product of one and a number x
Which of the following describes the graph of the equation
y = 2(x+2)
A. Line
B. Circle
C.Ellipse
D. parabold
The salesman has observed that many students are looking for cars that cost less
than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
Introducing vehicles costing less than $5,000 will alter the supply curve by adding a new segment for lower-priced cars, likely leading to an increase in the quantity supplied for this market segment. This reflects market segmentation and aligns with the demand for cheaper vehicles.
The introduction of cars less than $5,000 into the salesman's inventory may affect the distribution of car sales. When discussing economic models, a supply curve (such as curve So) indicates the quantity of goods that sellers are willing to supply at various prices. According to the scenario provided, Point J on the supply curve So shows that if the price is $20,000, the quantity supplied will be 18 million cars. However, if the price drops to below $5,000, this will most likely introduce a new segment on the supply curve, as the current supply data relates to higher-priced vehicles.
Introducing lower-cost cars will attract a different consumer base, often overlooked in premium markets. This could lead to an increase in the quantity supplied of cheaper cars, as the demand for this segment is likely to be different from premium cars. If the projection of selling 200 cars in 10 years holds true, it will introduce a new point on the supply curve, which will represent cars at a lower price point and possibly a higher quantity compared to the original supply curve for higher-priced cars.
It cannot be determined from the given information whether the overall effect will pull market equilibrium towards the lower end, but it introduces the concept of market segmentation where different products and prices can co-exist, catering to different consumer needs and preferences.
Six cakes cost 3.60. How much do seven cakes cost
Charlotte's annual salary is 29,354 dollars. She is hoping to win the World Lottery which has a grand prize of 6,156,782,221 dollars. Approximately how many times as large is the World Lottery's grand prize as Charlotte's annual salary?
The World Lottery's grand prize is approximately 209,701 times larger than Charlotte's annual salary when dividing the grand prize amount by her annual salary.
To determine approximately how many times larger the World Lottery's grand prize is compared to Charlotte's annual salary, we perform a division of the two amounts. Charlotte's annual salary is $29,354, and the World Lottery grand prize is $6,156,782,221.
To find out how many times larger the lottery prize is than Charlotte's salary, we use the following calculation:
Lottery Prize to Salary Ratio = World Lottery Grand Prize / Charlotte's Annual Salary
Lottery Prize to Salary Ratio = $6,156,782,221 / $29,354 ≈ 209,701
This means that the World Lottery's grand prize is approximately 209,701 times larger than Charlotte's annual salary.
Note: This is a simplified approximation and does not take into account any deductions or taxes that would be applied to either the grand prize or the salary.
Evaluate the expression. 9! − 5!