Find the absolute maximum and minimum of the function.
f(x,y) =9y² - 36x + 12 over the closed region 9x² +9y² ≤ 81. Absolute Maximum value is ...
Absolute Minimum Value is ...

Answer:13+49x

Step-by-step explanation:Combine Like Terms

48-35 = 13

13+39x

Answer:

75. is yr correct ans.

Step-by-step explanation:

hope it helps.

stay safe healthy and happy.

Answer:

x = 75

Step-by-step explanation:

The triangle has 2 congruent sides and is therefore isosceles with 2 congruent base angles, both of measure x

The sum of the 3 angles = 180° , that is

x + x + 30 = 180

2x + 30 = 180 ( subtract 30 from both sides )

2x = 150 ( divide both sides by 2 )

x = 75

There are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

Here, we have to solve this problem, we can use the concept of combinations, which involves counting the ways to choose a specific number of items from a larger set without regard to the order of selection.

Given the conditions that at least one member must be chosen from each group (artists, singers, writers) and there must be at least 3 artists, we can break down the problem into cases.

Case 1: Choosing 1 artist, 1 singer, and 5 members from the remaining groups (writers).

Case 2: Choosing 2 artists, 1 singer, and 4 members from the remaining groups (writers).

Case 3: Choosing 3 artists, 1 singer, and 3 members from the remaining groups (writers).

For each case, we will calculate the number of ways to choose members and then sum up the results from all three cases to get the total number of ways.

Let's calculate the number of ways for each case:

Case 1:

Number of ways to choose 1 artist: 6C1 (6 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 5 writers: 5C5 (1 way)

Total ways for case 1: 6C1 * 4C1 * 5C5 = 6 * 4 * 1 = 24

Case 2:

Number of ways to choose 2 artists: 6C2 (15 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 4 writers: 5C4 (5 ways)

Total ways for case 2: 6C2 * 4C1 * 5C4 = 15 * 4 * 5 = 300

Case 3:

Number of ways to choose 3 artists: 6C3 (20 ways)

Number of ways to choose 1 singer: 4C1 (4 ways)

Number of ways to choose 3 writers: 5C3 (10 ways)

Total ways for case 3: 6C3 * 4C1 * 5C3 = 20 * 4 * 10 = 800

Now, add up the total ways from all three cases:

Total ways = 24 + 300 + 800 = 1124

So, there are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.

To learn more about combination:

brainly.com/question/15015700

#SPJ12

Answer:A standard form is a form of writing a given mathematical concept like an equation, number, or an expression in a form that follows certain rules. Representing very large or very small numbers concisely, the standard form is used. For example, 4.5 billion years is written as 4,500,000,000 years.

Step-by-step explanation:

Answer:

Step-by-step explanation:

∠WZA + WZY = 180     {linear pair}

88 + ∠WZY = 180

∠WZY = 180 - 88

∠WZY = 92°

∠WXY + ∠WZY = 180     {Opposite angle in cyclic quadrilateral}

x + 92 = 180

       x = 180 - 92

x = 88°

Answer:

2a) 125

2b) 81

Step-by-step explanation:

For 2a:

Whenever one is multiplying there is a two exponents but one is out of the parentheses, you multiply the exponents

So I multiplied the 3 and 1 exponents to get 3 which I then multiplied the new exponent (3) with the base (5) to get 125

For 2b:

Whenever two exponents are multiplied with no parentheses meaning it is just an equation, we add the exponents together. Note, when the exponent is 0, the answer will always be 1.

3^0= 1

1 x 3^4= 81

209.125

Step-by-step explanation:

Multiply the two: 167.3 *1.25

The d score is a standardized measure of the degree to which the independent variable caused a change in the dependent variable, this is also known as the: d. effect size.

In Mathematics, there are two (2) main types of variables and these include the following:

An independent variable simply refers to a type of variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it stands alone because it cannot be changed by any variable being observed or measured.

A dependent variable can be defined as a type of variable which signifies the effect of an independent variable, and it is generally dependent on other factors because it is the part of an experiment that's being observed or measured.

In Statistics, d score is sometimes referred to as effect size and it is commonly used for the measurement of the degree to which an independent variable causes a change in a dependent variable.

Read more on independent variable here: brainly.com/question/82796

#SPJ1

The expression that does not belong is OC) (X - 6)-(-- 10). This expression does not have the same number of terms on both sides, as the left side has one term and the right side has two terms. Additionally, the left side has a coefficient of 1 for x, while the right side has a coefficient of -10 for x.

The expression OC) (X - 6)-(-- 10) does not follow the format of the other expressions, which are all of the form (ax + b) - (cx + d). This expression is not a valid linear expression, since its right side is not in the form cx + d. This expression follows the form (ax + b) - (cx + d) and would be the correct linear expression in this set.

Complete question:

Find (-1x + )-(--). 10 Question 14 The table shows the sales of plain and Asiago cheese bagels at a bakery for hours. Bagel Sales Bagel Cost ($) Number Sold After h Hours Asiago Cheese 1.50 12h + 7 Plain 1.50 7 - 4 After 6 hours, how much more will the bakery have made in sales of Asiago cheese bagels than the sales of plain bage Question 15 Derek owns a snack shop where he sells tins of buttered and caramel weeks. Popcorn Sales Popcorn Cost ($) Number Sold Over w Weeks Buttered 11 8W + 9 Caramel 11 6W - 1 After 12 weeks, how much more will he have made in sales of buttered Question 18 Which One Doesn't Belong? Identify the linear expression that does not belong with OA) (-5x + 3) - (-7x - 1) OB)(-3x + 3) - (-5x - 2) OC) (X - 6)-(-- 10) OD) (-7x + 2) - (-9x - 2)

To learn more about linear expressions:

https://brainly.com/question/25682757

The distance between the building and the ladder is 34.876 foot.

A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.

The ladder forms a right triangle with the building and the ground,

The length of the triangle is 40 foot

The angle made by the ladder is 29.32 degree

By using Trigonometric Ratios

cos 29.32 = Base /  Hypotenuse

cos 29.32 = Base / 40

0.8718 × 40 = Base

Base = 34.876 foot

Base is the distance between the building and the ladder.

Base of the ladder = 34.876 foot

To learn more about trigonometric functions from the given link

https://brainly.com/question/24336684

#SPJ4

Answer:

Step-by-step explanation:

Area Formula= 1/2(base 1 + base 2) x height

You are missing base 1, which would be equal to 17. This is because base 2, which is 23, subtracted by 6 or (3+3), is 17.

So- Base1 = 17, Base2 =23, Height = 17

Formula with variables added= 1/2(17 + 23) x 17

When this equation is solved, the answer is - 340

Now

Area of trapezium

Remember that

the area of the circle is

A=pi*(r^2)

we have

r=9.2/2=4.6 m ------> the radius is half the diameter

substitute

A=pi*(4.6^2)

using a calculator

(Note: the value of pi is the value that appear in the calculator)

Answer:5/8) * (4/7) + ( 3/8)* (2/7) = 13/28

Step-by-step explanation:

The explanation for my answer could go a bit longer but it’s pretty easy to understand the concept & a good approach to hit such questions right in few seconds. Hope it helps !!!!!!

(Remember: we always multiply for AND case & do addition for OR case)

Selection would be in 2 ways possible i.e ( WHITE AND WHITE ball “OR” BLACK AND BLACK ball ) because we have been asked to choose two balls of same color. You cant pick White & White AND Black & Black because in this way u ll end up picking 4 balls which is wrong. so we used “OR”

Now,,,,,Think it like , what is the probability of getting 1 white ball on your first selection out of all balls….???

(Most imp approach)- Don’t consider both selection only in one go !!! so just think it one by one. …..O.K!

Hopefully u too thought it = 5/8 ( i.e there are 5 white balls and you selected one from total 8 balls) ……………………………………….GOOD :)

Now, what about the next ball being white…………..is the most common mistake many could do.

Problem is we have 5 white balls & we have chosen 1 ball out from that,,,, Right?

So, there are only 7 balls left for next selection & How many are there white balls left to select now??? = 4 ( because we have already selected one, out from 5)….. :)

2. PROBABILITY OF GETTING WHITE BALL AGAIN IN SECOND CHANCE = 4/7

PROBABILITY OF GETTING BOTH WHITE = (5/8) * (4/7) (remember, getting the first ball changes the probability of another, since we wanted a white AND a white ball so we ll multiply them both )

3. Similarly, for black we have 2 scenarios, hopefully u thought =(3/8)

4. Can u tell me probability of getting another black now???? = (2/7) ( LIKE WE DID FOR WHITE BALLS)

ANSWER……Probability of getting white & white OR black & black =

= (5/8) * (4/7) + ( 3/8)* (2/7) = 13/28 (& - multiply, OR -addition )

Hope, my long explanation helped you to understand the easy approach for such questions. :)

Thanks for reading! :) have a good day :)

Answer:

1

Step-by-step explanation:

Answer:

Step-by-step explanation:

h^2=x^2+y^2

26^2=24^2+a^2

a^2=26^2-24^2

a^2=100

a=10

(a)  (1203)4 is equal to 99 in decimal and 12 in hexadecimal.

(b)  (5243)8 is equal to 2211 in decimal and 1523 in hexadecimal.

To convert numbers from different bases to decimal using the direct method, we multiply each digit of the number by the corresponding power of the base and sum the results. To convert to hexadecimal using the intermediary binary conversion method, we first convert the number to binary and then group the binary digits into groups of 4, starting from the rightmost digit, and convert each group to its hexadecimal equivalent.

(a) Converting (1203)4 to decimal:

(1203)4 = 1 * 4³ + 2 * 4² + 0 * 4¹ + 3 * 4⁰

= 64 + 32 + 0 + 3

= 99

Converting (1203)4 to hexadecimal:

First, convert (1203)4 to binary:

(1203)4 = (10010)2

Next, group the binary digits into groups of 4:

(10010)2 = (0001 0010)2

Finally, convert each group to its hexadecimal equivalent:

(0001 0010)2 = (12)16

Therefore, (1203)4 is equal to 99 in decimal and 12 in hexadecimal.

(b) Converting (5243)8 to decimal:

(5243)8 = 5 * 8³ + 2 * 8² + 4 * 8¹ + 3 * 8⁰

= 2048 + 128 + 32 + 3

= 2211

Converting (5243)8 to hexadecimal:

First, convert (5243)8 to binary:

(5243)8 = (101 010 100 011)2

Next, group the binary digits into groups of 4:

(101 010 100 011)2 = (0001 0101 0010 0011)2

Finally, convert each group to its hexadecimal equivalent:

(0001 0101 0010 0011)2 = (1523)16

Therefore, (5243)8 is equal to 2211 in decimal and 1523 in hexadecimal.

Learn more about Binary Conversion Method at

brainly.com/question/31675609

#SPJ4

Thus, in polar coordinates, the equation is represented as

\(�2=2�cos⁡(�)r 2 =2rcos(θ), with �2r 2\)

 having a positive coefficient.

To express the equation

\(�2+�2=2�+1x 2 +y 2 =2x+1\)

in polar coordinates, we substitute the polar coordinate representations

\(�=�cos⁡(�)x=rcos(θ) and �=�sin⁡(�)y=rsin(θ). This gives us:(�cos⁡(�))2+(�sin⁡(�))2=2(�cos⁡(\)

\(�))+1(rcos(θ)) 2 +(rsin(θ)) 2 =2(rcos(θ))+1\)

Expanding and simplifying, we have:

\(�2cos⁡2(�)+�2sin⁡2(�)=2�cos⁡(�)+1r 2 cos 2 (θ)+r 2 sin 2\)

Since

\(cos⁡2(�)+sin⁡2(�)=1cos 2 (θ)+sin 2 (θ)=1,\)we can further simplify to:

\(�2+0=2�cos⁡(�)+1r 2 +0=2rcos(θ)+1\)

Simplifying, we obtain:

\(�2=2�cos⁡(�)+1r 2 =2rcos(θ)+1\)

Thus, in polar coordinates, the equation is represented as

\(�2=2�cos⁡(�)r 2 =2rcos(θ), with �2r 2\)

 having a positive coefficient.

Learn more about polar coordinate here:

https://brainly.com/question/31904915

#SPJ11

i think i is 56 do you have answer choices?

Answer:

B.

Step-by-step explanation:

Since i is in the denominator, if i = 0, then the result will be undefined. Therefore, B cannot be a value of θ.

Given that Tyson has a $50 gift card to use at a store. He does not have any additional money to spend at the store. Tyson will purchase a belt that costs $8 and x number of shirts that cost $15 each. The mo appropriate domain of the function is C. 0 < x < 2 where x is an integer.

The function f(x) = 42 - 15x models the balance on the gift card after Tyson makes the purchases. The cost of each shirt is $15.The cost of a belt is $8.The total amount Tyson can spend is $50.

(i) If he buys only one shirt, the cost will be $15 + $8 = $23 and the balance on the gift card will be:$50 - $23 = $27(ii) If he buys two shirts, the cost will be $15 × 2 + $8 = $38 and the balance on the gift card will be:

$50 - $38 = $12

(iii) If he buys three shirts, the cost will be $15 × 3 + $8 = $53 and Tyson cannot purchase all three shirts because he only has $50. Thus, Tyson can buy at most 2 shirts. The domain of the function f(x) = 42 - 15x is such that the total cost of x shirts plus the cost of the belt is less than or equal to $50. Therefore:

15x + 8 ≤ 50

Subtracting 8 from both sides gives:

15x ≤ 42 Dividing both sides by 15 gives: x ≤ 42/15

The largest integer less than or equal to 42/15 is 2, thus the appropriate domain of the function is 0 ≤ x ≤ 2 where x is an integer.

You can learn more about domain at: brainly.com/question/30133157

#SPJ11

Answer:

9

Step-by-step explanation:

Answer:9

Step-by-step explanation:

The given problem involves finding specific values of a function and its derivatives using the Taylor series of the function.

Specifically, we are asked to find p(0), p'(0), p''(0), and p'''(0) for the function p(x) given by its Taylor series P(x) = -1/x^2 + 1/(2n + 1), where the series is taken over n from 0 to infinity.

To find p(0), we simply need to evaluate the Taylor series at x = 0, which gives us p(0) = -1/0^2 + 1/(2(0) + 1) = -1.To find p'(0), we can differentiate the Taylor series term by term and evaluate at x = 0. The derivative of -1/x^2 is 2/x^3, and the derivative of 1/(2n + 1) is 0. Evaluating at x = 0, we get p'(0) = 0.We can follow a similar process to find p''(0) and p'''(0), by differentiating the Taylor series term by term and evaluating at x = 0. The resulting expressions are p''(0) = 2(3)/0^5 = undefined, and p'''(0) = -2(3)(5)/0^7 = undefined.

Overall, the problem involves applying the principles of Taylor series and calculus to find specific values of functions and derivatives It also requires an understanding of differentiation and evaluation of expressions at specific points.

For more similar questions on topic

https://brainly.com/question/31399167

#SPJ11

Answer:

divide both sides by 2

Step-by-step explanation:

Step-by-step explanation:

Use power rule and chain rule.

y = cos²(5x³ − 2x)

dy/dx = 2 cos(5x³ − 2x) (-sin(5x³ − 2x)) (15x² − 2)

dy/dx = 2 cos(5x³ − 2x) sin(5x³ − 2x) (2 − 15x²)

Use double angle formula to simplify:

dy/dx = sin(10x³ − 4x) (2 − 15x²)

Histograms are used to determine the empirical distribution of a variable. Therefore, option (e) is the correct one.

Histogram is used to summarize discrete or continuous data measured on an interval scale. It is often used to describe key features of the distribution of data in a practical way.

A histogram divides the range of possible values ​​in a data set into different classes or groups. For each group, a rectangle is created with a base length equal to the range of values ​​in that particular group and a length equal to the number of observations that fall into that group.

Histograms are similar to column charts, but there are no gaps between the bars. Histograms generally have equal width bars.

Thus, it can be concluded that histograms are used to determine the empirical distribution of a variable. Therefore, option (e) is the correct one.

To learn more about histogram visit https://brainly.com/question/16819077

#SPJ4

Answer: b

Step-by-step explanation:

The equation of the circle centered at the origin and passing through the point (-4,0) is \(x^2+y^2=16\).

Equation of a circle

A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.

We know that,

Equation of the circle passing through the origin is given by:-

\(x^2+y^2=r^2\)

Where,

r is the radius of the circle, and

(x,y) are the coordinates of each point of the circle.

Hence, we can write,

The radius of the circle will be :-

\(\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units\)

Hence, r = 4 units.

Hence, the equation of the circle is given by:-

\(x^2+y^2=16\)

To learn more about radius, here:-

https://brainly.com/question/15047456

#SPJ4

Given the following inequality:

To solve it, you need to solve for "a" by applying the Subtraction property of Inequalities and subtract 18 from both sides, as you can see below:

To graph it on a number line we must put a dot or a circle where -11 is.

Since the symbol of the inequality is <, the dot or the circle must be unfilled and the line must go from -11 to the left (because it is the direction of the numbers that make the given inequality true).

Then, you get:

The correct option is C

The distribution is Approximately Normal

The sample size is 150, this is large.

The standard deviation is finite .

We say that the distribution is Approximately Normal