(5 points) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y=2, x = 3 – (y - 1)?;

The absolute minimum value is -18 at the point (7, 0), and the absolute maximum value is 35 at the point (7, 9) within the given triangular region

To find the absolute minimum and absolute maximum of the function f(x, y) = 10 - 4x + 7y on the closed triangular region with vertices (0, 0), (7, 0), and (7, 9), we need to evaluate the function at the critical points inside the region and at the boundary points.

Critical points:

To find the critical points, we need to find the points where the gradient of f(x, y) is equal to zero.

∇f(x, y) = (-4, 7)

Setting -4 = 0 and 7 = 0, we see that there are no critical points in the interior of the triangular region.

Boundary points:

We need to evaluate the function f(x, y) at the vertices of the triangular region.

(a) f(0, 0) = 10 - 4(0) + 7(0) = 10

(b) f(7, 0) = 10 - 4(7) + 7(0) = -18

(c) f(7, 9) = 10 - 4(7) + 7(9) = 35

Therefore, the absolute minimum value is -18 at the point (7, 0), and the absolute maximum value is 35 at the point (7, 9) within the given triangular region.

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Answer:

the answer is B

Step-by-step explanation:

8 + 14 = 2(4 + 7)

Answer:

C

Step-by-step explanation:

Given

- 12x - 2(x + 9) = 5(x + 4) ← distribute parenthesis on both sides

- 12x - 2x - 18 = 5x + 20, that is

- 14x - 18 = 5x + 20 ( subtract 5x from both sides )

- 19x - 18 = 20 ( add 18 to both sides )

- 19x = 38 ( divide both sides by - 19 )

x = - 2 → C

Answer:

x=-2

Step-by-step explanation:

-12x-2(x+9)=5(x+4)

-12x-2x-18=5x+20

-14x-5x=20+18

-19x=38

x=38/-19

x=-2

Answer:

4 hope that helped play adopt the application for rent

Answer:

3

Step-by-step explanation:

The interquartile range is where the 2nd and 5th dots are, on the opposite ends of the square, from 15-18.

Answer:

3

Step-by-step explanation:

The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁).

In a box plot:

From inspection of the given box plot:

Therefore:

IQR = Q₃ - Q₁

      = 18 - 15

      = 3

So the interquartile range of the given box plot is 3.

Answer:

D

Step-by-step explanation:

The correct option is " count 2 units below x=2 line."

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyper plane as a set of fixed.

Here, given that,

We have to find the reflection of point B(4,5) on the line x=2

Hence, from the given option the correct option is,

" count 2 units below x=2 line."

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Answer:

The triangle must be an isosceles triangle so as to only get one measurement

Step-by-step explanation:

The Pythagorean theorem states that the square of the hight and base is added then square rooted to get the hypotenuse

THE FORMULA: A square+b square=c square

The given statement "If a sequence has a limit of 0 as n approaches infinity then it's corresponding series must converge" is false.

This is due to the fact that the convergence of a sequence does not guarantee the convergence of its corresponding series. Even if a sequence converges to zero, the series derived from the sequence may or may not converge.

Here's an example to clarify this:Let a sequence be defined as aₙ = 1/n. It is clear that this sequence converges to zero as n approaches infinity since 1/n gets smaller and smaller as n approaches infinity.Now, let us define the corresponding series as

Sₙ = Σ(1/n) from n=1 to infinity.

We will now show that the series diverges.The sum of the first two terms in the series is:

S₂ = 1/1 + 1/2 = 1.5

The sum of the first three terms in the series is:

S₃ = 1/1 + 1/2 + 1/3 = 1.8333...

The sum of the first four terms in the series is:

S₄ = 1/1 + 1/2 + 1/3 + 1/4 = 2.0833...

It is clear that as n approaches infinity, the value of S_n becomes larger and larger without limit. As a result, the series diverges.Hence, we can conclude that even if a sequence converges to zero, the corresponding series derived from the sequence may or may not converge.

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The length of side XZ is 5 units and side YZ is 6 units.

A triangle is a three-sided polygon, which has three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the three angles of the triangle is equal to 180 degrees. To study about and build the world's seven sorts of triangles: equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene. The hypotenuse is the longest side of a right triangle, a "opposite" side is the one across from a given angle, and a "adjacent" side is the one close to a given angle.

Here,

XZ=3-(-2)

XZ=5 units

YZ=4-(-2)

YZ=6 units

Side XZ is 5 units long and Side YZ is 6 units long.

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On decomposing the vector 6i −3j −6k , we get the parallel vector as -i - j -k  and orthogonal vector as  i + j + k   .

The Vector is given as 6i −3j −6k ,

we have to decompose it in two components , Parallel Component and orthogonal Component .

the two components are parallel and orthogonal to i + j + k .

let us assume a = 6i - 3j -6k and b = i + j + k .

we write a = a₁ + a₂ , where a₁ is parallel to b and a₂ is orthogonal to b .

a₂ = xi + yj + 2k and a₁ = c.b ,.....equation(1)

a = 6i - 3j -6k = a₁ + a₂

                      = c(i+j+k) + xi + yj + 2k   ...from equation(1)

                      = (x+c)i + (y+c)j + (z+c)k

On comparing ,

we get ,

x + c = 6 , y + c = -3 and z + c = -6 ....equation(2)

also a₂.b = 0 .....because they are orthogonal ,

x + y + z = 0,

substituting the values ,

we get ,

b - c - 3 - c - 6 - c = 0

on solving , we have c = -1 .

substituting the values of c = -1  in equation(2) ,

we get x = 7 , y = -2 and c = -5 .

so ,the vectors are  a₁ = -i - j -k   and a₂ = 7i - 2j - 5k  .

Therefore , the parallel component is  -i - j -k and the orthogonal component is 7i - 2j - 5k .

The given question is incomplete , the complete question is

Decompose the vector 6i −3j −6k  into vectors which are parallel and perpendicular to the vector  i + j + k .

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Answer:

. A LINEAR REGRESSION is your answer

Correct option is D) and E)

(3,7π/6),(3,11π/6)

Point of intersection is the point where two lines or two curves meet each other.

The point of intersection of two lines of two curves is a point.

If two planes meet each other then the point of intersection is a line.

The term "point of intersection" refers to the intersection of two lines. The equations a1x+b1y+c1=0 and a2x+b2y+c2=0, respectively, are used to represent these two lines. The two lines' intersection point is shown in the following figure. The intersection of three or more lines can also be located.

let

5 + 4 sin(θ) = −6 sin(θ)

Then get

θ= -1/2

Then you can make it

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I understand that the question you are looking for is:

On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.

A) -3,7/6

B) (-3,11/6)

C) (3,7/6)

D) (3,11/6)

Answer:

10t + 400 would be the answer.

Step-by-step explanation:

every hour, there would be 10 gallons added to the pool, so time should be the letter "t" in the equation.

Also, there's already 400 gallons of water existing in the pool, so we need to add 400 gallons.

Therefore, 10t + 400 would be the answer.

Answer:

first of all who deleted my answer considering the fact that is was correct and i answer it first The answer is B

Step-by-step explanation:

hope this helps -_-

31). 9m=-2-52

m=-54÷9

ans=-9

I am unable to see number 49 so if you want me to answer it please tell so.

Answer/Step-by-step explanation:

31) m= -6

32) P=12

33) n = -19

34) x =2

35) r = -10

36)b=10

37) x=10

38) v=6

39)n=-2

40)x=15

41)x=-15

42)a=36

43)n=-6

44)p=0

45)k=-18

46)m=-8

47)x=7

48)n=10

50)x=-2

If You have any question or need the explanation for any question please tell me.

[RevyBreeze]

We see, there is a pair of sides that have similar lengths before and after the enlargement.

-> The scale factor = 30 : 18 (or) 35 : 21 = 5/3

Recheck :

18 x 5/3 = 30
18 x 5/3 = 30
21 x 5/3 = 35

Answer:

20 i think so

Step-by-step explanation:

mabye help full

The probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie is 12 / 22C2.

The probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie can be calculated by dividing the number of ways to select two sugar cookies by the total number of ways to select any two cookies.
Step-by-step explanation:
1. Determine the number of ways to select two sugar cookies: There are 4 sugar cookies in the bag, so the number of ways to select the first sugar cookie is 4. After eating the first sugar cookie, there are 3 sugar cookies left, so the number of ways to select the second sugar cookie is 3. Therefore, there are 4 * 3 = 12 ways to select two sugar cookies.
2. Determine the total number of ways to select any two cookies: There are a total of 6 + 5 + 4 + 7 = 22 cookies in the bag. So, the number of ways to select any two cookies is calculated by choosing 2 cookies out of 22, which is denoted as 22C2.
3. Calculate the probability: To find the probability, divide the number of ways to select two sugar cookies by the total number of ways to select any two cookies.
  Probability = (Number of ways to select two sugar cookies) / (Total number of ways to select any two cookies)
  Probability = 12 / 22C2
So, the probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie is 12 / 22C2.

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The amount of time that passes between iterations of the same behavior can vary depending on the specific behavior and the individual or situation involved. However, there is no specific time frame that can be universally applied to all behaviors.

When examining the frequency of a behavior, it is important to consider factors such as the complexity of the behavior, the availability of resources, and the motivation or reinforcement associated with the behavior. Additionally, individual differences and external influences can also affect the time between iterations of a behavior.

To determine the time between iterations, one can observe and record the occurrences of the behavior over a specific period. By analyzing the data collected, patterns can emerge, providing insights into the timing and frequency of the behavior.

In conclusion, the time between iterations of the same behavior is not fixed and can vary depending on various factors. Observing and recording the behavior over a period of time can help determine the frequency and time frame of the behavior.

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The equation could be used to solve for charles' rate if it is represented by x is 2x=54.

In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.

Bill riding a bicycle at an average rate of 9 mph.

Charles' rate is x.

So the relative rate = x−9 mph

Distance traveled by Bill in 4 hours = 9*4 =36 mph

Charles' overtook Bill in 2 hours. So

Relative Rate = Distance/Time

x−9=36/2

Multiply by 2 on both side. We get

2(x−9)=36

Simplifying

2x−18=36

Add 18 on both side, we get

2x=36+18

2x=54

Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.

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Answer:

640

Step-by-step explanation:

800-160=640...............................

Answer:

$800-$160

=$640

Hope it helps.

Given:

There are 5 numbers followed by 2 letters.

Solution:

To find the answer, we will have a plate number that consists of 5 numbers followed by 2 letters. In that 5 numbers, each place has 10 choices-from 0 to 9. It will be: 10 * 10 * 10 * 10 * 10 = 100,000 .

Now, for the letters, there are 26 letters in the alphabet. We have two places for the letters and each place have 26 choices-from A to Z that will give us: 26 * 26 = 676

We will now multiply the acquired data for both the numbers and letters to arrive at the correct answer.

100,000 * 676 = 67,600,000

ANSWER: 67,600,000 possible license plates

y > x - 3

y > x - 1

The above system of inequalities was given from the question

Firstly, we will need to graph the system of inequalities

y > x - 3

Change the inequality sign to equality sign

The equation becomes

y = x - 3

To find y, let x = 0

y = 0 - 3

y = -3

To find x, let y = 0

0 = x - 3

Make x the subject of the formula

0 + 3 = x

x = 3

For the system of inequality, y > x - 3

The points is (3, -3)

For the second system of inequality

y > x - 1

Change the inequality ss

Answer:

4h-1

Step-by-step explanation:

subtracted it with a scientific calculator and that was the answer

Answer:

2.25%  of 1,850 x 2 =  83.25

Step-by-step explanation:

2.25%  of 1,850 = 41.625

the answers are in the image

The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.

The function being used is;

f(x) = (x - 3)⁻²

If we separate this function according to x, we obtain;

f'(x) = -2/(x - 3)³

Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.

This suggests that;

0.06 - 0.25 = -2/(c - 3)³ x 6

-0.19 =  -12/(c - 3)³

(c - 3)³ = 63.157

c = 6.98

If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).

But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.

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The complete question is-

Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?

If two marbles are drawn from the bag without replacement the probability of (B|A) expressed in simplest form would be = 5/16.

To calculate the probability of the given event, the formula that should be used is given as follows;

Probability = Possible outcome/sample space.

For event A;

Possible outcome = 5

Sample space = 4+7+5 = 16

P(A) = 5/16 = 0.3125

For event B:

Possible outcome = 7

sample space = 16-1 = 15

P(B) = 7/15= 0.4667

But;

P(A/B) = P(A∩B) / P(B),

P(A/B) = 0.3125×0.4667/0.4667

= 0.3125 = 5/16

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The statement "if f'(x) = g'(x) for 0 < x < 6, then f(x) = g(x) for 0 < x < 6" is false. This statement is False. If f'(x) = g'(x) for 0 < x < 6, it means that the derivatives of both functions are equal on the interval (0, 6).

However, this does not necessarily mean that the functions themselves are equal on that interval.

In other words, there could be a constant difference between f(x) and g(x), which would not affect their derivatives.

To illustrate this, consider the functions f(x) = x^2 and g(x) = x^2 + 1. The derivative of both functions is 2x, which is equal for all values of x.

However, f(x) and g(x) are not equal on the interval (0, 6), as g(x) is always greater than f(x) by 1.

Therefore, the statement "if f'(x) = g'(x) for 0 < x < 6, then f(x) = g(x) for 0 < x < 6" is false.

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