find the centroid of the region in the first quadrant bounded by the given curves. y = x6, x = y6

Step-by-step explanation:

don't panic. just read carefully and write equations for every relation described in the text.

perimeter = 34 cm = side 1 + side 2 + side 3

side 1 = 2×side 3

side 3 = (side 1) / 2

side 2 = (side 1) + 4

now we use the last 2 equations in the first :

34 = side 1 + ((side 1) + 4) + (side 1)/2

68 = 2×(side 1) + 2×((side 1) + 4) + side 1

68 = 2×(side 1) + 2×(side 1) + 8 + side 1

68 = 5×(side 1) + 8

60 = 5×(side 1)

side 1 = 60/5 = 12 cm

side 2 = (side 1) + 4 = 12 + 4 = 16 cm

side 3 = (side 1)/2 = 12/2 = 6 cm

you see ? it is all just straight forward. no mystery.

the only trick is to find forms of the various equations to have only one variable in the main equation. like we did here with side 1 and side 3.

The limit exists and equals -4 when a = 28.

From the information, we want to find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2.

It should be noted that this will be illustrated as:

(4x² + ax + a + 12) / (x² + x − 2)

We will substitute x = -2 into the value of x in the Illustration. This will be:

(16 - 2a + a + 12) / (4 - 2 - 2)

16 - 2a + a + 12 = 0

-a = -28

a = 28

Using lhopital rule, we'll find the derivative. This will be:

8x + a / 2x + 2

Substitute x = -2

(-16 + 28) / (-4 + 1)

= 12 / -3

= -4

Therefore the limit exists and equals -4 when a = 28.

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Complete question

find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2

Answer: The first one is equivlent because you move the variable to the left collect like terms and then divide both terms.

Step-by-step explanation:

the correct answer from each drop-down menu. which formulas return true,.if the value in cell b4 is 12 and the value in c4 is 29.: A. =B4=12 AND C4=29

The correct answer is A. =B4=12 AND C4=29, as this is the only formula that returns true if the value in cell b4 is 12 and the value in c4 is 29.

Both B. =(B4=12) AND (C4=29) and D. =(B4+C4)=41 are correct, but they do not fit the given criteria.

C. =B4+C4=41 does not return true for the given values, as 12 + 29 does not equal 41.

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Answer: 1 batch

Step-by-step explanation:

1 batch = 24 - 36 cookies

So here we have 23 cups of sugar, and we know that each chocolate chip cookie uses 1 cup, so we can only make 23 cookies

Which is only 1 batch of cookies can be made.

Answer:

23 batches of cookies

Step-by-step explanation:

I think this problem is kind of straightforward:

1 bag = 23 cups

1 batch = 1 cup

We need to find how many batches = 1 bag

To find that out, we have to divide bags by batches, but we don't know the number of batches yet. (Also, they're not the same units)

Instead, we can use the respective cups of sugar to divide (because they do have the same units)

So we divide the number of cups of sugar in a bag (23) by the number of cups in a batch (1):

23 ÷ 1 = 23 batches

I hope this explanation was simple enough

The correct statement that establishes the identity is the third one: "The reciprocal of the cosine of an angle is equal to the secant of the angle."

Here's how you can prove this using the other three statements:

"The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle."

"The reciprocal of the sine of an angle is equal to the cosecant of the angle."

"The reciprocal of the cosine of an angle is equal to the secant of the angle."

"The reciprocal of the tangent of an angle is equal to the cotangent of the angle."

To prove the identity, we can start by substituting the first statement into the equation on the left side of the identity:

$1 + \tan^2 (-0) = 1 + \left( \frac{\sin (-0)}{\cos (-0)} \right)^2 = 1 + \frac{\sin^2 (-0)}{\cos^2 (-0)}$

Next, we can use the fourth statement to write the right side of the identity in terms of the cotangent:

$1 + \frac{\sin^2 (-0)}{\cos^2 (-0)} = 1 + \frac{1}{\cot^2 (-0)} = \frac{1}{\cot^2 (-0)}$

Now we can use the second statement to write the right side of the identity in terms of the cosecant:

$\frac{1}{\cot^2 (-0)} = \frac{1}{\frac{1}{\sin^2 (-0)}} = \csc^2 (-0)$

Finally, we can use the third statement to write the right side of the identity in terms of the secant:

$\csc^2 (-0) = \frac{1}{\sec^2 (-0)} = \sec^2 (-0)$

Therefore, the third statement establishes the identity.

Answer:

  34. x = 3 1/3

  35. x = 5.2

Step-by-step explanation:

Given figures involving triangles with angle bisectors and parallel segments, you want to solve for x.

In each case, you need to make use of two proportional relationships. An angle bisector divides the triangle proportionally. An segment parallel to one side of the triangle divides it proportionally.

Using the angle bisector relation, you have ...

  QP/PT = QS/ST

  x/3 = 5/ST   ⇒   x = 15/ST

Using the parallel segment relation, you have ...

  PT/QR = ST/SR

  3/2 = ST/3   ⇒   ST = 9/2

Using the value of ST in the equation for x gives ...

  x = 15/(9/2) = 30/9 = 10/3

  x = 3 1/3

Using the angle bisector relation, you have ...

  EF/ED = CF/CD

  7.2/9 = CF/6   ⇒   CF = 6(7.2/9) = 4.8

Using the parallel segment relation, you have ...

  CB/BA = CF/FE

  x/7.8 = 4.8/7.2

  x = 7.8(4.8/7.2)

  x = 5.2

__

Additional comment

In each case, we assigned a numerical value to the intermediate variable (ST, CF). We didn't actually need to do that.

Answer:

1/2 a cup of flour

Step-by-step explanation:

Sugar to flour ratio:
2 to 1
That means for every 2 sugar Harris needs 1 cup flour
There are twice as many cups of sugar of cups of flour
Since 1/2 times 2 is 1 that means the ratio is ture

2 to 1 = 0.5 to 1

Hope this helps :) im kinda bad at explaining

Answer:

1

Step-by-step explanation:

For function f(x), the average rate of change from x = a to x = b is:

average rate of change = (f(b) - f(a))/(b - a)

Here we have:

f(a) = f(-3) = -2.88

f(b) = f(2.5) = 2.62

average rate of change = (2.62 - (-2.88))/(2.5 - (-3)) = 1

Answer:

graph D

Step-by-step explanation:

if x = 0

y = 2 |-1| - 3

y = 2 (1) - 3

y = 2 - 3

y = -1

A (0, -1)

if x = 1

y = 2 |1-1|  - 3

y = 2 (0) - 3

y = -3

B (1,-3)

Answer:

100 isn't under the root, so the roots over the x cancel and you have 100x as the answer

Step-by-step explanation:

100 isn't under the root, so the roots over the x cancel and you have 100x as the answer

Answer:

only A ans bellow

Step-by-step explanation:

let k= -4

A. k * (k - 1) * ( k - 2)

= -4 * (-4 -1) * ( -4 -2)

= -4* (-5) * (-6)

= 20*-6

= -120

B. k * ( k+1)

= -4 * ( -4+1)

= -4 * (-3)

= + 12

C. k * (-50)

= -4 * (-50)

= + 200

D . (50 - k)

= 50 - (-4)

= 50 + 4

= + 54

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if k is negative then k(k-1)(k - 2) will be definitely negative.

A number system is defined as a system of writing to express numbers.

Given that k is a  negative integer.

We need to find which of the given options are defnitely negative.

Let us consider k as -3.

k(k-1)(k - 2)

-3(-3-1)(-3-2)

-3(-4)(-5)=-60

Which is negative.

k(k+1)=-3(-3+1)=6 +ve

k (-50)=-3(-50)=150 +ve

(50-k)​=50-(-3)=53 +ve.

Hence, if k is negative then k(k-1)(k - 2) will be definitely negative.

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The rate of change of function A is greater than the rate of change of function B.

The y-intercept of function A is less than the y-intercept of function B.

The rate of change is also called the slope of a linear equation and is defined as the rate of change of y-values divided by the corresponding change in x-values.

For function A, we are told that the line passes through the points (2, 3) and (-1, -3). The rate of change is gotten from the formula;

Rate of change = (y₂ - y₁)/(x₂ - x₁)

Rate of change = (-3 - 3)/(-1 - 2)

Rate of change = -6/-3

Rate of change = 2

For function B, we are given that the equation of the line is;

y = ¹/₂x + 2

Now, formula for equation of a line in slope intercept form is;

y = mx + c

where ;

m is slope and c is y-intercept

Thus, slope is 1/2 and y-intercept is 2

For function A, we can find the y-intercept as;

3 = 2(2) + c

c = 3 - 4

c = -1

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Answer: x

≥

3

−

3

y

Step-by-step explanation:

Answer:

The equation for the total cost of the gym membership over t months is CC = Jo + M * t, where Jo represents the one-time fee to join, M represents the monthly fee to remain a member, and t represents the number of months for which the membership is valid.

The slope of the graph is M, the monthly fee to remain a member. The interpretation of the slope in the context of the problem is that it represents the cost per month of remaining a member of the gym.

Answer:

time=speed÷distance

speed=distance×time

distance=speed ÷time

Step-by-step explanation:

from the answers we get a relationship between speed,distance and time.there by when with two you can find the other

The value of the fifth term in the given sequence as represented in the task content is; -35.

It follows from the task content that the value of the fifth term in the given sequence is to be determined.

On this note, it follows from the observation that the given sequence is arithmetic and the nth term, T (n) = a + ( n - 1 ) d.

where, a = first term = 1

and d = common difference = -8 - 1 = -17 - (-8) = -9.

Therefore, the fifth term is given as;

T (5) = 1 + ( 5 - 1 ) -9

= 1 + (4 × -9)

= 1 - 36

= -35.

On this note, the fifth term of the sequence as required is; -35.

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Made possible via methods. In light of this, 5, 6, 15, and 18 are in proportion. The same unit rates prove that.

A ratio, on the other hand, is the comparison of the sizes of two values, whereas a proportion is a part, share, or quantity in relation to an overall total. Each of the three measures has unique characteristics, and a rate is just one number divided by another.

Due to the consistency of the units and their equivalent, each ratio compares the same units—inches and feet—and is therefore similar. Compare two ratios using the same units when using proportions.

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The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The line t that passes through the points (0, 2) and (8, -4) is given as,

(y - 2) = [(- 6 - 2) / (8 - 0)](x - 0)

y - 2 = - 0.75x + 0

y = -0.75x + 2

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

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Answer:

x = -1

y = 3

Step-by-step explanation:

2x + y = 1

3x - y = -6

Let's find x first by adding both equations

5x = -5

x = -1

Now put -1 in the spot of the variable x

2(-1) + y = 1

-2 + y = 1

y = 3

Answer:

The answer is 1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The value of θ will -45° or 26.56°

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Given that, cosec²θ = cotθ + 3

Solving for θ,

∵ cosec²θ = cot²θ+1

∴ cot²θ+1 = cotθ + 3

cot²θ-cotθ-2 = 0

Factorizing and solving, we get

(cotθ+1)(cotθ-2) = 0

cotθ+1 = 0

cotθ = -1

θ = -45°

or, cotθ-2 = 0

cotθ = 2

θ = 26.56°

Hence, The value of θ will -45° or 26.56°

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To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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answer : y = 4/5x - 22/5

y = mx + b

get m or slope (aka "rate" or "speed")

(fun fact : see how the graph is a straight line? a lot of calculus is trying to get the rate or speed or slope of a curved graph)

(-3,-6) (2,-2)

(y2 - y1)/(x2-x1)

-2 + 6/2 + 3

m = 4/5

(if you make the 2 points a triangle bottom is 5 and the right side is 4)

line formula

y - y1 = m (x - x1)

y + 6 = 4/5 ( x + 2 )

y = 4/5x + 8/5 - 6

y = 4/5x + 8/5 - 30/5

y = 4/5x - 22/5

side note : since the graph doesnt go thru (0,0) the graph is NOT PROPORTIONAL

Answer:

3900

Step-by-step explanation:

20%=1/5

780 is 20%

780x5 equals total since 20% 80% is 3120

Answer:

w = 9

Step-by-step explanation:

Use a slope formula to solve. Subtract the y's put that on top and subtract x's and put that on the bottom. This calc should equal 2 that was given.

(8-6)/(10-w) = 2

2/(10-w) = 2

Cross-multiply.

2 = 2(10-w)

Distributive property

2 = 20 - 2w

Add 2w

2 + 2w = 20

Subtract 2

2w = 18

divide by 2

w = 18/2 = 9

Or you can logic it out...8-6 is 2 on top. Need a 1 on the bottom (bc 2/1 is 2) 10-9 is 1 for on the bottom. w = 1

The pool workers can conclude that there is not a statistically significant difference between the expected and observed results.

The chi-square value is 1.3892 and the p-value is 0.7081 The p-value of 0.7081 is greater than the 5% significance level, meaning that the null hypothesis can not be rejected.

This means that the difference between the expected and observed results is not statistically significant, and the observed results are likely due to random chance. This means that there is not a significant difference in the observed results from the expected results, and the null hypothesis is accepted.

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Answer:

The answer is C, 3/4 of a box

The requried, "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

To find the minimum sum of two positive numbers whose product is 47, we can use the concept of the arithmetic mean-geometric mean inequality (AM-GM inequality).

The AM-GM inequality states that for any two positive numbers, the arithmetic mean (average) is always greater than or equal to the geometric mean. Mathematically, it can be expressed as:

AM ≥ GM

For two positive numbers "a" and "b," the arithmetic mean is (a + b) / 2, and the geometric mean is √(ab).

Given that the product of the two numbers is 47 (ab = 47), we want to find the minimum value of their sum (a + b).

Using the AM-GM inequality:

(a + b) / 2 ≥ √(ab)

Substitute ab = 47:

(a + b) / 2 ≥ √47

Now, let's solve for the minimum sum (a + b):

a + b ≥ 2(√47)

a + b ≥ 2 * √(47)
a + b ≥  13.711.        

Since "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

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In the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, we know that:

The rate at which water is being filled is 4 ft³.

The radius of the cylinder is 2 ft.

Now, the time in which the level of water in the tank rises when the tank is half full:

Area of cylinder: πr²

πr² =  12.566 ft³

Next, multiply 4 by 12.566 to get how quickly the water is rising:

12.566 ft³/4 ft³/min = 3.14 m

According to this, a foot of water rises every roughly 3.14 minutes, or 1/3.14 - 0.318 ft/min, or 3.82 in/min.

Therefore, in the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.

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