Mathematics College

sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2
Find its area.

Answers

Answer 1

The enclosed area between the 2 equations, x = 7y² and x = 4 + 6y² is 32/3 sq units

Here equation 1 is x = 7y²

and equation 2 is x = 4 + 6y²

To find the area enclosed between the region, we need to first find the points where these two lines meet.

This implies,

eq 1 = eq 2

or, 7y² = 4 + 6y²

or, y² = 4

or, y = ±2

Now if we see the graph with respect to y, the area between the y-axis and eq 2 is greater than that of the y-axis and equation 1.

Now area is enclosed between 2 lines with respect to x. Hence it will be

= ∫eq 2 dy - ∫eq 1 dy with limts of 2 and -2

= ∫4 + 6y²dy - ∫7y²dy with limits 2 and -2

= [4y + 2y³ - 7/3 y³] with limits 2 and -2

= 8 + 16 - 56/3 + 8 + 16 - 56/3 sq. units

= 48 - 112/3

= 32/3 sq units

Hence the enclosed area is 32/3 sq units

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Sketch The Region Enclosed By The Given Curves. X = 7y2, X = 4 + 6y2Find Its Area.

Related Questions

25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. 15 developed at least 1 tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure

Answers

based on the number of mice that took part in the experiment, the total number of mice that had at least one effect is 20 mice.

how many mice had a health effect?

15 mice had at least 1 tumor while 4 mice had both a tumor and respiratory failure.

the number of mice with just a tumor is:

= 15 - 4

= 11 mice

the number of mice with respiratory failure alone is:

= 9 - 4

= 5 mice

the mice that had at least one symptom is:

= 11 + 5 + 4 mice with both

= 20 mice

question is:

what are the number of mice with at least one effect?

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which expression is equivalent to 7x^2 sqrt 2x^4 times 6 sqrt 2x^12 if x ≠ 0

Answers

The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

How to determine the equivalent expression?

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]

Evaluate the product

[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]

This gives

[tex]42x^2 \sqrt{4x^{16}[/tex]

Take the square root of 4

[tex]2*42x^2 \sqrt{x^{16}[/tex]

Take the square root of x^16

[tex]2*42x^2 *x^8[/tex]

So, we have:

[tex]84x^{10[/tex]

Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

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Answer:

Step-by-step explanation:

The equivalent expression of is

How to determine the equivalent expression?

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

Evaluate the product

This gives

Take the square root of 4

Take the square root of x^16

So, we have:

Hence, the equivalent expression of is

If f(x) = 3x4 + 2x3 - x + 15,
what would be the list of
possible rational roots?

Answers

Answer: A. ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]

Step-by-step explanation:

± [tex]\frac{1, 3, 5, 15}{1, 3}[/tex]

= ± [tex]1, 3, 5, 15, 1/3, 5/3, 5[/tex]

Rearranging, we get:

= ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]

Maths-4
What is the smallest number that is divisible by each of the numbers given below
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
5040
3780
1260
2520
None of the above

Answers

Answer:

5040 is the right answer

Step-by-step explanation:

5040/1=5040

5040/2=2520

5040/3=1680

5040/4=1260

5040/5=1008

5040/6=840

5040/7=720

5040/8=630

5040/9=560

5040/10=504

t
Use the table to the right, which shows the age distribution of those who earned less than
minimum wage in a recent year. If a worker is randomly selected from those surveyed, what
y is the probability that the person is younger than 65?
na
Ci
20
ar
The probability that the person is younger than 65 is
(Type a decimal rounded to three decimal places as needed.)
CID
Age
16-19
20-24
25-34
35-44
45-54
55-64
65 and older
Working Below Minimum
Wage (thousands)
350
412
318
200
107
51
49

Answers

The probability that a person chosen at random is younger than 65 is 0.967.

What is the probability?

Probability calculates the odds that a random event would happen. The odds that the random event happens lie between 0 and 1.

The probability that a person chosen at random is younger than 65 = (total number of people younger than 65 / total number of respondents)

(350 + 412 + 318 + 200 + 107 + 51 ) / (350 + 412 + 318 + 200 + 107 + 51 + 49)

1438 / 1487 = 0.967

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slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.

Answers

The height of the ramp above the ground is 1.55 meters.

The difference between the height of the tree is 33.20 meters

How to find sides of a right triangle?

The situation forms a right angle triangle.

Therefore, the height the ramp above the ground can be calculated as follows:

Using Pythagoras theorem,

sin 15 = opposite / hypotenuse

sin 15 = x / 6

cross multiply

x = 6 sin 15

x = 6 × 0.2588190451

x = 1.55291427062

x = 1.55

Therefore, the height of the ramp above the ground is 1.55 meters

tan 36 = opposite / adjacent

tan 36 = x / 60

x = 60 tan 36

x = 43.5925516803

x = 43.60 meters

tan 52 = y / 60

60 tan 52 = y

y = 76.7964979316

y = 76.79 meters

The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters

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Solve the following system of equations by elimination. What is the value of x? x = 1.5 x = -1.5 x = 8 x = -8

Answers

Using the elimination method, the value of x in the system of equations is calculated as: 8.

How to Solve a System of Equations by Elimination?

To solve a system of equations given using the elimination method, do the following:

Multiply 2x - 5y = 1 by 2 and multiply -3x + 2y = -18 by 5 to get the following:

4x - 10y = 2 --> eqn. 1

-15x + 10y = -90 --> eqn. 2

Add

-11x = -88

Divide both sides by -11

x = 8

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math stuff who ever answers right gets brainlest answer

Answers

Answer:

Median is 83

Range: 61

Step-by-step explanation:

The median is the number in the middle. The range is the max. number subtracted from the min number.

A company’s 5-year bonds are yielding 7% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r* ) is 2.75%. The average inflation premium is 2.05%, and the maturity risk premium is estimated to be 0.1 3 (t 2 1)%, where t 5 number of years to maturity. If the liquidity premium is 0.7%, what is the default risk premium on the corporate bonds

Answers

Based on the required rate of return, the real risk free rate, and the inflation premium, the default risk premium on the corporate bonds is 1.2%

How is the default risk premium found?

The default risk premium can be found as:

=real risk free rate + Inflation premium + default risk premium + liquidity premium + maturity risk premium

Solving gives:

= 0.07 - 0.0275 - 0.0205 - (0.1 x (t - 1)%)

= 0.07 - 0.0275 - 0.0205 - (0.1 x (5 years - 1)%)

= 1.2%

The default risk premium refers to the return that the bond is offering over what a risk-free bond would offer.

This means that the corporate bond described is offering 1.2% more than what a risk-free government bond would offer.

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a x = ±5
b. x = ±5i
C. x = ±3√√5
d. x = ±3√3
e. x = ±3i√√3
f. x= ±3i√√5

1. x^2+45=0
2. x^2=-25
3. x^2-25=0
4. x^2-45=0
5. x^2=27
6. x^2+27=0

Match the items

Answers

Answer:

1f, 2b, 3a, 4c, 5d, 6e

see image

Step-by-step explanation:

Solve the equations by getting x all by itself on one side. Then, square root to get rid of the exponent.

Any problem where you square root a negative will give you an i in the answer. This is because sqrt(-1) is i. Because i^2 = -1

Also, when you are simplifying square roots for your final answer, look for a perfect square number inside of the radical. Like Sqrt45 can be broken down to

Sqrt9•sqrt5

And because 9 is a perfect square, sqrt9 simplifies to just 3. See image.

1. F (-45 = -9 * 5)
2. B
3. A
4. C
5. D
6. E

Whenever you take the square root of a negative number, we create a complex number i

A cylindrical container has a radius of 17 inches and a height of 63 inches, how many gallons will it hold?

Answers

Answer:

=57198.98

Step-by-step explanation:

Volume of Cylinder = pi x radius^2 x height

= pi x 17^2 x 63

=57198.9774439

=57198.98

Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12)

Answers

Here, 12 is the mode.

Step-by-step explanation:

Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12) ?

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.

So let's talk in brief:-

First, we arrange it in ascending order.

3,3,6,6,9,9,12,12,12,12

and now as we see that we get 12 as the most repeated ones.

reference link-

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What is it? I am not sure

Answers

Answer: I think its A

Step-by-step explanation: maybe

A shoe repair operation uses a two-step sequence that all jobs in a certain category follow. All jobs can be split in half at both stations. For the group of jobs listed: JOB TIMES (minutes) A B C D E Workstation A 27 18 70 26 15 Workstation B 45 33 30 24 10 Click here for the Excel Data File a. Find the sequence that will minimize total completion time. b. Determine the amount of idle time for workstation B.

Answers

1. The sequence that will minimize the total completion time is sequence 4. B-A-C-D-E.

2. The determination of the amount of idle time for Workstation B is 37 minutes.

Johnson's Sequencing Rule:

According to Johnson's sequencing rule, start listing jobs with minimum completion time first.

If the job occurs at Workstation A, list it on the left side. If the job occurs at Workstation B, list it on the right side, as below:

Data and Calculations:

JOB TIMES (minutes) A B C D E

Workstation A 27 18 70 26 15

Workstation B 45 33 30 24 10

The first job with a minimum completion time is Job E at Workstation B.

The second job with a minimum completion time after Job E is Job B at Workstation A.

The third job with a minimum completion time after Job B is Job D at Workstation B.

The fourth job with a minimum completion time after Job D is Job A at Workstation A.

The last job is Job C at Workstation B.

The sequence that minimizes total completion time is as follows:

B A C D E

A B

Calculation of Idle Time at Workstation B:

Job Workstation A Workstation B Idle Time

In Out In Out Workstation B

B 0 0+18 = 18 18 18+33 = 51 18

A 18 18+27 = 45 51 51+45 = 96 19

C 45 45+70 = 115 115 115+30 = 145 0

D 115 115+26 = 141 145 145+24 = 169 0

E 141 141+15 = 156 169 169+10 = 179 0

Total Idle Time at Workstation B = 37 (18 + 19)

Thus, the sequence that minimizes the total completion time is sequence 4, while the idle time at Workstation B is 37 minutes.

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Question Completion with Answer Options:

1. A-B-C-D-E

2. E-D-B-C-A

3. D-C-B-A-E

4. B-A-C-D-E

5. C-A-B-D-E

Hence, write down the smallest integer value of x that satisfies 7(6+x) -x>0

Answers

Answer:

-6

Step-by-step explanation:

[tex]7(6+x)-x > 0[/tex]

[tex]42 + 7x-x > 0[/tex]

[tex]42+6x > 0[/tex]

[tex]6x > -42[/tex]

[tex]x > -7[/tex]

The smallest integer that satisfies the condition, [tex]x > -7[/tex], is -6.

Evaluate 4s^2 for s = 1/4. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.

Answers

Answer:

1/4

Step-by-step explanation:

Given [tex]\displaystyle{s=\dfrac{1}{4}}[/tex] and we have to evaluate [tex]\displaystyle{4s^2}[/tex]. We can do by substituting the given value s = 1/4 in 4s² term:

[tex]\displaystyle{4\cdot \left(\dfrac{1}{4}\right)^2}\\\\\displaystyle{4\cdot \dfrac{1}{16}}\\\\\displaystyle{\dfrac{1}{4}}[/tex]

Therefore the value is 1/4

Factor:
y(a−b)-(a−b)

Answers

Answer: [tex](a-b)(y-1)[/tex]

Step-by-step explanation:

Factoring out (a-b) gives [tex](a-b)(y-1)[/tex].

Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -y)
O (x, y) - (y, x)
O (x, y) -- (-x, -y)
O (x, y) - (-y, -x)

Answers

The rule that describes the transformation is (x, y) - (-y, -x).

What is transformation?Transformation is the process of using rules to transform some graphics into something else.When a shape is either reflected, rotated, or translated, the coordinates of the vertices that make up the shape change.The four different forms of transformations—Translation, Reflection, Rotation, and Enlargement—are depicted in the following illustrations.The underlying coordinate system remains fixed while an object transformation modifies the coordinates of each point on the object in accordance with some rule. • A coordinate transformation expresses each point of the object in the new coordinate system by defining it in terms of the old one.

The fourth option among the available choices depicts a 180° clockwise or counterclockwise rotation, in which is The vertices' x- and y-coordinates change to their opposites, i.e., x becomes -x and y becomes -y.

The rule that describes the transformation is (x, y) - (-y, -x).

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Mariana and her best friend are attending a concert in a large auditorium. They just climbed up 125 steps. The number of steps they climbed can be represented by

zero
positive
negative

Answers

The number of steps they climbed can be represented by positive

How to represent the number of steps?

From the question, we understand that they climbed up

Upward movements are usually represented by the positive sign

This means that:

Steps = 125 or +125

Hence, the number of steps they climbed can be represented by positive

Answers

The correct option regarding the correlation coefficient is given as follows:

strong negative linear relationship between protein amount and calories.

What is a correlation coefficient?

It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

In this problem, the coefficient is of -0.87, which is a negative value with absolute value greater than 0.6, hence the relationship is strong is the correct option is given as follows:

strong negative linear relationship between protein amount and calories.

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Which of the following similarity statements about the triangles in the figure is true?

Right triangle P Q R has angle Q marked as a right angle. A segment is drawn from point Q to side P R. The point where the segment intersects side PR is point S. Angle P S Q is marked as a right angle.

A. Triangle P Q R is similar to triangle P S Q, which is similar to triangle Q S R.
B. Triangle R Q P is similar to triangle S Q P, which is similar to triangle R S Q.
C. Triangle Q R P is similar to triangle Q S P, which is similar to triangle Q S R.
D. Triangle P R Q is similar to triangle Q P S, which is similar to triangle R Q S.

Answers

Answer:

Answer B is correct

Please help to solve these 3 questions

Answers

Based on the number of goals scored in the football matches, the mode is 4 goals. The median is 3 goals and the mean goals scored is 2.6 goals.

What are the statistics from the football matches?

The mode is the number of goals that was scored in the most matches. This number is 4 goals as this was scored in 6 matches.

To find the median, order the numbers:

0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6

The median is:

= (3 + 3) / 2

= 3

The mean is:

= (0 + 0 + 0 + 0 + 1 + 1 + 2 +2 +2 + 3 + 3 + 3 + 4 + 4+ 4 + 4 +4 + 4 + 5 + 6) / 20

= 2.6 goals

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The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. (-3, 1)

Answers

The information given illustrates that the graph of the function decreasing.

How to illustrate the information?

We say that a function is increasing on an interval if the function values increase as the input values increase within that interval.

Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval.

So according to the given graph on the interval (-3, 1) the graph is decreasing.

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Evaulate u^2-4u+2 when u=-2

Answers

You can just replace [tex]u[/tex] with 2:

[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]

Alternatively, you can complete the square.

[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]

When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.

Write the equation in slope-intercept form of the line that has slope
3 and y-intercept (0,1)

Answers

Answer:

y = 3x + 1

Step-by-step explanation:

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

y = mx + c

Where;

m is slope

c is y-intercept

Now, since we have coordinates, we will get the equation as;

(y - y1)/(x - x1) = m

(y - 1)/(x - 0) = 3

y - 1 = 3x

y = 3x + 1

What number represents the smallest value? .3 or .33

Answers

Answer:

Step-by-step explanation:

.33 is .03 greater than .3

The number which represents the smallest value between 0.3 and 0.33 is the number 0.3.

Given are two decimal numbers.

0.3 and 0.33

It is required to find the number which is the smallest between these two.

The number 0.3 can be written as 0.30.

And the other number is 0.33.

In order to find the smallest number, check the digits from left to right.

The first digit after the decimal point of both numbers is 3.

The second digit after the decimal point is 0 for 0.30 and 3 for 0.33.

Here 0 is smaller than 3.

So, 0.30 is smaller than 0.33.

Hence, the smallest value is 0.3.

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When first hired, Deondre was earning $5.85 per hour. He has worked his way up in the business and is currently making $12.30 an hour. What is the absolute and relative change in Deondre's hourly pay from when he was first hired to now?

Answers

Answer:

$6.45/hour

110.26%

Step-by-step explanation:

The absolute change is the difference between salaries now ands then.

12.30 - 5.85 = 6.45

The relative change in the percent increase.

percent increase = (new number - old number)/(old number) × 100%

percent increase = (12.3 - 5.85)/(5.85) × 100%

percent increase = 110.26%

find a whole number between 3.75 and the square root of 36

Answers

Answer:

Step-by-step explanation:

[tex]\sqrt{36}=6[/tex]

A whole number between 3.75 and 6 is 5.

could also be 4. 4 is between 3.75 and srt of 36

What is the domain of y = 4 log5 (x - 3)?
A. all real numbers
B. all real numbers greater than 4
C. all real numbers greater than 5
D. all real numbers greater than 3.

Answers

The domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.

How to determine the domain?

The function is given as:

[tex]y=4\log_5(x-3)[/tex]

Set the expression in bracket greater than 0

x -3 > 0

Add 3 to both sides

x > 3

Hence, the domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.

Answers

The sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0, the results tend to

How to interpret Garret studies?

From the question, we have the following highlights

The sample size is large enoughThe sample is at randomStudents who have a grade point average of 3.0 - 4.0 sleep for an average of 6.8 hoursStudents who have a grade point average of 2.0–3.0 sleep for an average of 6.4 hoursThere are no outliers

From the above highlights, the sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0

This is because 6.8 is greater than 6.4

This means that Garret's theory about the hours of sleep is correct

sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2 Find its area.

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sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2
Find its area.