sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2
Find its area.
Answers
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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Related Questions
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.
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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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
1) Can we predict the calories in a fast-food product if we know the amount of protein in that
product? Several fast-food products were examined and the number of calories and amount of
protein (in grams) were recorded. In the sample, the smallest and largest amounts of protein
were 4 grams and 22 grams, respectively. Analyzing the data resulted in the following
information:
Correlation of Protein and Calories = r = -0.87
The regression equation is Calories=302.5 -0.51 (Protein)
Interpret the correlation coefficient. There is a:
O strong negative linear relationship between protein amount and calories.
O weak negative linear relationship between protein amount and calories.
O strong positive linear relationship between protein amount and calories.
O weak positive linear relationship between protein amount and calories.
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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What number represents the smallest value? .3 or .33
Answers
Answer:
.3
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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What is it? I am not sure
Answers
Answer: I think its A
Step-by-step explanation: maybe
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%
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
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.
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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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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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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
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
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
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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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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]
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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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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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
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
HELP ASAP
Question
Garret studies number of hours sleep per night among students who have a grade point average of 3.0–4.0 versus students who have a grade point average of 2.0–3.0.
His theory is that students who get more sleep will have a higher grade point average than students who get less sleep because they are more rested and, therefore, better able to concentrate.
In his samples, the mean number of hours of sleep students with a grade point average of 3.0–4.0 received each night was 6.8. The mean number of hours of sleep students with a grade point average of 2.0–3.0 received each night was 6.4.
Assuming there are no outliers or skew, do the results support Garret's theory?
Select from the drop-down menus to correctly complete the statements.
Since the samples were large and randomly chosen, we can use the samples to understand the populations.
Because the sample mean for students with a grade point average of 3.0–4.0 is
Choose...
a. less than
b. about the same
c.greater than
the sample mean for students with a grade point average of 2.0–3.0, the results
Choose...
a. tend to
b. do not tend to
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 outliersFrom 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
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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.
find a whole number between 3.75 and the square root of 36
Answers
Answer:
5
Step-by-step explanation:
[tex]\sqrt{36}=6[/tex]
A whole number between 3.75 and 6 is 5.
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.
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].
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
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.
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
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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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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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.
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