The given curve is rotated about the y-axis. Find the area of the resulting surface.
y = 14
x2 −
12
ln x, 3 ≤ x ≤ 5
Answers
The surface area of the solid formed by rotating the curve y = 14\(x^{2}\) - 12ln(x) about the y-axis within the interval 3 ≤ x ≤ 5 is determined by calculating the derivative of y, substituting the values into the surface area formula, performing the integration, and evaluating the integral limits. The final result will provide the area of the resulting surface.
The surface area of the solid formed by rotating the curve y = 14\(x^{2}\) - 12ln(x) about the y-axis within the interval 3 ≤ x ≤ 5 needs to be determined.
To find the surface area, we can use the formula for the surface area of a solid of revolution. This formula states that the surface area is given by the integral of 2πy√\((1 + (dy/dx)^2)\) with respect to x, within the given interval.
First, we need to find dy/dx by taking the derivative of y with respect to x. Then, we can substitute the values into the formula and integrate over the interval to find the surface area.
The explanation will involve calculating the derivative of y, substituting the values into the surface area formula, performing the integration, and evaluating the integral limits to determine the final result.
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Related Questions
This chart shows what happens when each object is placed on a balance with a 10 kg weight on the other side.
A 3-column table with 2 rows titled effects of each object. The first row has entries Object 1, Object 2, Object 3. The second row has entries the balance tips toward the object, the balance remains balanced, the balance tips toward the weight.
Which statement is best supported by the information in the chart?
Object 1 is the heaviest object.
Object 3 is heavier than Object 1.
The weight is heavier than Object 2.
The weight is the heaviest object.
Answers
9514 1404 393
Answer:
Object 1 is the heaviest object.
Step-by-step explanation:
The first column of the table tells you ...
Object 1 is heavier than the 10 kg weight
The second column of the table tells you ...
Object 2 weighs 10 kg
The third column of the table tells you ...
Object 3 is lighter than the 10 kg weight
Then the relative weights are ...
Object 1 > Object 2 > Object 3
That is, Object 1 is the heaviest object.
Answer:
Object 1 is the Heaveyist!!!!
Step-by-step explanation:
3-column table with 2 rows titled effects of each object. The first row has entries Object 1, Object 2, Object 3. The second row has entries the balance tips toward the object, the balance remains balanced, the balance tips toward the weight.
Which statement is best supported by the information in the chart?
Object 1 is the heaviest object.----------!!!!!!!!!!!!!!!!!!!!!ΨΩΩΣΡξβνζ
Object 3 is heavier than Object 1.
The weight is heavier than Object 2.
The weight is the heaviest object.
A tree in Lashonda's backyard is 1 meters tall. It has been growing for 3 years. 4. What is the unit rate in meters per year?
Answers
Step-by-step explanation:
the answer is in the above image
There are three numbers. The second number is equal to the third number subtracted by the first number. The sun of the second and third numbers is 4 more than the first number.
Answers
Which numbers do you want?
Candice's Cupcakes recently sold 15 cupcakes, of which 6 were chocolate cupcakes. What is
the experimental probability that the next cupcake sold will be a chocolate cupcake?
Write your answer as a fraction or whole number.
Answers
Answer
2/5 i double checked on and ixl question so good luck
Step-by-step explanation:
The answer to the experimental probability that a chocolate cupcakes will be the next one sold is 0.5, or 50%.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
we know that,
The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials or experiments.
In this case, the event is selling a chocolate cupcake and the total number of cupcakes sold is 15.
Since 6 out of the 15 cupcakes sold were chocolate cupcakes,
the experimental probability of the next cupcake sold being chocolate cupcakes is:
Experimental probability = Number of times event occurred / Total number of trials
Experimental probability = 6/15
Experimental probability = 0.4
Therefore, the experimental probability that the next cupcake sold will be a chocolate cupcakes is 0.4 or 25%.
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What is 9+10?? Here are your answer choices
A) 21
B)21
C)21
D)21
LOL
Answers
Answer:
B
Step-by-step explanation:
9 plus 10 equals 21 because george washington was the first president of the United states and because Donald Trump lost the 2020 election
Use a graphing calculator or online application to find the solution to 3^-x = x^3 + x to the nearest tenth. The solution is approximately x = ?
the answer is not 0.5 or 0.48
Answers
Answer:
x = 0.5 to the nearest 1/10.
Step-by-step explanation:
3^-x = x^3 + x
y = x^3 - 3^-x + x = 0
Using a graphing calculator to draw the graph of the above:
The graph crosses the x-axis at x = 0.4798
Answer:
x≈ .5
Step-by-step explanation:
x ≈ 0.479822322350589
Rounding to the nearest tenth
x≈ .5
There is either an error in the equation or the solution key
What is the equation of the graphed line in slope intercept form?
(Graph is in the picture)
Answers
Answer:
y = 3x + 4
Step-by-step explanation:
y = mx + c where m is the slope and c is the y intercept.
Slope = \(\frac{rise}{run}\)
Slope (taken from points (0, 4) and (1, 7)) = \(\frac{7-4}{1-0}\)
= 3
y-intercept = 4
Equation: y = 3x + 4
Marshall is renting a bike for the day. It costs $13 for up to one hour. After one hour, the price increases to $20. After three hours, the price increases again to $50. The maximum time he can rent the bike is 10 hours total
Answers
The piecewise function that represents the situation is therefore:
Costs Possible hours
13 0 < x ≤ 1
20 1 < x ≤ 3
50 3 < x ≤ 10
How to find the piecewise function ?We see that up to one hour, the cost to Marshall would be $ 13 so the possible hours at that price is 0 < x ≤ 1 .
Likewise from one hour, the price goes up to $ 20 which means that possible hours become 1 < x ≤ 3 because the price will increase at 3 hours again.
From 3 hours, the price becomes $ 50 and there are a maximum of 10 hours so the hours become 3 < x ≤ 10 .
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You ride your bike up a steep mountain road at 5 miles per hour. How far do you go in 3 hours? Student solution: 5\div 3=1.75÷3=1.7. I ride 1.7 miles.
Answers
Answer:
15
Step-by-step explanation:
5x3 = 15 It's Simple Hope it helps
you want to determine the minimum total sample size needed to detect the desired effect of 50 mg/l lower than the true mean water hardness of the stock ponds using a significance level of 0.05 and a power of 0.8.
Answers
To determine the minimum total sample size needed to detect a desired effect of 50 mg/l lower than the true mean water hardness of the stock ponds, you would use a significance level of 0.05 and a power of 0.8. This ensures the statistical test has adequate sensitivity to identify the effect while maintaining a low risk of false-positive findings.
The minimum total sample size needed to detect the desired effect of 50 mg/l is lower than the true mean water hardness of the stock ponds, a significance level of 0.05 and a power of 0.8 are required. The sample size calculation requires knowledge of the expected effect size, variability of the data, and significance level
. Using statistical software, the calculation can be done to obtain the minimum sample size required to achieve the desired level of significance and power. It is important to ensure that the sample size is sufficient to detect the desired effect size and to minimize the risk of a type II error.
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7x= -8 + 5x
help me solve this step by step !
Answers
Answer:
Step-by-step explanation:
First, you'll want to combine like terms by bringing the
x's together. This can be done by adding 7x to both sides.
4 − 7x = 5x
to get
4 = 12x
To solve for x, you must divide both sides of the equation by the coefficient of x which is 12 and then simplify.
x = 4/12
x = 1/3
x is therefore equal to 1/3.
A company sells cases of Mountain Dew. The revenue generated by selling x cases is described as LaTeX: \text{R(x)=50x} . The cost to produce the cases is described by the function LaTeX: \text{C(x)=25x+100.} The company’s profits for selling the cases of Mountain Dew is the difference between the revenue and cost amounts. Which function describes P, the profit for selling x cases?
A company sells cases of Mountain Dew. The revenue generated by selling x cases is described as LaTeX: \text{R(x)=50x} . The cost to produce the cases is described by the function LaTeX: \text{C(x)=25x+100.} The company’s profits for selling the cases of Mountain Dew is the difference between the revenue and cost amounts. Which function describes P, the profit for selling x cases?
LaTeX: \text{P(x)=25x+100}
LaTeX: \text{P(x)=75x-100}
LaTeX: \text{P(x)=25x-100}
LaTeX: \text{P(x)=75x+100}
Answers
Answer:the person below is correct
Step-by-step explanation:
What is the value of x in X² 9?
Answers
The value of x in the given equation x² = 9 is x = ± 3.
In x² = 9, we need to remove the power of 2 in order to separate just x.
This implies finding the square root √x² which is equal to x.
However, there are 2 possible answers to any square root, a positive or a negative answer.
x = √9
x = ± 3
0r we can solve this equation by the splitting method.
Rearrange the equation
x² = 9
(x - 3)(x + 3) = 0
On solving, we get
x = +3 and x = -3
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Please answer this question ty
Answers
Answer:
m<1 = 45 M<2 = 135 M<3 = 45
Step-by-step explanation:
Answer: M<1 = 45, M<2 = 135, m<4 = 45
Step-by-step explanation:
Angles such as 1 to 4 and 2 to 3 have the same angle, so you take the total of 3 and 2 (270) and subtract it from 360 to to get the values of angles 1 and 4 combined. divide this in half to separate the two angles to get 45 degrees.
135+135=270
360-270=90
90/2=45
does each equation represent exponential decay or exponential growth? drag and drop the choices into the boxes to correctly complete the table. note: if an equation is neither exponential growth nor exponential decay, do not drag it to the table.
Answers
The equations that represent exponential growth are L = 0.25(12)^t, W = 0.5(2.1)^t, f(t) =2/3(6)^t and exponential decay are W=9/8(3/5)^t, f(t) = (3/4)^t, L = 4.2(0.6)^t.
An exponential function refers to a relationship where the rate of change of a variable depends on the value of the variable itself. In mathematics, an exponential function is a function of form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. It is a type of mathematical function helpful in finding the growth or decay of population. Exponential growth refers to the function whose base of the function is greater than 1 and exponential decay refers to the function whose base of the function is less than 1. Hence, The equations that represent exponential growth are L = 0.25(12)^t, W = 0.5(2.1)^t, f(t) =2/3(6)^t and exponential decay are W=9/8(3/5)^t, f(t) = (3/4)^t, L = 4.2(0.6)^t. g(x) = 1.3x is neither a growth or decay exponential as it has no exponent.
Note: The question is incomplete, and the complete question is attached.
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6. sınıf atanan sınav kesirlerle işlemler ve ondalık gösterimler cevaplarını atar mısınız lütfen çok ihtiyacım var 12 MAYIS'a KADAR YAPMAM LAZIM LÜTFEN
Answers
Answer:
Hallelujah, hallelujah, Hallelujaaaahhh yes lord for the rest of our days.
YES
Step-by-step explanation:
a farmer has 312 feet of fencing to enclose 2 adjacent rectangular pig pens sharing a common side. the common side divides the total area in half. what is the maximum area for each pig pen?
Answers
The maximum area for each pig pen is 156 square feet. The total length of fencing available is 312 feet. We also know that the two pig pens share a common side, so we can assume that the other three sides of each pen are independent rectangles.
The length of the common side "x" and the width of each pen "y". Since the total area is divided in half by the common side, we can write an equation:
2(xy/2) = x*y
xy = 156
A = xy
y = 156/x
Substituting this expression for y into the formula for the area, we get:
A = x(156/x)
A = 156 - x^2/2
This is a quadratic equation in standard form, with a = -1/2, b = 0, and c = 156. The vertex of the parabola is at x = -b/2a = 0, which means that the maximum area occurs when x is at the midpoint of the fencing available, which is 156/2 = 78
feet.
y = 156/78 = 2
The dimensions of each pig pen are 78 feet by 2 feet, and the maximum area of each pen is:
A = 78*2 = 156 square feet.
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Marcus has x songs downloaded on his phone. He downloads 20 more songs to his phone.
Enter an expression in the box to represent the number of songs Marcus now has on his phone.
Answers
Answer:
x + 20 = y
Step-by-step explanation:
x + 20 = y
where x= number of songs
y = total songs marcus has
-4x>6y - 54
I’m not sure how to completely solve this
Answers
1) Divide both sides by-4.
\(x < - \frac{6y - 54}{4} \)
2) Factor out the common term 6.
\(x < - \frac{6(y - 9)}{4} \)
3) Simplify 6(y-9)/4 to 3 ( y - 9) / 2.
\(x < - \frac{3(y - 9)}{2} \)
Therefor, the answer for x is x < - 3(y - 9)/2.
Solving for Y:\( - 4x + 54 > 6y\)
\( \frac{ - 4x + 54}{6} > y\)
\( \frac{ - 2(2x - 27)}{6} > y\)
\( - \frac{2(2x - 27)}{6} > y\)
\( - \frac{2x - 27}{3} > y\)
\(y < - \frac{2x - 27}{3} \)
Therefor, the answer for Y is y < - 2x-27/3.
find the area of the figure below:
Answers
To solve for 1 rectangle you do:
9 • 5 = 45
And for the other rectangle you do:
6 • 3 = 18
Add up the areas:
45 + 18 = 63
63m^2
Answer:
63 m^2 would be your answer
Step-by-step explanation:
finding the area is preety easy
look at pic
y
− 10
=
1
8
(
x
− 8
)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
x answer: x = ( y + 134 ) / 18
y answer: y = 18x - 134
Step-by-step explanation:
y - 10 = 18( x - 8 )
y - 10 = 18x - 144
x answer:
y - 10 = 18x - 144
y + 134 = 18x
( y + 134 ) / 18 = x
y answer:
y - 10 = 18x - 144
y = 18x - 134
Given the point (-6, 1) & slope = 1/3, what is the equation of the line? *
Answers
Answer:
y=1/3 + 3
Step-by-step explanation:
y= 1/3x + b
(1) = 1/3(-6) + b
1 = -2 +b
3 = b
y=1/3 + b
find the area of the surface formed by revolving the polar equation over the given interval about the given line. p
Polar equation r = eaθ
interval 0 ≤ θ ≤ π/2
axis of revolutionθ = π/2
Answers
Answer:
We are asked to find the area of the surface formed by revolving the polar equation r = eaθ over the interval 0 ≤ θ ≤ π/2 about the line θ = π/2.
To find the surface area of the solid formed by revolving the polar curve r = eaθ over the interval 0 ≤ θ ≤ π/2 about the line θ = π/2, we need to use the formula for surface area of a surface of revolution, which is given by:
A = ∫αβ 2πr(s)√(1 + [r'(s)]^2) ds
where α and β are the limits of integration, r(s) is the polar curve, and r'(s) is the derivative of the polar curve with respect to s.
In this case, our polar curve is r = eaθ, so r'(θ) = aeaθ. We also know that the axis of revolution is θ = π/2, so our limits of integration will be α = 0 and β = π/2. Substituting these values into the formula, we get:
A = ∫0^(π/2) 2π(e^(aθ))√(1 + a^2(e^(aθ))^2) dθ
Simplifying this expression, we get:
A = 2πa ∫0^(π/2) e^(aθ)√(1 + a^2(e^(aθ))^2) dθ
This integral can be evaluated using a trigonometric substitution and integration by parts, but the process is quite lengthy and complex. Therefore, we will leave the result in this form as the final answer.
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In this division problem what is the divined of 2/3 divided by 6/5
Answers
Answer:
5/9
Step-by-step explanation:
brainliest when possible.
A square has vertices at (1,1), and (2, -1). Where are the two vertices located? How do you know you have created a square?
Answers
If you graph the point
(1,1)
and
(2,-1)
you see this. Shown below:
The figure above is maddie's bedroom .maddie is going to paint just the walls blue how many square feet will be painted blue
Answers
Can someone please help me on this question! Thank you very much!!
Answers
Answer:
(9√3 - 3π) cm² or ≈ 6.16 cm²
Step-by-step explanation:
Refer to attached pictures
We have equilateral triangle with side of 6 cm and inscribed circle, we need to find the shaded area inside the triangle not covered by the circle.
The shaded are is the difference of areas of the triangle and circle
Area of equilateral triangle is calculated as per formula:
A= √3 /4 × a², where a is side of triangleA= √3 /4 × 6² = 9√3 cm²Area of circle is calculated as per formula:
A= πr², where r is the radius of circleLet's find the value of r:
Δ ADB is the right triangle with angles 30° and 60°
It has sides of 3 cm, 6 cm and AD= m cm
As per attached, m is the long leg and equal to a√3, so
m = 3√3also,
AD= AO+OD= AO +rWe can find AO in the same way as above using Δ AOF
AO= 2r as it is the hypotenuse and the hypotenuse is twice a short leg in the right triangle with angles 30° and 60°
So,
AD= 2r+r= 3r ⇒ r= AD/3 = 3√3/3= √3 cmNow we can get the area of circle:
A= πr²= π×√3²= 3π cm²Shaded are is:
(9√3 - 3π) cm² or ≈ 6.16 cm²
Please help me I'm stuck. I will give 30 points for this one. Given triangle ABC tilde triangle PQR and your scale factor Complete the hotspots for these similar triangles and show work
Answers
The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:
(1). angle B = 68°
(2). PQ = 5cm
(3). BC = 19.5cm
(4). area of ∆PQR = 30cm²
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}
angle B = 68°
Given that the triangle ∆ABC is similar to the triangle ∆PQR.
(2). PQ/7.5cm = 12cm/18cm
PQ = (12cm × 7.5cm)/18cm {cross multiplication}
PQ = 5cm
(3). 13cm/BC = 12cm/18cm
BC = (13cm × 18cm)/12cm {cross multiplication}
BC = 19.5cm
(4). area of ∆PQR = 1/2 × 12cm × 5cm
area of ∆PQR = 6cm × 5cm
area of ∆PQR = 30cm²
Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:
(1). angle B = 68°
(2). PQ = 5cm
(3). BC = 19.5cm
(4). area of ∆PQR = 30cm²
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Please help me I suck at proof :(( I don’
Answers
Answer:it's just like baldi's equations just multiply the digits that are u there it is hard to see
Step-by-step explanation:
circular cloud of poison gas from a factory explosion is expanding so that hours after the explosion the radius of the cloud is meters. how fast is the area of the cloud increasing hours after the explosion?
Answers
The rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the square of the radius of the cloud.
Therefore, the rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the radius of the cloud. The rate of expansion can be calculated using the equation . Therefore, the rate at which the area of the cloud is increasing can be calculated as .
The area of a circle is determined by the square of its radius. Thus, when the radius of the cloud is expanding at a rate, the area of the cloud is increasing at a rate that is proportional to the square of its radius.
Therefore, in order to calculate the rate at which the area of the cloud is increasing, we must calculate the rate of expansion of the radius of the cloud and then multiply it by the square of the radius of the cloud. To calculate the rate of expansion of the radius of the cloud, we can use the equation .
After we have calculated the rate of expansion, we can then multiply it by the square of the radius of the cloud to calculate the rate at which the area of the cloud is increasing.
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