The area of the resulting surface of this infinite curve is π units.
In this question,
The infinite curve is y = e^−2x, x ≥ 0.
The curve is rotated about x-axis.
Since x ≥ 0, the limits will be 0 to ∞.
Then the area of the resulting surface is,
[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]
Now substitute,
u = -2x
⇒ du = -2dx
⇒ dx = [tex]-\frac{1}{2} du[/tex]
Then,
[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]
Now substitute u and du, we get
⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]
⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]
Thus the area of the resulting surface is
[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]
⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]
⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]
⇒ [tex]A= -\pi [0-1} \,]\\[/tex]
⇒ [tex]A= \pi[/tex]
Hence we can conclude that the area of the resulting surface is π units.
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what is the value of sin30°+cos60°
The answer is 1.
Here, we need to know the trigonometric values of sin 30° and cos 60°, which are :
sin 30° = 0.5cos 60° = 0.5Hence, sin 30° and cos 60° :
0.5 + 0.515. On the way to the museum, 50% of the students rode on the first bus.
What fraction of the students rode on the second bus? Show your work
in the space below. Remember to check your solution.
Answer:
1/2
Step-by-step explanation:
Since 50% is half the number of students it means that half of the students took the first bus which leaves the other half to take the 2nd bus
can someone help me pls
Explanation:
The sector is the pizza slice. We subtract off the area of the triangle to find the yellow shaded area.
78.6794 - 70.4956 = 8.1838
If the length of the minor axis of an ellipse is 6 units and the length of the major axis is 10 units, how far from the center are the foci located? a. 4 units b. 2 units c. units d. units e. 5 units
The distance from the center to where the foci are located exists 8 units.
How to determine the distance from the center?The formula associated with the focus of an ellipse exists given as;
c² = a² − b²
Where c exists the distance from the focus to the center.
a exists the distance from the center to a vertex,
the major axis exists 10 units.
b exists the distance from the center to a co-vertex, the minor axis exists 6 units
c² = a² − b²
c² = 10² - 6²
c² = 100 - 36
c² = 64
[tex]c = \sqrt{64}[/tex]
c = 8
Therefore, the distance from the center to where the foci are located exists 8 units.
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what time 2 equals 25
Answer:
the answer to "2 times what equals 25?" is 12.5.
Find the inequality represented by the graph.
The inequality of the graph is expressed as: y > 1/2x + 2.
How to Find the Inequality of a Graph?The graph given has a broken line and the shaded part is above the boundary line, therefore, we would use the sign, ">" in our inequality. The inequality would be expressed as y > mx + b.
Find the slope (m):
Slope (m) = rise/run = 1 units/2 units
m = 1/2
b = 2 (y-intercepts)
Substitute m = 1/2 and b = 2 into y > mx + b
y > 1/2x + 2.
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Graph Y equals |x|-5
Answer:
graph C
Step-by-step explanation:
when X= 0
Y ---> -5
so , answer is graph C
Answer:
c
Step-by-step explanation:
the graph of | x | has its vertex at the origin and has shape V
the graph of | x | - 5 is the graph of | x | translated 5 units vertically down.
That is graph c represents | x | - 5
Which inequality explains why these three segments cannot be used to construct a triangle? ef fd > de ed ef < df ed ef > df ef fd < de
We have the segments EF, FD, and DE.
Therefore, the correct answer is
ED + EF < DF
EF + FD < DE
What is Triangle Inequality Theorem?
The Triangle Inequality Theorem states that the totality of any side of a triangle must be greater than the measure of the third side in this problem.
We have the segments EF, FD, and DE.
To construct a triangle three inequalities must be met
case 1: EF + FD > DE
case 2: FD + DE > EF
case 3: EF + DE > FD
Therefore, the correct answer is
ED + EF < DF
EF + FD < DE
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Which unit rate is the lowest price per ounce
Choice a: 10 ounces of chocolate chips for $1.66
Choice b: 20 ounces of chocolate chips for $3.22
1: choice a
2: choice b
3:unit rates are equal
4:Cannot be determined
Answer:
2: choice b
Step-by-step explanation:
a: $1.66 / 10 oz = $0.166/oz
b: $3.22 / 20 oz = $0.161/oz
Answer: 2: choice b
Sami cuts out a rectangle that has a perimeter of 48 inches and a length of 13 inches. they cut out another rectangle that is the same length and twice as wide. what is the perimeter of the new rectangle?
Answer:
70 inches
Step-by-step explanation:
the width of the original rectangle:
48/2 - 13 = 24 - 13 = 11
the new rectangle:
length: 13
width: 2(11) = 22
perimeter: 2(13+22) = 2(35) = 70
The perimeter of the new rectangle is 70 inches.
What is Area of Rectangle?The area of Rectangle is length times of width.
The perimeter of a rectangle is given by the formula P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
The first rectangle has a perimeter of 48 inches and a length of 13 inches.
48 = 2(13 + w)
24 = 13 + w
w = 11
So the first rectangle has a length of 13 inches and a width of 11 inches.
The second rectangle has the same length of 13 inches and twice the width of the first rectangle, which means it has a width of 22 inches.
P = 2(13 + 22)
= 2(35)
= 70
Therefore, the perimeter of the new rectangle is 70 inches.
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________13. Write an equation of a circle centered at the origin with radius 3.
Answer:
13. x^2 + y^2 = 3
14. B
Step-by-step explanation:
13. Since it's centered at the origin, (0, 0), the values of h and k in (x - h)^2 + (y - k)^2 = r^2 are equal to zero. So we simply have x^2 + y^2, and since the radius is the square root of 3, squaring the radius gives us 3.
14. B is the only circle with both a radius of 3 that's also shifted to the right 1 and down 2, since it's centered at (h, k), which is (1, -2).
Hope this helps! Brainliest, please :)
If X = 2 centimeters, Y = 5 centimeters, and Z = 5 centimeters, what is the area of the object?
Answer: [tex]35 cm^2[/tex]
Step-by-step explanation:
Area of trapezium =
2X = 2 + 2 = 4 cm
2Z = 5 + 5 = 10 cm
Y = 5 cm
[tex]\dfrac{ \left( 4+10 \right) }{ 2 } \times 5[/tex]
|
|--------> 35 [tex]cm^2[/tex]
What would you do if you found two values that were twice as big as the next highest value?
If I discovered two numerical values that were twice as big as the next highest value, I would expunge them because they can affect the final results.
What is a numerical data?A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only.
This ultimately implies that, a numerical data is a data set consisting of numbers rather than words.
What is an outlier?An outlier can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.
Assuming I am counting the number of expert tutors on Brainly and I discovered two numerical values that were twice as big as the next highest value, I would expunge them because they can affect the final results.
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Expand and simplify (2+√3)² - (2-√3)²
Answer:
8√3
I hope this helps you
A laptop is on sale for 45% off the regular price. If the sale price is $299.75, what was the original price?
The original price of the laptop is calculated as $545
How to find the original Price?We are given;
Sales Price of Laptop = $299.75
Now, the laptop is on sale for 45% off regular price.
If original price is x, then we can express that;
(100% - 45%) * x = 299.75
Thus;
55%x = 299.75
0.55x = 299.75
x = 299.75/0.55
x = $545
Thus, the original price of the laptop is calculated as $545
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Solve the inequality and enter your solution as an inequality comparing the variable to a number x+25>50
Let's solve your inequality step-by-step.
x+25>50
Step 1: Subtract 25 from both sides.
x+25−25>50−25
x>25
Answer:
x>25
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For a population with µ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of __________
Answer:
calculate the number of atom in 3 mol helium
what is a constant
for example
[tex]y=x^{3} -3x^{2} +Kx+8[/tex] where K is the constant
what does that mean
Answer:
see explanation
Step-by-step explanation:
K is a constant means that K is a fixed numerical value
Select the correct answer. what is the completely factored form of this expression? y2 − 12y 32 a. (y 4)(y 8) b. (y − 4)(y − 8) c. (y 18)(y 2) d. (y − 18)(y − 2)
Answer:
b. (y - 4)(y - 8)
Step-by-step explanation:
Please Help me i will give brainlist !Which of the choices below show the pre-image quadrilateral ABCD, rotated 180° about the origin?
Answer:
The first choice.
Step-by-step explanation:
The second choice is a translation and the third choice is a reflection.
Evaluate the expressions. 32) 12+ 32÷3-6
Answer:
16.66666667
Step-by-step explanation:
=12+10.66666667-6
=22.66666667-6
=16.66666667
neeed help more more please uwu
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]
[ Multiply both sides by 2 ]
[tex]\qquad \sf \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]
a = 2b = 17 c = 10[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 289 - ( - 80)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 369[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]
[tex]\qquad \sf \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]
Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. leave your answer in terms of π.
If the radius of the circle exists 2.4 kilometers and is intercepted by a central angle measuring 150° then the length of the arc exists 5π inches.
What was the relation between the central angle and its intercepted arc?If the vertex of an angle exists in the center of the circle and the two sides of the angle are radii in the circle, then this angle exists named a central angle.Each central angle exists subtended by the opposite arc, the name of the arc exists the starting point and the finish point of the angle.There exists a relation between the central angle and its subtended arc the measure of the central angle equals half the measure of its subtended arc.The length of the subtended arc relies on the measurement of its central angle and the length of the radius and the measure of the arc.The measurement of the circle exists at 360°.The length of the circle exists at 2πr.The radius of the circle r = 2.4 kilometers
The measure of the central angle exists at 150°.
The length of the arc = central angle/360 × 2πr
The length of the arc = 150°/360° × 2 × π × 2.4 = 2π
The length of the arc exists 2π kilometers.
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I NEED THIS ANSWER QUICK (5 1/6 - x) ∙ 2.7 - 5 3/4 = -1.25 what is x
Answer:
x = 3 1/2
Step-by-step explanation:
You could simplify the given equation first, then solve the resulting 2-step linear equation. It might work better to undo the operations done to the variable.
Solution(5 1/6 -x)(2.7) -5 3/4 = -1 1/4 . . . . . given
(5 1/6) -x)(2.7) = 4 1/2 . . . . . . . add 5 3/4 to both sides
(5 1/6 -x) = 4.5/2.7 = 5/3 . . . divide by 2.7
31/6 -10/6 = x . . . . . . . . . . add x-5/3, use common denominators
21/6 = x = 7/2
x = 3 1/2
A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = –4.
In which direction does the parabola open?
up
down
right
left
The direction does the parabola open is right. Option C
What is the equation of a parabola?
It is important to note that the general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h
where
⇒ (h , k) denotes the vertex.
Also, the standard equation of a regular parabola is y² = 4ax.
From the equation given , we have
The vertex of the parabola is at (0, 0)Directrix of the parabola is x = -4We know that when the vertex of the parabola is (0, 0) and the directrix is x = - a, the parabola will have the form;
y² = 4ax
It is important to note that ;
If the x - axis has a positive value, the parabola shifts to the leftif the x- axis has a negative value, the parabola shift to the rightFrom this, we can see that the parabola would open in the right direction
Thus, the direction does the parabola open is right. Option C
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The graph of any function and the graph of its inverse are symmetric with respect to the
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
A function should be one - to - one and onto in order to have inverse.
and to find the point on its inverse function we swap the value of x - coordinate and y - coordinate.
like (x , y) becomes (y , x)
The only way we get (y , x) is by taking image of point (x , y) about line : y = x
[tex] \qquad \large \sf {Conclusion} : [/tex]
we can conclude that the graph of a function and it's inverse is symmetric about equation (line) : y = x
What step would be necessary if you wished to conduct a poll with a margin of error of zero?
The necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.
What is a poll?An opinion poll, often known as a poll or a survey, is a human research survey of public opinion from a specific sample. Opinion polls are often designed to depict a population's opinions by asking a series of questions and then extrapolating generalities in ratio or within confidence intervals. A pollster is somebody who conducts polls.If we were to conduct a poll with a margin of error of zero, we would need to recruit every responder in the population to participate.As it is given in the description itself, if we were to conduct a poll with a margin of error of zero, we would need to recruit every responder in the population to participate.
Therefore, the necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.
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Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?
35°
70°
75°
140°
By applying the theorem of intersecting secants, the measure of angle XYZ is equal to: A. 35°.
How to determine angle <XYZ?By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the theorem of intersecting secants.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle XYZ will be given by this formula:
<XYZ = ½ × (m<WZ - m<XZ)
Substituting the given parameters into the formula, we have;
<XYZ = ½ × (175 - 105)
<XYZ = ½ × 70
<XYZ = 35°.
By applying the theorem of intersecting secants, we can infer and logically deduce that the measure of angle XYZ is equal to 35°.
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Answer: 35
Step-by-step explanation:
Which of the following steps were applied to ABCD to obtain A'B'C'D'?
A. shifted 3 units right and 4 units down
B. shifted 2 units right and 3 units down
C. shifted 3 units
right and 3 units down
D. shifted 2 units right and 4 units down
The answer is B.
To obtain A'B'C'D' from ABCD, we can clearly see that it has been shifted 2 units right and 3 units down.
(01.02 mc)matt is showing his work in simplifying (6.2 − 1.6) − 4.4 7.8. identify any error in his work or reasoning. step 1: (6.2 − 1.6) − 4.4 7.8 step 2: 6.2 (− 1.6 − 4.4) 7.8 (commutative property) step 3: 6.2 − 6 7.8 step 4: −14 − 6 = 8 (commutative property) step 5: 14 − 6 = 8 he wrote commutative instead of distributive in step 4. he wrote commutative instead of distributive in step 2. he wrote commutative instead of associative in step 4. he wrote commutative instead of associative in step 2.
The correct option is (d)
He wrote commutative instead of associative in step 2.
What is the commutative property?According to the commutative property, a mathematical principle, the product of a multiplication does not depend on the order in which the numbers are multiplied.
Commutative property: a+b = b+a
Associative property: (a+b) + = a+(b+c)
Now consider the provided expression.
(6.2 − 1.6) − 4.4 + 7.8
Step 1:
(6.2 − 1.6) − 4.4 + 7.8
Step 2 Use Associative property
6.2 + (−1.6 − 4.4) + 7.8
Step 3: Simplify
6.2 − 6 + 7.8
Step 4: Use commutative property
14 − 6
Step 5: Simplify
14 − 6 = 8
Hence, the wrong step is step 2.
He wrote commutative instead of associative in Step 2.
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I understand that the question you are looking for is:
Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning. Step 1: (6.2 − 1.6) − 4.4 + 7.8 Step 2: 6.2 + (− 1.6 − 4.4) + 7.8 (commutative property) Step 3: 6.2 − 6 + 7.8 Step 4: −14 − 6 = 8 (commutative property) Step 5: 14 − 6 = 8
(a)-He wrote commutative instead of distributive in Step 4.
(b)-He wrote commutative instead of distributive in Step 2.
(c)-He wrote commutative instead of associative in Step 4.
(d)-He wrote commutative instead of associative in Step 2.
