The area of the region enclosed by the curve y² = x²(1 − x²) is 1/6.
To find the area, we can integrate the square root of the expression inside the curve from x=0 to x=1. This gives us the definite integral ∫(0 to 1) √(x²(1 − x²)) dx = 1/6.
The equation y² = x²(1 − x²) represents a curve that is symmetric about both the x-axis and the y-axis. To find the area enclosed by this curve, we need to integrate the square root of the expression inside the curve from x=0 to x=1.
We can simplify the expression inside the square root as follows: x²(1 − x²) = x² - x⁴. So, the area of the region can be found by evaluating the definite integral ∫(0 to 1) √(x² - x⁴) dx.
We can use substitution to evaluate this integral. Let u = x² - x⁴, then du/dx = 2x - 4x³. Rearranging, we get x(2 - 4x²) dx = 1/2 du. So, the integral becomes 1/2 ∫(0 to 1) √u du.
Integrating this gives us (1/2) * (2/3) * u³/² evaluated from 0 to 1, which simplifies to 1/3. However, since we used the substitution u = x² - x⁴, we need to multiply the result by 2 to account for the other half of the curve, giving us a final answer of 1/6.
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help guys soal integral
Answer:
E. [tex] \purple { \bold{ \frac{2}{3} ( \frac{x - 1}{x} ) \sqrt{\frac{x - 1}{x} } + c }}[/tex]
Step-by-step explanation:
[tex] \int \sqrt{ \frac{x - 1}{ {x}^{5} } } dx \\ \\ = \int \sqrt{ \frac{x - 1}{ {x}^{4} .x} } dx \\ \\ = \int \frac{1}{ {x}^{2}}\sqrt{ \frac{x - 1}{ x} } dx \\ \\ = \int \frac{1}{ {x}^{2}}\sqrt{ 1 - \frac{1}{ x} } dx \\ \\ let \: 1 - \frac{1}{ x} = t \\ \\ \implies \: \frac{1}{ {x}^{2} } dx = dt \\ \\ \implies \int \frac{1}{ {x}^{2}}\sqrt{ 1 - \frac{1}{ x} } dx = \int \sqrt{t} dt \\ \\ = \int {t}^{ \frac{1}{2} } dt \\ \\ = \frac{t ^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} t ^{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} \sqrt{ {t}^{3} } + c \\ \\ = \frac{2}{3} t\sqrt{ {t} } + c \\ \\ = \frac{2}{3} (1 - \frac{1}{x} ) \sqrt{1 - \frac{1}{x} } + c \\ \\ \red{ \bold{= \frac{2}{3} ( \frac{x - 1}{x} ) \sqrt{\frac{x - 1}{x} } + c }}\\ \\ [/tex]
suppose you plunk $5000 into a one-year certificate of deposit (CD) that pays simple interest at 3% per annum. The interest you earn after one year would be $150:
The simple interest for a deposit of $ 5,000 at 3 % rate of interest for 1 year would be $ 150
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as S
Now , the value of S is
The principal amount = $ 5,000
The rate of interest R = 3 %
The time period T = 1 year
So , the Simple Interest is given by the equation
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
Simple Interest S = ( 5000 x 3 x 1 ) / 100
On simplifying the equation , we get
Simple Interest S = 150000 / 100
Simple Interest S = $ 150
Therefore , the value of S is $ 150
Hence , the simple interest for the deposit is $ 150
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Evaluate each of the numerical expressions below.
1. 42 +9
2. (5 + 8)
PLEASE HELP ITS DO RN
Answer:
1. 51
2. 13
Step-by-step explanation:
1. 42 + 9
42 + 9 = 51
2. (5+8)
5 + 8 = 13
2/3n+1/2=3/4 I need this fast pls
Answer:
n = ⅜
Step-by-step explanation:
Answer: n = 1/6
Step-by-step explanation:
2/3n + 1/2 = 3/4
-1/2 -1/2
2/3n = 1/4
multiply both sides by 2/3
n = 1/4 *2/3
n = 2/12
reduce
n = 1/6
You buy 5 candy bars for $2.00. Find the cost of 18 candy bars? First
write a proportion to find the unit rate(price per one candy bar). Then use
the unit rate to to find the cost of 18 candy bars?
Answer- $7.50
Step-by-step explanation: edg
Which is the correct value for tanN? *
A tanN=16/20
B tanN=16/12
C tanN=12/20
D tanN=12/16
Answer:
D
Step-by-step explanation:
3/4 = 12/16
3) Solve the System of Equations using Elimination/Combinations.
-2x-y=-4
x+2y=5
Answer:
[tex]y = 2 \\ x = 1[/tex]
Step-by-step explanation:
[tex]y = 2 \\ x = 1[/tex]
Algebra 1 Please help! thank u sm
Answer:
1. Slyvia is wrong. You treat the numbers normally when dividing the left side, so 3.61/4.1 = .88. When dividing the exponents, you subtract the numerator from the denominator, so -11-7 = -18. So, you do have .88 * 10^-18, at first, but when you are working in scientific notation you want the decimal to be greater than so, which requires us to add an additional -1, to make it 8.8 instead of 0.88. This is because we want to move the decimal place left one more time. This results in our final answer being 8.8 * 10^-19, which is not Slyvia's answer.
2. Dylan's answer is correct. He subtracted the exponents correctly, then moved the decimal place over one place towards the left.
3. Ethan is wrong. He added the exponents, instead of subtracting. However, you cannot do this, because when you are dividing exponents, you must subtract.
Step-by-step explanation:
I have this acronym I learned called MADSPM, which has helped me a lot. I never learned it in Algebra, but I wish that they had taught it. Each letter corresponds with an exponent rule. If this makes sense, here is what it stands for:
When you multiply, you add.
When you divide, you subtract.
When there are parentheses, you multiply.
In this case, it was solely division. So, you just need to remember division = subtraction, when it comes to exponents.
Hopefully this helped. If you need me to explain it better, please let me know, and I will try. Thanks much & have a wonderful day!
Find the exact value of sin space 2 theta when tan theta equals negative 12 over 5 where fraction numerator 3 pi over denominator 2 end fraction less or equal than theta less or equal than 2 straight pi.
Answer:
-120/169
Step-by-step explanation:
Sin2theta = 2sintheta costheta
Given that tan theta = -12/5
Opposite = -12
Adjacent = 5
Using Pythagoras theorem
Hyp = √(-12)²+5²
Hyp = √144+25
Hyp = √169
Hyp = 13
Cos theta = adj/hyp
Cos theta = 5/13
Sin theta = opp/hyp
Sin theta = -12/13
Substitute
Sin2theta = 2(-12/13)(5/13)
Sin2theta = -120/169
Hence sin 2theta = -120/169
What is the expanded form of this number?
570.086
A (5×100)+(7×10)+(8×1100)+(6×1100)
B (5×100)+(7×10)+(8×110)+(6×1100)
C (5×100)+(7×10)+(8×110)+(6×11,000)
D (5×100)+(7×10)+(8×1100)+(6×11,000)
Answer:
B
Step-by-step explanation:
I think it is No am not sure exactly
The expanded form of this number 570.086 is,
⇒ (5 × 100) + (7 × 10) + (8 × 1/100) + (6 × 1/1000)
What is Place value?The value represented by a digit in a number on the basis of its position in the number is called a Place value.
Given that;
The number is,
⇒ 570.086
Now, We can expand the number as;
⇒ 570.086
⇒ 500 + 70 + 00 + 8/100 + 6/1000
⇒ (5 × 100) + (7 × 10) + (8 × 1/100) + (6 × 1/1000)
Thus, The expanded form is,
⇒ (5 × 100) + (7 × 10) + (8 × 1/100) + (6 × 1/1000)
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x * 5 * 25 * 4 ÷ 5, if x = 813 simplified form please
Answer:
81,300
Step-by-step explanation:
convert 5.70 lbs to grams and explain please help
Answer:
2585.48.
Step-by-step explanation:
The formula to convert pounds to grams is to approximately multiply 5.70 by 454, which is equal to 2585.48.
I need help with this plz
Can anyone answer 20-24
Mrs. Montgomery earns a 6.5% commission on her total sales. Last month, she had sales of $55,780.
How much commission did Mrs. Montgomery earn last month?What was her total pay for the month?
Answer:
Commission: $3625.70
Total (sales + commission): $59405.70
Step-by-step explanation:
6.5% of 55780 = 0.065 × 55780 = 3625.7
55780 increase 6.5% =
55780 × (1 + 6.5%) = 55780 × (1 + 0.065) = 59405.7
Television is measured by the diagonal. A 55-inch tv has an actual diagonal length of 54.8 inches. Its height is 27 inch Mr.Schlagers entertainment center is 49 inches wide will the tv fit the entertainment center?
Answer:
47.68 inches
Step-by-step explanation:
As seen in the diagram attached below we can see that the tv is a rectangle. We are given the diagonal and the height which means we have to find the length. Since the tv diagonal forms a right triangle we can use the Pythagorean theorem to solve for the length. This theorem would be the following.
[tex]a^{2} + b^{2} = c^{2}[/tex]
where a and b are the sides of the triangle and c is the diagonal.
[tex]27^{2} + b^{2} = 54.8^{2}[/tex]
[tex]729 + b^{2} = 3,003.04[/tex]
[tex]b^{2} = 2,274.04[/tex]
[tex]b = 47.68[/tex]
Finally, we can see that the length of the TV is 47.68 inches
(5-8) (1,4) m = -3
find the slope
Answer:
slope is -3
Step-by-step explanation:
m is the slope, this may have been a trick question.
by the points given the slope is 1
PLEASE HELP ME GUYS!! ITS URGENT
(2, 0); y > x – 5
y < 2x + 1
Y <-X + 3
tell whether the ordered pair is a solution of the system of linear inequalities
Answer:
ang hirap pag aralan mo po muna
What are the coordinates of the image after a dilation
with the center at the origin and a scale factor of 2?
(0, 0) (10, 0) (10,4) (0, 4)
(-2.2) (8, 2) (8.-2) (-2,-2)
(1, 1) (6, 1) (6, 3) (1, 3)
(0, 0) (0, 2) (5.0) (5,2)
Explanation:
The scale factor 2 means we multiply the coordinates of every original point by 2. A point like (-1,1) moves to (-2,2) after doing so
As another example, (4,1) moves to (8,2) after multiplying both coordinates by 2.
Find the length of the third side. If necessary, round to the nearest tenth.
17
25
Answer:
the real answer is 48 but if you round it to the nearest tenth it's 50
Step-by-step explanation: I hope my answer helps, if it does help can I get the brainliest answer, thanks.
Asystem of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the - y = 4x + 5 y = 4x - 5 2y = 8x - 10 - 2y = 8 - 10
Step-by-step explanation:
step 1. The first equation 4x - y = 5 has a slope of 4. The 2nd equation simply cannot have the same slope for there to be 1 solution.
step 2. -y = 4x + 5. This has a slope of -4 so "yes" it could work.
step 3. y = 4x - 5. "no".
step 4. 2y = 8x - 10. The slope is 8/2 = 4. "no".
step 5. -2y = 8x - 10. The slope is 8/-2 = -4. "yes".
???
[tex]( \frac{ {2x}^{3} }{ {8y}^{ - 4} }) ^{ - 3} [/tex]
Answer:
I'm not sure
Step-by-step explanation:
Sorry
HELP.... BRAINLIEST FOR ANYONE WHO ANSWERS
Kelly walks 1/3 mile to school. Justin’s walks 75% longer. How far does Justin walk to school?
Answer:
7/12 miles i think
Step-by-step explanation:
3/4 x 1/3 = 1/4
1/3 + 1/4 = 7/12 miles
Solve for x and show work need help just stuck on this one ☝
Answer:
X=11
Step-by-step explanation:
6 x 11 is 66, after adding 2 its 68. They are equal because they are vertical angles :)
Answer:
11
Step-by-step explanation:
I did:
68 - 2= 66
66 divided by 11= 6
To check my work I did:
6 * 11= 66
66 + 2= 68
Hope this helps!
Find the value of r so that the line through (8,r) and (4,5) has a slope of -4
Answer:
r = - 11
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to - 4
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 5) and (x₂, y₂ ) = (8, r)
m = [tex]\frac{r-5}{8-4}[/tex] = [tex]\frac{r-5}{4}[/tex] = - 4 ( multiply both sides by 4 )
r - 5 = - 16 ( add 5 to both sides )
r = - 11
I NEED HELP PLEASEEE!!!!
Answer:
1/4
Step-by-step explanation:
You are being asked to find 1/3 of 3/4. To find a fraction of a number, you multiply them:
1/3 * 3/4
(cross multiply)
3/12
(simplify (divide top and bottom by three))
1/4
help please I cant figure this put
Answer:
C
Step-by-step explanation:
Because the circle is not shaded in, it doesn't count the number it's on:
So it would be a < or >.
Because this is on a number line and the shaded part goes to the left, it will be < because it points to the left.
The non-shaded circle is on 4, so your answer, x, will be:
x < 4
But the answer choices don't have this, meaning you have to simplify all of them.
The first one is:
x + 9 < 5
x < -4
x - 5 < 9
x < 14
x + 5 < 9
x < 4
x - 9 < 5
x < 14
So it would be C.
The graph shown here is the graph of which of the following rational
functions?
FOO
5
A. F(x) = x(x+1)
B. F(x) = 4+1
X(X-2)
C. Fx) =
(x - 2)(x + 1)
Answer:
the graph of the rational function is B
Answer:
Step-by-step explanation:
B
3.
Which equation best describes the graph?
A. y = 2x + 3
B. y = 1/2x + 3
C. y = 1/2x – 3
D. y = 2x – 3
Answer:
Its C
Step-by-step explanation:
The y starts at negative 3 and it is going up by 1 and over 2
Hope this Helped
Answer:
C. y = 1/2x - 3
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
1
2
y-intercept:
(
0
,
−
3
)
x
y
0
−
3
6
0