Answer:
A and D
Step-by-step explanation:
Given the function:
[tex]\displaystyle{f(x)=\sqrt{5-x^2}}[/tex]
In order to find the first-order derivative of square root function, we have to convert the form of surd to exponent form. Therefore:
[tex]\displaystyle{f(x)=\left(5-x^2\right)^{\frac{1}{2}}}[/tex]
Since the exponent is a constant and that the base is an expression with variable, we can apply the chain rule (power rule variation):
[tex]\displaystyle{f(x) = u^n \to f'(x) = nu^{n-1} \cdot \dfrac{du}{dx}}[/tex]
Therefore:
[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-1} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-\frac{2}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}[/tex]
Deriving 5 - x²:
[tex]\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = 0 - 2x^{2-1}}\\\\\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = -2x}[/tex]
Thus:
[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot (-2x)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}(-2x)\left(5-x^2\right)^{-\frac{1}{2}} }\\\\\displaystyle{f'(x)=-x\left(5-x^2\right)^{-\frac{1}{2}} }[/tex]
You can also convert to the square root form of:
[tex]\displaystyle{f'(x)= \dfrac{-x}{\sqrt{5-x^2}}}[/tex]
Therefore, A and D are correct.
Tentukan!!! A. Sin A tos A dam tg A
Answer: if u don't know that this language is than ill tell u.
its just random words that someone typed in. I'm being honest this is not a language this is some random typed words. trust me pls I'm being honest fr.
Step-by-step explanation: what I did was going a a type of book that has all the language on it so u get to know the language.
Fill in each blank so that the resulting statement is true.
The shaded set of numbers shown on the y-axis on the graph can be expressed in interval notation as _______. This set represents the function's _______.
The shaded set of numbers shown on the y-axis on the graph can be expressed in interval notation as interval notation as
{y∣-11≤y<∞} or [-11,∞). This set represents the function's range.
How to explain the informationEndpoints that are part of an interval are indicated by square brackets. Endpoints that are not part of an interval are indicated by parentheses. When using or, parentheses are always used.
As a result, the set of shaded numerals displayed on the interval notation can be used to express the y-axis as {y∣-11≤y<∞} or [-11,∞)
This set displays the functional domain.
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Yolanda is building a fence around her garden. For every 2 feet of fencing, the cost is 12.
Complete the table below showing the length of the fence and the cost.
The complete table:
The fence → cost
3 → $18
5 → $30
7 → $42
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Yolanda is building a fence around her garden.
For every 2 feet of fencing, the cost is 12.
The unit rate = 12/ 2 = $6 per feet
The complete table:
The fence → cost
3 → $18
5 → $30
7 → $42
Therefore, the complete table is given above.
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What is the slope-intercept equation of the line that includes (0, 12) and
(4,36)?
The slope-intercept equation of the line that includes the points (0, 12) and (4, 36) is y = 6x + 12.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the linear equation representing the line which passes through the points (0, 12) and (4, 36) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 12 = (36 - 12)/(4 - 0)(x - 0)
y - 12 = 6(x - 0)
y = 6x + 12
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Shipping costs $6 on purchases up to $50, $8 on purchases over $50 and up to $100, and $10 on purchases over $100 and up to $200. Write a function for the cost C (x) of shipping based on the purchase price x.
Answer:
f(x) = {
C(x) = 6, 0 < x ≤ 50
C(x) = 8, 50 < x ≤ 100
C(x) = 10, 100 < x ≤ 200
}
Step-by-step explanation:
If ya know how to do this help college algebra
The equation of the line passing through point (-8, 7) and parallel to a line -9x+8y = -24, is y = 9x/8 + 16
What is slope-intercept form?The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Given that, a line is passing through point (-8, 7) and parallel to a line -9x+8y = -24,
We need to find the equation of the line,
Converting the parallel line equation into slope-intercept form,
-9x + 8y = -24
8y = 9x - 24
y = 9x/8 - 3
Here, slope = 9/8
We know that, two lines which are parallel have equal slopes,
Therefore, the slope for the asked line is 9/8
Now, the equation of line is =
y = 9x/8 + c
To find c, put x = -8 and y = 7 in the equation,
7 = -9 + c
c = 16
Therefore, the equation =
y = 9x/8 + 16
Hence, the equation of the line passing through point (-8, 7) and parallel to a line -9x+8y = -24, is y = 9x/8 + 16
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Ted places $1500 in a ten-year certificate of deposit (CD) account at a local bank. The CD account earns interest, compounded annually, at the same rate for 10 years. Let A(n) represent the amount, in dollars, in Ted's account after n years between n = 0 to n = 10. Part A: Write an explicit expression for the function A(n) if Ted's account has $1535.25 after 1 year. Part B: Explain how you determined your answer.
Part A. An explicit expression for the function A(n), the final amount (future value) after n years is 1,500 x 1.0235^n.
Part B. The function for determining the future value of the CD at 2.35% annual compounded interest rate is derived by comparing the present value and the future value and using the difference to calculate the compound interest rate.
What is the future value?The future value is the present value compounded at an interest rate.
The future value formula or function is as follows:
FV = PV(1+r)^{n}
FV = future value
PV = present value
r = annual interest rate
{n} = number of periods interest held
Initial deposit in a ten-year certificate of deposit (CD) = $1,500
Deposit period = 10 years
Amount after 1 year = $1,535.25
Compound interest rate = 2.35% annually ($1,535.25 - $1,500)/$1,500 x 100)
Function for A(n) = 1,500 x 1.0235^n
Thus, from the future value after 1 year, we can derive the compound interest rate.
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Raina, Kareem, and Eric have a total of $138 in their wallets. Raina has 6 more than Kareem. Eric has 4 times what Kareem has. How much does each have?
Kareem has $22, Raina has $28, Eric has $88.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Raina, Kareem, and Eric have a total of $138 in their wallets.
let Kareem has x dollar.
Then Raina has (x+6) dollar
and, Eric has 4x dollar
So, x+ 4x + x + 6 = 138
6x + 6 = 138
6x = 132
x= 22
Thus, Kareem has $22.
Raina has = 22 +6 = $28
and, Eric has =4x = $88
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I NEED HELP W THIS.............
The equation of the line that is parallel to 2x - y = 7 and passes through the point (10, 0) is y = 2x - 20.
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
To find an Equation that is parallel to 2x - y = 7 and passes through the point (10, 0)
Since, Both equations are parallel thus, the slope of the given equation will be the Same.
equation of the first line in slope intercept form: y = 2x - 7
Thus, Slope = 2
From the general formula of the linear equation in slope-intercept form:
y=mx+b,
where m is the slope
b is the y-intercept
in our case,
Slope = 2
So Line,
y = 2x + b
Since line passes through (10, 0)
b= -20
Thus,
Equation of line y = 2x - 20
Therefore, The equation of the line that is parallel to 2x - y = 7 and passes through the point (10, 0) is y = 2x - 20.
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9(98) using the distributive property
Answer: 882
Hope this helps :)
Step-by-step explanation:
Since there is only one other term in the parenthesis, there will only be one step.
Distribute the 9 to 98.
9 * 98 = 882
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{9(98)}\\\mathsf{= 98(9)}\\\mathsf{= 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98 + 98}\\\mathsf{= 196 + 196 + 196 + 196 + 98}\\\mathsf{= 392 + 392 + 98}\\\mathsf{= 784 + 98}\\\mathsf{= 882}\\\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathsf{882}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What is the area of this polygon?
Enter your answer in the box,
units?
Answer: it's 39.
Step-by-step explanation: for this figure, you want to divide it into two parts: The triangle and the rectangle.
The triangle has a base of 6, and a height of 3.
The formula for area of a triangle is 1/2 bh.
So the area of the triangle is 9!! 6 x 3 is 18.. divided by two is 9.
Then the rectangle, a= b(h)
the height is 6 while the base is 5.
When you multiply thsoe two you get 30.
The cheerleaders are having a fundraiser for new uniforms. They are selling pizzas at the football game on Friday night. The cheerleading coach put an amount of money in the money box before the sale to use for change. During the game, the cheerleaders take turns selling pizzas. When the girls finish their turn selling, they chart the ongoing total pizza sales and money in the box. Some of the data are shown below. PLEASE PLEASE HELP
Answer: pls see the analysis.
Step-by-step explanation:
triangle with base 7.5 m and height 1.6 m The area of this triangle is ? m2.
Answer: [tex]6 \text{ m}^2[/tex]
Step-by-step explanation:
[tex]A=\frac{1}{2}bh=\frac{1}{2}(7.5)(1.6)=6 \text{ m}^2[/tex]
What do you know to be true about the values of p and q?
pº
80⁰
20⁰
45°
55
q
A. p
B. p= q
C. p> q
D. Can't be determined
The value of p and q are set to be equal ( option B)
What is the sum of angle in a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
The sum of angles In a triangle is 180.
Therefore to find p
p+80+20 = 180
p = 180-(100)
p = 80
To find angle q
q+45+55 = 180
q = 180-(45+55)
q = 180-100
q = 80
q = 80= p
therefore the values of p and q are equal
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solve
2x + y = -3
3x - 2y= -22
Answer: x = -4
Step-by-step explanation: Multiply both sides of the top equation by 2 so you can cancel the y's.
4x + 3x = -28.
7x = -28
x = -4
(100 POINTS!) What is the measure of each interior angle of the regular polygon pictured below? If necessary, round to the nearest tenth.
Answer: All angles of the regular polygon in the image are 90 degrees
Step-by-step explanation: Hello!
All interior angles of a four-sided polygon add up to 360 degrees. Since this is a square, all interior angles are congruent. There are four interior angles that are congruent and they all add up to 360 degrees. This can be represented by the equation:
s (side) x 4 = 360
Divide each side by 4 by the division property of equality.
s x 4/4 = 360/4
s = 90 degrees.
Each angle of the polygon is 90 degrees.
"The common property for all [] four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees."
-https://byjus.com/maths/interior-angles-of-a-polygon/#:~:text=The%20common%20property%20for%20all%20the%20above%20four-sided,will%20be%20equal%20to%3A%20360%2F4%20%3D%2090%20degrees.
Answer:
The measure of each interior angle of the regular polygon pictured below is 151.7°. This can be calculated using the formula 180n - 360, where n is the number of sides of the polygon. In this case, n = 8, so the measure of each interior angle is 180(8) - 360 = 151.7°.
Which shows the expression below simplified?
(6 × 10^7) × 0.007
A.
1.3 x 10^-21
B.
4.2 x 10^4
C.
4.2 x 10^-21
D.
4.2 x 10^5
Answer:
The expression (6 × 10^7) × 0.007 simplified is 4.2 x 10^5.
Step-by-step explanation:
Anita purchased a stuffed animal for $10.04. The cashier gave Anita $4.76 in change. How much money did Anita give the cashier?
Answer:
14.8
Step-by-step explanation:
Answer: Anita gave $14.80 to the cashier.
Step-by-step explanation:
Add $10.04 and $4.76 together to find your total.
$10.04 + $4.76 = $14.80
Meaning, Anita gave $14.80 to the cashier.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each quadratic equation with its solution set.
2x²8x+5=0
2x²9x-1=0
2x²
-
2x²9x+6=0
9+√33
4+√6
2
10x3=0
9+√89
2x²8x-3=0
Answer:
[tex]\dfrac{9\pm \sqrt{33}}{4} \longrightarrow \boxed {2x^2\:-\:9x+6=0}}[/tex]
[tex]\dfrac{4\pm \sqrt{6}}{2} \longrightarrow \boxed{2x^2 - 8x +5=0}[/tex]
[tex]\dfrac{9\pm\sqrt{89}}{4} \longrightarrow \boxed{2x^2\:-\:9x-1=0 }[/tex]
[tex]\dfrac{4\pm \sqrt{22}}{2} \longrightarrow \boxed{2x^2\:-\:8x-\:3=0}[/tex]
Step-by-step explanation:
Use a quadratic equation solver calculator
Here are the roots for each equation
Equation Roots
[tex]2x^2 - 8x +5=0\quad\quad\quad \quad \dfrac{4\pm \sqrt{6}}{2}[/tex]
[tex]2x^2\:-\:10x-\:3=0\quad\quad\quad \dfrac{5\pm \sqrt{31}}{2}[/tex]
[tex]2x^2\:-\:8x-\:3=0\quad\quad\quad \dfrac{4\pm \sqrt{22}}{2}[/tex]
[tex]2x^2\:-\:9x-1=0 \quad\quad\quad \dfrac{9\pm\sqrt{89}}{4}[/tex]
[tex]2x^2\:-\:9x+6=0\quad\quad\quad \dfrac{9\pm \sqrt{33}}{4}[/tex]
The quadratic equations are solved and the tiles are matched with the following equations
a) 2x²- 8x + 5 = 0 → x = ( 4 ± √6 ) / 2
b) 2x² - 8x - 3 = 0 → x = ( 4 ± √22 ) / 2
c) 2x² - 9x - 1 = 0 → x = ( 9 ± √89 ) / 4
d) 2x² - 9x + 6 = 0 → x = ( 9 ± √33 ) / 4
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
a)
2x²- 8x + 5 = 0
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
x = ( 4 ± √6 ) / 2
b)
2x² - 8x - 3 = 0
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
x = ( 4 ± √22 ) / 2
c)
2x² - 9x - 1 = 0
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
x = ( 9 ± √89 ) / 4
d)
2x² - 9x + 6 = 0
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
x = ( 9 ± √33 ) / 4
Hence , the quadratic equations are solved
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24,783 is invested, part at 15% and the rest 9%. If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 9% by $894.09, how much is invested at each rate?
If 24,783 is invested, part at 15% and the rest 9%. If the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 9% by $894.09: 51,960 is invested at 15%, and 22,823 is invested at 9%.
How to find the amount invested?Let's x represent the amount invested at 15%
Let the amount invested at 9% = 24,783 - x.
Interest earned at 15% is 0.15 * x
Interest earned at 9% is 0.09 * (24,783 - x)
We can set up the equation: 0.15x = 0.09 * 24,783 - 0.09x + 894.09
Solving for x:
0.06x = 24,783 * 0.09 + 894.09
0.06x = 2223.47 + 894.09
0.06x = 3117.56
x = 51,960
So,
(24,783 - x)
24,783 - 51,960
= 22,823
Therefore 51,960 is invested at 15%, and 22,823 is invested at 9%.
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4
10. Given the function below, what is f(-6)-f(9)?
2x
15
x odd
[|x, xeven
f(x)=3
MATH - 1
PART 1
The domain of the composite function f(-6) - f(9) for the function f(x) = 2x + 15 is equal to -30.
What is composite function?A function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domain of the function f(-6) - f(9) as follows:
f(-6) = 2(-6) + 15 {put -6 for x }
f(-6) = -12 + 15
f(-6) = 3
f(9) = 2(9) + 15 {put 9 for x }
f(9) = 18 + 15
f(9) = 33
f(-6) - f(9) = 3 - 33
f(-6) - f(9) = -30
Therefore, the domain of the composite function f(-6) - f(9) for the function f(x) = 2x + 15 is equal to -30.
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Possible question:
Given the function f(x) = 2x + 15. What is f(-6) - f(9)?
Which shows a proportional relationship represented by the equation y = 1/2x
The relationship is proportional, when, there is no added constant, which shows a proportional relationship represented by the equation y = 1/2x.
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol "::" or "=".
here, we have,
y = 1/2x
If the relationship is proportional, there is no added constant. The relation that is proportional is ...
y = 1/2x
Hence, The relationship is proportional, when, there is no added constant.
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What is the constant proportional of 1.5 and 3.9
The constant of proportionality is the ratio between two quantities that are in proportion. If two quantities are proportional, their ratio is always the same, and this constant ratio is called the constant of proportionality.
Given the two quantities 1.5 and 3.9, the constant of proportionality can be found by dividing one by the other:
k = 3.9 / 1.5
k = 2.6
So the constant of proportionality between 1.5 and 3.9 is 2.6.
O) The ratio of students wearing sneakers to students wearing something else is 8:2. If there
are 18 more kids wearing sneakers, how many are wearing sneakers?
****
How do I solve this? My 11y/o doesn’t have a text book for me to explain it to me
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
What is the 12 to 8 ratio?Convert the ratio to a fraction, multiply it by a common factor, and divide it again to obtain the corresponding ratio of 6:4. Therefore, 12/8 is the same as 6:4.
What is the ratio and proportion formula?Any two quantities can be compared using the ratio formula a: b a/b. The ratio, on the other hand, proportion formula is expressed as a:b::c:d⟶ab=cd a : b :: c : d ⟶ a b = c d
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factor the trinimial x2-2x-35
The factored form of the trinomial x² - 2x - 35 is ( x - 7 )( x + 5 ).
How to determine the factor of a trinomial?Given the trinomial in the question;
x² - 2x - 35
To simplified in a factored form,
Consider the trinomial in its standard form; ax² + bx + c.
Now, find a pair of integers whose product is c and whose sum is b.
In this case, we use -7 and 5
The product of -7 and 5 = -35
The sum of -7 and 5 = -2
Next, we write the factored form using the integers -7 and 5
( x - 7 )( x + 5 )
Therefore, the factored form is ( x - 7 )( x + 5 ).
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How do you write 9.2 in words? IXL
please help fast here is screesnshot
The standard form of the given quadratic equation is;
x² - x - 6
What is the standard form of the quadratic equation?The standard form of a quadratic equation can be written in the form;
ax² + bx + c =0 (In terms of variable x), where a ≠ 0.
The equation is expressed in the question as;
(x + 2)(x - 3)
To convert to standard form, we will just multiply out the bracket to get;
x² + 2x - 3x - 6
= x² - x - 6
Thus, that final expression is the standard form of the given quadratic expression
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Simplify the expression:
2.5(6.1 - 2.3h)
Answer:
15.25 - 5.75 h
this my be it but i'm not shore
1 6/11 ft of fabric is needed to make a rug? while 4 1/2 ft of fabric is required to make pillows/ Producing a rug is 2 2/7 times faster than pilliws/ How much more fabric is needed to make pillows versus a rug
3.1 ft more fabric should be produced to make pillows versus a rug.
What is a fraction?A fraction is a number expressed in the form of {x/y}, where y ≠ 0.
Given is that 1[tex]\frac{6}{11}[/tex] ft of fabric is needed to make a rug while 4[tex]\frac{1}{2}[/tex] ft of fabric is required to make pillows. Producing a rug is 2[tex]\frac{2}{7}[/tex] times faster than pillows.
We can write -
1[tex]\frac{6}{11}[/tex] x 4[tex]\frac{1}{2}[/tex] = 2[tex]\frac{2}{7}[/tex] x {y}
{17/11 x 9/2} = {16/7 y}
{y} = {6.96 x 7}/16
{y} = 3.1
Therefore, 3.1 ft more fabric should be produced to make pillows versus a rug.
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solve the following for x
Answer:
x = 27
Step-by-step explanation:
[tex]\displaystyle 4x^{\frac{2}{3}}-5=31\\4x^\frac{2}{3}=36\\x^{\frac{2}{3}}=9\\x=9^\frac{3}{2}\\x=27[/tex]