Find the slope of the tangent line to the given polar curve at the point specified by the value of theta.
r = 6 cos(theta),
theta = ????/3
*its not negative square root of 3

It is proved that the function h(x)=(1-x^2) ^1/3 is its own inverse by showing that h(h(x)) =x.

The inverse of a function f is denoted by f-1 and it exists only when f is both one-one and onto function. Note that f-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x.

(f o f-1) (x) = (f-1 o f) (x) = x

For a function 'f' to be considered an inverse function, each element in the range y ∈ Y has been mapped from some element x ∈ X in the domain set, and such a relation is called a one-one relation or an injunction relation. Also the inverse f-1 of the given function has a domain y ∈ Y is related to a distinct element x ∈ X in the codomain set, and this kind of relationship with reference to the given function 'f' is an onto function or a surjection function. Thus the inverse function being an injunctive and a surjection function, is called a bijective function.

The given function is h(x) = (1-x²)^1/3

We have to find h(h(x)).

Put h(x) in place of x in above function:

h(h(x)) = (1-((1-x²)^1/3)²)^1/3

After solving the above equation, we get

h(h(x)) = x

Thus, it is proved that the function h(x)=(1-x^2) ^1/3 is its own inverse by showing that h(h(x)) =x.

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Percent error in the measurement is 8.3 % ( round to one decimal )

Percent of error show how big the error between measurement and actual value in comparison of actual value, and shown in percentage.

Simple formula to find percent of error is :

% error  = | (T - E) / T | x 100%

Where :

T is actual value

E is estimated / measured value

From the question, we know following information :

1. Measured Value = 13 inches

   --> E = 13 inches

2. Actual value = 1 foot. We know that 1 foot equal to 12 inches

   --> T = 12 inches

% error = | (T - E) / T | x 100%

            = | (12-13)/12 | x 100%

            = | -1/12 | x 100%

            = | -0.083 | x 100%

            = 0.083 x 100%

            = 8.3 %

Hence percent error of the measurement is 8.3%

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Answer: 9.2%

Step-by-step explanation: did the test and got it correct, hope this helps

Answer:

[tex]\text{In terms of Gazebos, the perimeter of Gazebo A = \textbf{46 m}}[/tex]

Step-by-step explanation:

Since the two pentagons are similar the ratio of each side of the smaller pentagon to the corresponding side of the larger pentagon is the same

We are given that in pentagon ABCDE, side AB = 10 and the corresponding side FG of pentagon FGHJK = 15

[tex]\text{Therefore } \\\\\dfrac{\overline {AB}}{\overline{FG}} =\dfrac{10}{15} = \dfrac{2}{3}$ \textrm(divide numerator and denominator by 5)}\\[/tex]

The ratios of all the other sides of ABCDE to the corresponding sides of FGHJK must also be [tex]\displaystyle {\dfrac{2}{3}}[/tex]

Therefore it follows that the perimeter of ABCDE = 2/3 x perimeter of FGHJK

Perimeter of FGHJK = sum of sides  [tex]= 15 + 9 + 12 + 15 + 18 = 69 \;m[/tex]

[tex]\textrm{Perimeter of ABCDE } = \dfrac{2}{3} \cdot 69 = 2 \cdot 23 = 46\text{ m}\\\\[/tex]

[tex]\text{In terms of Gazebos, the perimeter of Gazebo A = \textbf{46 m}}[/tex]

The width of the farm in the drawing is 2 centimeters.

The formula used to calculate the width of the farm in the drawing is: the actual width of the goat pen divided by the scale of the drawing. In this case, 8 meters divided by 4 meters (1 centimeter = 4 meters) is equal to 2 centimeters. So, the width of the farm in the drawing is 2 centimeters.

To calculate the width of the farm in the drawing, we must first understand the scale of the drawing. The scale of the drawing is 1 centimeter = 4 meters. This means that for every 1 centimeter in the drawing, it represents 4 meters in the actual farm.

Next, we must determine the actual width of the goat pen. In this case, it is 8 meters.

Finally, we can calculate the width of the farm in the drawing by dividing the actual width of the goat pen (8 meters) by the scale of the drawing (1 centimeter = 4 meters). 8 meters divided by 4 meters is equal to 2 centimeters. So, the width of the farm in the drawing is 2 centimeters.

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6.56168 feet  and inches is around two metres.

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Stephen Curry is 75 inches tall.

Let's call Stephen Curry's height h.

Since the shadow length of Shaq is proportional to his height,

we can write the following ratio:

shadow length of Shaq / Shaq's height = shadow length of Curry / Curry's height

This gives

17'' / 85'' = 15'' / h

Solving for h:

h = 15'' * 85'' / 17'' = 75''

So Stephen Curry is approximately 75 inches tall.

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The system of equations have one solution.

Two or more expressions with an Equal sign is called as Equation.

The system of equations

10x - 8y = -1...(1)

3x + 5y = -17..(2)

Multiply equation 1 with 3 and equation 2 with 10

30x-24y=-3..(3)

30x+50y=-170...(4)

Subtract equation 4 from equation 3

30x-24y-30x-50y=-3+170

-74y=167

Divide both sides by 74

y=2.25

Now plug in y value in equation 1

10x-8(2.25)=-1

10x-18=-1

10x=17

Divide both sides by 10

x=17/10

Hence, the system of equations have one solution.

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The scale of figure A to Figure B is given by 9 : 5 and option C is the correct answer.

Shapes in various dimensions can be scaled using the Scale Factor. In geometry, we study many geometrical forms that exist in both two- and three-dimensions. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.

The scaling factor indicates how much a figure has increased or decreased from its initial value.

The scale of figure A to Figure B is given by:

Scale factor = Segment of figure A / segment of figure B

SF = 36 / 20

SF = 9 / 5

Hence, the scale of figure A to Figure B is given by 9 : 5 and option C is the correct answer.

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Linear combination of u and v is c1u + c2v where c1,c2 are scalars, eg. (1, -12), (2.5, -7), (6.5, -4.5).

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

A linear combination of vectors u and v is a vector of the form c1u + c2v, where c1 and c2 are scalars. There are infinitely many possible linear combinations of u and v, here are three examples:

c1u + c2v = (1) (3, -2) + (2) (-1, -5) = (3 + -2, -2 - 10) = (1, -12)

c1u + c2v = (0.5) (3, -2) + (-1) (-1, -5) = (1.5 + 1, -2 - 5) = (2.5, -7)

c1u + c2v = (2) (3, -2) + (-0.5) (-1, -5) = (6 + 0.5, -2 - 2.5) = (6.5, -4.5)

that these are just three examples, there are many more possible linear combinations of u and v.

Linear combination of u and v is c1u + c2v where c1,c2 are scalars, eg. (1, -12), (2.5, -7), (6.5, -4.5).

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When a plane is inclined at a 45-degree angle and intersects a cylinder's base along its diameter with radius "r," it results in the division of the cylinder into two identical right circular cones.

Imagine a cylinder with a radius "r."

The plane passes through the cylinder's base, creating a line that bisects the circular base into two equal halves.

This intersection between the inclined plane and the cylinder forms a cross-section that resembles an isosceles right triangle.

By symmetrically splitting the cylinder along its central axis, the inclined plane generates two congruent right circular cones, each with a 45-degree angle at its apex. The curved line formed by the intersection represents the boundary between the two cone halves.

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The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

Substituting the parameters, we have the following:

y - y₁ = m(x - x₁)

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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The distance from a to the line passing through b and c is 7/5.

To find the distance from a point to a line, you can use the cross product and the dot product.

First, find the vector pointing from a to b and the vector pointing from b to c:

u = b - a = (3, -5, 0) - (0, 3, -5) = (3, -8, 5)

v = c - b = (3, 0, -5) - (3, -5, 0) = (0, 5, -5)

Next, find the cross product of these two vectors, which gives a vector orthogonal to the plane defined by the line:

n = u x v = (-40, 0, 40)

Finally, find the dot product of n and a - b, which gives the magnitude of the projection of a - b onto n:

d = |n . (a - b)| / |n| = |(-40, 0, 40) . (-3, -8, -5)| / |(-40, 0, 40)| = 57 / √(40^2 + 40^2) = 57 / √1600 = 57 / 40 = 7/5

Therefore, the distance from a to the line passing through b and c is 7/5.

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Step-by-step explanation:

up/down shifts are easy. they just indicate a constant change to the calculated y-values (result values) of f(x).

a shift up is therefore just adding a constant to f(x).

a shift down is just subtracting a constant from f(x).

in our case that would be f(x) + 3 = x³ + 3.

left/right shifts are more difficult to understand.

a shift to the left means that the same y-/result values happen as for f(x) also for g(x), just a bit "earlier" (to the left) on the x-axis.

a shift to the right means via the same principle the y-values for f(x) happen unchanged but "later" (to the right on the x-axis) for g(x).

so, 5 units to the left means that g(x) has the same y-value as f(x+5). f(x+5) happens 5 units earlier (at x).

and so, the full g(x) is

g(x) = f(x+5) + 3 = (x+5)³ + 3 =

= (x² + 10x + 25)(x + 5) + 3 =

= x³ + 5x² + 10x² + 50x + 25x + 125 + 3 =

= x³ + 15x² + 75x + 128

Answer: 2A/H

Step-by-step explanation:

A = région

H = la taille

x = base

1/2*x*H = A

1/2*x = A/H

x = 2A/H

None of the statements is true, as they all refer average to the false statement that exactly one, two, three, or four of the statements is false. This statement itself is false, and so none of the other statements can be true.

None of the statements is true because they all refer to the false statement that exactly one, two, three, or four of the statements is false. This statement itself is false, and so none of the other statements can be true. The statement that exactly one of the statements is false is false because it is referring to itself as the false statement, which means that it is not actually false. Similarly, the statement that exactly two of the statements are false is false because it is referring to itself as one of the two false statements, which means that it is not actually false. The statement that exactly three of the statements are false is also false because it is referring to itself as one of the three false statements, and the statement that exactly four of the statements are false is false because it is referring to itself as one of the four false statements. Therefore, none of the statements is true.

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Answer:

12: A = 40 and C = 32

13: A = 45 , C=72 and D=72

Step-by-step explanation:

Angles inscribed by the same arc are equal.

Answer:

21 Bikini Styles

Step-by-step explanation:

Hello!

If at Krysta's Swimwear 25% of the 84 swimsuit styles are bikinis there are 21 bikini styles.

Step-by-step explanation:

[tex]84[/tex] × [tex]0.25=21[/tex]

Hope this helps!

(2t)^-6 = 1/(2t)^6 is expression of only positive exponents.

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

the given expression is, (2t)^-6.

Now,

To simplify this using only positive exponents we are going to use the rule for negative exponents: b^(-n) = 1/b^n .

Notice that in this case :

b= 2t

so, we get,

(2t)^-6 = 1/(2t)^6

Hence, (2t)^-6 = 1/(2t)^6 is expression of only positive exponents.

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The parametrize line will be r(t)=(1,2,1)+t(1,2,2).

How to parametrize a line?

In order to parametrize a line, you need to know at least one point on the line, and the direction of the line. If you know two points on the line, you can find its direction. The parametrization of a line is r(t) = u + tv, where u is a point on the line and v is a vector parallel to the line. There are lots of possible such vectors u and v. To find one such vector v, find the difference between any two points on the line.

Example: If we want to parametrize the straight line passing through (1,1,1) and (4,6,2), we can take u = (1,1,1) and v = (4,6,2) - (1,1,1) = (3,5,1). So one possible parametrization for this line is r(t) = (1,1,1) + t(3,5,1). We can also write this as:

x(t) = 1 + 3t

y(t) = 1 + 5t

z(t) = 1 + t

Now,

For points (1, 2, 1) and (2, 4, 3)

u=(1,2,1)

v=(2,4,3)-(1, 2, 1)

v=(1,2,2)

so the parametrized line will be r(t)=(1,2,1)+t(1,2,2).

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Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.

For continuously compounded interest: FV = PV x e (i x t), where e is the mathematical constant approximated as 2.7183.

What is meant by process?

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18 pounds of candy costing $1.05 and 12 pounds of candy costing $1.35 are needed to be mixed to get a 30 pounds of mixture costing $1.17

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the amount of candy costing $1.05, y represent the candy costing $1.35.

The mixture is worth $1.17 a pound and is about 30 pounds. Hence:

1.05x + 1.35x = 1.17(30)    (1)

Also:

x + y = 30    (2)

From both equations:

x = 18, y = 12

18 pounds and 12 pounds of candy are needed to be mixed

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Answer:

PQ=17.088

Step-by-step explanation:

If M is the midpoint of PQ, then PM is half the length of PQ. So we cna find our answer by first finding PM.

Imagine a right angle triangle with PM as its hypotenuse. Since P(x,y)=(5,-15), and M(x,y)=(13,-18), we know that the length of the vertical side of this triangle is the difference between P and M's y (vertical) coordinates, and the length of the horizontal side of this triangle is the difference between P and M's x (horizontal) coordinates. This means the vertical side is equal to -15-(-18)=3 and the horizontal side is equal to 13-5=8. Since we know the lengths of the other two sides and PM is the hypotenuse, we can use pythagorus to find the length of PM:

PM = [tex]\sqrt{3^{2} +8^{2} } =\sqrt{9 +64 }=\sqrt{73} =[/tex]8.544

Since PM is half PQ, PQ=2(8.544)=17.088

The length of the rectangular garden will be 13 feet.

Let x be the length of the rectangular garden.

If the length of the garden is to be 5 feet longer than the width, then the expression for the width should be "x - 5".

If the area of the garden will be 104 square feet, then the equation for the area will be:

A = x(x - 5) = 104 square feet

Simplify the equation and solve for the value of x.

x² - 5x - 104 = 0

(x + 8)(x - 13) = 0

x = -8 ; x = 13

(choose the positive value since dimensions should always be positive)

Therefore, the length of the rectangular garden is 13 feet.

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Answer:

i agree good job mate I'm not zooded while doing homework

Step-by-step explanation:

I didn't clear a then another then two more

Triangle congruence: Two triangles are deemed to be congruent if all three of their matching sides and angles have the same magnitude.

Slides, rotations, flips, and turns can be used to make these triangles appear identical.

One of the following conditions must be satisfied for two triangles to be considered congruent:The three equivalent side pairings are equal in all three cases. According to the question, there are four congruent triangles, and each of these triangles has equal-sized and length sides.

ASA, AAS, and HL make up the four triangles.

Divided by BD, ABCD.

BDA = BCD in the given context.

ST is parallel to UN and congruent to VU in the second.

That too is admitted

The FH divides the EHG in the third statement.

FRH and FGH are equivalent.

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Answer:

Below

Step-by-step explanation:

Slope-intercept form of a line  is   y = mx + b     m is slope    b is intercept

so it is just   y = -3/4 x -4

The value of N equals to -9.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

n+9/9=0

Now,

n+9/9=0

n+9=0

n=-9

Therefore, the answer of this algebra will be -9.

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Answer:

B) 4 - 3r

Step-by-step explanation:

B.  4 - 3r is the mathematical expression.

The sum of x + y is always equal to 14.

What is positive integers?

Positive integers are the numbers that we use to count: 1, 2, 3, 4, and so on. A collection of positive integers excludes numbers with a fractional element that is not equal to zero and negative numbers.

Since x and y are positive integers, we can find the possible values of x and y by finding the factors of 13. The positive integer factors of 13 are 1 and 13. Therefore, the possible pairs of x and y are (1, 13) and (13, 1).

The sum of the two values for x and y in each pair is 14.

So, The sum of x + y is always equal to 14.

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Sharon completed a walkathon by walking a total of 9. 52 miles. Sharon would need 3.4 hours to complete the walk if she urinated on average 2. 8 times each hour.

Detailed explanation:

The distance that Shareen must travel is 9.52 miles.

Shareen travels at a mean speed of 2.8 mph.

We need to determine how long it took Shareen to finish the walk.

the average speed formula,

v = length/duration

[tex]$t & =\frac{d}{v} \\[/tex]

[tex]$t & =\frac{9.52}{2.8} \\[/tex]

[tex]$t & =3.4 \text { hour }[/tex]

As a result, the walk will take 3.4 hours to complete.

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