Coplanar circles that have the same center, but not necessarily the congruent radii are called?

The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

For given question,

We have been given a function f(x) = 6 + 9x² - 6x³

We need to find the local maximum and local minimum of the function  f(x)

First we find the first derivative of the function.

⇒ f'(x) = 0 + 18x - 18x²

⇒ f'(x) = - 18x² + 18x

Putting the first derivative of the function equal to zero, we get

⇒ f'(x) = 0

⇒ - 18x² + 18x = 0

⇒ 18(-x² + x) = 0

⇒ x (-x + 1) = 0

⇒ x = 0    or    -x + 1 = 0

⇒ x = 0     or    x = 1

Now we find the second derivative of the function.

⇒ f"(x) = - 36x + 18

At x = 0 the value of second derivative of function f(x),

⇒ f"(0) = - 36(0) + 18

⇒ f"(0) = 0 + 18

⇒ f"(0) = 18

Here, at x=0, f"(x) > 0

This means, the function f(x) has the local minimum value at x = 0,  which is given by

⇒ f(0) = 6 + 9(0)² - 6(0)³

⇒ f(0) = 6 + 0 - 0

⇒ f(0) = 6

At x = 1 the value of second derivative of function f(x),

⇒ f"(1) = - 36(1) + 18

⇒ f"(1) = - 18

Here, at x = 1, f"(x) < 0

This means, the function f(x) has the local maximum value at x = 1,  which is given by

⇒ f(1) = 6 + 9(1)² - 6(1)³

⇒ f(1) = 6 + 9 - 6

⇒ f(1) = 9

So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.

Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

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Answer:

11÷7=[tex]\frac{11}{7}[/tex]

v= 11/7

Based on the calculations, the coordinates of the mid-point of BC are (1, 4).

First of all, we would determine the initial y-coordinate by substituting the value of x into the equation of line that is given:

At the origin x₁ = 0, we have:

y = 2x + 1

y₁ = 2(0) + 1

y₁ = 2 + 1

y₁ = 3.

When x₂ = 2, we have:

y = 2x + 1

y₂ = 2(2) + 1

y₂ = 4 + 1

y₂ = 5.

In order to determine the midpoint of a line segment with two (2) coordinates or endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate is given by:

Midpoint = (x₁ + x₂)/2

Midpoint = (0 + 2)/2

Midpoint = 2/2

Midpoint = 1.

Midpoint on y-coordinate is given by:

Midpoint = (y₁ + y₂)/2

Midpoint = (3 + 5)/2

Midpoint = 8/2

Midpoint = 4.

Therefore, the coordinates of the mid-point of BC are (1, 4).

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Answer:

4. 4.125 inches by 3.5 inches.

5. 8.4 hours.

Step-by-step explanation:

4. multiply 16.5 and 14 by .25 because each foot in the house is .25 of an inch on the paper.

5. 252 miles / 9 hours = 28 mph. Add 2 so you get 30 mph. 252 miles / 30 mph = 8.4 hours.

Answer: 46.7 in/3

Step-by-step explanation:

Answer:

[tex]\textsf{a)} \quad v=12t^2-6t-18[/tex]

[tex]\textsf{b)} \quad a=24t-6[/tex]

c)   1.5 s

d)  -19.25 m

e)   24.5 m

Step-by-step explanation:

Displacement

[tex]x=4t^3-3t^2-18t+1[/tex]

(where t ≥ 0 and x is in meters)

To find the equation for velocity, differentiate the equation for displacement:

[tex]\implies v=\dfrac{\text{d}x}{\text{d}t}=12t^2-6t-18[/tex]

(where t ≥ 0 and v is in meters per second)

To find the equation for acceleration, differentiate the equation for velocity:

[tex]\implies a=\dfrac{\text{d}v}{\text{d}t}=24t-6[/tex]

(where t ≥ 0 and a is in meters per second squared)

The particle comes to rest when its velocity is zero:

[tex]\begin{aligned}v & = 0\\\implies 12t^2-6t-18 & = 0\\6(2t^2-t-3) & = 0\\2t^2-t-3 & = 0\\2t^2-3t+2t-3 & = 0\\t(2t-3)+1(2t-3) & = 0\\(t+1)(2t-3) & = 0\\\implies t & =-1, \dfrac{3}{2}\end{aligned}[/tex]

As t ≥ 0, the particle comes to rest at 1.5 s.

Substitute the found value of t from part (c) into the equation for displacement to find where the particle comes to rest:

[tex]\implies 4(1.5)^3-3(1.5)^2-18(1.5)+1=-19.25\: \sf m[/tex]

We have determined that the particle is at rest at 1.5 s.

Therefore, to find how far the particle traveled in the first 2 seconds, we need to divide the journey into two parts: before and after it was at rest.  

The first leg of the journey is the first 1.5 s and the second leg of the journey is the next 0.5 s.

At the beginning of the journey, t = 0 s.

[tex]\textsf{when }t=0: \quad x=4(0)^3-3(0)^2-18(0)+1=1[/tex]

Therefore, when t = 0, x = 1

When t = 1.5 s, x = -19.25 m (from part (d)).

⇒ Total distance traveled in first 1.5 s = 1 + 19.25 = 20.25 m

When t = 2, x = -15 m.

Therefore, the particle has traveled 19.25 - 15 = 4.25 m in the last 0.5 s of its journey.

Total distance traveled:

1 + 19.25 + 4.25 = 24.5 m

Refer to the attached diagram

When the particle is at rest, it changes direction.  If we model its journey using the x-axis, for the first leg of its journey (0 - 1.5 s) it travels in the negative direction (to the left). At 1.5 s it stops, then changes direction and travels in the positive direction (to the right), arriving at -15 at 2 seconds.

The solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .

According to the given question.

We have a differential equation

[tex]y^{"} + 4y^{'} + 4y = 2x^{3}[/tex]

The above differerntial equation acn be written as

[tex](D^{2} +4D+ 4)= 2x^{3}[/tex]

Now, the auxillary equation for the above differential equation is given by

[tex]m^{2} + 4m + 4 = 0[/tex]

[tex]\implies m^{2} + 2m + 2m + 4 = 0[/tex]

⇒ m (m + 2) + 2(m + 2) = 0

⇒ m(m + 2)(m + 2) = 0

Therefore,

[tex]C.F = (C_{1} + C_{2}x)e^{-2x}[/tex]

Now,

[tex]PI = \frac{1}{D^{2} +4D+4} 2x^{3}[/tex]

[tex]\implies PI = \frac{1}{4(1+\frac{D^{2}+4D }{4} )} 2x^{3}[/tex]

[tex]\implies PI = \frac{1}{4} [1+(\frac{D^{2}+4D }{4} )]^{-1} 2x^{3}[/tex]

[tex]\implies PI = \frac{1}{4} [ 1 - (\frac{D^{2} +4D}{4} )+(\frac{D^{2} +4D}{4} )^{2} -(\frac{D^{2}+4D }{4}) ^{3} ...]2x^{3}[/tex]

[tex]\implies PI =\frac{1}{2} [ x^{3} -\frac{1}{4} (6x)-3x^{2} +3x^{2} -6][/tex]

[tex]\implies PI = \frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]

Therefore, the solution of the differential equation will be

y = CI + PI

[tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex]

Hence, the solution of the differential equation is [tex]y = (C_{1} + C_{2} x)e^{-2x} +\frac{1}{2} [x^{3} -\frac{3}{2} x-6][/tex] .

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the value of b is = 10.

The equation of a hyperbola is x^2/24^2 - y^2/ (10)^2= 1.

The geometric characteristics of a hyperbola or the equations for which it is the solution set characterize it as a particular kind of smooth curve that lies in a plane. Mirror reflections of each other that resemble two infinite bows make up a hyperbola's two connected components or branches.

The general formula for hyperbola = (x - h)²/a²- (y - k)²/(b)² = 1

x²/24 - y²/(b)² = 1

(x - 0)²/24 - (y -0)²/(b)² = 1

a=24,h=0 and k=0

Now equation of the directrix

x=a²/c...(1)

and we know x=576/26...(2)

Therefore from 1 and 2 we get

24²/c=576/26.

isolate the c so we get,

C=26

C= center of focii

c = √(a² + b³)

c² = a² + b²

b = c² - a²

b = 10

So we get the value of b is 10.

Therefore the equation of a hyperbola is x²/24² - y²/ (10)² =  1.

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Answer: x is -1/2,0 and y is 0,2

Step-by-step explanation:

Answer:

(4,0) , (0,2)

Step-by-step explanation:

Similar to the previous question.

x-intercept is where the line touches the x-axis , and y = 0.

when y = 0,

8x + 16(0) = 32

8x = 32

x = [tex]\frac{32}{8}[/tex]

x = 4

Therefore the coordinates of the x-intercept is (4,0)

y-intercept is where the line touches the y-axis, and x = 0.

when x = 0,

8(0) + 16y = 32

16y = 32

y = [tex]\frac{32}{16}[/tex]

y = 2

Therefore the coordinates of the y-intercept is (0,2)

Answer:

50.24 ft^2.

Step-by-step explanation:

Area = pi r^2

Here the radius r = 4

Therefore the area of the circle

= pi * 4^2

= 16 pi

= 16 *3.14

= 50.24 ft^2.

The steps to solve a quadratic formula include:

In algebra, a quadratic equation is a equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

A quadratic equation is an equation that could be written as ax² + bx + c = 0

when a 0. The factoring method is illustrated:

To solve a quadratic equation by factoring, put all terms on one side of the equal sign, leaving zero on the other side.

Set each factor equal to zero.

Solve each of these equations.

Check by inserting your answer in the original equation.

Example 1

Solve x² – 6 x = 16.

Following the steps,

x² – 6 x = 16 becomes x² – 8x + 2x – 16 = 0

Factor.

( x – 8)( x + 2) = 0

Therefore, x = 8 and -2.

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A graph which shows the image of ABCD is: A. on a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1).

A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on transformation of parallelogram ABCD, we can infer and logically deduce that a graph which shows the image of ABCD is that on a coordinate plane, with parallelogram A'B'C'D' having points (-2, 5), (0, 3), (0, -1.2), (-2, 1) as shown in the image attached below.

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Answer:

a

Step-by-step explanation:

given y varies directly as x² and inversely as z³ then the equation relating them is

y = [tex]\frac{kx^2}{z^3}[/tex] ← k is the constant of variation

to find k use the condition y = 12 when x = 4 and z = 2 , then

12 = [tex]\frac{k(4)^2}{2^3}[/tex] = [tex]\frac{16k}{8}[/tex] ( multiply both sides by 8 )

96 = 16k ( divide both sides by 16 )

6 = k

y = [tex]\frac{6x^2}{z^3}[/tex] ← equation of variation

when y = 1.728 and z = 5 , then

1.728 = [tex]\frac{6x^2}{5^3}[/tex] = [tex]\frac{6x^2}{125}[/tex] ( multiply both sides by 125 )

216 = 6x² ( divide both sides by 6 )

36 = x² ( take square root of both sides )

[tex]\sqrt{36}[/tex] = x , that is

x = 6

Comparing it to a system of equations, the expression is represented as follows:

18g + 5.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, we consider g as the variable. Then:

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Answer:

x = 36

Step-by-step explanation:

3x and 2x are a linear pair and sum to 180° , that is

3x + 2x = 180

5x = 180 ( divide both sides by 5 )

x = 36

Between 2 seconds and 2.5 seconds, the rock hits the ground after it is dropped.

What are distance and time?

As you can see at 2s the height of the rock is 0.4m and at 2.5s it is -10.6m, which tells us that in between these values the height would have been 0m, as the movement of the rock is uniform in direction and hence, the rock will hit the ground between 2s and 2.5s.

The rock hits the ground between 2 seconds and 2.5 seconds after it is dropped.

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Using the binomial distribution, there is a 0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are:

p = 0.5, n = 13

The probability that at most eleven of the thirteen babies are girls is:

[tex]P(X \leq 11) = 1 - P(X > 11)[/tex]

In which

P(X > 11) = P(X = 12) + P(X = 13)

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 12) = C_{13,12}.(0.5)^{12}.(0.5)^{1} = 0.0016[/tex]

[tex]P(X = 13) = C_{13,13}.(0.5)^{13}.(0.5)^{0} = 0.0001[/tex]

So:

P(X > 11) = P(X = 12) + P(X = 13) = 0.0016 + 0.0001 = 0.0017

[tex]P(X \leq 11) = 1 - P(X > 11) = 1 - 0.0017 = 0.9983[/tex]

0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.

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Answer:

x = 4, y = 1

Step-by-step explanation:

y = (1/4)x  

2x + 4y = 12

replace y with something x

2x + 4(1/4)x = 12

3x = 12

x = 4

so y = 1

The domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

So long as x ≥ -9/4, the function f(x) will be defined.

Given: "f(x) = Startroot 4 x + 9 Endroot + 2" should be written as

[tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

Note that [tex]$\sqrt{(4x + 9)}[/tex] exists a variation of the basic function [tex]y = \sqrt{x}[/tex], whose domain exists [0, ∞ ).

The domain of [tex]$f(x) = \sqrt{(4x + 9) }+ 2[/tex] exists seen by taking the "argument" 4x + 9 of [tex]\sqrt{(4x + 9)}[/tex]and setting it equivalent to zero:

4x + 9 ≥ 0

simplifying the equation, we get

4x ≥ -9

x ≥ -9/4

This exists the domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

So long as x ≥ -9/4, the function f(x) will be defined.

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Answer:

B

Step-by-step explanation:

I tink old up

no its BBBBB

Answer:

Step-by-step explanation:

Use periodic compound formula:

[tex]F=P\cfrac{(1+r/n)^{nt}-1}{r/n}[/tex]

Substitute the values and calculate:

[tex]F=200\cfrac{(1+0.032/12)^{12*2}-1}{0.032/12} =4950.12[/tex]     rounded

Step-by-step explanation:

Use periodic compound formula:

[tex] \sf \: F=P\cfrac{(1+ \frac{r}{n})^{nt}-1}{\frac{r}{n}}[/tex]

Substitute the values and calculate:

[tex]\sf \: F=200\cfrac{(1+ \frac{0.032}{12})^{12 \times 2}-1}{\frac{0.032}{12}}[/tex]

[tex]\sf \: F=200\cfrac{( \frac{ 12 + 0.032}{12})^{24}-1}{\frac{0.032}{12}}[/tex]

[tex]\sf \: F=200\cfrac{( {11.002 }{})^{24}-1}{0.002} [/tex]

[tex]\sf \: F=200 \times 24.7506[/tex]

[tex]\sf \: F=4950.12rounded[/tex]

Answer:

2nd option, x > 1.10

Step-by-step explanation:

[tex]7e^{2x}-5 > 58[/tex]

Add 5 to both sides,

[tex]7e^{2x}-5+5 > 58 +5\\7e^{2x} > 63[/tex]

Divided both sides by 7,

[tex]\frac{7e^{2x}}{7} > \frac{63}{7}[/tex]

[tex]e^{2x} > 9[/tex]

Apply Exponent Rule,

[tex]2x > 2ln(3)[/tex]

[tex]\frac{2x}{2} > \frac{2ln(3)}{2}[/tex]

x > ln(3) or x > 1.09861

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Answer:

c^2 = a^2 + b^226^2 = 10^2 + b^2 676 = 100 + b^2 576 = b^2 shortest side length = 24 units

Step-by-step explanation:

Answer:

30°

30 is the value of x that’s makes AB//CD.

Step-by-step explanation:

the angles of measures 2x + 40 and 3x + 10 are two Alternate interior angles

If these two angle were congruent then the lines AB and CD

would be parallel .

2x + 40 = 3x + 10

⇔ 40 - 10 = 3x - 2x

⇔ 30 = x

⇔ x = 30

Answer:

a) x = 3

b) x = 10

c) x = 28

Explanation:

a)

[tex]\sf 6x + 3 = 21[/tex]

collect term

[tex]\sf 6x = 21-3[/tex]

simplify

[tex]\sf 6x = 18[/tex]

divide both both sides by 6

[tex]\sf x = 3[/tex]

b)

[tex]\sf 15(x - 5) = 75[/tex]

distribute

[tex]\sf 15x - 75 = 75[/tex]

collect terms

[tex]\sf 15x = 75 + 75[/tex]

combine

[tex]\sf 15x = 150[/tex]

divide both sides by 15

[tex]\sf x = 10[/tex]

c)

[tex]\sf \frac{3}{4} x +5 = 26[/tex]

collect like terms

[tex]\sf \frac{3}{4} x = 26-5[/tex]

combine

[tex]\sf \frac{3}{4} x = 21[/tex]

cross multiply

[tex]\sf x = \frac{ 21 (4)}{3}[/tex]

simplify

[tex]\sf x =28[/tex]

75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

So normally the least positive integer of all the numbers is the number 1 but when you talk about least positive integer, often times you are talking about the special function called the ceiling function

The smallest of the numbers in the set {1, 2, 3, …} is 1.

So, the number 1 is the smallest positive integer.

7300

If we Take Square root of 7300 we have to subtract 75 from 7300 to get a perfect square.

7300-75=7225

(85)^2=7225

75 to be subtracted

√7300 ≥ 85

Perfect Square = 85² =  7225     or (7300-7225 = 75)

75  is  the least positive integers which , when subtracted 7300 would make a result a perfect square

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The inclination to the nearest tenth of a degree exists 0.24146

The given scenario includes a right-angled triangle where the length of the ramp exists hypotenuse and the rise of ramp exists the perpendicular.

Given: H = 4.6 m and P = 1.1 m

We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse

Let x be the angle then

sin x = P/H

sin x = 1.1/4.6

sin x = 0.23913

[tex]$$sin^{-1} x[/tex] = 0.24146

The inclination to the nearest tenth of a degree exists 0.24146

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The answer is A = m².

We know the general formula for finding the area of a square is :

Area = side²

Now, we are given the side is equal to m.

Hence, the expression which can be used to find the area is :

A = m²

The equation s for each scenario in which case, the former, Prize A is represented as a linear equation while the latter, Prize B is represented as an exponential function are;

It follows from the task content that in scenario which pertains to Prize A, the initial price which represents the y-intercept is; $5,000 while the slope which represents the increase per month is; $100.

Consequently, we have; Prize A = $5,000 + $100m

While, for Prize B, in which case the function via exponential, we have;

Prize B = $2,000(1.1)^m.

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Answer:

See attached image.

Step-by-step explanation:

If x=y, the (x,y) = (x,x) or (y,y).  All points have the same x and y values.

The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.

According to the statement

We have given that the

AB = 8 and B lies at −7, and we have to find the position of the A on the number line.

Let a be a point on number line and b be the second point on number line.

And The distance between two numbers on number line is calculate by subtracting the smaller number from larger number.

Here

AB = 8

B = -7

We have to look at the options one by one.

For A = -1

As A>B

AB = -1-(7) = -1+7 = 6

For A = 1

As A>B so

AB = 1-(-7) = 8

So with A = 1 , AB = 8

This is one of the right answers.

For A=15

As A>B

AB = 15-(-7) = 22

For A=-15

As B>A

AB = -7 -(-15) = 8

As with A=1 and A=-15, the distance between AB is 8 so these are the correct answers.

So, The value of A is A(1,-15) and the distance between AB is 8 so these are the correct answers.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Suppose A and B are points on the number line. If AB = 8 and B lies at −7, where could A be located?

Select ALL that apply.

A −1

B 1

C 15

D −15

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