2. How does m 3. Using Geogebra’s angle measure tool, prove your claim from Problem 2.

The surface area of a cone with circumference base of 24π inches and slant height of 20 inches is 384π inches² in terms of π.

surface area = πr(r + l)

where

Therefore,

l = 20 inches

24π = 2πr

r = 12

Therefore,

surface area  = π(12)(12 + 20)

surface area = 12π(12 + 20)

surface area = 12π × 32

surface area = 384π inches²

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Answer:

B)  384 π square inches

Step-by-step explanation:

E2020

Derivative and Maximum Value of a Function

The critical points of a function are those where the first derivative is zero or does not exist.

Out of those points, we may find local maxima or minima or none of them.

One example of a function with a derivative that does not exist is:

This function has a local maximum at x=0 where the derivative does not exist.

The graph of this function is shown below:

Answer:

x=(3a+5)/(2a-b)

Step-by-step explanation:

first we distribute the a to the 2x and -3

2ax -3a=bx+5

we move the -3a over by adding 3a

2ax=bx+5+3a

then we move the bx over

2ax-bx=5+3a

we can now group the left side like this

x(2a-b)=5+3a)

to find x all we must do is divide both sides by (2a-b)

x=(3a+5)/(2a-b)

The value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Measure of arc ML=76 Degrees and

Measure of Angle JLK = 54 Degrees

We have to find the value of x

O is the centre of the circle.

As we see the figure angle L is corresponding to 54 degrees.

x=54

Hence, the value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.

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The given Mayan number which is: :|| :|| in decimal (base 10) is 42.

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

In order to obtain the decimal equivalent (base 10) of a Mayan numeral, it is imperative to comprehend the positional significance of each constituent symbol.

The numerical system employed here assigns a weight to each digit that corresponds to a certain power of 20. Specifically, the weight associated with the least significant digit is 20 raised to the exponent of 0, while the weight of the digit to its immediate left is 20 raised to the exponent of 1, and so forth.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represent a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represent a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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Answer:

0.5

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The measure of each interior angle in a regular 23-sided polygon is 164.35°.

In Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:

Interior angle = [180 × (n - 2)]/n

Where:

n represents the number of sides of a regular polygon.

When n = 23, the measure of each interior angle in this regular 23-sided polygon can be calculated as follows;

Interior angle = [180 × (n - 2)]/n

Interior angle = [180 × (23 - 2)]/23

Interior angle = [180 × (21)]/23

Interior angle = 3,780/23

Interior angle = 164.35°

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Answer:

The difference between value of y at x=11 is 385, the correct option is third

Step-by-step explanation:

Answer:

784

Step-by-step explanation:

each 1 PT = 16 FL Oz

49*16=784

Answer:

-23

Step-by-step explanation:

h(-5) = 4 * -5 - 3 = -20 - 3 = - 23       .... x ≥ -5

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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Answer:

it could be multiple things it depends what its really asking, id say X+11=25

Step-by-step explanation:

X+11=25

X=14

I don't actually know, im not smart, I'm just answering for the points

Answer:

(8, 8)

Step-by-step explanation:

Since the 3 replaces the x in (x, y), that means you would add the 5 to the three, making 8. Same thing for the 7 and the y. 7 plus 1 is 8.

The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.

A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.

From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).

The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.

Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.

To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.

To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.

Substituting these values into the equation for g(x), we have:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4

Therefore, the exact expression for g(x) is:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.

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The frequency of the wave in the stretched wire, evaluated using the formula for a standing wave in a vibrating string are as follows;

(a) The frequency of the first harmonic is about 28.013 Hz

(b) The frequency of the second harmonic is about 56.026 Hz

(c) The third harmonic frequency is about 84.039 Hz

A stretched string vibrates such that the wavelength of the wave in the string is proportional to the length of the string.

The frequency of a stretched string can be found with the formula;

\(f_1 = \dfrac{\sqrt{\dfrac{T}{m/L} } }{2\cdot L}\)

Where;

T = The tension in the wire = 578 N

m = The mass of the string = 0.341 g

L = The length of the string = 54.0 cm = 0.54 m

Therefore;

f₁ = (√(578/(0.341/0.54))/(2×0.54) ≈ 28.013

(b) A general formula for the frequency of a standing wave is presented as follows;

\(f_n= \dfrac{n \cdot v}{2\cdot L}\)

Where;

\(f_n = \dfrac{n\times \sqrt{\dfrac{T}{m/L} } }{2\cdot L}\)

Therefore, the second harmonics, f₂ = 2·f₁

f₂ = 2 × (√(578/(0.341/0.54))/(2×0.54) ≈ 56.026

(c) The third harmonics, f₃ = 3 × f₁

Therefore;

f₃ = 3 × (√(578/(0.341/0.54))/(2×0.54) ≈ 84.039

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The two integers that are between -83 and +83 are -82 and +82.

What is integers ?

In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.

There are multiple pairs of integers that are between -83 and 83.

Here are two examples:

-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -50 0 50 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:

-83 -75 0 75 83

|----------------|----------------|----------------|----------------|

The integers between -83 and 83 are represented by the shaded portion of the number line.

In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.

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Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

Answer:

f(3) = 6

Step-by-step explanation:

If f(1)=10, then f(1+1)=f(1)-2

f (2) = 10 - 2 = 8

Therefore f(3) = f(2) - 2 = 8 - 2 = 6

Answer:

because the first one isn't the exact same as the second it equals something different and if u think about it it wouldn't look the exact same but in the front of the small one only has one and the first one has two

Answer:

D) 2x2

Step-by-step explanation:

i got i right on the test

Answer:

2x2

\

Step-by-step explanation:

Answer:

a) False

b) True

c) True

d) False

Step-by-step explanation:

Answer: x = -3

Step-by-step explanation:

2 x 2 + x - 1 = 0

4 + x - 1 = 0

3 + x = 0

x = -3

Answer:

X=-3

Step-by-step explanation:

See steps below:)

Here is the final matching of multiplication expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173

81.4 x 32.1 ≈ 2,618

32.9 x 4.81 ≈ 158

46.7 x 31.7 ≈ 1,479

59.3 x 3.57 ≈ 212

Match each multiplication expression on the left with the best estimate of its product on the right:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9

81.4 x 32.1

32.9 x 4.81

46.7 x 31.7

59.3 x 3.57

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

Estimates for the remaining expressions:

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

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The rate of depreciation is 5.19% and the value of the car in the year 2006 is $11,078.35.

A car was valued at $26,000 in the year 1990. The value depreciated to 13,000 by the year 2003.

The exponent is given as,

$13,000 = $26,000 (1 - r)ⁿ

Here, n represents the number of years from 1990.

Then the rate is calculated as,

$13,000 = $26,000 (1 - r)¹³

1/2 = (1 - r)¹³

0.94807 = 1 - r

r = 0.0519 or 5.19%

The value of the car in the year 2006 is calculated as,

A = $26,000 (1 - 0.0519)¹⁶

A = $26,000 (0.94807)¹⁶

A = $26,000 x 0.426

A = $11,078.35

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Answer:

The answer is 22,650

So, option b for you

Step-by-step explanation:

To find the sum of even numbers from 2 to 300, the formula we use is,

N ( N + 1 )

Where N is given by,

N = [( first number + last number)/2] - 1

So here, N = [ (2 + 300 ) / 2 ] - 1 = 150

And hence Sum = 150 * 151 = 22650

Answer:

11.9 cm

Step-by-step explanation:

1 in ≈ 2.54 cm

4.7 in ≈ 2.54(4.7) cm

2.54(4.7) = 11.938 cm

11.938 cm rounded to the nearest tenth is 11.9 cm.

Answer: 11.9

Step-by-step explanation:

The conversion rate is 1 inch to 2.54 centimeters. Using this we can setup the equation \(4.7 in * \frac{2.54 cm}{1 in}\). The inches units will cancel and you will end up with 11.938 cm. Rounded to the nearest tenth and you get 11.9.