Now consider just a small mass element of the string. What is the vertical velocity of the string at the origin at time, t

The function g(x) = (2/3)ˣ is the graph of the function f(x) = (3/2)ˣ reflected over y-axis.

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.

f = {(a, b)| for all a ∈ A, b ∈ B}.

Given, the function

f(x) = (3/2)ˣ

g(x) = (2/3)ˣ

We have to compare the graphs of the functions f(x) and g(x).

Exponential function is of the form: y = abˣ

Where a is the initial value and b is the growth factor.

a) If b > 1, then the function is an exponential growth function.

b) If 0 < b < 1, then the function is an exponential decay function.

f(x) = y = (3/2)ˣ

The function is an exponential growth function.

The rule of reflection over y-axis:

(x, y) → (-x, y)

Applying the rule, we get,

(3/2)ˣ = (3/2)⁻ˣ

= (2/3)ˣ

= g(x)

Therefore, g(x) is graph of f(x) reflected over y-axis

Hence, graph of the function f(x) = (3/2)ˣ  reflected over y-axis is function g(x) = (2/3)ˣ .

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(a) The sum of the interior angles of the nonagon is 1260°.

(b) The sum of the interior angles of the dodecagon is 1800°.

(c) The sum of the interior angles of the 23-gon is 3780°.

What is a convex polygon?

A convex polygon is a closed figure with all of its interior angles less than 180° and all of its vertices pointing outward. The term convex refers to a shape with a curve or a projecting surface. To put it another way, all of the lines across the outline are straight and point outwards.

The formula for the sum of the interior angle is (n -2)180°.

The number of sides of the nonagon is 9.

Putting n = 9 in (n -2)180°, to find the sum of interior angle of nonagon:

The sum of the interior angle is (9 -2)180° = 1260°.

The number of sides of dodecagon is 12.

Putting n = 12 in (n -2)180°, to find the sum of interior angle of dodecagon:

The sum of the interior angle is (12 -2)180° = 1800°

Putting n = 23 in (n -2)180°, to find the sum of interior angle of 23-gon:

The sum of the interior angle is (23 -2)180° = 3780°.

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A function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.

An element of one non-empty set and an element of another non-empty set are said to have a special relationship when they are connected by a function in mathematics.

An assignment of an element from set Y to each element of set X, where set X is the domain and set Y is the codomain, is what is meant when a function is applied from a set X to a set Y.

We have given that f(t) is given by the Sales of $10,000 increase by 65% each year, i.e.

As sales of $10,000 increase by 65% each year.

The situation is represented by an exponential growth function.

The initial amount a = 10,000

The rate of growth r = 65% = 0.65

Therefore, the function will be:

                                                   t = a(1 + r)ⁿ                                                  

Where,

t represents the final amount.

a represents the initial amount

r represents the rate of growth

1+r represents the growth factor

n represents the time.

⇒  t = a(1 + r)ⁿ      

⇒  t = 10,000(1 + 0.65)ⁿ    

⇒  t = 10,000(1.65)ⁿ    

Thus, a function in terms of t that represents the situation of sales that is of $10,000 and increase by 65% each year is t = 10,000(1.65)ⁿ.    

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The result of simplifying the quadratic polynomial (9x2- 8x-3) + (2x+8) is 9x2 - 6x + 5.

In mathematics, the intersection point is the place on the y-axis where the slope of the line passes. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are highlighted in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten so that they appear to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

given

(9x2- 8x-3) + (2x+8)

9x2 - 8x - 3 + 2x + 8

9x2 - 6x + 5

Thus, the result of simplifying (9x2- 8x-3) + (2x+8) is 9x2 - 6x + 5.

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Answer:

Isosceles triangle

Step-by-step explanation:

Isosceles triangle has more than 90 but less than 180, which means Isosceles triangle is equal to 120.

Answer: 1. linear equation

2. non-linear equation

3. non-linear equation

4. non-linear equation

5. linear equation

Step-by-step explanation:

not sure

Therefore , the solution of the given problem of triangle comes out to be x = 32.376 side of the hypotunse length.

Since a triangle has four or even more sections, it is a polygon. It has an easy geometric form. Triangle ABC refers to a square with angles A, B, & C. A singular plane and square are produced by Euclidean geometry whenever the sides are still not collinear. A triangle is a polygon if it has 3 components and three corners. Where a triangle's three sides come together are known as the corners. A triangle's angles add up to 180 degrees.

Here,

Given:

Triangle having :

=> Sin 78° =  h /30

=> 0.9781 = h /30

=> h = 30 * 0.9781

=>h =29.343

and

For x :

=> Sin 65° = 29.343 /x

=> 0.9063 = 29.343 /x

=> x = 29.343 / 0.9063

=> x = 32.376

Therefore , the solution of the given problem of triangle comes out to be

x = 32.376 side of the hypotunse length.

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The likelihood of the spinner to land on a consonant rather than a vowel is C. Less likely.

The likelihood of the spinner landing on a consonant rather than a vowel can be found by the formula :

= Number of consonants / Number of outcomes on the spinner

= 4 / 9

= 0. 44

This likelihood is less than 50 % which is what would have made the likelihood equally likely. However, it is not much lower than 50 % so the likelihood would be less likely.

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RS and QR are -8 and -5, respectively, in the rectangle P Q R S. Consequently, v is equal to 23.

here, QR is 3 v - 77, RS is 4 v - 97, and PS is v-23.As a result,                   PS = v - 23 ⇒ v = 23. As a result, v has a value of 23. So,                           RS = 4 × 23 - 97 = -5 is used to calculate its value.So,                               QR = 3 × 23 - 77 = -8 is used to determine its value. A All of the internal angles of a rectangle's four sides are equal to 90 degrees.

Every corner or vertex has a right angle where the two sides meet. It differs from a square in that the length of the opposing sides of the rectangle are equal. First, determine the width w using the area of rectangle formula, which is "w = A/l," to determine the length and width of a rectangle.

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Answer:

Well yeah its -18

Step-by-step explanation:

Answer: No it doesnt

Step-by-step explanation:

12+9 = 21 which is greater than 15 meaning it cannot create a triangle

The domain of the piecewise function as described in the task content is; ( −∞ , ∞ ).

It follows from the task content that the domain of the piecewise function which is as described in the task content be determined.

The domain of a function is the set of all possible input values of that function.

For the first piece, since the curve increases from left ( -∞ ) through a point and ends at a closed point (-2, -2). Hence, the set of inputs for the first piece in interval notation is; ( -∞, -2 ].

Also, for the second piece which is linear with an open point at (-2, -1) and ends at an endpoint (2, 1). Hence, the domain of the second piece is; [-2, 2].

Finally, the third piece is curved with an endpoint at (2, 1) and continues to increase tonthe right. Hence, the domain of the third piece is; [2, ∞)

Ultimately, by combining all sets of input values as determined; ( -∞, -2 ], [-2, 2] and [2, ∞); the domain of the whole piecewise function is; (−∞,∞).

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By plotting the given points (0,-5) , (1,-17/3 ) for  y=-2/3x-5 and the points for-2x+3y=-15 are (0,-5) , (1,-13/3) and (2,-11/3) we get the required graph.

What is linear equation ?

Linear equation can be defined as the equation in which highest degree is one.

Given Equation,

y=-2/3x-5 and -2x+3y=-15

So,

use the slope form is

y= mx+b , where m is slope and b is the y-intercept.

find the valued of m an b using the form y = mx+b

m = -2/3 and b=-5

The slope of line is the value of m and y-intercept the value of b

slope = -2/3

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding 2y values.

create a table for x and y values.

x    y

0   -5

1    -17/3

and soon

Similarly for -2x+3y=-15

x    y

0   -5

1    -13/3

2    -11/3

and soon

And Hence plot the points in the graph.

Therefore, By plotting the given points (0,-5) , (1,-17/3 ) for  y=-2/3x-5 and the points for-2x+3y=-15 are (0,-5) , (1,-13/3) and (2,-11/3) we get the required graph.

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The point represents the number of small gloves is 16 and the number of large gloves is 2.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given  Wanda sews small and large gloves,

time for small gloves = 45 minutes

time for large gloves = 120 minutes

total time = 16 hours = 960 minutes

let x be the number of small gloves and y be the number of large gloves,

inequality equation is 45x + 90y ≤ 960

and the cost of small gloves = $2

cost of large  gloves = $4

total amount = $40

equation 2x + 4y ≤ 40

let us assume the system of inequality in form of a linear equation,

45x + 90y = 960

2x + 4y = 40

by solving the equations

the equation is written as

x = 20 - y

45(20 -y) + 90y = 960

y = 2

and x = 16

so the minimum values for x and y are 16 and 2 to maximize the profit Wanda should not decrease the production of small gloves from 16 and large gloves to 2.

Hence the point of maximization is (16, 2).

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the complete question is in image.

The equation (t6)(t-14) is identical to tn when n = 8. A mathematical expression is composed of numbers .

You can multiply, divided, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Contrasting phrases and emotions is possible. An algebraic expression is any mathematical statement that has elements, quantities, and an arithmetic operation. As an illustration, the phrase 4m + 5 consists of the terms 4m and 5, as well as the given equation's variable m, which are all split by the algebraic sign +.

given

(t^6) (t^-14) = t^n

= 6 -14 = n

n = 8

The equation (t6)(t-14) is identical to tn when n = 8.

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Step-by-step explanation:

I don't know because you have it to far

Answer: 45 min

Step-by-step explanation:

A scale factor of 1/3 is not an enlargement. A scale factor of less than 1 is considered a reduction and not an enlargement.

An enlargement is a transformation that increases the size of a figure, it is characterized by a scale factor greater than 1. A dilation with a scale factor greater than 1 will increase the size of a figure and thus is considered an enlargement.

A dilation with a scale factor of 1/3 will decrease the size of a figure, as each point on the figure will be moved one-third as far from the origin as it was before the dilation. This means that the dilated figure will be smaller than the original figure and will have a scale factor of 1/3.

It's important to note that if the scale factor is less than 1, the dilation will reduce the size of the figure and if the scale factor is greater than 1, the dilation will increase the size of the figure.

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A polynomial function v (x) in standard form for the volume of the piece of marble is v(x) = 18a^3.

What is volume?

Volume is a term used in mathematics to describe the volume of three-dimensional space occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m^3, cm^3, in^3, etc. Volume is also referred to as capacity on occasion.

Given:

A rectangular piece of marble is cut such that the width is triple the length and the height is double the width.

We have to write a polynomial function v (x) in standard form for the volume of the piece of marble.

Let 'a' is the length of the marble.

⇒  Width of marble = 3a      (width is triple the length)

⇒ Height of marble = 2(3a) = 6a           (height is double the width)

⇒ Volume of marble = length x width x height

                                  = a x 3a x 6a

   Volume of marble = 18a^3

Hence, a polynomial function v (x) in standard form for the volume of the piece of marble is v(x) = 18a^3.

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The function rule for the line is,

f(x) = -2/3x -2.

The correct option is B.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

From the diagram,

the function has y-intercept at -2 and x-intercept at -3.

To find the slope:

First, we interpreted two points (-3, 0) and (0, -2).

Then the slope,

m =  (y₂- y₁) / (x₂ - x₁)

m = (-2, 0)/(0 + 3)

m = -2/3

Now, the equation is,

f(x) = -2x/3 - 2

Therefore, the equation is,

f(x) = -2x/3 - 2

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Answer: 734.4 inch

Step-by-step explanation:

Answer:

734.4 is the correct answer

Answer: 3

Step-by-step explanation: -4 1/3 divided by 2 1/5 = -1  32/33

Answer:

-1 32/33

Step-by-step explanation:

Negative divided by positive is negative.

We know the answeer will be negative.

Now ignore the signs, and just divide the mixed numerals.

1. Convert the mixed numerals to fractions.

2. Divide.

3. Convert quotient back to mixed numeral.

4. Make answer negative.

1.           4 1/3 ÷ 2 1/5 = 13/3 ÷ 11/5

2.          = 13/3 × 5/11 = 65/33

3.          = 33/33 + 32/33 = 1 32/33

4.          Answer: -1 32/33

Therefore , the solution to the given problem of trigonometry comes out to be Sin( θ) = Cos(90 -  θ).

Correlations between triangles' angles and sides are studied in the mathematics discipline known as trigonometry. Since every straight-sided form can be reduced to a collection of triangles, trig can be found throughout geometry. The relationships between trigonometric and other branches of mathematics, in particular calculus, either real or complex, integrals, square root, and integrals, are astonishingly complicated.

Here,

Below is a list of the trigonometric values that are missing:

Angle A =  θ-90.

28° sin = 62° cos

Cos 33° equals Sin 57°.

Cos 31° equals Sin 59°.

Sin( θ) = Cos(90 -  θ).

Therefore , the solution to the given problem of trigonometry comes out to be Sin( θ) = Cos(90 -  θ).

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Answer:

[tex]\frac{3}{5}[/tex] miles per minute

Step-by-step explanation:

3/10 ÷ 1/2

3/10 x 2 = 6/10 = 3/5

Answer:

The height of the cylinder is 10 cm.

Step-by-step explanation:

1. The volume of a cylinder is given by

-V = pi r^2 h  where r is the radius and h is the height

- 90 pi = pi r^2 h

2. We know the radius is 3

-90 pi = pi (3)^2 h

-90 pi = 9 pi h

3. Divide each side by 9 pi

- 90 pi /9 pi = 9 pi h / 9pi

- 10 =h

The height of the cylinder is 10 cm.

Answer:

B.) An isosceles triangle has at least two sides with equal measures.

Step-by-step explanation:

There are two equal sides and two equal angles in an isosceles triangle. There should be at least 2 equal sides for an Isosceles triangle. This means, even an equilateral triangle is an Isosceles triangle. In this case, at least two equal sides are 8 inches each. This is why the correct answer is 'Yes; an isosceles triangle has at least two sides that have equal measures.'

The additive inverse of 14 /- 15 is -14 /+ 15.

The antithesis of a number is the additive inverse. It is found by changing the sign of the number. To find the additive inverse of 14 /- 15, start by changing the sign of the number from a negative sign to a positive sign. The result is 14 /+ 15. This is the additive inverse of 14 /- 15. The additive inverse of any number is the same number, but with the opposite sign. For example, the additive inverse of -14 is 14, and the additive inverse of 14 is -14. The additive inverse of any number always adds up to zero when added together, which is why it is called the "additive inverse".

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