As x gets very large, which function becomes largest and remains so?

A y = 5x^3
B y = 4x^2
C y = ^3x
D y = 7x

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:  112112v

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Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112Answer:

Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112

The equation is solved and the values of a and b is simplified as

a) The possible values of ab = 4

b) The possible values of a + b = 4

c) The possible values of a and b = 2

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)

To find all possible values of ab, we can use the identity:

a⁴ + b⁴ = (a² + b²)² - 2a²b²

Substituting the given values, we have:

16 = (a² + b²)² - 2a²b²

We also know that a + b=4, which means that b = 4 - a.

Substituting this into the equation above, we have:

16 = (a² + (4-a)²)² - 2a²(4-a)²

Simplifying, we get:

16 = (2a² - 8a + 16)² - 32a² + 64a³ - 32a⁴

Expanding, we get:

16 = 4a⁴ - 64a³ + 288a² - 512a + 272

Rearranging and factoring, we get:

4a⁴ - 64a³ + 288a² - 512a + 256 = 0

Dividing by 4, we get:

a⁴ - 16a³ + 72a² - 128a + 64 = 0

This is a quartic equation, which can be factored as:

(a-2)⁴ = 0

Therefore, the only possible value of a is 2, which means that the only possible value of b is 2 as well.

So, ab = 2 x 2 = 4

(b)

We know that a + b = 4, and since a = 2, we have b = 4 - a = 2

Therefore, the only possible value of a + b is 4

(c)

From part (b), we know that the only possible value of a + b is 4. From part (a), we know that the only possible values of a and b are both equal to 2.

Therefore, the only possible solution is a = 2 and b = 2

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The value of x in degrees will be 6° and 11° using properties of parallel lines.

They are typically equal-distance, parallel straight lines. The lines here are parallel. They never come together no matter how far you extend them in any one way.

Pairs of equal-sized angles that are both obtuse or acute and are generated on the same side of the transversal are known as corresponding angles. Each pair of comparable angles on the same side of the crossing transversal is equal to the other.

The alternative angle theorem states that alternate interior angles or alternate exterior angles that come from cutting two parallel lines are congruent.

In the above figure,

8x + 7 = 55

8x  = 55 - 7

x = 6

Measure of the angle will be 8 × 6 + 7 = 49

In 11)

10x + 10 = 9x + 21 (by using first corresponding angles and then alternate angles)

⇒x = 11

The value of x in degrees will be = 11° using properties of parallel lines.

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By using the fact that the sum of the interior angles must be 180°, we wil see that:

x = 110°.

First, remember that the sum of the interior angles of a triangle is alway equal to 180°.

We also can see that the interior angle that is adjacent to x can be written as:

a = 180° - x

Then the sum of the interior angles will give:

30° + 80° + (180° - x) = 180°

30° + 80° - x = 0

110° - x = 0

110° = x

That is the value of x.

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The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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Answer:

2y+x=7

Step-by-step explanation:

The equation of a line is in the form:

[tex]y = mx + c[/tex]

where m is the gradient and c is the y-intercept.

In the equation y=2x+3 the gradient is 2, so to find the perpendicular gradient, it is the negative reciprocal, or in other words, flip the number upside down and make it negative:

[tex]2 = \frac{2}{1} [/tex]

[tex] \frac{2}{1} \: flipped \: upside \: down = \frac{1}{2} [/tex]

[tex] make \: \frac{1}{2} \: negative = - \frac{1}{2} [/tex]

So the gradient for the point (1, 3) is -1/2

Using y=mx+c to find c (the y-intercept) where y=1, m=-1/2, x=1, substitute these values in:

[tex]y = mx + c[/tex]

[tex]3 = - \frac{1}{2} (1) + c[/tex]

[tex]3 = - \frac{1}{2} + c[/tex]

[tex]3 + \frac{1}{2} = c[/tex]

[tex]c = \frac{7}{2} [/tex]

So the equation is:

[tex]y = - \frac{1}{2} x + \frac{7}{2} [/tex]

We need to write this in the form ax+by=c, so multiply everything by 2 to get rid of the fractions on the right:

[tex]2y = - x + 7[/tex]

Bring x to the left side by adding it:

[tex]2y + x = 7[/tex]

This is now in the form ax+by=c

The domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

Given is a graph of the function.

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -

Domain → [-5, 10)

Range → [-3, 3)

Therefore, the domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

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Answer:

(0, 28)

Step-by-step explanation:

Overview

To answer the question given, we have to find the point on the line that goes through the points given in the table when the x-axis represents the month of the year (1 is Jan, 2 is Feb, etc.) and the y-axis represents the average temperature for that month.

Method 1

I've attached a graph of the line for reference.

When we look at the graph of the line that goes through the points given in the table, we can determine that its y-intercept is (0, 28).

Method 2

To determine the y-intercept of the line without actually graphing it, we can construct an equation using the given points.

We know that the line's slope is defined as [tex]\dfrac{\textrm{rise}}{\textrm{run}}[/tex].

Using that information, we can solve for the line's slope by using any two of the given points. I will use the points for January (1, 42) and February (2, 56).

[tex]\textrm{slope} = \dfrac{56-42}{2-1} = \dfrac{14}{1} = 14[/tex]

Then, we can plug this value into the point-slope form equation

[tex]y - b = m(x - a)[/tex]

along with one of the given points [tex](a,b)[/tex] -- I'll use January (1, 42):

[tex]y-42=14(x-1)[/tex]

Next, to solve for the y-coordinate of the line's y-intercept, we can plug 0 into the equation for x and solve for y.

[tex]y - 42 = 14(0 - 1)[/tex]

[tex]y - 42 = 14(-1)[/tex]

[tex]y - 42 = -14[/tex]

[tex]y = -14 + 42[/tex]

[tex]y = 28[/tex]

Finally, we can plug the solved y-coordinate and 0 for the x-value (because we solved for when y when x = 0) into the format of a Cartesian coordinate:

(0, 28)

i) The absolute change of the CPI from 2009 to 2014 is given as follows: 22,199.

ii) The absolute change of the Tuition from 2009 to 2014 is given as follows: $26.5.

iii) The relative change of the CPI from 2009 to 2014 is given as follows: 10.35%.

iv) The relative change of the Tuition from 2009 to 2014 is given as follows: 26.59%.

Tuition has increased more in this time period.

The absolute change between two amounts is given by the absolute value of the difference of these two amounts.

Hence for the CPI from 2009 to 2014 is given as follows:

236736 - 214537 = 22,199

For the Tuition, it is given as follows:

126.15 - 99.65 = $26.5.

The relative change is given by the absolute change divided by the initial value and multiplied by 100%, hence:

Due to the higher relative change, the Tuition increased more in this time period.

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Answer:

B

Step-by-step explanation:

after 0 it's 1 and 4 is after 5

Answer:

0.01 %

Step-by-step explanation:

The interest rate is the percentage of the principal (the amount borrowed) that is charged as interest over a certain period of time.

To find the interest rate, we can use the formula:

Interest Rate = Interest / Principal x Number of days / 365

We know that the principal is 600$, the interest is 14.25$ and the number of days is 90

so we can substitute the values into the formula:

Interest Rate = 14.25 / 600 x 90 / 365

Interest Rate = 0.02375 * 90 / 365

Interest Rate = 0.0104

Rounded to the nearest thousandth, the interest rate is 0.010 or 0.01 %

Answer:

Step-by-step explanation:

The f(9) means that the value of x would be 9 in any given equations or functions.

For example:

[tex]f(x) = 2x^{2} + 5\\f(9) = 2(9)^{2} + 5\\f(9) = 2(81) + 5\\f(9) = 162 + 5\\f(9) = 167[/tex]

On the other hand, f(x) = 9 means that the value of a certain function is simply equal to 9.

The cyclist's average speed is

14.93

mph.

Total

distance

covered is=2+8=10

Total time =10+30=40

=40/60 min

=.0.67 hours.

Convert miles per min to miles per hour,

average speed= 10 miles/0.67 hours,

=14.93 mph.

The average speed is =4.93 mph

The total distance covered is 2 + 8 = 10 miles. The total time taken is 10 minutes + 30 minutes = 40 minutes. To convert minutes to hours, divide the time in minutes by 60. So, the total time taken in hours is 40 minutes / 60 = 0.67 hours. To convert miles per minute to miles per hour, multiply the speed in miles per minute by 60. So, the average speed in miles per hour is

10 miles / 0.67 hours = 14.93 mph

The average speed is =14.93 mph

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Answer:

$9 left

Step-by-step explanation:

1.50 x 2 = $3

1.50 x 2 = $3

2.50 x 2 = $5

5 + 3 + 3 = $11

$20 - $11 = $9

Answer:

Step-by-step explanation:

1.50+1.50+3

1.50+1.50+3

2.50+2.50= 5

5 + 3 + 3 = 11

20 - 11 = 9

The FOIL method to find the product (x + 5)(x² - 3x) is x³ + 2x² - 15

You should note the following about FOIL method

It stands for "First, Outer, Inner, Last"

It is the sum of:

· multiplying the First terms,

· multiplying the Outer terms,

· multiplying the Inner terms, and

· multiplying the Last terms

That is  (a+b)(c+d) = ac + ad + bc + bd

Use FOIL (First, Outside, Inside, Last)

The give expression is

x(x²) = x³

x(-3x) = -3x²

5(x²) = 5x²

5(-3x) = -15x

Combine like terms:

x³ - 3x² + 5x² - 15x

x³ + 2x² - 15

Therefore the FOIL method is x³ + 2x² - 15

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Answer:3 square root 27c7 • 3 square root 250c2 can be simplified by applying the property of square roots, (√a * √b) = √(ab) .

So, 3 square root 27c7 • 3 square root 250c2 = √(27c7 * 250c2) = √(27250c7c2) = √(675c7*c2) = √(675c9) = √(675) * √(c9) = 15c3

Therefore, 3 square root 27c7 • 3 square root 250c2 = 15c3 is the equivalent expression.

Step-by-step explanation:

The convergence of the series ∑∧∞ 4.7.10…(3n+1) /1.2.3….n is π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106

You should understand that any series that is not convergent is said to be divergent or to diverge

The reciprocals of the positive integers produce a divergent series

This can be written as π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106 .... For x ∈ R, the (infinite) geometric series ∑n≥0 xn converges if |x| < 1 and ...

This is to say that the convergence series is the reciprocal of the series.

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Answer:

The zeroes of the equation are -2 and -6.

Step-by-step explanation:

(x + 2)(x + 6) = 0

=> x = -2, -6

Hope it helps.

Answer:

-5 and -3

Step-by-step explanation:

-2x + 1 > 6

[tex]-2(-\frac{5}{2}) + 1 > 6\\6 > 6[/tex]

Not an answer

-2(-5) + 1 > 6

11 > 6

An answer

-2(-2) + 1 > 6

5 > 6

Not an answer

[tex]-2(-\frac{3}{2}) + 1 > 6\\4 > 6[/tex]

Not an answer

-2(0) + 1 > 6

1 > 6

Not an answer

-2(-3) + 1 > 6

7 > 6

An answer

Answer:

y = -3

Step-by-step explanation:

The midline of a sinusoidal function is y = a where "a" is halfway between the minimum and maximum y-values of the function.

From inspection of the given graph:

Therefore, the y-value that is halfway between the minimum and maximum points is:

[tex]\implies y=\dfrac{y_2+y_1}{2}=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3[/tex]

Therefore, the equation of the midline of the given sinusoidal function is:

Answer:

2,260.80 cubic millimeters

Step-by-step explanation:

The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Answer:

y = -x - 3

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Given that the point (-8,5) lies on the line and the slope of the line is m=-1, we can use the point-slope form of a linear equation to write the equation of the line.

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

So substituting the given point (-8,5) and slope m=-1 into the point-slope form, we get:

y - 5 = -1(x + 8)

Simplifying, we get:

y = -x - 3

This equation is the slope-intercept form of the line that passes through the point (-8,5) and has a slope of -1.

Answer:

Step-by-step explanation:

Linear functions can be used in many real-world applications such as:

Economics: Linear functions can be used to model the relationship between the price of a product and the quantity of the product that will be sold.

Engineering: Linear functions can be used to model the relationship between force and displacement in elastic materials.

Sciences: Linear functions can be used to model the relationship between the concentration of a substance in a solution and the time it takes for that substance to be consumed or produced.

Business and Finance: Linear functions can be used to model the relationship between the cost of a product and the number of products produced.

Graphing: Linear functions can be used to graph the relationship between different variables.

Transportation: Linear functions can be used to model the relationship between the distance traveled and the time it takes to travel that distance at a constant speed.

Construction: Linear functions can be used to model the relationship between the height of a building and the number of floors in the building.

Weather forecasting: Linear functions can be used to model the relationship between temperature and time of the day.

I'm going to provide a real life case for this answer. I own and manage an online soccer jersey store and the process behind it is quite simple:

1. Receive order

2. Buy jerseys from supplier

3. Resell at an slighly higher price

4. Pay taxes + shipping

Now, say that "x" is the amount of jerseys my store sells in a month. I can use functions to create an expression that tells me what is the total net revenue I get from selling "x" amount of jerseys a month.

For example, say that the jerseys cost $50 and you sell them for 60$. You also need to pay the shipping for each jersey (say it is $5 per jersey). Then, we can form a function like this:

[tex]y=60x-50x-5x[/tex]

As you can tell, the money that comes back to the seller ($60 dollars per jersey) is expressed as a possitive coefficient for variable "x" (number of sold jerseys). And, all the other costs, which is money that you spend in order to sell the jerseys, are expressed with a negative coefficient meaning that they are not net revenue, it isn't profit. Now, to see how much money you can make by selling 2 jerseys, simplify the function and substitute variable "x" (number of sold jerseys) by 1:

[tex]y=60x-55x\\ \\y=5x[/tex]

Say "y" is the net revenue:

[tex]y=5(2)\\ \\y=10[/tex]

You can also use functions to determine things such as, how many jerseys do I need to sell in order to make $750 of net revenue? In that case you do the following:

[tex](750)=5x\\\\x=\frac{750}{5} \\ \\x=150[/tex]

From this analysis, you can conclude that you need to sell 150 jerseys ij order to amke a net revenue of $750.

In conclusion, linear functions can be used to see how a variable value (normally called "x") can affect in the results in multiple daily situations: how many miles can your car run with a full tank, how much time do I need to work so I can buy a product, how much money I can spend in something so I can have saving of "x" amount at the end of the year, etc...

Answer:

Step-by-step explanation:

a. To minimize the average cost, we need to find the value of x that minimizes the cost function C(x) = x² - 40x + 500.

This is the same as finding the minimum value of the parabola represented by the function. The vertex of the parabola is the point at which the parabola reaches its minimum or maximum value. The vertex form of a parabola is given by C(x) = a(x - h)² + k, where (h, k) is the vertex.

By comparing the given function with the vertex form of a parabola, we can find the vertex:

C(x) = x² - 40x + 500

= a(x - h)² + k

= (x - h)² + k

The x-coordinate of the vertex h = 40/2 = 20

So the minimum average cost occurs when 20 televisions are made per week.

b. To find the minimum average cost, we need to substitute the value of x = 20 into the cost function:

C(x) = x² - 40x + 500

= 20² - 40*20 + 500

= 400 - 800 + 500

= 100

So the minimum average cost is $100 per television.

If the average cost is $200 per television, we can set C(x) = 200 and solve for x:

200 = x² - 40x + 500

0 = x² - 40x + 300

This is a quadratic equation that can be solved by factoring or by using the quadratic formula.

we can factor it as

0 = (x-50)(x-6)

x = 50 or x = 6

The number of televisions made per week if the average cost is $200 per television is 50 or 6. Since 50 is much higher than 20, the minimum average cost, it is not physically possible to make 50 televisions with the average cost of $200 per television. So the answer is 6 televisions per week.

Answer:

s(5+7)

Step-by-step explanation:

Since 's' is the Highest Common Factor that will go outside the brackets.

[tex]s(5+7).[/tex]

[tex]5s+7s[/tex]

As you can tell, a common term between "5s" and "7s" is variable "s". Hence, we may factorize using that variable.

[tex]s(\frac{5s+7s}{s} )\\\\s(\frac{5s}{s} +\frac{7s}{s} )\\ \\s(5+7)[/tex]

Final answer: [tex]s(5+7)[/tex].

The area of a outdoor carpet is 42 square feet.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

In the given figure, the outdoor carpet consist two triangles and one rectangle.

Here, rectangle measures length=11 ft and width = 3 ft, small triangle has base= 2 ft and height =3 ft and large triangle has base= 4ft and height =3 ft.

So, area of rectangle is 11×3 = 33 square ft

Area of small triangle = 1/2 ×Base×Height

= 0.5×2×3

= 3 square feet

Area of large triangle = 1/2 × 4×3

= 6 square feet

Total area = 33+3+6

= 42 square feet

Therefore, the area of a outdoor carpet is 42 square feet.

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Answer:

D

Step-by-step explanation:

the midsegment of a trapezoid is half the sum of the parallel sides, that is

midsegment = [tex]\frac{WT+VU}{2}[/tex] = [tex]\frac{17.5+6.1}{2}[/tex] = [tex]\frac{23.6}{2}[/tex] = 11.8

The maximum allowed ratio for the cord such that the maximum allowable normal stress is 8.77 kilopascals is equal to 2.081.

Let assume that the cork is made of a ductile material, in this case we find that the normal stress (σ), in kilopascals, and shear stress (τ), in kilopascals, are described below:

Normal stress

σ = F / A

Shear stress

τ = (3 · V) / (2 · A')

Where:

Let assume that cork is at static equilibrium and at inminent motion, then the shear and normal forces are, respectively:

F = P

V = P / 2

And the transversal areas are introduced below:

A = π · R²

A' = 2 · R · H

Where:

If we know that σ = 8.77 kPa and τ = 4.98 kPa, then the maximum allowed ratio between the cork height and the cork radius is:

8.77 = P / (π · R²)

8.77 = [1 / (π · R)] · (P / R)

4.98 = 1.5 · (0.5 · P) / (2 · R · H)

4.98 = [0.75 / (2 · H)] · (P / R)

Then, we eliminate P / R of the two equations:

8.77π · R = 13.24 · H

H / R = 8.77π / 13.24

H / R = 2.081

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The value of log10 5 as required to be determined using the given information is; 0.3979 + P..

It follows from the task content that; the value of log10 5 is to be determined based on the given information.

Since the given expression is; log10 2 = P;

The expression which can be inferred from the equation above is;

10^P = 2..............(i)

However, let; log10 5 = x

Therefore; 10^x = 5..........(ii)

By dividing the equation (ii) by (i); we have that;

10^(x - P) = 2.5

Therefore, from the converse of logarithmic law;

x - P = log10 2.5

x = P + log10 2.5

where, log10 2.5 = 0.3979

x = 0.3979 + P

Ultimately, the value of log10 5 as required is; 0.3979 + P.

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f(x) and g(x) are inverses using composition

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

To confirm the inverse relationship using composition.

For valid inverse f(g(x)) must be equal to g(f(x))

f(x) = ∛(x) + 13; g(x) = (x - 13)³:

f(g(x)) = f((x - 13)³)

f(g(x)) = ∛((x - 13)³) + 13

f(g(x)) = x - 13 + 13

f(g(x)) = x

g(f(x)) = g(∛(x) + 13)

g(f(x)) =  (∛(x) + 13 - 13)³

g(f(x)) =  (∛(x))³
g(f(x)) =  x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

f(x) = x³ + 1; g(x) = ∛(x - 1):

f(x) = x³ + 1; g(x) = ∛(x - 1)

f(g(x)) = f(∛(x - 1))

f(g(x)) =  (∛(x - 1))³ + 1

f(g(x)) =  x - 1 + 1

f(g(x)) =  x

g(f(x)) = g(x³ + 1)

g(f(x)) = ∛((x³ + 1) - 1)

g(f(x)) = ∛(x³)

g(f(x)) = x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

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