Need help with my math please. 31-41.

The area of the resulting surface of this infinite curve is π units.

In this question,

The infinite curve is y = e^−2x, x ≥ 0.

The curve is rotated about x-axis.

Since x ≥ 0, the limits will be 0 to ∞.

Then the area of the resulting surface is,

[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]

Now substitute,

u = -2x

⇒ du = -2dx

⇒ dx = [tex]-\frac{1}{2} du[/tex]

Then,

[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]

Now substitute u and du, we get

⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]

⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]

⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]

⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]

Thus the area of the resulting surface is

[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]

⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]

⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]

⇒ [tex]A= -\pi [0-1} \,]\\[/tex]

⇒ [tex]A= \pi[/tex]

Hence we can conclude that the area of the resulting surface is π units.

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Answer: x = 2

Step-by-Step Solution:

Given:

OH = WO = LW

OH = 2x + 1

WO = 3x - 1

LW = 5

To Find:

The value of 'x'

Solution:

We know, OH = WO = LW

So, equate any two of the values given :-

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

Hence, x = 2.

The steps to use to construct a frequency distribution table using sturge’s approximation is as below.

The steps to construct a frequency distribution table using Sturge's approximation are as follows;

Step 1: Find the range of the data: This is simply finding the difference between the largest and the smallest values.

Step 2; Take a decision on the approximate number of classes in which the given data are to be grouped. The formula for this is;

K = 1 + 3.322logN

where;

K= Number of classes

logN = Logarithm of the total number of observations.

Step 3; Determine the approximate class interval size: This is obtained by dividing the range of data by the number of classes and is denoted by h class interval size

Step 4; Locate the starting point: The lower class limit should take care of the smallest value in the raw data.

Step 5; Identify the remaining class boundaries: When you have gotten the lowest class boundary, then you can add the class interval size to the lower class boundary to get the upper class boundary.

Step 6; Distribute the data into respective classes:

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Answer:

20

Step-by-step explanation:

To solve this you have to make a system of equations.

Since the father and son's age sum up to 60, the first equation will be:

f + s = 60

Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:

6 - (5s) = f

Now, you have to solve the first equation to let it equal to s

f + s = 60

f = 60 - s

Plug in

6 - 5s = 60 - s

     +s          +s

6 - 4s = 60

-6         -6

---------------------

-4s = 54

-----   -----

 -4     -4

   s ≅ 14

14 + 6 = 20

Answer:

20.

Step-by-step explanation:

x = father's age and y = son's age,

x + y = 60

x - 6 = 5(y - 6)

x - 5y = -24

Subtract this from first equation:

6y = 84

y = 14

So the son's age is 14.

Six years time son will be 20.

The measures of variation that can be used by Paul are interquartile range and mean absolute deviation.

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1)

First quartile = 1/4 x (n + 1)

The mean absolute deviation is the average of the distance of a data set from its mean.

Mean absolute deviation =  ∑ l x - m(x) l

Mean, median and mode are measures of tendency. They are used to measure the number at the center of a dataset.

Here are the options:

Mean absolute deviation

mean

interquartile range

median

mode

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mean absolute deviation
mean

median

interquartile range

mode

The equation of the parabolic shape of the gate is:

(x - 40)² = -64(y - 25)

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:

y = a(x - h)² + k

y = a(x - 40)² + 25

When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:

0 = 1600a + 25

a = -25/1600

a = -1/64.

Hence the equation is:

y = -1/64(x - 40)² + 25

(x - 40)² = -64(y - 25)

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The area of the given semicircle is 56.574 sq. units. Half of the area of the circle is the area of the semicircle.

The area of the semicircle is

A = [tex]\frac{1}{2}[/tex] πr² sq. units

Where r - radius

A semicircle is nothing but half part of the circle. So, its area is also half of the circle's area.

It is given that,

The radius of the semicircle is

r = 6

So, its area in terms of π is

A = [tex]\frac{1}{2}[/tex] πr²

   =  [tex]\frac{1}{2}[/tex] × π × 6²

   = 18π sq. units

On substituting π = 3.143, we get

A = 18 × 3.143 = 56.574 sq. units

Thus, the area of the given semicircle in terms of π is 18π or in terms of π =3.143 is 56.574 sq. units.

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Answer:

C

Step-by-step explanation:

The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.

Option C is the correct answer.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

Inequalities where we need to find the coordinates and see which inequalities represent the graph.

y < 4 (x- 1)² - 11 ____(1)

y < -4 (x-1)² - 11 _____(2)

y < 4 (x-1)² - 16 ______(3)

From (1),

y =  4 (x- 1)² - 11

x = 0, y = 4 x 1 - 11 = 4 - 11 = -7

From (2),

y = -4 (x-1)² - 11

y = -4 x 1 - 11 = -4 - 11 = -15

From (3),

y = 4 (x-1)² - 16

x = 0, y = 4 x 1 - 16 = 4 - 16 = -12

We see that,

y < 4 (x-1)² - 16  gives us the coordinates (0, -12) on the graph.

Similarly,

x = 1, y = 4 x 0  - 16 = 0 -16 = -16

x = 1, y = 4 x 1 - 16 = 4 - 16 = -12

(1, -16) and (2, -12) coordinates are on the graph.

Thus,

The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.

Option C is the correct answer.

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Answer:

Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession.  He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point.  It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.

Step-by-step explanation:

We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods.  The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.

Differentiate

y = -16x² +85x

The first derivative produces an equation that gives us the slope of the line at any point x.  At the ball's top height, it stops and reverses direction, a point at which the slope is zero.

y = -16x² +85x

d(y)/d(x) = -32x + 85

0 = -32x + 85

32x = 85

x = 2.66 feet horizontal distance when the ball reaches its peak.

At x = 2.66, y is 112.9 feet high

When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.

Graph:

See attached plot of the function.

Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.

After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.

Profit function in terms of x = 33x + 390.

What is a profit in business?

Given that revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial

[tex]2x^{3} + 30x - 130[/tex]

The cost, in dollars, of producing the skateboards can be modeled by

[tex]2x^{3} -3x - 520[/tex]

Profit function = Revenue - cost

                         = [tex]2x^{3} + 30x - 130 - ( 2x^{3} - 3x - 520)[/tex]

                          = 33x + 390

Therefore, profit function in terms of x = 33x + 390

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Answer: 4096.

Step-by-step explanation:

[tex](8^3)^8\div(8^4)^5=\\8^{3*8}\div8^{4*5}=\\8^{24}\div8^{20}=\\8^{24-20}=\\8^4=\\4096.[/tex]

The identity Sin(α)/Tan(α) = Cos(α) is valid

Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-

Sine Function:

sin(θ) = Opposite / Hypotenuse

Cosine Function:

cos(θ) = Adjacent / Hypotenuse

Tangent Function:

tan(θ) = Opposite / Adjacent

Lets prove this identity by proceeding with the LHS

= Sin(α)/Tan(α)

= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))

= Sin(α)xCos(α) / Sin(α)

= Cos(α)

Hence verified

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The given condition on the basis of truth table is true.

According to the statement

we have given that the some condition p and q. and we have to find that  the given condition is true or false on the basis of the truth table.

So, The given conditions are:

If 3 + 2 = 5, Then 5 + 5 = 10

Now,

The Truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It is a mathematical table that shows all possible outcomes that would occur from all possible scenarios that are considered.

So, the given conditions are properly verified with the truth table. So, it is true.

So, The given condition on the basis of truth table is true.

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The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.

Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.

The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.

So, each term is ⁿCₓaˣbⁿ⁻ˣ.

Comparing (a + b)ⁿ with (2t + s)⁷,

So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ

= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ

So, the coefficient term is ⁷Cₓ(2)ˣ

Now for the term t²s⁵, x = 2.

So, the coeficient term is  ⁷Cₓ(2)ˣ =  ⁷C₂(2)²

= 7!/2!(7 - 2)! × 4

= 7!/2!5! × 4

= 7 × 6 × 5!/(2! × 5!) × 4

= 7 × 6/2 × 4

= 7 × 3 × 4

= 84

So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

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The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

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Answer:

Step-by-step explanation:

4x - 10 + x + 7 = 4x

5x - 3 = 4x

-3 = -x

x = 3

4(3) - 10 = 12 - 10 = 2

3 + 7 = 10

10+2 = 12

4(3)= 12

If a, b and c vectors are in cyclic order , the scalar product is equals to  zero which makes Option C to be correct.

A vector  can be regarded as quantities that posses both magnitude and a direction this is the opposite to scalar quantity which posses just the magnitude without any direction.

Geometrically,  the  vector can be described as the  line segment,  having its  length as  the magnitude  with the arrow over it  showing direction.

The scalar product  can be gotten with the  multiplication  of the magnitudes of vectors .

Hence, If a, b and c vectors are in cyclic order , the scalar product is equals to  zero .

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CHECK THE COMPLETE QUESTION IN THE ATTACHMENT

Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

The correct option is C.

One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.

Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.

Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:

x + y = 18

We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,

1x + 1.5y = 21

Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:

X+1.5Y = 21, and X+Y = 18

equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

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If Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party and he divided the pizza evenly among his 4 students, each student will get 5/3 pizzas.

Given the data in the question;

First we convert the mixed fraction into an improper fraction.

6 2/3 = ( 6×3 + 2 )/3 = 20/3

Since McConnell divides the pizza evenly among his 4 students.

We will divide 20/3 by 4

20/3 ÷ 4

20/3 × 1/4

(20 × 1) / (3 × 4 )

20/12

5/3

Therefore, if Mr. McConnell brings in 6 2/3 pizzas for his students' pizza party and he divided the pizza evenly among his 4 students, each student will get 5/3 pizzas.

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Since Point R divides PQ in the ratio 1:3. the x-coordinate of Q is 3

The question has to do with line division

This is the division of a line into a given ratio.

Since Point R divides PQ in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3.

Let

Since R divides PQ in the ratio, 1:3, we have that

PR/RQ = 1/3

(x₂ - x₁)/(x₃ - x₂) = 1/3

Substituting the values of the variables into the equation, we have

(x₂ - x₁)/(x₃ - x₂) = 1/3

(-1 - (-3))/(x₃ - (-3)) = 1/3

(-1 + 3)/(x₃ + 3) = 1/3

2/(x₃ + 3) = 1/3

x₃ + 3 = 2 × 3

x₃ + 3 = 6

x₃ = 6 - 3

x₃ = 3

So, the x-coordinate of Q is 3

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Answer:

Zero

Step-by-step explanation:

Answer:

8.5 g/cm^3

Step-by-step explanation:

Density = mass/volume

          = 34 g / 4 cm^3 =  8.5 g/cm^3

Answer:

8.5 grams per cubic centimeter.

Step-by-step explanation:

Density = mass / volume

             =  34 / 4

             = 8.5 grams / cubic centimeter.

Answer:

[tex]4x^{6} y^{10}[/tex]  A.

Answer:

17.2 units

Step-by-step explanation:

You would use the Pythagorean Theorem to solve. The height (a) is 4 units. The base (b) is 6 units.

4^2 + 6^2 = sqrt(52)

This would mean that the hypotenuse is 7.211102550927979 units or 7.2 units (the square root of 4^2 + 6^2).

Now you would need to just add all three sides.
6 + 4 + 7.2 = 17.2 units

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Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

From the question we can say that the Hexagon has three shapes inside it,

Also it is given that,

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.

From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.

A pentagon is shown inside a regular hexagon.

An equilateral triangle is shown inside a square.

The expression for total shaded region would be written as,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,        

⇒ Shaded area  = area of the hexagon – area of the pentagon + area of the  square – area of the equilateral triangle.

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Answer:

Regular Hexagon

Regular Pentagon

Square

Equilateral Triangle

Step-by-step explanation:

E2020 Geometry B!! :3

Answer is Healthclub A costs $33 less in monthly fees than Healthclub B

The number next to the “x” is your rate.

So Healthclub A charges $33 less than B

A charges 27 monthly fee

B charges 60 monthly fee

60-27=33

Answer:

[tex]a = 8[/tex]  or [tex]a = -\frac{14}{3}[/tex]

Step-by-step explanation:

[tex]13(a+4)+24(a+5) = 3(a^{2} +9a+20)[/tex]

[tex]3a^{2} -10a-112=0[/tex]

[tex](3a+14)(a-8)=0[/tex]

[tex]a = 8[/tex]  or [tex]a = -\frac{14}{3}[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13}{a + 5} + \cfrac{24}{a + 4} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13(a + 4) + 24(a + 5)}{(a + 5)(a + 4)} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13a + 52+ 24a + 120}{a {}^{2} + 5a + 4a + 20} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ 37a + 172}{a {}^{2} +9a + 20} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3( {a }^{2} + 9a + 20) = 37a + 172[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} + 27a + 60 = 37a + 172[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} + 27a - 37a + 60 - 172 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} - 10a - 112= 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} - 24a + 14a - 112 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3a(a - 8) + 14(a - 8) = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: (a - 8) + (3a + 14) = 0[/tex]

So, required values of " a " are :

[tex]\qquad \sf  \dashrightarrow \: a = 8 \: \: \: or \: \: \: a = - \cfrac{ 14}{3} [/tex]

Universities A had an income under $20,000 25% graduates.

A two way table is a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.

Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.

A had an income under $40,000 25% graduates.

We have to add 30 45 together and get 75 because those are the students that have income under $40,000 dollars in both Universities

Then u convert have to convert it to a percentage and get 25%.

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The above question is not complete:

Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.

How many graduates from University A had an income under $40,000?

________graduates.

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The answer is 25%

its what khan says :>