The carrying capacity of a drain pipe is directly proportional to the area of its cross section.If cylindrical pipe drain can carry 36L/sec,determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second .

Answer:

[tex]\boxed{x = 8 \;m}[/tex]

Step-by-step explanation:

Nice drawing! :)

From the figure we see that the rectangle has a length of 30 m and a width of 20 m

The total area of the rectangle PQRS = 20 x 30 = 600 m²

The square footage of the planted area = area of figure MNSR = 388 m²

Therefore the rest of the area (the unshaded portion) is:
600 - 388 = 212 m²

This is the combined area of the two triangles ΔPNM and ΔMRG

Let's find the area of each of these triangles. Each of them is a right triangle which makes calculations easier

Area of a right triangle = (1/2) x base x height

ΔPNM has base = 30 - x and height = 20 -x

Area of ΔPNM

= (1/2) (30-x)(2-x)

We can use the FOIL method to evaluate (30-x)(2-x)

(30-x)(20-x)  

= 30·20 + (30)(-x) + x(20) + (-x)(-x)

= 600 - 30x + 20x + x²

= 600 -50x + x³

We usually rewrite with coefficients in decreasing magnitude of x degree

Area of ΔPNM

[tex]=\dfrac{x^2 - 50x + 600}{2}[/tex]

Let's now find the area of ΔMRQ with a base of x and a height of 20

Area of ΔMRQ
[tex]=\dfrac{1}{2}\cdot 20 = \dfrac{20x}{2}[/tex]

Adding both terms together we get
[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} \\[/tex]

We have computed the area of the unshaded region as 212

So the above sum must be equal to 212

[tex]\dfrac{x^2 - 50x + 600}{2} + \dfrac{20x}{2} = 212[/tex]

Multiply throughout by 2 to get rid of the denominator:

[tex]\rightarrow \;\;x^2 - 50x + 600 + 20x = 212\times 2 = 424\\\\\rightarrow \;\;x^2 -30x + 600 =424\\[/tex]

Move 424 to the left:

[tex]x^2-30x+600-424=424-424\\\\x^2-30x+176=0[/tex][tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]

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

[tex]\textrm{Factoring } x^2-30x+176=0\\\\\\\textrm{We get}\\\\x^2-30x+176=\left(x-8\right)\left(x-22\right)\\\\[/tex]

So
[tex]x^2-30x+176=0 \rightarrow (x -8)(x-22) = 0\\\\[/tex]

So x = 8 or x = 22 are two possible solutions to this quadratic

If x = 22, it will be greater than the width of 20 and also 20-x = -2 so it is not a valid solution for this situation

Therefore we get the final answer as [tex]\boxed{x = 8 \;m}[/tex]

Answer:

28.71

I looked it up.

Answer:

28.71

Step-by-step explanation:

To be honest with you, I looked it up

We can use the formula:

[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]

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

20) The point-slope form of a line is[tex]y - y1 = m(x - x1)[/tex], where [tex](x1, y1)[/tex] is a point on the line and m is the slope. The slope of the line can be found by using the coordinates of two points on the line. To find the slope between the points [tex](1, 3)[/tex] and [tex](-4, 5)[/tex], we can use the formula:

[tex]m = (y2 - y1) / (x2 - x1) = (5 - 3) / (-4 - 1) = 2/5[/tex]

The point-slope form of the line is then:

[tex]y - 3 = (2/5)(x - 1)[/tex]

To convert this to slope-intercept form (y = mx + b), we can solve for y:

[tex]y = (2/5)x + (3 - (2/5)) = (2/5)x + (12/5)[/tex]

21) The line is parallel to [tex]y = -2x - 5[/tex], so we know that the slope of the line is -2. We can use the point [tex](4, -7)[/tex]and the slope -2 to write the equation in point-slope form:

[tex]y - (-7) = -2(x - 4)[/tex]

or

[tex]y + 7 = -2x + 8[/tex]

To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:

[tex]y = -2x + 1[/tex]

22) The line is perpendicular to [tex]y = -3/2x + 1[/tex], so we know that the slope of the line is the negative reciprocal of [tex]-3/2[/tex]. The slope of the line is [tex]2/3[/tex]. We can use the point [tex](3, 5)[/tex] and the slope [tex]2/3[/tex] to write the equation in point-slope form:

[tex]y - 5 = (2/3)(x - 3)[/tex]

or

[tex]y = (2/3)x + (5 - (2/3)3) = (2/3)x + (5 - 2) = (2/3)x + 3[/tex]

To convert this to slope-intercept form [tex](y = mx + b)[/tex], we can solve for y:

[tex]y = (2/3)x + 3[/tex]

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The manager of the clothing store always orders 2 small T-shirts and 3 small T-shirts for every 4 medium T-shirts.

What in mathematics is a linear equation?

According to Wolfram MathWorld A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The manager plans to order 24 medium T-shirts and we want to find out how many small T-shirts the manager should order.

We can use the information given to set up an equation to represent the relationship between the number of small T-shirts and medium T-shirts. Let S be the number of small T-shirts and M be the number of medium T-shirts.

We know that:

S = 2 + (3/4)M

We are given that the manager plans to order 24 medium T-shirts, so we can substitute this value into the equation:

S = 2 + (3/4) * 24

We can simplify and solve for S:

S = 2 + (3/4) * 24

S = 2 + 18

S = 20

Therefore, the manager should order 20 small T-shirts.

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Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo. Do note that since this is a right-angled triangle, Pythagoras' Theorem can be used to find the length of one side：

[tex]c^{2} = a^{2} + b^{2}[/tex]

The difference in the monthly payments for a 20-year mortgage and a 30-year mortgage on a $135,000 loan at 3.32% APR is $430.

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The first digit to the right of the decimal point indicates the number of tenths. For example, the decimal 0.3 is the same as the fraction 3/10. 

a) The polygon has 11 sides

b) The Sum of the Interior Angles of the 11 sided Polygon = 1620 degrees

What is a polygon ?

The definition of a polygon is a closed, two-dimensional, plane shape created by connecting three or more line segments. During our study of geometry, polygons are a common sight.

A polygon's sides are constructed from segments of straight lines joined end to end. The sides or edges of a polygon are the line segments that make up its shape. The vertex or corners formed by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon.

There are 11  sides, So, n=11

Sum of the Interior Angles of a Polygon = 180 (n-2) degrees

So,

The Sum of the Interior Angles of the 11 sided Polygon
= 180 (11-2) degrees

= 180 ( 9)

= 1620 degrees

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To find the mass of the lamina, we need to integrate the density function over region D. The density function is given by? (x, y) = 7ky, where k is a constant. The region D is bounded by y = [tex](1 ? x^2)[/tex]  and y = 0, and the limits of integration are [tex]0 < = y < = (1 - x^2)[/tex] .

So, the mass of the lamina is:

[tex]m = ∫∫?(x, y) dx dy = ∫∫ 7ky dx dy\\= 7k ∫∫ y dx dy = 7k * ∫ (1 - x^2) dy dx\\= 7k * ∫(0 to 1 - x^2) y dy\\= 7k * (1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/2 * [((1-x^2)^3/3] - 0))= 7k * (1/2 * (1/3 - x^6))[/tex]

To find the center of mass (x bar, y bar) of the lamina, we need to find the x and y coordinates of the center of mass.

The x-coordinate is given by

[tex](x bar) = 1/m * ∫∫ x ?(x, y) dx dy = 1/m * ∫∫ x * 7ky dx dy \\= 7k * ∫ (x * y) dx dy\\= 7k * (x * 1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (x * 1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (x * (1/2 * (1/3 - x^6))\\The y-coordinate is given by\\(y bar) = 1/m * ∫∫ y ?(x, y) dx dy = 1/m * ∫∫ y * 7ky dx dy= 7k * ∫ (y^2) dx dy\\= 7k * (1/3 * ∫(0 to 1 - x^2) y^3 dy)\\= 7k * (1/3 * [y^4/4] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/3 * (1/4 - x^6/2))[/tex]

It's worth noting that the mass and center of mass of the lamina depend on the constant k, which is not specified in the problem.

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Answer:

(0,5) and (3,320)

Step-by-step explanation:

Plug in the ordered pair into the function and see if it makes sense.

Plug in 5 for y and 0 for x:

5= 5(4)^0
4^0 = 1 (anything to the power of 0 except 0 is one)
5x1 = 5
5=5
(0,5) works

320 = 5(4)^3

4^3 = 64

64x5 = 320

320=320

320=320 (3,320) works

(0,5) and (3,320) both work.

The <HDI of the circle is 70 degree. A circle is divides into 360 equal degrees.

A circle is divides into 360 equal degrees.

In relation to a circle, angles are measured in degrees or radians, with one full rotation being equal to 360 degrees or 2 Pi radians.

so, <EDI = 140 degree.

so

A circle is  360 equal degrees.

360 - 140 =  220

< IDH = <EDF = 2x

<FDG = <GDH = 2y

so

2x + 2y = 220

2 * 70  + 2 * 40 = 220 degree

so,

<HDI = 70 degree.

so

The <HDI of the circle is 70 degree.A circle is divided into 360 equal degrees.

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Answer:

c=2a/h-b

Step-by-step explanation:

On solving the provided question we can say that the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

here,

the expression of the emaily number will be as =[tex]\frac{1}{4}n - 3[/tex]

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Option A, The degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex], and [tex]n_1[/tex], [tex]n_2[/tex] is 15.

To calculate the degrees of freedom for a small-sample test of hypothesis for [tex]H_1[/tex] and [tex]H_2[/tex], assuming [tex]o_{12}[/tex], [tex]o_{22}[/tex] and [tex]n_1[/tex], [tex]n_2[/tex], you would use the following formula:

df = ([tex]o_{12}^2[/tex]/n_1) + ([tex]o_{22}^2[/tex]/n_2)

In this case, the degrees of freedom would be:

df = ([tex]o_{12}^2[/tex]/16) + ([tex]o_{22}^2[/tex]/16) = 15 and represents the number of values that are free to vary in the sample.

So, the answer would be A. 15

It's important to note that this formula is only used for small sample sizes. For large sample sizes, the degrees of freedom are approximated using the Welch-Satterthwaite approximation.

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The sine of an angle is the ratio of height to the hypotenuse. The value of sin 50° = 0.7660.

What is an angle?

An angle is a figure in Plane Geometry generated by two rays or lines that share a common endpoint. The term "angle" is derived from the Latin word "angulus," which meaning "corner". The two rays are referred to as the sides of an angle, while the common terminus is referred to as the vertex.

The sine of an angle is the ratio of height to the hypotenuse of a right triangle.

The reference angle is 50.

Now sin 50 = 0.766044.

The 5 digits after the decimal point is 4. 4 is less than 5 thus the 4 digits after the decimal point remain the same.

sin 50 = 0.7660

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Answer:

the answer is 338.13

Step-by-step explanation:

289,00×.17=49.23

49.13+289.00

hope this helps:)

The terms in given expression like variables, coefficient, constant are respectively, y, 1, -9

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

An expression,

⇒ y-9

In given expression, y is term which is variable

And coefficient of y is 1

constant term is -9

Therefore, we can write our terms are,  y, 1, -9

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CuI's molar solubility is determined to be 1.27 x 10⁻¹².

The quantity of ions dissolved per litre of solution is measured by molar solubility. The quantity of ions that are dissolved in this situation's amount of solvent is represented as solubility.

Think about the equation.

Cu+(aq) CuI.(s) + I- (aq)

Let's assume that CuI (s) has a molar solubility of "S" mol/L.

Thus,

Product of solubility = [Cu+(aq)] + [ I-(aq)] → [Cu+(aq)] Ksp

[ I-(aq)] ———(1)

We are aware of

For CuI, the solubility product Ksp is 1.27 x 10⁻¹².

Consequently, from equation (1)

1.27 × 10⁻¹² = S.S

S² =1.27 × 10⁻¹²

= (1.27 × 10⁻¹² )½ = 1.127 x 10⁻⁶ M

Therefore, CuI has a molar solubility of 1.127 x 10-6 M.

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The tip was $7.77 in total, and it is a 18.5% of the bill cost.

Here we know that the bill was $42, while the family spend a total of $49.77

Then the amount for the tip is equal to the difference between the bill and the amount that the family spends.

Tip = $49.77 - $42  = $7.77

Now we want to see which percentage of the bill this is, to check that, we need to take the quotient between the tip and the bill, and multiply that by 100%, we will get:

percentage = ($7.77/$42)*100%

percentage = (0.185)*100% = 18.5%

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The Fencing Mrs. Jones will need in centimeters is 1220 cm

The fencing is a measure of the perimeter of the region to be covered

With the dimensions in meters deduced form the problem as 3.4 m by 2.7 m. the perimeter is calculated using the formula

= 2( length * width)

= 2(3.4 + 2.7)

= 2(6.1)

= 12.2 m

To convert 12.2 m to cm we use the factor, 1 m i= 100 cm, therefore

= 12.2 * 100

= 1220 cm

the perimeter is 1220 cm

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Therefore, We can use the Gaussian elimination method to find the basis of H.

In linear and multilinear algebra, the procedure of Gauss elimination involves first solving one of the simultaneous linear equations for one variable (in terms of all the others) and then substituting this expression into the other equations to discover the answers.

A linear equation is an algebraic equation in which each term has an exponent of 1, which, when plotted on a graph, always yields a straight line. One example with one variable is where ax+b = 0, where a and b are fundamental values and x is the variable.

Selecting the polynomials Pi(t) = 1 + t and P2(t) = 1 - t from the set S. These are linearly independent since they cannot be written as a linear combination of the other polynomials in the set and checking if the span of Pi(t) and P2(t) is equal to H. Then expressing the remaining

polynomials P3(t), P4(t), and Ps(t) in terms of Pi(t) and P2(t) and checking if they can be written as a linear combination of Pi(t) and P2(t) or not.

P3(t) = 4 can be written as 4 * Pi(t) - 4 * P2(t)

P4(t) = 1 + 7t can be written as Pi(t) + 7 * P2(t)

Ps(t) = 1 + 2t + 7t^2 can be written as Pi(t) + 2t * P2(t) + 7 * P2(t)^2

From this, we can see that all the polynomials in S can be written as a linear combination of Pi(t) and P2(t). So, the span of Pi(t) and P2(t) equals H. Hence, { Pi(t), P2(t) } is a basis for the subspace H.

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A right Riemann sum has the formula  A=∑ni=1Δxf(xi) A = ∑ i = 1 n Δ x f ( x i ) where x is the width of each of the n rectangles and f(xi) is the height.

A specific method of approximating an integral with a finite sum in mathematics is known as a Riemann sum. Riemann is the name of a German mathematician who lived in the 19th century. Approximating the area of functions or lines in graphs, as well as the length of curves and other approximations, is a highly typical application. The picked points in each subinterval of the partition are all in the upper Riemann sum, given an interval partition. The interval is often separated into subintervals of equal size.

Riemann  sum formula is A=∑f(xi)Δx A = ∑ f ( x i ) Δ x ,

where A is the curve's area under the evaluable interval,

f(xi) f ( x i ) is each rectangle's height (or the average of the two heights in the case of a trapezoid)

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On solving the provided question, we can say that By addition, people could be at a game = 42,500 - 275 = 42225

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.

By addition,

Stadium capacity = 42,500

General admission seating = 31,750

Reserved seating = 10,475

42,500-( 31,750 + 10,475 ) =42,500- 42225 = 275

people could be at a game = 42,500 - 275 = 42225

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Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.

Every point in the plane of a circle is equally separated from the center and is a closed, two-dimensional object. Each line tracing the circle contributes to the formation of the line of reflection symmetry. Additionally, each angle has rotational symmetry around the center.

Here,

calculation

The formula for arc length is (/2) 2r.

because of length of an arc equals r.

16 = 4θ

=> θ = 4

4r is the length of an arc.

Four times the radius, the subtended arc is longer.

Angle A is subtended by an arc if its length and radius are equal.

=> θ = 16 /4

=>4 rad

Therefore , the circumference of the circle is 4 centimeters, while the length of the subtended arc is 16 centimeters.

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As a result, the East Pacific Rise rate of change extends by around 6 to 16 centimeters annually, compared to the Mid-Atlantic Ridge's 2 to 5 cm.

The relation of one quantity's changes to someone else's change is known as the rate of change. The rate of change in linear relationships is constant. Here are a few instances with varying rates: Every week, forty rats are added to the rat population. When an automobile is moving at 68 km, its distance traveled grows by 68 mph over time. When calculating the change in distance for a car employing 27 miles per gallon, the duration is multiplied x 27 mile for each gallon.

Here,

Using the data in the inquiry

Conclusion: As a result, we may say also that East Pacific Rise is expanding more quickly than the Mid-Atlantic Ridge.

The East Pacific Rise expands roughly 6 to 16 centimeters year, whereas the Mid-Atlantic Ridge distributes about 2 to 5 centimeters annually.

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In the question given, only option a, c and e are correct because the bars in a histogram do not touch, the bars also represent the frequency and the histogram can have a horizontal axis with different intervals

A histogram is a graphical representation of data that uses bars of different heights to show the frequency of a particular variable. It is used to show the distribution of numerical data.

In the given question, we can simply select the right choices and eliminate the wrong ones.

In option A, the bars in a histogram don't touch. This is true because in histogram, the bars do not touch.

In option B, this is false because we can't find the exact value of the median with only the histogram.

In option C, this is true because the bars represents the frequency of the data.

In option d, this is false as the histogram must not go up the same interval along the horizontal axis.

In option e, this is true because the histogram can have a horizontal axis with different intervals.

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The complement of A∪B is A′∩B ′.

A set of components in the universal set that are not a part of the initial set is known as the complement of a set in mathematics. Discover what a subset and its complement are, how to calculate a subset's complement, and the proper notation to use when writing a subset and its complement.

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B) ′=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕ

A′∩B′=(U−A)n(U−B)

={3,4,6}n{1,2,7}=ϕ

Hence ( A∪B)′=A′∩B ′.

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Answer:

Let a, b and c be integers with a≠0 and b≠0, and let d=gcd(a,b). If d does not divide c, then the linear Diophantine equation ax+by=c has no solution.

Therefore ,the mean of given data is 36, Simply dividing the total number of values by the sum of all the values in the data set yields it.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Here,

Given :

=> Mean=summation of fxi

=> Mean = 3600 /100 = 36

Therefore , the solution of the given problem of mean is comes out to be

Mean  = 36.

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