Differentiate the given function.
y=x² √4x-3

Answer:

Perimeter = 8π cm

Area = (32π - 64) cm²

Step-by-step explanation:

ABCD is a square.

Therefore:

The perimeter of the shaded part is the sum of two congruent quarter circles, i.e. half the length of the circumference.

The arcs AC are quarter circles of a circle with radius 8 cm.

Therefore the perimeter of the shaded area is:

[tex]\implies \sf Perimeter=Half\;circumference=\dfrac{1}{2} \cdot 2\pi r=\pi r=8\pi\;cm[/tex]

To find the area of the shaded area, subtract the two unshaded areas from the area of the square.

As the two unshaded areas are congruent we only need to find the area of one unshaded area.

The area of one unshaded area is the area of the square minus the area of the sector ADC (which is a quarter of a circle with radius 8 cm).

[tex]\begin{aligned}\implies \textsf{Area of one unshaded area}&=\textsf{Area of square}-\textsf{Area of $\frac{1}{4}$ circle}\\&=64-\dfrac{1}{4} \pi r^2\\&=64-\dfrac{1}{4} \pi \cdot 8^2\\&=64-\dfrac{1}{4} \pi \cdot 64\\&=(64-16 \pi)\; \sf cm^2\end{aligned}[/tex]

Now we have found the area of one unshaded area, to calculate the area of the shaded area simply subtract two unshaded areas from the area of the square:

[tex]\begin{aligned}\implies \textsf{Shaded area}&=64-2(64-16\pi)\\&=64-128+32\pi\\&=(32\pi-64)\; \sf cm^2 \end{aligned}[/tex]

The conceptual schema and the E-R diagram are attached.

(i) Before making the E-R diagram we discuss the entity relational model for the given problem. So the E-R diagram is the graphical representation of different entities and attributes.

Assumptions for the given problem:

(i) University: a university has its name, address, email id, and mobile number

the university gives admission to students and also university and different departments.

(ii) Student: a student has attributes name, contact number, and social security number as the primary number, address, student number, birth date has its name, department, sex, class, department, and degree program.

(iii) Department: the department has its name, department code, office number, phone

(iv) Courses: each course has its name, description, course number, number of semester hours, level, and offering department.

(v) Section: section has an instructor, semester, year, course, section number

(vi) Grade report: a grade report contain a student section, letter grade, and numeric grade

To learn more about the E-R diagram:

https://brainly.com/question/13266919

#SPJ4

An absolute maximum point is where the function reaches its highest value.

A function may have more than one location (x values) or point (ordered pairs) where these values occur, but there can be only one absolute minimum value and one absolute maximum value (in a given closed interval).

A point where the function achieves its highest value is known as an absolute maximum point. Similar to this, an absolute minimum point is the location at which the function's maximum value is obtained.

Minimum refers to the bare minimum that can be done. For instance, if anything requires seven dollars as the minimum payment, you cannot make a payment of six or less (you must pay at least seven). More than the bare minimum is acceptable, but not less. Maximum refers to the greatest quantity of anything.

Therefore, the correct answer is option C) (3, h(3)) is neither an absolute maximum nor an absolute minimum.

The complete question is:

Suppose that h(x) is a continuous function and is defined for all x greater than or equal to 1. You are given that h(x) has critical points at x = 1, x = 3, and x = 5. If h'(x) is negative on the interval 1 < x < 3, positive on the interval 3 < x < 5, and positive on the interval x > 5, what can be said about the point (3, h(3))?

A) (3, h(3)) is an absolute maximum.

B) (3, h(3)) is an absolute minimum.

C) (3, h(3)) is neither an absolute maximum nor an absolute minimum.

d) Nothing can be determined about the point (3, h(3)).

To learn more about absolute maximum refer to:

https://brainly.com/question/29178335

#SPJ4

Answer: 14 boys & 28 girls

Step-by-step explanation:

the number of girls= 2x

the number of boys= x

now create an algebraic equation:

x + 2x = 42

     3x = 42

        x = 14 (boys)

multiply 14 by 2 as the number of girls is two times the number of boys.

14 x 2 = 28 girls

Step-by-step explanation:

We can prove without use of calculator.

Use exponent product rule:

[tex]a^{n+m} = a^{n}*a^{m}[/tex]

Rewrite with exponent power rule:

[tex](9*9*9*9)-(3^{2}*3^{2}*3^{2}*3)[/tex]

Since [tex]3^{2}=9[/tex], we can eliminate 3 pairs via subtraction, leaving us with:

[tex]9-3=6[/tex]

6 is divisible by 6.

Easy without calculator :)

Hope this helps.

Width of the rectangle is 14/3 feet.

Rectangle is a two dimensional figure which has four sides and four angles and all the angles are right angles.

Area of a rectangle = Length × Width

Length = 3/7 feet

Area = 2 feet²

Substituting in the equation for the area,

2 = 3/7 × Width

Width = (2 × 7) / 3

          = 14/3 feet

Hence the measure of width of the rectangle is 14/3 feet.

Learn more about Rectangle here :

https://brainly.com/question/29123947

#SPJ1

y = 30 ( 0.95 ) t y=30(0.95)^t y=30(0.95)t is an exponential decay function. Because 0.95 < 1 0.95<1 0.95<1. Therefore, 0.95 0.95 0.95 is the decay factor 1 − r 1-r 1−r.

What is meant by function ?

To learn more about function refer to

brainly.com/question/22340031

#SPJ1

Answer:

9/-7

Step-by-step explanation:

the reason is all you have to do is reverse the fraction

Answer:

-9/7

Step-by-step explanation:

The multiplicative inverse of -7/9 is_____?

-7/9 × (- 9/7) = 1

Part A: The path of the ball in relation to the curved path of the thrower

Part A: The path the ball takes is perpendicular to the hand, bat, or feet  at the point of last contact

Part A:

A real-world example of tangents is the direction of a ball immediately after it is released and the circular path of the motion, that provides the force input that is given to the ball to cause it to move in the required direction

The tangent is the path the ball takes immediately after it is moving without contact with the bat, hand, or feet that causes it to move.

The circular path is the motion of the hand, leg, bat, or feet that makes before the ball is released.

The radius is the hand, leg, or bat that rotates in a circular path, so as to move the ball

Part B:

The radius, such as the leg kicking a ball is perpendicular to the tangent which is the path of the ball because a kick sends the ball into the air, the orientation of the leg at the point the ball leaves is perpendicular to the angle of elevation with which the ball is launched.

To know more about Tangent:

https://brainly.com/question/23506113

#SPJ4

The mathematical sentence can be written as the equation below,

k + t = 11

Here we want to write the the mathematical sentence below:

"The sum of a number k and t is 11"

As an algebraic equation, so let's analyze each part of the mathematical sentence.

"sum" refers to an addition, in this case between two numbers represented by k and t, then we can write:

k + t

And that is equal to 11, then the equation will just be:

k + t = 11

Learn more about writing equations by reading:

https://brainly.com/question/18831322

#SPJ1

The linear combination of the general solution of system of equations is.

[tex]X=(7,-3,0)+S1(-2,0,1)\\[/tex].

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution.

A linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results.

Write vector form of the equations, then the vector with variable can expressed as a linear combination of vectors on right sides.

[tex](x1,x2,x3)=(7-2S1,-3,S1)\\=(7,-3,0)+(-2S1,0,S1)\\\\=(7,-3,0)+S1(-2,0,1)[/tex]

So, the linear combination of vectors is.

[tex]X=(7,-3,0)+S1(-2,0,1)\\[/tex]

The complete question is,

the general solution to a linear system is given. express this solution as a linear combination of vectors.

x1=7-2S1

X2=-3

X3=S1.

learn more about linear combination.

https://brainly.com/question/29551145

#SPJ4

Answer:

Jelly bean is 8 pound

Brach's variety is 4 pound

Step-by-step explanation:

jelly belly = x

brach's variety = y

5.99x + 3.99y = 63.88 _______(1)

x = 2y ______(2)

5.99x + 3.99y = 63.88

5.99(2y) + 3.99y = 63.88

11.98y + 3.99y = 63.88

15.97y = 63.88

15.97y/15.97 = 63.88/15.97

y = 4

Substitute y = 4 into equ 2

x = 2y

x = 2(4)

x = 8

Therefore, Steven bought 8 lb of jellybean and 4 lb of brach variety

The equivalent way to write the expression is 12x-15. The solution has been obtained by simplifying the expression.

What is simplified expression?

Simplified expression is that expression which does not contains any like terms. When in an expression, all the like terms are combined and all of the specified brackets are solved, then only unlike terms are left in the simplified expression which cannot be further reduced.

We are given 3(4x-5).

There are no like terms in the given expression.

Therefore, as the next step, we  need to solve the bracket for simplifying the expression.

Thus, we obtain

⇒ 3*4x - 5*3

⇒ 12x -15

Hence, the equivalent way to write the given expression is 12x-15.

Learn more about simplified expression from the given link

https://brainly.com/question/13742517

#SPJ1

Option A is correct i.e., Yes, the statement is an exponential function because the population decreases daily by a proportional rate.

Exponents in mathematics are usually defined as when a number or an expression is given a specific power. The number to which the power is assigned is multiplied power times itself to get the final value. It is depicted by raised symbol written beside the number or expression.

It is written as a∧b where a is the base and b is the power and is called b to the base a or a raised to bth power. An example of the same can be 2∧3= 2x2x2=8, [tex]a^{3}[/tex]=axaxa, etc.

There are some properties of exponents like

To know more about exponents visit

https://brainly.com/question/25263760

#SPJ4

Answer:

9

Step-by-step explanation:

parenthesis

exponents

multiply

división

add

Subtract

do it in this order and it makes it 10 times easier

The scientific method is a systematic set of method that scientists follow to gain information. we will explore how the scientific method is used in the study of nutrition.

To make the things simple, you might want to think of the scientific method as a pro way to ask questions and find answers. With this in mind, it makes sense that the stride of the scientific method starts when researchers ask questions.

For example, a research scientist might awe whether people who eat an apple a day visit their family doctor hardly times a year than those who do not eat apples.

The scientific method is a nice tool for analyzing nutrition. It has been used to set nutrition advice, understand how nutrients support health and learn how nutrition supports athletic account.

To know more about Nutrition:

https://brainly.com/question/10685158

#SPJ4

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 19.37}}{\left( \cfrac{15}{100} \right)19.37} ~~ \approx ~~ 2.91[/tex]

To determine how much effort the gas undergoes as it changes from its original condition to its final one, Nora and Bob utilize the area underneath the line separating the two states and the first rule of thermodynamics.

When a gas changes from its initial condition to its final state, Nora and Bob explain how to compute the work that is done. They talk about compressing gas, thus something is being done to the gas.

You suggest using the area under the line separating the final and initial states to calculate the work done as well as the application of the first equation of thermodynamics, q=w.

To learn more about the work done at

https://brainly.com/question/13662169?referrer=searchResults

#SPJ4

The fixed point of the function f(x) = x^2 + 1 is c = 0.

f(x) = x^2 + 1

c = 0

To find the fixed point of the function f, we can set the equation f(x) = x^2 + 1 equal to x, since the fixed point is when f(x) is equal to x.

Therefore, we can solve for x by setting x^2 + 1 = x. Re-arranging the equation, we get x^2 - x + 1 = 0.

Using the quadratic formula, x = (-(-1) ± √(1 - 4(1)(1))/(2(1))

Simplifying this expression, x = (-1 ± √3)/2.

Since we are looking for a real number, we can eliminate the negative solution and set x = (1 + √3)/2.

Therefore, the fixed point of the function f is c = 0.

The fixed point of the function f(x) = x^2 + 1 is c = 0.

Learn more about point here

https://brainly.com/question/28224145

#SPJ4

Step-by-step explanation:

[tex]x = \frac{13}{8} \\ y = \frac{ - 7}{8} \\ 2y + x = - \frac{14}{8} + \frac{13}{8} = - \frac{1}{8} [/tex]

Answer:

-1/8

Step-by-step explanation:

x + y = 3/4

x -y = 5/2

2x = 13/4       3/4 + 5/2 = 3/4 + 10/4 = 13/4  Next divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{\frac{13}{4} }{2}[/tex]      [tex]\frac{13}{4}[/tex] ÷[tex]\frac{2}{1}[/tex] = [tex]\frac{13}{4}[/tex] x [tex]\frac{1}{2}[/tex] = [tex]\frac{13}{8}[/tex]

x = [tex]\frac{13}{8}[/tex]

plug in 13/8 for x in either of the two original equations.

x + y = 3/4

13/8 + y = 3/4  Subtract 13/8 from both sides

y = -7/8        3/4 - 13/8 = 6/8 - 13/8 = -7/8

Check:

substitute x = 13/8 and y = -7/8 back into the original two equations to see if the equations ae true

x + y = 34

13/8 - 7/8 = 3/4

6/8 = 3/4

3/4 = 3/4  Checks

x - y = 5/2

13/8 - (-7/8) = 5/2

13/8 + 7/8 = 5/2

20/8 = 5/2

5/2 = 5/2 Checks

Find the value of 2y + x

2(-7/8) + 13/8

-14/8 + 13/8

-1/8

S=72, P=108, Q=144, and R=36 are the degree measures for each quadrilateral angel.

Since the sum of all angles is 360.

∠S+∠P+∠Q+∠R=360

2y+3y+4y+y=360

10y=360

y=36.

Hence, we get ∠S=72, ∠P=108, ∠Q=144 and ∠R=36.

A polygon with four sides, four vertices, and four angles is called a closed quadrilateral. It is made by joining four non-collinear points together. In all cases, the inner angles of quadrilaterals add up to 360 degrees.

The fact that the sum of the interior angles is always equal to 360 degrees is a property shared by all of the above four-sided shapes. Each interior angle of a regular quadrilateral, such as a square, will be equal to: 90 degrees is 360/4.

They split in two directions. There are both regular and irregular quadrilaterals. The diagonals of a regular quadrilateral must cross each other and have four equal sides and angles. The only quadrilateral that meets all of these requirements is square

Learn more about Interior angles:

brainly.com/question/16054741

#SPJ1

Answer:

69

Step-by-step explanation:

Graphical techniques are widely used to assess whether the data support the fractionation of a single source or the mixture of two putative sources.

For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.

To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.

We generate a graph for each equation in order to solve systems of equations or simultaneous equations graphically. Then, we search for the intersection of the two graphs. The system of equations would have a solution at the coordinates of the point of intersection.

Let x be the number of hats and y be the number of pairs of sunglasses.

The constraints exists:

2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)

y <= 100 (because the supplier can only provide 100 pairs of sunglasses)

x + y >= 210 (because you want to sell at least 210 items in total)

x, y >= 0 (because the number of items sold cannot be negative)

Lose in every hat is $3 and in Pair of Sunglasses is $ 2

Total loss in promotion or cost of promotion is

3x + 2y

For least purchase,

x + y = 210

⇒ x + x/2 = 210

⇒3x/2 = 210

⇒ x =140

y = 140/2 = 70

So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

To learn more about Graphic method refer to:

brainly.com/question/12931624

#SPJ1

For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

What is meant by total?

Let x be the number of hats and y be the number of pairs of sunglasses.

The constraints exists:

2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)

y <= 100 (because the supplier can only provide 100 pairs of sunglasses)

x + y >= 210 (because you want to sell at least 210 items in total)

x, y >= 0 (because the number of items sold cannot be negative)

Lose in every hat is $3 and in Pair of Sunglasses is $ 2

Total loss in promotion or cost of promotion is

3x + 2y

For least purchase,

x + y = 210

⇒ x + x/2 = 210

⇒3x/2 = 210

⇒ x =140

y = 140/2 = 70

So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

To learn more about total refer to

https://brainly.com/question/25109150

#SPJ1

The quantity of chlorine that has a 60% concentration is 310 ml.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that,  60% chlorine solution must be mixed with an 18% chlorine solution to produce 542.5 mL of 42% solution

Let "x" be the quantity of chlorine that has a 60% concentration

So, the quantity of chlorine that has 18% concentration = 542.5 - x

thus, As per the given data expression formed as given below:

0.6 * x + 0.18 (542.5 - x) = 542.5 * 0.42

0.6x - 0.18x + 0.18 *542.5 = 542.5 *0.42

0.42x = 130.20

x = 310

therefore, the quantity of chlorine that has a 60% concentration is 310 ml.

Learn more about expression here:

https://brainly.com/question/23246712

#SPJ1

Picking a king from a deck of cards, swapping it out for a queen, then continuing. These occurrences would constitute Dependent events.

'What is dependent probability?'

A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.

A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.

Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.

know more about variables here

https://brainly.com/question/17344045#

#SPJ4

The c1 and c2 are arbitrary constants.

What is the arbitrary constant?

y=mx+c is the general equation of a straight line in two dimensions, where m and c are arbitrary constants that represent the gradient of the line and the y-intercept. And ∫2x dx=x 2+c where c is an arbitrary constant whose value can be determined by a boundary condition.

y = c1ekx + c2e-kx is a general solution to the homogeneous linear differential equation y' + ky = 0. This means that any specific solution to this equation can be obtained by plugging in appropriate values for c1 and c2.

The general solution y = c1ekx + c2e-kx is a linear combination of ekx and e-kx.

The differential equation y' + ky = 0 is a first-order, linear differential equation.

The general solution y = c1ekx + c2e-kx is valid for all values of x.

The general solution y = c1ekx + c2e-kx is a sum of two linearly independent solutions to the differential equation.

The general solution y = c1ekx + c2e-kx is a particular solution if c1 and c2 are determined by initial or boundary conditions.

The general solution y = c1ekx + c2e-kx is a general solution if c1 and c2 are arbitrary constants.

The general solution y = c1ekx + c2e-kx is a unique solution if c1 and c2 are determined by initial or boundary conditions, otherwise, it is not unique.

The general solution y = c1ekx + c2e-kx is a solution to the homogeneous differential equation y' + ky = 0, it does not contain any particular solution for the non-homogeneous differential equation.

Hence,  The c1 and c2 are arbitrary constants.

To learn more about arbitrary constants visit,

https://brainly.com/question/13243284

#SPJ4

Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb.

R and S should be two equivalence relations on X.

I want to demonstrate that the relationship RS is equivalent, but I am unable to demonstrate that it is transitive and reflexive.

regarding transitivity

There are random x and y with (x,y)RS, z with (x,z)R and (z,y)S, and what else?

Do I need to use R=S=S=R somewhere else?

As opposed to (x,y)R, I use the notation xRy. For some a, the term "xRSy" specifically refers to "xRaSy." Additionally, writing (xRy and yRz) is more convenient than writing xRySz. I would generally suggest drawing these relationships as graphs, with the vertices representing the points and the edges denoting the relationship.

assumption R=S=R.

Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb. Then, as R,S are equivalence relations, xRcSz follows from xRaRcSbSz, and xRSz follows.

I'm sure you can now independently demonstrate reflexivity.

To Learn more About  SoR=RoS Refer To:

https://brainly.com/question/25421984

#SPJ1