The graph of a function f is shown below.
Find one value of x for which f(x) = 1 and find f(-1)

With help of integration, The volume of the  solid that results when the region bounded by y=√x , y=0, and x=16 is revolved about the line x=16 will be 42.66 cubic unit.

What exactly is integration?

The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).

Integral Fundamental

A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.

From a to b, use ∫f(x)dx

indefinite integral

Integrals are defined without upper and lower limits. It looks like this:

A indefinite Integral is written as:

∫f(x)dx = F(x) + C

Where C might be any constant and the function f(x) is referred to as the integrand.

Now,

for volume of the   solid that results when the region bounded by y=√x , y=0, and x=16 is revolved about the line x=16.

volume= ∫√x dx for x=0 to 16

=x*√x/3/2

=64*2/3

=128/3

=42.66 cubic unit

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Answer:

(3x + 2y) (3x - 2y)

Step-by-step explanation:

a² - b² = (a + b) (a - b)

where a = 3x and b = 2y

The expression for (h·g)(x) is 4x²+17.8x+19.8.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x)=9+4x and h(x)=x+ [tex]2\frac{1}{5}[/tex].

Now, (h·g)(x)=h(x)×g(x)

= (x+ [tex]2\frac{1}{5}[/tex])×(9+4x)

= (x+11/5)×(9+4x)

= 9x+99/5+4x²+44x/5

= 9x+19.8+4x²+8.8x

= 4x²+17.8x+19.8

Therefore, the expression for (h·g)(x) is 4x²+17.8x+19.8.

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The requried measure of the angle ∠2 = ∠5 = ∠15 = 125, ∠11 = 88, ∠3 = ∠9 = ∠13 =  102°, ∠4 = ∠14 = 78°, ∠7 = 37, ∠8 = 41, ∠1 = ∠6 = ∠10 = 16 = 55°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
from figure,
∠2 = ∠5 = ∠11 + ∠12 = ∠15 = 125

From the above expression,
∠2 = ∠11 + 37°
125 - 37 = ∠11
∠11 = 88°

Similarly.
∠3 = ∠9 = ∠13 = ∠18 = 102°
∠4 = ∠7+∠8 = ∠14 = ∠17= 78°
∠1 = ∠6 = ∠10 = 16 = 55°

Thus, the requried measure of the angle ∠2 = ∠5 = ∠15 = 125, ∠11 = 88, ∠3 = ∠9 = ∠13 =  102°, ∠4 = ∠14 = 78°, ∠7 = 37, ∠8 = 41, ∠1 = ∠6 = ∠10 = 16 = 55°.

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The endpoints of an edge are its end-vertices. When two vertices are endpoints of the same edge, they are said to be neighbouring.

The limit of the normalised even iterations of a linear transformation can be used to obtain the similarity matrix. The square matrix in the particular case when G A=G B=G contains the similarity score between the vertices I and j of G as its I j)-th element.

The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.

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The fraction does the third girl gets is 3c - b/3c

A fraction can be defined as the part of a whole number or element.

The different types of fraction are;

From the information given, we have that;

3 girls shares an amount of money

The eldest = b/3x

The youngest = b/6c

This is represented as;

1 - b/3c + b/6c

Add the fractions

1 - 2b - b /6c

add the values

1 - 3b/6c

1 - b/3c

3c - b/3c

Hence, the expression is 3c - b/3c

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The statement is true. Matrix multiplication is not commutative, so the product of the transposes of the matrices must be applied in the same order as the initial product, not in a reverse order.

The statement that the transpose of a product of matrices equals the product of their transposes in the same order is true. Matrix multiplication is not commutative, which means that the order in which the matrices are multiplied matters. That is, for two matrices A and B, AB does not necessarily equal BA. Thus, when taking the transpose of a product of matrices, the order in which the transposes of the matrices are multiplied must be the same as the order in which the original matrices were multiplied. Otherwise, the result will not be the same. For example, if two matrices A and B are multiplied to give AB, the transpose of AB will be (AB)^T = B^T A^T, not A^T B^T. This is why the product of the transposes must be applied in the same order as the initial product.

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the measurement of the ∠R will be 101 degrees.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.

Given TPRS is a parallelogram. in that ∠T = (4x +1) and ∠S = (3x +4)°

Since in a parallelogram, opposite angles are equal Thus,

∠P = ∠S = 3x + 4

∠R = ∠T = 4x +1

Since we know the sum of all angles of a quadrilateral is 360°

3x +4 + 4x +1 + 3x +4 + 4x +1 = 360

14x + 10 = 360

14x = 350

x = 350/14

x = 25

Thus,

∠R = 4x +1

∠R = 4 *25 + 1

∠R = 101°

therefore, the measurement of the ∠R will be 101 degrees.

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Drone 1 is traveling faster than Drone 2.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The table and equation below show the proportional relationship between time, in seconds, x, and distance traveled, in feet, y, for two drones.

For drone 1;

The equation is,

⇒ y = 6x

For drone 2;

x = 8, 10, 13

y = 24, 30, 39

Now, For drone 1;

The distance in 8 seconds is,

⇒ y = 6x

⇒ y = 6 × 8

⇒ y = 48

The distance in 10 seconds is,

⇒ y = 6x

⇒ y = 6 × 10

⇒ y = 60

Thus, Drone 1 is traveling faster than Drone 2.

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The final value of the investment is $689.10. Fill the table accordingly.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

First year

Interest earned = 9/100 * $580 = $52.20

Second year

Balance + Interest = $580 + $52.20

Total balance = $632.20   (Note: Total balance = Balance + Interest )

Interest earned = 9/100 *  $632.20 = $56.90

Third year

Balance + Interest = $632.20 + $56.90

Total balance = $689.10

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(a) f(x) =  [tex]log_2(x)[/tex] is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2

(e) v(t) = [tex]5^t[/tex]is an exponential function

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is a trigonometric function.

(a) f(x) = [tex]log_2(x)[/tex] is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex] is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex] is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = [tex]5^t[/tex] is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex] is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  [tex]log_2(x)[/tex]    

(b) g(x) = ∜x    

(c) h(x) = [tex]2x^3/(1 - x^2)[/tex]    

(d) u(t) = 1 - 1.1t + [tex]2.54t^2[/tex]                    

(e) v(t) = [tex]5^t[/tex]    

(f) w(θ) = sin θ [tex]cos^{2}\theta[/tex]

From the two plans for a set price the second graph in this issue is the right one.

The following is the definition of a linear function's slope and intercept:

y = mx + b.

where:

The rate of change is represented by the slope m.

The starting quantity is represented by the intercept b.

We have it for the plan with the fixed price:

Compared to the other plan, the slope is higher.

There is no intercept.

As a result, it is less expensive for fewer trips.

We have the following for the plan with the set price plus the fee:

Compared to the other plan, the slope is smaller.

There is an intercept that exceeds zero.

As a result, paying for more visits results in lower expenditures.

Hence, the second graph in this issue is the right one.

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Answer:

Step-by-step explanation:

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Answer:

The first one is 3/5 & The second one is 3/8 & The the third one is 1/8

Step-by-step explanation:

Hope this helps :)

Answer:

60

Step-by-step explanation:

15x3=45

5x3=15

15+45=60

Alexander's white paint will be more lighter.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that in art class students are mixing black and white paint to make gray paint. Allison mixes 1 cup of black paint and 2 cups of white paint. Alexander mixes 6 cups of black paint and 11 cups of white paint.

We will compare the percent of white paint in a mixture.

We can write -

Therefore, Alexander's white paint will be more lighter.

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Answer:

Step-by-step explanation:

I am not sure what you mean with that question but a short definition of bullying is:

Bullying can result in physical injury, social and emotional distress, self-harm, and even death. It also increases the risk for depression, anxiety, sleep difficulties, lower academic achievement, and dropping out of school.

The rule for the arithmetic sequence in this problem is defined as follows:

[tex]a_n = 4.5 - 0.625(n - 1)[/tex]

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The general rule of an arithmetic sequence is given as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

The common ratio for the sequence is given as follows:

d = 3.25 - 3.875 = 3.875 - 4.5 = -0.625.

The first term of the sequence is given as follows:

[tex]a_1 = 4.5[/tex]

Hence the rule is defined as follows:

[tex]a_n = 4.5 - 0.625(n - 1)[/tex]

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The cardinal number of G = 0 for the given set G = {x|x ∈ N and x is a negative}.

A set is defined as a group of objects in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent parts can be included in anything.

The set is given in the question, as follows:

G = {x|x ∈ N and x is a negative}

We have to determine the cardinal number of set G = {x|x ∈ N and x is a negative}

Cardinal numbers, also known as Cardinals of a Set, are the numbers used to count the number of elements in a Set.

Simply expressed, the cardinal number of a set equals the number of items in a set.

Let A = {a, b, c, d}  be a set then Cardinal number of A is 4

Given G = {x|x ∈ N and x is a negative}

Here, x belongs to N, and a negative number

Since Natural Number (N) = 1, 2, 3, 4 ...

There is no negative value that corresponds to N.

Thus, G = { } or G is an empty set.

Hence, the cardinal number of G = 0

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The question seems incomplete, the complete question would be as:

Find the cardinal number of set G = {x|x ∈ N and x is a negative}

is really "x", which oddly enough is the 100%, but we also know that 0.40% of "x" is 29, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 29& 0.40 \end{array} \implies \cfrac{x}{29}~~=~~\cfrac{100}{0.40}\implies \cfrac{x}{29}=\cfrac{100}{~~ \frac{ 40}{100 } ~~}\implies \cfrac{x}{29}=\cfrac{10000}{40} \\\\\\ \cfrac{x}{29}=250\implies x=7250[/tex]

Answer: When the domain of the non-invertible function f(x)=(x+5)^2−8 is [−5,∞), the inverse of the function is not defined, and the domain of the inverse function is empty.

Step-by-step explanation:

The logistic model for the population P is P = 75x = 400.

The number of deer population after 10 years is 1150.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Deer:

Population capacity = 2500

Initial population = 400

Population after 4 years = 700

Now,

We can make two ordered pairs:

(0, 400) and (4, 700)

Now,

We can write an equation as,

P = mx + c

m = (700 - 400) / (4 - 0) = 300/4 = 75

And,

(0, 400) = (x, y)

400 = 75 x 0 + c

c = 400

So,

P = 75x + 400

This is the equation for the number of deers after x years.

Now,

The number of deers after 10 years.

x = 10

P = 75 x 10 + 400

P = 750 + 400

P = 1150

Thus,

The number of deer after 10 years is 1150.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2545.10\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]2545.10 = 2000\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4} \implies \cfrac{2545.10}{2000}=\left( 1+\cfrac{r}{100} \right)^4 \\\\\\ \cfrac{2545.10}{2000}=\left( \cfrac{100+r}{100} \right)^4\implies \sqrt[4]{\cfrac{2545.10}{2000}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[4]{\cfrac{2545.10}{2000}}=100+r\implies 100\sqrt[4]{\cfrac{2545.10}{2000}}-100=r\implies \boxed{6.2\approx r}[/tex]

Answer:

y=-3x+7

its the same thing  

Step-by-step explanation:

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

when pulling one card out of 52 cards, the totally possible cases for the result are 52.

now, all we need to do is "counting" or calculating the desired cases for each problem.

a 3 or a heart is pulled.

it is important to really read this carefully : 3 OR a heart. not 3 and a heart (that would ask for the probability to pull the 3 of hearts card, as no other card would satisfy the criteria).

we have 13 cards of heart.

and we have 4 cards of the value 3. but one of them is already included in the 13 cards of heart.

so, we need to add only 3 to these 13 and get 16 desired cards.

the probability is therefore

16/52 = 4/13 = 0.307692308... ≈ 0.308

a face card OR a club is pulled.

face cards are Jack, Queen and King (the ones with faces on the cards). so, 3 per suit, 4 suits = 12 cards.

we have 13 cards of club.

3 of these cards are already in the group of face cards, so we need to add only 10 to to this group for the desired cases. and the probability is

22/52 = 11/26 = 0.423076923... ≈ 0.423

a face card AND a heart is pulled.

we have 13 cards of heart.

and now it is AND to be a face card (not OR like in the previous question).

there are only 3 face cards of heart. the probability is

3/52 = 0.057692308... ≈ 0.058

Answer:

C(t) = 0.50 * t + 2.50

Step-by-step explanation:

The function C(t) to represent the cost of a taxicab ride can be written as:

C(t) = 2.50 + 0.50 * t

where t is the distance traveled in tenths of a mile.

The slope of the graph of this function is 0.50, which represents the cost per tenth of a mile.

The y-intercept of the graph of this function is 2.50, which represents the fixed fee that must be paid regardless of the distance traveled.

So, the equation of the graph of this function is:

C(t) = 0.50 * t + 2.50

The required  sum of the first n odd numbers is equal to n².

The first few odd numbers are 1, 3, 5, 7, 9, 11, and so on. When we add up the first few of these numbers, we get the following sums:

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

We can see that the nth odd number is equal to 2n - 1. And the sum of the first n odd numbers is equal to n². This can be verified geometrically by considering a square with sides of length n.

The sum of the first n odd numbers can be thought of as the sum of the diagonal elements of the square, which forms a square of length n.

Thus, the sum of the first n odd numbers is equal to n².

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Answer:

The cost is 250

Step-by-step explanation:

Let's call the cost of the bench "x". The cost of the garden table is then 3x. The combined cost of the two items is $1000, so we can set up the following equation:

x + 3x = 1000

Combining like terms, we have:

4x = 1000

Dividing both sides by 4, we find:

x = 250

So the cost of the bench is $250.