How would y-x2=5 be written in function notation

The volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 48π

Volume of the Solid:

Volume refers the measure of how much space an object takes up and it is measured by the number of unit cubes it takes to fill up the solid.

Given,

Here we have to use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

xy = 6, x = 0, y = 6, y = 8.

Here we know that,

xy = 6

Then the value of x is obtained as,

=> x = 6/y

Now, the volume of the solid is calculated with the given interval [6,8] as.

=> V = 2π ∫₆⁸ y x (6/y)/dy

=>  2π∫₆⁸ 6/dy

When we differentiate the equation, then we get,

=> 24π[y]₆⁸

=> 24π [8 - 6]

=> 24π [2]

=> 48π

Therefore, the volume of the solid is 48π.

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Answer:

√32

Step-by-step explanation:

c = [tex]\sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]

The values of the addition given will be:

6 + 9 = 15

0 + 9 = 9

2 + 3 = 5

11 + 90876 = 90887

Addition simply means sum. It is one of the basic operations that are used in Mathematics. In this case, the addition of two whole numbers will bring about the total amount of the value combined.

Therefore the addition will be the sum of the numbers. This will be:

6 + 9 will be:

= 6 + 9

= 15

0+9 will be:

= 0 + 9

= 15

2+3 will be:

= 2 + 3

= 5

11+90876 will be:

= 11 + 90876

= 90887

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Podras comprar un total de 8 docenas, y sobrara $1.30

Sabemos que una docena de bananos cuesta $2.65, y queremos ver cuantas docenas se peden comprar con $22.50, para ver esto, debemos tomar el cociente entre la cantidad de dinero que tenemos y el precio de una docena.

Obtendremos:

$22.50/$2.65 = 8.49

Redondenado al proximo numero entero obtenemos 8, es decir, se pueden comprar 8 docenas.

La cantidad que sobra es:

$22.50 - 8*$2.65 = $1.30

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The value of the equation is 2² x A ²

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be D

D = 2 power 8 multiply by A power 5  /  4 power 3 multiply by a power 3​

So , on substituting the values in the equation , we get

D = 2⁸ x A⁵ / 4³ x A³

Now , 2⁸ /  4³ can be simplified as

4³ = 2⁶

So ,

2⁸ /  2⁶ = 2 ⁸⁻⁶

            = 2²

And , A⁵ / A³ can be simplified as

A⁵ / A³ = A⁵⁻³

           = A²

So , the equation becomes ,

D = 2⁸ x A⁵ / 4³ x A³

D = 2² x A²

D = ( 2A )²

Hence , the value of the equation is D = 2² x A²

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Given equation to us is , [tex](m-3)r^2+9r-2=0[/tex] .

The given equation is a quadratic equation and it has two real solutions if it's discriminant is greater than or equal to 0 .

For a quadratic equation in standard form of

[tex]ax ^{2} + bx + c = 0[/tex]

the discriminant is given by b² - 4ac .

On comparing wrt to Standard form, we have ;

Now we have,

[tex]\longrightarrow b^2-4ac \geq 0\\\\\longrightarrow 9^2-4(m-3)(-2)\geq 0\\\\\longrightarrow 81 +8(m-3)\geq 0 \\\\\longrightarrow 81 +8m-24\geq 0 \\\\\longrightarrow 8m \geq 24-81 \\\\\longrightarrow 8m \geq -57 \\\\\longrightarrow \underline{\underline{ m \geq \dfrac{-57}{8}}}[/tex]

Therefore for all values greater than or equal to -57/8 the equation will have a real solution .

And we are done!

The equation (m-3)r² + 9r -2 = 0 will have two real solution for the value of m, greater than or equal to -57/8.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The standard form of equation of power two is ax²+bx+c =0 .

The given equation,

(m-3)r² + 9r -2 = 0

Compare the given equation with standard equation ax²+bx+c =0,

The value of a=m-3, b=9 and c=-2

An equation has two real solutions if a discriminant of the equation is greater than or equal to zero.

⇒D ≥ 0

⇒b²-4ac ≥ 0

Substitute the value of a, b and c,

⇒9² - 4×(m-3)(-2) ≥ 0

⇒81 +8m - 24 ≥ 0

⇒8m ≥ -57

⇒ m ≥ -57/8

For the values of m greater than or equal to -57/8, the equation have two real solutions.

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The number of tiles with the dimensions 3 cm x 3 cm are needed to cover the grid is 4.

Given that, a grid is 6 cm x 6 cm.

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.

Here,

Area of a grid is 6×6 =36 cm²

a) Area of a tile with 1 cm x 1 cm is

1×1 =1 cm²

Number of tiles = 36/1 =36

b) Area of a tile with 2 cm x 2 cm is

2×2 =4 cm²

Number of tiles = 36/4 =9

a) Area of a tile with 3 cm x 3 cm is

3×3 =9 cm²

Number of tiles = 36/9 =4

Therefore, the number of tiles with the dimensions 3 cm x 3 cm are

needed to cover the grid is 4.

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Glens have 110 coins in his entire collection.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Glens coins from Denmark are eleven 11.

These 11 coins are 10% of his entire coins.

We need to find how many coins Glens has.

Let x be the entire collection of Glens coins

10/100x=11

0.1x=11

Divide both sides by 0.1

x=110

Hence, Glens have 110 coins in his entire collection.

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The corresponding probabilities of the random variables x = (0, 1, 2, 3, 4, 5, and 6) are  (0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0)

Since we are dealing with a binomial probability distribution. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . π^r  . q^n-r

Given: n = 4 and π = 0.30, q = 1 - π = 1 - 0.30 = 0.70 and x = (0, 1, 2, 3, 4, 5, 6)

P(x = 0) = 4C0 × 0.3⁰ × 0.7⁴⁻⁰ = 0.2401

P(x = 1) = 4C1 × 0.3¹ × 0.7⁴⁻¹ = 0.4116

P(x = 2) = 4C2 × 0.3² × 0.7⁴⁻² = 0.2646

P(x = 3) = 4C3 × 0.3³ × 0.7⁴⁻³ = 0.0756

P(x = 4) = 4C4 × 0.3⁴ × 0.7⁴⁻⁴ = 0.0081

P(x = 5) = 0

P(x = 6) = 0

Note: P(x = 5) and P(x = 6) are 0 because their x (5 and 6) is greater than the n (4)

Therefore, the probabilities of the random variables x(0, 1, 2, 3, 4, 5, and 6) are  0.2401, 0.4116, 0.2646, 0.0756, 0.0081, 0, and 0 respectively

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a. The hypothesis to be tested are given as follows:

b. The p-value is of: 0.0047.

c. The decision is of: Reject the null hypothesis.

d. The conclusion is of: There is enough evidence to conclude that the mean rate is less for people who exercise regularly.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the heart rate is less, than is, if the difference is not negative, hence:

[tex]H_0: \mu_d \leq 0[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the heart rate is less, that is, if the difference is negative, hence:

[tex]H_1: \mu_d > 0[/tex]

The parameters to the p-value are given as follows:

We have a left-tailed test, as we are testing if the mean is less than a value, hence, using a t-distribution calculator, the p-value is of:

0.0047.

Since the p-value is less than the critical value, the decision and the conclusion are given as follows:

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The rate for the balance to triple in 46 years is  2.42% .

$500 is compounded annually for 46 years. No other deposits are made.

The rate needed for the balance to triple in that time can be calculated as follows:

The interest rate as a percent can be calculated as follows:

For the principal to be tripled, the amount will be 500(3) = 1500 dollars

[tex]r = n((\frac{A}{P} )^{\frac{1}{nt} } -1)[/tex]

where

P = 500

A = 1500

n = 1

t = 46 years

r[tex]r = 1((\frac{1500}{500})^{\frac{1}{1(46)} } - 1 )[/tex]

[tex]r = 1((\frac{1500}{500})^{\frac{1}{46} } - 1 )[/tex]

r = 0.0241704

Then convert r to R as a percentage

R = r * 100

R = 0.0241704 * 100

R = 2.42% per year

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The surface area of the figure in square inches will be 17.5 inch².

It is defined as a six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.

It is given that, Rectangular prism with dimensions 0.5 feet by 1.5 feet by 4 inches.

Length(l) = 0.5 ft = 6 inch

Width(w) = 1.5 ft = 18 inches

Height(h) = 4 inches

The surface area of the figure in square inches is found as,

S = 2(lw + lh + wh)

S=2(6×8 + 8×4 +4×6)

A = 17.5 inch²

Thus, the surface area of the figure in square inches will be 17.5 inch².

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The probability that a student chosen at random is in the choir or band or both is 0.911

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In mathematics terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain.

Total number of students in the school = 450

number of students in choir = 110

number of students in band = 240

number of students in both = 60

Probability a student chosen at random is in the choir or band or both is

110/450 + 60/450 + 240/450

= 410/450 which is 0.911

In conclusion, the probability of a student being in music, or band or both is 0.911

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Step-by-step explanation:

Zhang invests $2,600 in two different accounts. The first account paid 11%, the second account paid 5% in interest. At the end of the first year he had earned $220 in interest. How much was in each account?

11% = 0.11

in account 1: $220/0.11 = $2,000

in account 2: $2,600 - $2,000 = $600

$2,000 At 11%

$600 At 5%

The perimeter of the given triangle with given lengths is; 78

The perimeter of a triangle is defined as the sum total of the 3 side lengths of the triangle.

Now, we are given the triangle as QRS.

We are given that;

A is the midpoint of QR

B is the midpoint of RS

C is the midpoint of SQ

Thus;

QA = RA = 10

BR = SB = 15

SQ = 28

Thus;

Perimeter of Triangle = 2(10) + 2(15) + 28 = 78

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Answer: x = -8

Step-by-step explanation:

1. Add 10 to both sides

-3x = 14 + 10

2. Simplify 14 + 10 to 24

-3x = 24

3. Divide both sides by -3

x = [tex]-\frac{24}{3}[/tex]

4. Simplify [tex]\frac{24}{3}[/tex] to 8

x = -8

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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If your cost of money is 6.4 percent, what is the current value of the lease is equal to $820.0054.

In Economics, a lease can be defined as a contractual agreement between a lessor and lessee, which avails the lessee an opportunity to make use of an asset, while making payments in instalment to the lessor for a specific period of time.

Mathematically, the current (present) monetary value of a lease can be calculated by using this formula:

Current value, PV = [Annuity × (1 + r) × [1 - (1 + r)^{-n}]/r]

Where:

Note: r = 0.064/12 = 0.0053333

Substituting the given parameters into the formula, we have;

Current value, PV = [144 × (1 + 0.0053333) × [1 - (1 + 0.0053333)^{-36}]/0.0053333]

Current value, PV = [144 × (1.0053333) × [1 - (1.0053333)^{-36}]/0.0053333]

Current value, PV = [144 × (1.0053333) × [1 - 0.8257290]/0.0053333]

Current value, PV = [144 × (1.0053333) × [0.174271/0.0053333]

Current value, PV = 25.095024 × 32.6760167

Current value, PV = $820.0054.

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Answer:

1,2,3,4,6,8,12,24 sub set

An equation that represents the situation is 780/x and the initial number of participants is 95.

Equation:

An equation is the combination of number, variables and the mathematical operators such as addition, subtraction, multiplication and division etc.

Given,

The chess club plans to fundraise $780, which is to be divided evenly among the members. Initially there are x participants, but then 2 more participants come forward, causing each participant to fundraise $8 less.

Here we need to find the equation that represents the situation and then we have to find the initial number of participants.

According to the given question,

Total amount for fundraise = $780

Number of participants = x

Here we know that the amount is divided evenly among the members.

So, the equation is written as.

=> 780/x

And the other part of the condition is, 2 more participants come forward, causing each participant to fundraise $8,

So, it can be written as,

=> 780 / (x+2)  = 8

=> x + 2 = 780/8

=> x + 2 = 97

=> x = 95

Therefore, there are 95 initial number of participants.

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The number of point on this graph that represent a relative minimum is one, which is point b.

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair (x, y)on a graph.

A relative minimum can be defined as the lowest point or valley point on the graph of a function. Additionally, all of the points that are located to the left and right of the lowest point (valley point) on a graph must be larger than the relative minimum.

By critically observing the graph of function f(x), we can reasonably and logically deduce the following information:

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The algebraic expression of raise t to the 10th power then add the result to 3 is t¹⁰ + 3

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

Given: raise t to the 10th power then add the result to 3

Note: t is the variable here

Let's write algebraic expression now:

raise t to the 10th power => t¹⁰

then add the result to 3 => t¹⁰ + 3

Therefore, the algebraic expression is t¹⁰ + 3

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The correct representation of the solution to the inequality given; –3(2x – 5) < 5(2 – x) are;

It follows from the task content that the correct representation of the inequality given in the task content be determined.

The given inequality can be evaluated for the solution set as follows;

–3 (2x – 5) < 5 (2 – x)

-6x + 15 < 10 - 5x

-6x + 5x < 10 - 15

-x < -5

By dividing both sides by -1; we have;

x > 5.

On this note, the required representation is; An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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The value obtained after solving the expression will be equal to (-1, 1).

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.

Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given in for the mention in the question,

x² = 36

x = ±6

Therefore, the values are -6, and +6.

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Answer:

-35/-7=5

Step-by-step explanation:

Diviser par de nombre négatif alors sa devient positif pareil pour la multiplication

Answer:

Step-by-step explanation:

2x+3x+8-3x-2 = 2x + 6

Answer:

The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.

Step-by-step explanation:

The end behavior of a function is what happens to the value of the function as x approaches negative infinity and as x approaches positive infinity.

Graphing the function is very helpful to visualize the end behavior.

Here, the graph has the shape of a V with the vertex on the x-axis going up in value on both sides forever.

The function here is f(x) = 3|x|.

Let's try a few values for x to get an idea.

We will deal with x approaching positive infinity first.

f(0) = 3|0| = 0

Let's get larger and larger values for x, approaching positive infinity.

f(10) = 3|10| = 30

f(10,000) = 3|10,000| = 30,000

f(1,000,000) = 3|1,000,000| = 3,000,000

As you can see, as x increases, the value of f(x) also increases. As x approaches positive infinity, f(x) also approaches positive infinity.

Now let's look at values of x approaching negative infinity.

f(0) = 3|0| = 0

Let's get smaller and smaller values for x, approaching negative infinity.

f(-10) = 3|-10| = 30

f(-10,000) = 3|-10,000| = 30,000

f(-1,000,000) = 3|-1,000,000| = 3,000,000

As you can see, as x decreases, the value of f(x) increases. As x approaches negative infinity, f(x) approaches positive infinity.

The end behavior of the function is that it approaches positive infinity as x decreases to negative infinity, and it also approaches positive infinity as x approaches positive infinity.

The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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Answer:

x = 3

Step-by-step explanation:

The cement kinds will be listed in order of highest to lowest unit rate of pounds per day: C > A > D > B.

The table shows the rates at which each type is sold. A workday is 8 hours, and each pound of cement sells for 4.50.

Type A cement,

Forty pounds were sold in one day.

unit rate = 40 pounds per day

Type B cement,

6y = 2x, where x is in pounds and y is in hours

Since the workday is 8 hours, so substitute the value of x = 8 and we get

6y = 2(8)

6y = 16

y = 16/6 = 2.67

This means the unit rate = 2.67 pounds per day

Type C cement,

After 3 hours, 45 worth had been sold.

After 8 hours,

The worth had been sold = 8×45/3 = 120

unit rate = 120 pounds per day

Type D cement,

The ratio of days to pounds sold was 2: 60.

So, unit rate = 60/2 = 30 pounds per day

So the types of cement in order from highest to lowest unit rate of pounds per day will be :

C > A > D > B

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