Show that the two-variable function f given by f(x, y) = 2x^2 − xy is
differentiable at any point (a, b). What is the derivative of f at (a, b)?

The estimated force on the projectile when it is traveling at 750 ft/sec is approximately 696.7 lbs.

One possible interpolating polynomial for these data points is a polynomial of degree 3, also known as a cubic polynomial. Using software or a calculator to fit a cubic polynomial to the data points, the resulting equation is:

F(v) = -0.00000016v³ + 0.0004v² - 0.08v + 0.4

To estimate the force on the projectile when it is traveling at 750 ft/sec, we can substitute 750 for v in the equation above:

F(750) = -0.00000016(750³) + 0.0004(750²) - 0.08(750) + 0.4

F(750) ≈ 696.7

The estimated force on the projectile when it is traveling at 750 ft/sec is approximately 696.7 lbs.

Learn more about The Possible Interpolating Polynomial here:

https://brainly.com/question/13427238

#SPJ4

For the given image, the value of iota (i) is -i and 1.  

Thus, the development of complex numbers has given rise to imaginary roots. The sign I which stands for Iota, is used to represent -1. (Imaginary number). In essence, I refers to the imaginary component, often known as the iota. I's value is -1. A square root with a negative value represents an imaginary value. Imaginary numbers can be calculated using any of the standard arithmetic operators. An imaginary number has a negative value when squared.

Complex numbers are expressed using the imaginary unit number, where I is defined as imaginary or unit imaginary. Here, we'll go over the chart and principles for imaginary numbers that are employed in mathematical computations.

The value of iota (i²) = -1

The given expressions can be represented in the following way -

i³ = i² × i = -1 × i = -i

i⁸ = i² × i² × i² × i² = -1 × -1 × -1 × -1 = 1

To learn more about iota(i) from given link

https://brainly.com/question/29369374

#SPJ1

The expression that does not equal the length of one of the pieces in feet is C) 4/20

The expression that show the length of one of the pieces of feet would be the expressions that lead to the solution:

= Length of board cut by David / Number of equal pieces

= 20 / 4

= 5 ft each

Option A mirrors the equation above and so is equal to the length of one of the pieces. Option B also equals the equation above as the signs ÷ and / are both for division.

Option C does not equal the length of one of the pieces as it gives:

= 4 / 20

= 1 / 5 ft

Find out more on expressions at https://brainly.com/question/14655835

#SPJ1

Options for this question are:

A)20/4

B)20 ÷ 4

C)4/20

Answer:

31-17=14

Step-by-step explanation:

When you reverse it it equals the same answer

Answer:

31-14=17

Step-by-step explanation:

When We Reverse It,Will Be it Self.

The value of this constant, by assuming that the pressure at some reference height y₀ is p₀, is p - p₀ = p.g(y₀ - y).

dp = -pg dy

At height y = y₀ and p = p₀

∫dp = ∫-pg dy

⇒p = -pgy + C        Eqn(1)

Where c is the constant of integration

We know that y = y₀ and p = p₀

⇒p₀ = -pgy₀ + C

⇒C = p₀ + pgy₀

Put the value of C in Eqn(1)

⇒p = -pgy + p₀ + pgy₀

⇒p - p₀ = -pgy + pgy₀

⇒p - p₀ = pg(y₀ - y)

To know more about pressure, here

https://brainly.com/question/30244346

#SPJ4

Using expression {River=x(race)} River's length is 7.38 times the race's length, approximately.

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

We know that

The river is 310 miles long.

The race is 42 miles long.

So, if we want to know know how many times as long as the race is the river, we just need to use this expression

River=x(race)

Where x represents the factor that expresses the ratio between both, solving for x we have

x=river/race=310/42≈7.38

Therefore,

            River's length is 7.38 times the race's length, approximately.

To know more about expressions visit the link

https://brainly.com/question/13947055?referrer=searchResults

#SPJ1

Right question:-

The Annual Mug Race 42 mile is the

longest river sailboat race in the world. The

event is run along the St. Johns River, which

is 310 miles long. About how many times as

long as the race is the river?

Trigonometry is best used in navigation to estimate where to point the compass to get a straight line. It will be simple to pinpoint a location as well as find distance and see the horizon using a compass and trigonometric functions in navigation.

The area of mathematics known as trigonometry examines the correlation between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are used to study this relationship. The concept of trigonometry was developed by the Greek mathematician Hipparchus, and the word trigonometry is a derivative of Latin from the 16th century.

One of the most significant area of mathematic is rigometry. The words "Trigonon" and "Metron," which mean respectively "triangle" and "measure," are combined to form the word "trigonometry." It is the investigation of how a right-angled triangle's sides and angles relate to one another. Therefore, using formulas and identities based on this relationship aids in determining the measure of a right-angled triangle's unknown dimensions.

Learn more about trigonometry

https://brainly.com/question/29002217

#SPJ1

Full question:

What is the best use of trigonometry?

well, we know in 2002 it was 25,056, then it ballooned to 36,720 in 2010, the difference is really 36720-25056 = 11664.

now, if we take 25,056(origin amount) to  be the 100%, what's 11664 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 25056 & 100\\ 11664& x \end{array} \implies \cfrac{25056}{11664}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 58 }{ 27 } ~~=~~ \cfrac{ 100 }{ x }\implies 58x=2700\implies x=\cfrac{2700}{58} \implies x\approx \stackrel{\%}{46.55}[/tex]

Answer:

The equation 49^2 + 16^2 = 784 can be rewritten as (x/24.5)^2 + (y/8)^2 = 1.

The standard form of an ellipse is (x/a)^2 + (y/b)^2 = 1, where a and b are the lengths of the major and minor axes, respectively. In this case, a = 24.5 and b = 8.

To graph the ellipse, we can use the equation in the standard form and plot points that satisfy the equation. The center of the ellipse is (0,0) and it has a major axis of 24.5 and minor axis of 8.

The graph of this ellipse will look like an oval, with the center at the origin, major axis along the x-axis and minor axis along the y-axis.

Answer:

There are several lines of evidence that scientists use to determine the relative age of the Earth and its various features. These include:

Stratigraphy: This refers to the study of rock layers and the sequence in which they were formed. Scientists use stratigraphy to determine the relative ages of different rock layers and the fossils they contain. The principle of superposition states that in any undisturbed sequence of rocks, the oldest rock layers will be at the bottom and the youngest will be at the top.

Fossil record: Fossils are the remains of plants and animals that lived in the past. By studying the fossils in rock layers, scientists can determine the relative ages of different rock formations and the organisms that lived in them. Fossils of extinct species found in lower rock layers are older than those found in higher rock layers.

Radiometric dating: This is a method that uses the decay of radioactive isotopes in minerals to determine the absolute age of rocks and minerals. Scientists can use radiometric dating to determine the age of a rock or mineral, and by comparing the ages of different rocks and minerals, they can determine the relative ages of different rock formations and the Earth's surface features.

Answer:

Step-by-step explanation:

2(x-5)=9-3x+6+8+3x+7

2x-10=9-3x+14+3x+7                  {Adding the constant no.s +6 and +8}

2x-10=30-3x+3x                          {Adding all the constants +14 , +7, +9}

2x-10=30-0                                 {+3x and -3x cancels out}

2x-10=30                                    

2x=30-10                              {coefficient with variable i.e 2x on one side}

2x=20                         {20 divides by 2 if we bring coefficient 2 to right side}

x=10 Ans

If two marbles are drawn at random and not replaced, the probability that two red marbles are drawn is; 1/3

The parameters given for marbles in the bag are;

Number of red marbles = 6

Number of blue marbles = 4

Thus;

Total number of marbles = 6 + 4

Total number of marbles = 10 marbles

Now, probability of first selection being red marble = 6/10

Probability of second marble being red if first was not replaced = 5/9

Thus;

P(first two being red marbles) = (6/10) * (5/9)

= 1/3

Read more about Probability of selection at; https://brainly.com/question/251701

#SPJ1

The area of triangle, using the formula A is 146.9 in^2

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It can be used to calculate the area of a triangle by using the length of its sides.

The most commonly used formula to calculate the area of a triangle is known as Heron's formula. This formula uses the lengths of the triangle's three sides, known as a, b, and c. Then use the formula A = 1/2 x[tex]\sqrt{(a + b+ c)(-a + b + c)(a - b + c)(a + b -c)}[/tex] to calculate the area of the triangle.

To calculate the area of a triangle using Heron's formula, first measure the length of each side of the triangle. Then use the lengths of the sides to calculate s using the formula above. Once you have calculated s, plug the values for a, b, and c into Heron's formula to calculate the area of the triangle.

A = 1/2ab⋅sin(C)

= 1/2(21 in. )(14 in.)⋅sin(88)

= 1/2(294 in.2 )⋅sin(88)

= 1/2(294 in.2 )⋅0.9945

A = 146.9 [tex]in^{2}[/tex]

To learn more about area of triangle, visit

brainly.com/question/17335144

#SPJ1

Answer:

53

a. Graph of equation attached

b.
Domain:
[tex]-\infty \: < x < \infty \:[/tex]
Interval notation: [tex]\left(-\infty \:,\:\infty \:\right)[/tex]

Range:
[tex]f(x) > 1\\\\[/tex]

Interval notation: [tex]\left(1,\:\infty \:\right)[/tex]

c. See explanation below and on attached graph

d. See explanation below

Step-by-step explanation:

53

The function to be used for answering questions is
[tex]f(x) = 8\left(\dfrac{1}{4}\right)^{x+4}+1[/tex]

a. Graph

Graph is plotted using online graphing tool. 2 points identified are (-4, 9) and (-3, 3)

b. Domain and Range

First let's understand what domain and range are

Definition of domain

The domain of a function, y = f(x),  is the set of input(x)  values for which the function is real and defined

The function has no undefined points nor domain constraints.  You can see that the graph goes to infinity for negative and positive x values Therefore,  the domain is :

[tex]-\infty \: < x < \infty \:[/tex]

which can be expressed in interval notation as:

[tex]\left(-\infty \:,\:\infty \:\right)[/tex]

Definition of range

The range of a function y = f(x) is the set of values for y over the domain for which the function is defined

As [tex]x \rightarrow \infty[/tex], [tex]y \rightarrow 1[/tex]

y never quite reaches 0 but its value approaches 1 and therefore the range is
[tex]f(x) > 1\\\\[/tex]

In interval notation:
[tex]\left(1,\:\infty \:\right)[/tex]

c. End Behavior

The end behavior of a function  f(x)  refers to how the function behaves when the variable x  increases or decreases without bound. In other words, the end behavior describes the ultimate trend in the graph of f(x) as [tex]x \rightarrow \pm \infty[/tex]

In this particular function we see that as [tex]x\to \:+\infty \:,\:f\left(x\right)\to \:1\\[/tex]

and as [tex]x\to \:-\infty \:,\:f\left(x\right)\to \:\infty\\[/tex]

d. Point (-3, 3)
By pure chance I chose this point as one of the points asked for in part a because I was looking for integer values I don't think it matters that there is repetition

(-3, 3) is plotted on the graph as point A

3. Evaluate f(-3)
We have
[tex]f(x) = 8\left(\dfrac{1}{4}\right)^{x+4}+1[/tex]

To find f(-3) substitute -3 for x in the above function:

[tex]f(-3) = 8\left(\dfrac{1}{4}\right)^{-3+4}+1\\\\= 8\left(\dfrac{1}{4}\right)^1} + 1\\\\\\= 8\left(\dfrac{1}{4}\right) + 1\\\\= 2 + 1 \\\\= 3[/tex]

So f(-3) = 3

Answer:

a)  See attachment 1.

b)  Domain: (-∞, ∞)

     Range: (1, ∞)

c)  As x → -∞, f(x) → ∞

    As x → ∞, f(x) → 1⁺

d)  See attachment 2.

e)  See below.

Step-by-step explanation:

Given exponential function:

[tex]f(x)=8\left(\dfrac{1}{4}\right)^{x+4}+1[/tex]

To find the y-intercept, input x = 0 and solve for y:

[tex]\implies f(0)=8\left(\dfrac{1}{4}\right)^{0+4}+1[/tex]

[tex]\implies f(0)=8\left(\dfrac{1}{4}\right)^{4}+1[/tex]

[tex]\implies f(0)=8\left(\dfrac{1}{256}\right)+1[/tex]

[tex]\implies f(0)=\dfrac{1}{32}+1[/tex]

[tex]\implies f(0)=\dfrac{33}{32}[/tex]

[tex]\implies f(0)=1.03125[/tex]

Therefore, the y-intercept is (0, 1.03125).

Substitute x = -2 into the function to find a second point on the curve:

[tex]\implies f(-2)=8\left(\dfrac{1}{4}\right)^{-2+4}+1[/tex]

[tex]\implies f(-2)=8\left(\dfrac{1}{4}\right)^{2}+1[/tex]

[tex]\implies f(-2)=8\left(\dfrac{1}{16}\right)+1[/tex]

[tex]\implies f(-2)=\dfrac{1}{2}+1[/tex]

[tex]\implies f(-2)=\dfrac{3}{2}[/tex]

[tex]\implies f(-2)=1.5[/tex]

Therefore, a second point on the curve is (-2, 1.5).

The domain of a function is the set of all possible input values (x-values).  

The domain of the given function is unrestricted:

The range of a function is the set of all possible output values (y-values).

As the exponential part of the function is always positive, the range of the given function is restricted:

As x approaches negative infinity, the function approaches positive infinity:

As x approaches positive infinity, the function approaches f(x) = 1.

See attachment 2.

Substitute x = -3 into the function:

[tex]\implies f(-3)=8\left(\dfrac{1}{4}\right)^{-3+4}+1[/tex]

[tex]\implies f(-3)=8\left(\dfrac{1}{4}\right)^{1}+1[/tex]

[tex]\implies f(-3)=8\left(\dfrac{1}{4}\right)+1[/tex]

[tex]\implies f(-3)=2+1[/tex]

[tex]\implies f(-3)=3[/tex]  

Hey there!

Hope this helps!

The transformation with respect to dilation will only preserve the angle measure i.e. B.

What is dilation in mathematics?

Dilation is a process of changing the size of an object or shape by decreasing or increasing its dimensions by some scaling factors. For example, a circle with radius 10 unit is reduced to a circle of radius 5 unit. The application of this method is used in photography, arts and crafts, to create logos, etc. In Geometry, there are four basic types of transformations. They are:

Some features of shapes that remain unchanged during the dilation transformations are:

Now,

As in dilation Each angle of the figure remains the same.

Hence,

              The transformation with respect to dilation will only preserve the angle measure

To know more about dilation visit the link

https://brainly.com/question/13176891?referrer=searchResults

#SPJ1

Answer:

I'm not sure if this is what you meant but 5,345 + 806 = 6,151

Step-by-step explanation:

Answer:6151

Step-by-step explanation:

5345 + 806 = 6151

The amount loaned at 6% was $9200. The solution has been obtained by making and solving the equations.

What is an equation?

A claim that two expressions are equal and connected by the equals sign "=" is the mathematical definition of an equation. The two expressions need not be entirely composed of variables; one expression may have variables while the other may not.

We are given that a bank loaned out $12,000 and a part of it at the rate of 6% per year and the rest at the rate of 16% per year.

Let the amount loaned at 6% be 'x'

So, amount loaned at 16% will be '12,000 - x'

The total interest received was $1000.

Therefore,

⇒6%x + 16%(12000-x) = 1000

⇒0.06x + 1920 - 0.16x = 1000

⇒920 = 0.1x

⇒9200 = x

Hence, the amount loaned at 6% was $9200.

Learn more about equation from the given link

https://brainly.com/question/2972832

#SPJ1

Answer:

X=3

Step-by-step explanation:

If you enter log5(125)= x into your calculator that should be your answer

1. The abbreviation for femtogram is - fg.

2. The abbreviation for decimeters is - dm.

3. The abbreviation for microliter is - μL or ul.

4. The abbreviation for femtosecond is - fs.

1. Femtogram (fg): A unit of mass measurement in the International System of Units (SI). It is equal to [tex]10^{-15}[/tex] grams and is commonly used to measure the mass of small particles or atoms.

2. Decimeter (dm): A unit of length measurement in the International System of Units (SI). It is equal to 0.1 meters and is commonly used to measure small distances.

3. Microliter (μL or ul): A unit of volume measurement in the International System of Units (SI). It is equal to [tex]10^{-6}[/tex] liters and is commonly used to measure very small volumes of liquids.

4. Femtosecond (fs): A unit of time measurement in the International System of Units (SI). It is equal to [tex]10^{-15}[/tex] seconds and is commonly used to measure very short periods of time, such as in atomic and molecular physics, chemistry, and photonics.

Read more about Units:

brainly.com/question/141163

#SPJ4

The complete question is -

write the abbreviation for each of the following: match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer.

1. The abbreviation for femtogram is -

2. The abbreviation for decimeter is -

3. The abbreviation for microliter is -

4. The abbreviation for femtosecond is -

The all the real values of x , such that for the function f(x) = 19x² + 10x satisfies f(x) = 0 are 0 , -10/19  .

The function is  ⇒ f(x) = 19x² + 10x  ;

taking x common from both terms and writing it in factor form ,

we get ;

⇒ x(19x + 10) = 0  ;

we know that the product of any two number is zero only when one of them is 0 ,

that means ;

⇒ x = 0   or   19x + 10 = 0   ;

⇒ x = 0   or   19x = -10  ;

⇒ x = 0   or  x = -10/19  .

Therefore , all the real values of x such that f(x) = 0 are 0 , -10/19 .

The given question is incomplete , the complete question is

List all real values of x such that the function f(x)=0. If there are no such real x, type none in the answer blank. If there is more that one real x, give a comma separated list (e.g. 1,2).

f(x) = 19x² + 10x .

Learn more about Functions here

https://brainly.com/question/29159787

#SPJ4

Answer:

n< -1

Step-by-step explanation:

1. Rewrite so n is on the left side of the inequality.

−5n+2n>3

2.Add 5n and 2n

-3n >3

3. Divide each term then simplify.

The quantity which represents the 0.031 in the given formula of compound interest, the value represents the annual compound interest rate 3.1%, So option A is correct

A loan or deposit amount is subject to compound interest as interest. In everyday life, it is the most prevalent idea. Both the principal and the interest accrued over time affect the compound interest for a given amount. Between compound and simple interest, this is the primary distinction.

[tex]A = P[1 + r/n]^{nt}[/tex]

Where,

A = compound interest

P = Principle Amount

r  =  Interest rate

n = number of period for which interest is calculated

t = time

Given that,

A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t

[tex]A = 2400[1 + 0.031/4]^{4}[/tex]

So, here we can see that r is equal to 0.031

It represents the annual compound interest rate of the compound interest

Hence, it is a annual compound interest which has value of 3.1%

To know more about compound interest check:

https://brainly.com/question/14295570

#SPJ1

The height of the roof will be 10.75 units.

Given is to find the height of the roof.

The upward motion is modelled by the equation -

S = - t² + 3t + 4

The height of the roof is equal to maximum height attained. For the maximum height attained -

dS/dt = 0

d/dt (- t² + 3t + 4) = 0

- 2t + 3 = 0

2t = 3

t = 3/2                                                    .... Eq(1)

The  height of the roof will be -

S(max) = - t² + 3t + 4

S(3/2) = - (3/2)² +(3 x 3/2) + 4

S(3/2) = 9/4 + 9/2 + 4

S(3/2) = 2.25 + 4.5 + 4

S(3/2) = 10.75 units.

Therefore, the height of the roof will be 10.75 units.

To solve more questions on algebraic expressions, visit the link below -

brainly.com/question/1041084

#SPJ1

The volume is the product of the area of the base, 2x(2x+5), and the height, 2x-3.

What is Volume?

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

What is Area?

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given that;

Height= 2x - 3

Length= 2x + 5

Width= 2x

We have the following equation for the rectangular box in this instance:

2x(2x + 5)(2x- 3)

We may come up with an equivalent formula for the volume by using the distributive property of multiplication.

We have then ;

[tex](4x^2+10x)(2x-3)[/tex]

Once more writing, we have:

[tex](8x^3+20x^2)+(-12x^2-30x)[/tex]

Including related terms, we have:

8x^3+8x^2-30x

To learn more about Volume click here:

https://brainly.com/question/24284033

#SPJ1

Answer:  Total area = 40 cm² + 25.12 cm² = 65.12 cm²

Step-by-step explanation:

https://brainly.com/question/925961

Answer:65.1

Step-by-step explanation:

The equation y = x² represents a parabola as a curve

Two or more expressions with an Equal sign is called as Equation.

The equation y = x² represents a parabola as a curve

The equation is given as:

y = x²

The above equation has a degree of 2

Polynomials that have a degree of 2 are referred to as quadratic equations

The curve of a quadratic equations are called parabola

Hence, the equation y = x² represents a parabola as a curve

Read more about parabola at:

brainly.com/question/4061870

#SPJ1

Answer:

4 daysb

Step-by-step explanation:

Here the number of animals and the number of days are in inverse proportion. Hence the food will last 4 days.

The food will last for 6 days for 20 animals.

If there were 10 more animals in the cattle, the total number of animals would be 20+10 = 30.

The food will last for the same 6 days but now it would be divided among 30 animals.

Therefore, the food would last for 6 days / 30 animals = 0.2 days per animal.

So, the food will last for 0.2 days if there were 10 more animals in the farmer's cattle.

If Canada specializes in producing wheat and the US specializes in producing TV sets, both countries will benefit from trade.

To determine this if Canada produces wheat, the opportunity cost is 1/2 TV set. If the US produces wheat, the opportunity cost is 2 TV sets. So, Canada has a comparative advantage in producing wheat. Similarly, the US has a comparative advantage in producing TV sets.

Let's say Canada produces 100 bushels of wheat, and the US produces 100 TV sets. If they trade with each other, Canada can exchange 50 bushels of wheat for 50 TV sets, and the US can exchange 50 TV sets for 50 bushels of wheat. Both countries would benefit from this trade.

Canada would end up with 50 TV sets and 50 bushels of wheat, while the US would end up with 50 bushels of wheat and 50 TV sets. Both countries would be better off than if they had not traded.

Opportunity cost in mathematics is a term that is used to describe the cost of one alternative in terms of the benefits forgone by the best alternative. It can also be represented in terms of mathematical equations.

To learn more about the  mathematical equations, visit:

brainly.com/question/29514785

#SPJ4