is {(1,9), (-3,4), (1, -7)} a function?

The derivative of the vector-valued function r(t) = (-7t/(t^2 - 7), -t^2/t^3 + 6, 6/(6t - 1)) is r'(t) = (7(2t^2 - 7)/(t^2 - 7)^2, (-3t^4 + 12t^2 - 18)/(t^3)^2, -36/(6t - 1)^2).

To find the derivative of each component function, we apply the rules of differentiation. For the first component, -7t/(t^2 - 7), we use the quotient rule to differentiate it, resulting in the expression 7(2t^2 - 7)/(t^2 - 7)^2.

For the second component, -t^2/t^3 + 6, we simplify the expression and then differentiate it using the quotient rule. This yields (-3t^4 + 12t^2 - 18)/(t^3)^2.

For the third component, 6/(6t - 1), we differentiate it using the power rule and chain rule, leading to -36/(6t - 1)^2.

Thus, the derivative of the vector-valued function r(t) is r'(t) = (7(2t^2 - 7)/(t^2 - 7)^2, (-3t^4 + 12t^2 - 18)/(t^3)^2, -36/(6t - 1)^2). Each component of r'(t) represents the derivative of the respective component of r(t) with respect to t.

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Answer:

x = 10

Step-by-step explanation:

We can use ratios to solve

Side over bottom

5         5+3

---- = --------

x         16

Using cross products

5 * 16 = (5+3)*x

80 = 8x

Divide by 8

10 = x

x = 10.  This is a dilation. To find x, you must first find what you are dilating and by how much. 8 is the starting value, and 5 is the newer value. 5 divided by 8 is .625. Then multiply.625 by 16, to get 10, or x

Answer:

4x²-5x +4  X=3

Step-by-step explanation:

The expression below has 3 terms. The first step is to plug in the 3 for all the  x´s. Then find what 3 squared is. Next is to multiply the 9(3²) with the 4 to get 36. Now the expression is 36 - 5 x 3 + 4. Next is to multiply the -5 and the 3 to get 15. Now combine all like terms to get 55.

Explanation

Step 1

apply distributive property

Step 2

add similar terms and order

so, the answer is

I hope this helps you

Answer:

16in or 1ft 4in

Step-by-step explanation:

Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.

initial height = 5

final height =20

height to travel =20-5 =15

\(15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0\)

solving we get, t = 0.255 or -2.44

since, -2.44 is not possible,

t = 0.255 seconds.

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\( \sqrt{117} \)

You first find the average of the first two test scores. When you find the average, you add the two numbers together and then divide by two which gives you 89. You then plug in different scores above the number 89 and find the average of those (89 and x) to see which gives you an average of 92. It’s mostly a guess and check type of problem.

To find all points with a specific x-coordinate, you need to have the equation of the curve or the data points representing the graph. If you have an equation, you can substitute the desired x-coordinate into the equation and solve for the corresponding y-coordinate.

If you have data points, you can look for the points that have the specified x-coordinate.

For example, let's say you have the equation of a line: y = 2x + 3. If you want to find all points with an x-coordinate of 5, you can substitute x = 5 into the equation to find y. In this case, y = 2(5) + 3 = 13. So the point (5, 13) has an x-coordinate of 5.

to find points with a specific x-coordinate, you need the equation of the curve or the data points. You can substitute the desired x-coordinate into the equation or look for the points that have the specified x-coordinate in the given data.

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Answer:

x=-9

Step-by-step explanation:

STEP 1: Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

\(9(x-5)-14x=-7(x+9)\)

STEP 2: Simplify 9(x−5)−14x.

\(-5x-45=-7(x+9)\)

STEP 3: Simplify −7(x+9).

\(-5x-45=-7x-63\)

STEP 4: Move all terms containing x to the left side of the equation.

\(2x-45=-63\)

STEP 5: Move all terms not containing x to the right side of the equation.

\(2x=-18\)

STEP 6: Divide each term by 2 and simplify.

\(x=-9\)

Answer:

x= -9

explanation in the pic above

hope it helps.

Approximately $1,061.88 is the payment of interest that Khalid should pay today in the bank paying 7% semi-annually.

Given, Khalid wants to have BD 30000 in his account by the end of 96 months. Interest rate = 7% (semi-annually)

We have to find how much should he pay interest today in the bank. For calculating this, we have to follow the below steps:

To calculate the payment of interest, we have to use the formula of Present Value of an Annuity or PV(Present value) of an annuity. In this formula, we have to calculate the present value of all the future payments, which he will be paying until the end of 96 months. Using the formula of Present Value of an Annuity or PV(Present value) of an annuity:

PV = PMT * [(1 - (1 + r/n)^-nt)/(r/n)]

Where, PV = Present Value

PMT = Payment amount

r = interest rate

n = number of times interest is compounded per year

t = time in years

For Semi-annually, the compounding period is 2.

PV = PMT * [(1 - (1 + r/n)^-nt)/(r/n)]

PV = Payment * [(1 - (1 + r/n)^-nt)/(r/n)]

PV = Payment * [(1 - (1 + 0.07/2)^-(96*2))/(0.07/2)]

PV = Payment * [(1 - (1.035)^-192)/(0.035)]

PV = Payment * [(1 - 0.000044)/0.035]

PV = Payment * 28.23130

Therefore, the amount Khalid should pay today in the bank paying 7% semi-annually is:

PV = Payment * 28.23130

$30,000 = Payment * 28.23130

Payment = $1,061.88

Approximately $1,061.88 is the payment of interest that Khalid should pay today in the bank paying 7% semi-annually.

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Responda:

a) 3 e 4

Explicação passo a passo:

Deixei :

Número de cães = x

Número de gatos = y

2x + 3y = 17 - - - - (1)

x - y = 1 - - - - (2)

De (2)

x = 1 + y

Coloque em (1)

2 (1 + y) + 3y = 17

2 + 2y + 3y = 17

2 + 5y = 17

5y = 17 - 2

5y = 15

y = 15/5

y = 3

x = 1 + y

x = 1 + 3

x = 4

Número de cães = x = 4

Número de gatos = y = 3

The derivative of f(x) = | -x³ + 4 | is f'(x) = (-3x²) * (d/dx|-x³ + 4|).

To find the derivative of the function f(x) = | -x³ + 4 |, we will first need to examine the expression inside the absolute value function and then use the chain rule.



1. Identify the inner function: g(x) = -x³ + 4
2. Find its derivative: g'(x) = -3x²
3. Determine the sign of g(x) to know how to differentiate the absolute value:
  - If g(x) > 0, the derivative of |g(x)| is g'(x).
  - If g(x) < 0, the derivative of |g(x)| is -g'(x).
  - If g(x) = 0, the derivative is undefined.

4. Apply the chain rule to find the derivative of the function: f'(x) = (d/dx |g(x)|) * g'(x)

Hence, the derivative of f(x) = | -x³ + 4 | is f'(x) = (-3x²) * (d/dx | -x³ + 4 |) in an unsimplified form. Further simplification requires knowing the sign of g(x).

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The value of y(x) when y(0) = -7 is;y = -cos(7x)/7 - 48/7.

Set up an integral for solving dy/dx = sin (7x) when y(0) = −7.The differential equation is as follows;dy/dx = sin(7x)By taking the antiderivative of both sides;∫dy/∫sin(7x) = ∫dx ∫dy = -cos(7x)/7 + C1, where C1 is the constant of integration.Then by solving for C1, we get;y(0) = -cos(0)/7 + C1 => C1 = y(0) + 1/7

Hence the general solution is;y = -cos(7x)/7 + y(0) + 1/7B) Evaluate your answer to the previous part to find y(x).

From the solution we obtained in part (a), we can plug in the values of x and y(0) into the general solution as follows;y = -cos(7x)/7 + (-7) + 1/7y = -cos(7x)/7 - 48/7Therefore the value of y(x) when y(0) = -7 is;y = -cos(7x)/7 - 48/7.

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Answer:

I think 10 is the correct answer.

Answer:

x = 7

Step-by-step explanation:

2(3x-9)=2x+10

6x - 18 = 2x + 10

4x = 28

x = 7

Answer:

x = 7

Step-by-step explanation:

In order to find the value of x, isolate it in the equation.

1) First, distribute the 2 to the terms inside the set of parentheses.

\(2 (3x - 9) = 2x + 10 \\6x - 18 = 2x + 10 \\\)

2) Next, move all the x terms to one side and all the other terms to the other side. Subtract both sides by 2x and add both sides by 18.

\(6x - 18 = 2x + 10 \\4x = 28\)

2) Divide both sides by 4 to finally isolate x.

\(4x = 28 \\x = 7\)

Thus, x = 7.

Answer:

Yes.

because 2:3 =0.666...

Step-by-step explanation:

Answer:

yes i agree

Step-by-step explanation:

i agree because 0.66 is 2/3 of 1 if you take 1 and divide it by 3 you get 0.33 which would be 1/3 so 2/3 would be 0.66

The probability that the student is a junior is 0.5.

The probability that the selected student takes calculus is given by:

P(C) = probability that the selected student takes calculus= probability of seniors taking calculus + probability of juniors taking calculus= 0.4 x 1/2 + 0.2 x 1/2= 0.2

Now,Let's find the probability that a calculus student selected is a junior.i.e., we need to find P(J|C).We know that,

P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)

We already know,P(C) = 0.2

Also,P(C|J) = probability that a junior student takes calculus= 0.2

So,P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)= 0.2 × 1/2 / 0.2= 1/2= 0.5

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Answer:

3ft²

Step-by-step explanation:

We see that this figure is a rhombus, with the diagonals d1=3ft, and d2=2ft

The area of a rhombus is d1×d2/2

3×2/2=3ft²

Step-by-step explanation:

a basic internet search : area of a diamond or - more general - a kite.

it is

ab/2

with a, b being the diagonals.

as we can see, the long b diagonal is 3 ft long, the short diagonal is 2 ft long.

so, the area is

3×2/2 = 3 ft²

Answer:

20

Step-by-step explanation:

The total degrees in a circle is 360 degrees

x+40+2x+110+3x+90 = 360

==> 6x = 120

x = 20

Answer:

The answer would be x=20

We can tell if a character is direct or Indirect  by the five methods which are action, reactions, physical description,  inner thoughts,  and speech.

The Characterization in literature is the process that the authors use to develop characters and create images of characters for audience.

There are two different approaches for characterization, which are Direct Characterization and Indirect Characterization.

The methods by which we can know that a character is Direct or Indirect are :

(i) Physical description - In this the character's physical appearance is described. For example, How the character dresses might reveal something about the character.

(ii) Action - Is the character a good person or a bad person can be told by his Action .

(iii) Inner thoughts - The inner thoughts of character reveals the personality .

(iv) Reactions - The Effect on other characters also reveals about the personality of character .

(v) Speech - What character says provides a great insight for the reader.

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Unearned income may vary depending on investment performance, interest rates, and changes in government policies.

Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms.

In 10 years, an individual's earned and unearned income may vary greatly depending on their career and investment choices, economic conditions, and personal circumstances.

Some individuals may see increases in earned income as they gain more experience or take on higher-paying positions, while others may see fluctuations or decreases in earned income due to changes in the job market.

Similarly, unearned income may vary depending on investment performance, interest rates, and changes in government policies.

Hence, unearned income may vary depending on investment performance, interest rates, and changes in government policies.

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Answer:

4 gifts

Step-by-step explanation:

4÷4=0

so you get each other a gift so there none to spare

Answer:

12 gifts

Step-by-step explanation:

If there are 4 people, and each person brings a gift for each of the other three people, that means that there are 12 gifts at the party. Let's say there are four people: A, B, C, and D. Person A would have to bring 3 gifts to give  B, C, and D. Similarly, B would bring a gift each for A, C, D. C would bring a gift for A, B, D. Lastly, D would bring a gift for A, B, and C. Each person brings three gifts to give to the other three people at the party, and 3*4 people is 12. I hope that makes sense.

The identities to be proven are: 1) div (F times G) = G middot curl (F) - F middot curl (G), and 2) curl (curl(F)) = grad (div(F)) - nabla^2 F.

1) To prove div (F times G) = G middot curl (F) - F middot curl (G), we can expand the divergence of the vector field F times G using the product rule. The divergence of F times G is given by div (F times G) = div(F) times G + F times div(G). Applying the curl product rule, we have curl(F times G) = G times curl(F) + F times curl(G). Taking the divergence of both sides, we get div(curl(F times G)) = G middot curl(F) + F middot curl(G). Since div(curl(F times G)) is equal to div(F times G), we conclude that div(F times G) = G middot curl (F) - F middot curl (G).

2) To prove curl(curl(F)) = grad(div(F)) - nabla^2 F, we can start by expanding the curl of F. The curl of F is given by curl(F) = (nabla cross F), and the curl of the curl of F is curl(curl(F)) = (nabla cross (nabla cross F)). Applying the vector identity for the curl of a curl, we have curl(curl(F)) = grad(div(F)) - nabla^2 F, where grad(div(F)) represents the gradient of the divergence of F and nabla^2 F represents the Laplacian of F.

By assuming that the appropriate partial derivatives exist and are continuous, we have proven the identities div (F times G) = G middot curl (F) - F middot curl (G) and curl (curl(F)) = grad (div(F)) - nabla^2 F.

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The correlation coefficient is 0.9541. This can be determined from the information provided in the ANOVA table, specifically the regression sum of squares (SSR) and the total sum of squares (SST).

The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger relationship, and values closer to 0 indicate a weaker relationship.

To calculate the correlation coefficient, we can use the formula:

r = sqrt(SSR/SST)

From the ANOVA table provided, we can see that SSR = 12,323.64 and SST = 13,538.4. Plugging these values into the formula gives:

r = sqrt(12,323.64/13,538.4) = 0.9541

Therefore, the correlation coefficient for this model is 0.9541, indicating a strong positive linear relationship between the independent variable and the dependent variable

Complete Question:

Using the following information. Coefficients -12.8094 Intercept Independent variable 2.1794 ANOVA df SS MS F 1 90.0481 Regression Residual Total 12,323.64 1,214.762 13,538.4 12,323.64 136.8550 8 1° 9 What is the correlation coefficient? Multiple Choice 0.9103 0.9541 -0.9541

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Answer:

T.A = 54 + 9/2 √3

Step-by-step explanation:

∵ The figure is triangular prism

∴ T.A = perimeter of the base × height + 2 × area of the base

∵ The base is an equilateral Δ with side length 3"

∴ The perimeter of the base = 3 × 3 = 9 inches

∴ The area of the base = 1/4 S² √3 = 1/4 (3)²√3 = 9/4 √3 inches²

∵ The length of the height of the prism = 6"

∴ T.A = 9 × 6 + 2 × 9/4 √3 = 54 + 9/2 √3

∴ T.A = 54 + 9/2 √3 inches²

Answer:

89° to the nearest degree.

Step-by-step explanation:

Answer:

The real number is - 6 and the imaginary number is 2.

Answer:

Step-by-step explanation:

the real numbers are -6 and 2

the imaginery is i

The volume of a square based pyramid is 927.7 cubic centimeter.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a square base pyramid with the side length of the base is 16.6 and the height of the pyramid is 10.1 m.

We know that, the volume of square based pyramid =a²h/3.

Here, volume = 16.6²×10.1/3

= 275.56×10.1/3

= 927.7 cubic centimeter

Therefore, the volume of a pyramid is 927.7 cubic centimeter.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the volume of a pyramid with a square base, where the side length of the base is 16.6 and the height of the pyramid is 10.1 m. Round your answer to the nearest tenth of a cubic meter.

Answer:

20x20=400 so 20 is your integer

Step-by-step explanation:

20 × 20 = 400.

Step-by-step explanation: