MATHEMATICS COLLEGE

What is the common difference of the arithmetic sequence 5 8 11 14

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

The gap between every single number of this sequence is 3.

14 - 11 = 3

8 - 5 = 3

This gap is called the common difference. You can find it by subtracting values in the sequence that are next to each other.

Answer 2

Answer: The answer is for sure 3

Related Questions

Given the age in years, t, of a water-transport pipe, the formula R = 17 + 4 t can be used to predict the rate of water leakage (in gallons per minute) from the pipe as it carries water from the headquarters of a farming cooperative to farmland a mile away. What is the meaning of the constant 17 in the function R ?A. Initially the pipe leaks at 4 gallons per year. B. Initially the pipe leaks at 17 gallons per year. C. Initially the pipe leaks 17 gallons. D. Initially the pipe leaks at 4 gallons per minute. E. Initially the pipe leaks 4 gallons. F. Initially the pipe leaks at 17 gallons per minute.
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What is the next term of the arithmetic sequence 24, 16, 8, 0,

The ordered pairs in the table below represent a linear function. x y 6 2 9 8 What is the slope of the function? One-fourth One-half 2 4

Answers

Answer:

The answer is C) 2

Step-by-step explanation: I hope you get this right also.

Answer:

Step-by-step explanation:

Suppose f(x,y)=xy, P=(−4,−4) and v=2i+3j. A. Find the gradient of f. ∇f= i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (∇f)(P)= i+ j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf= Note: Your answer should be a number D. Find the maximum rate of change of f at P. Note: Your answer should be a number E. Find the (unit) direction vector in which the maximum rate of change occurs at P. u= i+ j Note: Your answers should be numbers

Answers

Answers:

Gradient of f: $\nabla f = y\hat{i} + x\hat{j}$

Gradient of f at point p: $\nabla f = -4\hat{i} -4\hat{j}$

Directional derivative of f and P in direction of v: $\nabla f(P)v = -20\n$

The maximum rate of change of f at P: $| \nabla f(P)| = 4√(2)$

The (unit) direction vector in which the maximum rate of change occurs at P is: $v = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}$

Step by step solutions:

Given that:

$f(x,y) = xy$

$P = (-4,4)\n$

$v = 2i + 3j$

A: Gradient of f

$\nabla f = ((\partial f)/(\partial x), (\partial f)/(\partial y)) = (y,x) = y\hat{i} + x\hat{j}$

B: Gradient of f at point P:

Just put the coordinates of p in above formula:

$\nabla f = -4\hat{i} -4\hat{j}$

C: The directional derivative of f and P in direction of v:

The directional derivative is found by dot product of $\nabla f(P) \: \rm and \: \rm v$ :

$\nabla f(P)v = [-4,4][2,3]^T = -20\n$

D: The maximum rate of change of f at P is calculated by evaluating the magnitude of gradient vector at P:

$| \nabla f(P)| = √((-4)^2 + (-4)^2) = 4√(2)$

E: The (unit) direction vector in which the maximum rate of change occurs at P is:

$v = ((-4)/(4√(2)), (-4)/(4√(2))) = -(1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}$

That vector v is the needed unit vector in this case.

we divided by $4√(2)$ to make that vector as of unit length.

Learn more about vectors here:

brainly.com/question/12969462

Answer:

a) The gradient of a function is the vector of partial derivatives. Then

$\nabla f=((\partial f)/(\partial x), (\partial f)/(\partial y))=(y,x)=y\hat{i} + x\hat{j}$

b) It's enough evaluate P in the gradient.

$\nabla f(P)=(-4,-4)=-4\hat{i} - 4 \hat{j}$

c) The directional derivative of f at P in direction of V is the dot produtc of $\nabla f(P)$ and v.

$\nabla f(P) v=(-4,-4)\left[\begin{array}{ccc}2\n3\end{array}\right] =(-4)2+(-4)3=-20$

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

$||\nabla f(P)||=√((-4)^2+(-4)^2)=√(32)=4√(2)$

e) The maximum rate of change occurs in the direction of the gradient. Then

$v=(1)/(4√(2))(-4,-4)=((-1)/(√(2)),(-1)/(√(2)))= (-1)/(√(2))\hat{i}-(1)/(√(2))\hat{j}$

is the direction vector in which the maximum rate of change occurs at P.

Find the area of the shape

Answers

Answer:

The area is 91 cm²

Step-by-step explanation:

The shape is a kite.

area of a kite = ½(p*q)

Where, p and q are the diagonals of the kite.

p = 13 cm

q = 7 + 7 = 14 cm

The area of the kite = ½(13 * 14)

= ½(182)

Area = 91 cm²

6(5 + 3x) is equivalent too

Answers

Answer:

30+18 x

Step-by-step explanation:

Simplify the following expression.
11x^2+9–2x–8x^2 - 6x

Answers

Answer:

3x^2-8x+9

Step-by-step explanation:

11x2+9−2x−8x2−6x

Subtract 8x2 from 11x2.

3x2+9−2x−6x

Subtract 6x from −2x.

3x2+9−8x

Move 9.

3x^2−8x+9

Hope this helps! :) Plz mark as brainliest

Answer: 3x^2-8x+9

Step-by-step explanation:

11x2+9−2x−8x2−6x

Subtract 8x2 from 11x2.

3x2+9−2x−6x

Subtract 6x from −2x.

3x2+9−8x

Move 9.

3x^2−8x+9

Thank you :)

The ratio of Sunita's age to Mark's age is currently 3 to 4, and in 12 years, it will be 5 to 6. What is Mark's current age?A) 18

B)24

C)30

D)36

Answers

Answer:

24 years.

B is correct option.

Step-by-step explanation:

Let Sunita's current age is x and that of Mark's is y.

Hence, we have

$(x)/(y)=(3)/(4)\n\nx=(3)/(4)y.......(1)$

Now, in 12 years the ratio will be 5 to 6. Thus, we have

$(x+12)/(y+12)=(5)/(6)$

Cross multiplying, we get

$6x+72=5y+60$

Plunging, the value of x from equation (1)

$6((3)/(4)y)+72=5y+60\n\n(9y)/(2)+72=5y+60\n\n(y)/(2)=12\n\ny=24$

Therefore, Mark's current age is 24 years.

Mark's current age is 24

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