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3 years ago

What is the nth term rule of the quadratic sequence below? -5, -3,3, 13, 27, 45, 67, ...

Mathematics

2 answers:

SCORPION-xisa [38]3 years ago

5 0

Answer:

$u_{n} = 2n^{2} -4n-3$

Step-by-step explanation:

a +b + c = - 5 First term in sequence

3a + b = 2 Difference between first two terms

2a = 4 Difference between the difference of the first two terms and the second third terms (the difference between -5 and -3 is 2 the difference between -3 and 3 is 6; the difference between 6 and two is 4)

2a = 4 so a = 2; 3(2) + b = 2 → 6 + b = 2 so b = -4; 2 - 4 + c = -5 → -2 + c = -5 so c = -3

Svetllana [295]3 years ago

4 0

Answer:

the pattern is +2, +6, +10, +14, +18 etc

so its in increment of 4

the rest is trivial

Step-by-step explanation:

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What is the approximate equation of this line of best fit in slope-intercept form?

Anni [7]

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3 years ago

Read 2 more answers

Explain why 1.234 + 5.7 is rational please help i need this submitted!!

saw5 [17]

Answer:

This is rational because it has two integers

Step-by-step explanation:

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Example

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3 years ago

mrs. grady surveyed 30 students, 11 of which said they liked basketball, 16 of which said they liked hockey, and 3 of which said

Neko [114]

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3 years ago

Can anyone please help me to do this with steps

qwelly [4]

Answer:

x = 58°

Step-by-step explanation:

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3 years ago

Consider the surface f (x comma y comma z )f(x,y,z)equals=negative 2 x squared plus 2 y squared minus 3 z squared plus 3 equals

trapecia [35]

Answer:

a) (8,8,-6)

b) 4x+4y+3z = -3

Step-by-step explanation:

The surface is given by the equation

f(x,y,z) = 0 where

$f(x,y,z)=-2x^2+2y^2-3z^2+3$

The gradient of this function is the vector

$(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})=(-4x,4y,-6z)$

If we evaluate it in the point P = (-2,2,1) we obtain the point

(8,8,-6)

The vectors with their tails at P are of the form

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

as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0

$(-2-x,2-y,1-z)\cdot(8,8,6)=0\Rightarrow -16-8x+16-8y+6-6z=0\Rightarrow 4x+4y+3z=-3$

and the equation of the desired plane is

4x+4y+3z = -3

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4 years ago