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Keith_Richards [23]
3 years ago
14

How do find the nth term in a non-linear sequence

Mathematics
1 answer:
erastovalidia [21]3 years ago
6 0

Answer:an =n-1d

a+1d

a-2d

so that 29 is the sequence

Step-by-step explanation:

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Find sum of three consecutive even integers if the largest integer is Y
KATRIN_1 [288]

Answer:

3y -- 6

Step-by-step explanation:

if the largest number is y, then the other two integers would be (y -- 2) and (y -- 4).

Therefore the sum of the integers would be

y + (y -- 2) + (y -- 4) = 3y -- 6.

7 0
3 years ago
There is a circle with a center of 0,0 on a coordinate plane. There is one point on the circle's circumference in which the x:y
abruzzese [7]

Answer:

Step-by-step explanation:

Suppose the radius is 1. The parametric equations for the circle are

x = cosθ

y = sinθ

x:y = 3:1

tanθ = ⅓

cosθ = 3/√(1²+3²) =  3/√10

sinθ = 1/√10

The solutions are (3/√10, 1/√10) and (-3/√10, -1/√10).

6 0
3 years ago
Which rule best described the following pattern 5,6,15,16,25,26,35​
ad-work [718]
The pattern is increasing by 10 then a ding 1 to the next number. Hope this helps! :)
6 0
3 years ago
How many solutions are there for the system x^2+4y^2=100 and 4y-x^2=-20
never [62]
There are 5 solutions for this system.

x^2 + 4y^2 = 100  ____1
4y - x^2 = -20  ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80   (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y :  y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2    x = /100 - 4y^2  (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
6 0
3 years ago
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much
Y_Kistochka [10]

Answer:

x = ∛ 2*V/5  

y = ∛ 2*V/5

h  = V/ ∛ 4*V²/25

Step-by-step explanation:

Dimensions of the aquarium base is  x*y

We call c₁ cost per unit area of the sides, then cost per unit area of slate is equal 5c₁.

let call h the height of the aquarium then volume of the aquarium is:

V = x*y*h      where   h =  V / x*y

As the base is a rectangular one there are 2 sides x*h .  and 2 sides  y*h

According to this:

Ct (cost of aquarium )  = cost of the base  + cost of the sides

cₐ  ( cost of the base) = 5*c₁*x*y

c₆ (cost of the sides ) = c₁*2*x*h   +   c₁*2*y*h

C(t)  =  5*c₁*x*y +2* c₁*x* V/x*y  +  2* c₁*y* V/x*y    or

C(t)  =  5*c₁*x*y  + 2*c₁*V/y   *2*c₁* V/x

Taking partial derivatives en x and y we have:

C´(x)  =  5*c₁*y - 2*c₁*V/x²

C´(y)  =  5*c₁*x - 2*c₁*V/y²

C´(x)  = C´(y)        ⇒  5*c₁*y - 2*c₁*V/x²  =   5*c₁*x - 2*c₁*V/y²

or    5*y - 2*V/x²  =   5*x - 2*V/y²

(5*y*x² - 2*V)/x²  = ( 5*y²x - 2*V) /y²

(5*y*x² - 2*V)*y²  = ( 5*y²x - 2*V)*x²

5*y³*x² - 2*V*y²  =  5*y²x³  - 2*V*x²

5*y³*x² - 5*y²x³  =  2*V * ( y² - x²)

by symmetry  x =  y

Then using x = y  and plugging that value on the derivatives

C´(x) =  5*c₁*y - 2*c₁*V/x²

C´(x) =  5*c₁*x - 2*c₁*V/x²

C´(x) = 0          ⇒     5*c₁*x - 2*c₁*V/x²  = 0

5*x  - 2*V/x² = 0      ⇒  5*x³ - 2*V = 0   ⇒   5*x³  = 2*V  ⇒ x³ = 2*V/5

x = ∛ 2*V/5       and   y = ∛ 2*V/5    and   h  =  V/ x*y    h  = V/ ∛ 4*V²/25

7 0
3 years ago
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