35 x 30 = 35 x ____tens, <br> ____=____tens, <br> ___=___

The sum of the second and third terms of G.P is six times the fourth term. Find the two possible values of the common ratio

andrew-mc [135]

Answer:

Step-by-step explanation:

Let “a” be the first term and ”r” the common ratio of the GP. Then,

f(n) = ar^(n - 1).

f(2) + f(3) = 6f(4). (given)

ar + ar^2 = 6ar^3, or

1 + r = 6r^2, or

6r^2 - r - 1 = 0,

(3r + 1)(2r - 1) = 0.

r = -1/3, or 1/2.

If the common ratio is positive and the second term is 8 we have,

ar = 8, or

a*1/2 = 8, or a = 16.

f(n) = 16*(1/2)^(n - 1) = 2^4*2^(1 - n), or

f(n) = 2^(5 - n).

The first six terms of the GP are : 16, 8, 4, 2, 1, 1/2,…

××××××××××

Checking : f(2) + f(3) = 6f(4), (given).

LHS = 8 + 4 = 12.

RHS = 6* 2 = 12.

LHS = RHS.

8 0

2 years ago

Solve the system using substitution.

Maru [420]

Answer:

Given: The following system:

4x + y − 2z=18 ......[1]

2x-3y+3z = 21 ......[2]

x-3y=6 ......[3]

we can write equation [3] as;

3y = x-6 ......[4]

Multiply by 3 in equation [1] to both sides of an equation we get,

$3 \cdot(4x+y-2z)= 3\cdot 18$ or

12x+3y-6z=54 ......[5]

Substituting the equation [4] in [2] and [5] we get;

2x-(x-6)+3z=21 or

2x-x+6+3z=21

Simplify:

x+3z=15 .....[6] [combine like terms]

12x+x-6-6z =54

Simplify:

13x-6z=60 ......[7] [Combine like terms]

On Solving equation [6] and [7] simultaneously,

x+3z=15

13x-6z=60

we get the value of x

i.e, x=6

Substitute the value of x in equation x+3z=15 we get

6+3z=15 or

3z=9

Simplify:

z=3

Also, substitute the value of x=6 in equation [3] we get the value of y;

x-3y=6

6-3y=6 or

-3y = 0

Simplify:

y = 0

Therefore, the solution to the system of three linear equation is, (6, 0 , 3)

5 0

3 years ago

What is the length of the line segment between point (-5,8) and point (-5,-4).

dedylja [7]

Answer:

12 would be the distance between the two points

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

True/False (4z + y) is the sum of two terms

frutty [35]

True. The answer is the product of 4 and a number plus another number.

4 0

3 years ago

Read 2 more answers

The average daily high temperature in Seattle is modeled by the function T = –15 cos(πm/6)+ 61, where T is the temperature in °F

Sliva [168]

Answer:

$m = 6$

Step-by-step explanation:

$T = -15cos(\frac{\pi m}{6}) +61$

$76 = -15cos(\frac{\pi m}{6}) +61$

$76-61 = -15cos(\frac{\pi m}{6})$

$15 = -15cos(\frac{\pi m}{6})$

$\frac{15}{-15} = cos(\frac{\pi m}{6})$

$-1 = cos(\frac{\pi m}{6})$

$cos^{-1}( -1) = \frac{\pi m}{6}$

$\pi = \frac{\pi m}{6}$

$6\pi = \pi m$

$m = 6$

7 0

1 year ago

35 x 30 = 35 x ____tens, ____=____tens, ___=____.

35 x 30 = 35 x __tens, =tens, _=____.