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3 years ago

Find the sum to infinity of a geometric series having a second term of -9 and fifth term of 1/3 g

Mathematics

1 answer:

Eduardwww [97]3 years ago

5 0

Answer:

S infinity= -51/4

Step-by-step explanation:

First term

ar= -9

Fifth term

ar⁴= 1/3

Solving for the value of the r and a

ar= -9

ar⁴= 1/3

Dividing each other

r³=1/3 * -1/9

r³=-1/27

r= 3√-1/27

r= -1/3

Solving for a

ar= -9

a(-1/3)= 9

a= 9*-3

a= -27

Sum of a go to infinity is given by the formula

S infinity= a/(1-r)

S infinity= -27/(1-(-1/3))

S infinity= -27/(1+1/3)

S infinity= -27 * 3/4

S infinity= -51/4

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Extended Problems, Extraneous Solutions

diamong [38]

Answer:

1a. 2 is the solution

1b. -3 is because square root of 1 doesn't equal -1.

1c.-3

Step-by-step explanation:

$(x + 2 = \sqrt{3x + 10}$

Square both sides

$(x + 2) {}^{2} = 3x + 10$

Remeber perfect square Rule

$(x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2}$

So now we got

$x {}^{2} + 4x + 4 = 3x + 10$

${x}^{2} + x + 4 = 10$

${x}^{2} + x - 6 = 0$

Factor into binomial.

$(x + 3)(x - 2) = 0$

So our solution is 3 or 2. However, let's check our work.

$- 3 + 2 = \sqrt{3( - 3) + 10}$

$- 1 = \sqrt{1}$

However square root of 1 is 1. It could be 1 but in Math, We only take the principal square root which is positive always. So -3 isn't a solution.

So let try 2.

 $2 + 2 = \sqrt{3(2) + 10} = 4 = \sqrt{16} = 4 = 4$ 

So this is indeed the solution.

Make up equation for 2 and 3. Ask me if you need help.

5 0

2 years ago

Susan enlarged to scale a rectangle with a height of 4 cm and length of 11cm on her computer. The length of the new rectangle is

ladessa [460]

The answer is 6. To answer this you would need to do 16.5/11 to get 1.5 (that's how much the rectangle got enlarged). Then you would do 4 times 1.5 to get your new height size, which is 6.

4 0

3 years ago

The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x2 + 5x

nikdorinn [45]

Answer:

width: 15 inches; length: 20 inches

Step-by-step explanation:

The equation tells you the product of width (x) and length (x+5) is 300, so you're looking for factors of 300 that differ by 5.

300 = 1·300 = 2·150 = 3·100 = 4·75 = 5·60 = 6·50 = 10·30 = 12·25 = 15·20

The factors in the last pair on this list differ by 5, so we have ...