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3 years ago

Find the first four terms of this geometric sequence a1 = 5 And r = 6

Mathematics

1 answer:

Elena-2011 [213]3 years ago

4 0

General term of a geometric sequence is
a(n)=a(1)×r^(n-1)
a1=5
a2=5×6=30
a3=5×6²=180
a4=5×6³=1080

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Help! You can look at the picture please

viva [34]

Answer:

$\frac{3x}{3 - 2x}$

Step-by-step explanation:

Here,

f(x) = y

$y = \frac{3x}{2x + 3}$

or , swapping x with y

$x = \frac{3y}{2y + 3}$

now to solve for y we get

$y = \frac{3x}{3 - 2x}$

now we put f inverse x instead of y

${f}^{ - 1} (x) = \frac{3x}{3 - 2x}$

I am done.

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4 years ago

Read 2 more answers

The length of a rectangle is 6 more than twice the width. if the area is 40 cm^2, find the length and breadth of the rectangle

ra1l [238]

Answer: 3.217 & 12.434

Step-by-step explanation:

If we use w to represent the width, the length will be 6 more than 2 times w.

Hence, the length is $2w+6$ .

The area of a rectangle would be its length times its width, so let's make an equation to represent it's area.

$A=w(2w+6)$

We can also substitute 40 in for A as it's given in the question.

$40 = w(2w+6)$

Distributing w by multiplying it by both terms in the parentheses, we get

$40 = 2w^2+6w$

We can make the equation simpler by dividing both sides by 2.

$20 = w^2+3w$

Subtracting both sides by 20 will make the left-hand side 0.

$0=w^2+3w-20$

Now that we have put this quadratic equation into standard form (ax²+bx+c), we can find its solutions using the quadratic formula.

For reference, the quadratic formula is

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a is 1, b is 3, and c is -20.

Substituting, we get

$w=\frac{-3\pm\sqrt{3^2-4(1)(-20)}}{2(1)}$

$w= \frac{-3\pm\sqrt{9+80}}{2}$

$w=\frac{-3+\sqrt{89}}{2}\hspace{0.1cm}or\hspace{0.1cm}\frac{-3-\sqrt{89}}{2}$

Since the second solution results in a negative number, it cannot be the length of w.

$w=\frac{-3+\sqrt{89}}{2}\approx3.217$

The width/breadth of the rectangle is 3.217 cm.

To calculate the length, let's substitute the width into the expression for the length:

$l=2(3.217)+6$

$l=12.434$

The length of this rectangle is 12.434 cm.

6 0

2 years ago

What is the approximate length of the radius of a circle with a circumference of 63 inches?

Sergeeva-Olga [200]

Answer: 63/2π

Step-by-step explanation: C=πd

63=πd

D=63/π

r=1/2d

1/2×63/π=63/2π

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3 years ago

Someone pls help with geometryyy

andrezito [222]

What's the problem about geometry? Which section?

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3 years ago

An amount of $32,000 is borrowed for 10 years at 5.75% Interest, compounded annually. If the loan is paid in full at the end of

Leya [2.2K]

Answer:

Total cost of the loan $55,969.8.-

Step-by-step explanation:

Giving the following information:

An amount of $32,000 is borrowed for 10 years at 5.75% Interest, compounded annually.

To calculate the total cost of the loan, we need to use the Future Value (FV) formula:

FV= PV*(1 + i)^n

PV= loan

i= interest rate

n= number of periods

FV= 32,000*(1.0575^10)

FV= $55,969.8

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3 years ago