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3 years ago

If (x/100-1)(x/100+1)=kx^2-1 k=

1 answer:

3 0

(x/100-1)(x/100+1)=kx^2-1
(x/100-1)(x/100+1)=(x/100)^2 - 1^2 because it's a difference of squares ( (a-b)(a+b) = a^2-ab+ab-b^2 = a^2 - b^2):
(x/100)^2 - 1^2=kx^2 - 1
(x/100)^2 - 1=kx^2 - 1
(x/100)^2=kx^2
(x^2)/(100^2)=kx^2
1/(100^2)=k
1/10000=k
k=0.0001

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Find the first four terms of the sequence<br> An=2a n-1,where a1=3

yKpoI14uk [10]

The first four terms of the sequence are 3 , 6 , 12 , 24

Step-by-step explanation:

We need to find the first four terms of the sequence $a_{n}=2a_{n-1}$

where $a_{1}=3$ to find them do that

Substitute n by 2 in the rule to find $a_{2}$
Substitute n by 3 in the rule to find $a_{3}$
Substitute n by 4 in the rule to find $a_{4}$

∵ $a_{n}=2a_{n-1}$

- Substitute n by 2 to find the 2nd term

∴ $a_{2}=2a_{2-1}$

∴ $a_{2}=2a_{1}$

∵ $a_{1}=3$

∴ $a_{2}=2(3)$

∴ $a_{2}=6$

- Substitute n by 3 to find the 3rd term

∴ $a_{3}=2a_{3-1}$

∴ $a_{3}=2a_{2}$

∵ $a_{2}=6$

∴ $a_{3}=2(6)$

∴ $a_{3}=12$

- Substitute n by 4 to find the 4th term

∴ $a_{4}=2a_{4-1}$

∴ $a_{4}=2a_{3}$

∵ $a_{3}=12$

∴ $a_{4}=2(12)$

∴ $a_{4}=24$

The first four terms of the sequence are 3 , 6 , 12 , 24

Learn more:

You can learn more about the sequences in brainly.com/question/1522572

#LearnwithBrainly

3 0

3 years ago

Ten times a number is fifty

Rashid [163]

Answer:

Step-by-step explanation:

if you multiply 10 and 5, you will get 50

7 0

3 years ago

Read 2 more answers

Two high-speed ferries leave at the same time from a city to go to the same island. The first ferry, the Cat, travels at 34 m

djyliett [7]

Answer:

They will be 5 miles apart in 1 hour

Step-by-step explanation:

Here, we want to calculate the time it will take for the two ferries to be 5 miles apart

Mathematically; distance = speed * time

Let the number of hours be x

In x hours, the cat will have traveled 34 * x = 34x miles

In x hours, the Bird will have traveled 29 * x = 29x miles

So;

34x - 29x = 5

5x = 5

x = 5/5

x = 1 hour

4 0

3 years ago

18 is 75 percent of what number

dimulka [17.4K]

18 is 75% of x.

$75\%= \frac{75}{100}=\frac{3 \times 25}{4 \times 25}=\frac{3}{4} \\ \\
\frac{3}{4}x=18 \\
x=18 \times \frac{4}{3} \\
x=6 \times 4\\
x=24
$

18 is 75% of 24.

8 0

3 years ago

Solve the equation the square root of the quantity x plus 4 minus 3 equals 1 for the variable.

Kruka [31]

Answer:

x = 12

Step-by-step explanation:

sqrt(x+4) - 3 = 1

First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.

sqrt(x+4) = 1 + 3

sqrt(x+4) = 4

To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.

(sqrt(x+4))^2 = 4^2

x + 4 = 16

subtract 4 to finish up.

x = 12

Check:

sqrt(12 + 4) - 3 = 1

sqrt16 - 3 = 1

4 - 3 = 1

1 = 1 Check!

6 0

2 years ago