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3 years ago

16, -6.4, 2.56, ..., 6th term The 6th term of the sequence is

Mathematics

1 answer:

AlekseyPX3 years ago

4 0

Answer:

the 6th term is = -0.16384

Step-by-step explanation:

Notice this is a geometric sequence with first term 16, and common ratio (-0.4)

Therefore the first 6 terms of the sequence are:

a1 = 16

a2 = 16 * (-0.4) = -6.4

a3 = -6.4 * (-0.4) = 2.56

a4 = 2.56 * (-0.4) = -1.024

a5 = -1.024 * (-0,4) = 0.4096

a6 = 0.4096 * (-0.4) = -0.16384

The the 6th term is = -0.16384

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Sin(20)=x/670 ????????

mash [69]

Answer:

229.2

Step-by-step explanation:

Remark

There's a lot in this question. The x is not just any x. It is defined and limited by its relationship with the sine function.

The Sin is defined as Opposite over Hypotenuse in a right triangle. The 670 is the Hypotenuse. You know that by the definition of Sine.

So one thing you should always keep in mind: the x because of where it is in the definition, will always be smaller than the Hypotenuse. So you should get a value less than 670.

Formula

Just as you have it

Sin(20) = x / 670

Solution

Multiply both sides by 570

670 * sin(20) = x

sin(20) = 0.3420

x = 670 * 0.3420

x = 229.2

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3 years ago

Does this table of values represent a linear relationship? Explain your answer.

eduard

Answer:

Yes

Step-by-step explanation:

Yes, because there is a constant rate of change. It is and will always be constantly increasing by 1.5.

To be a linear line you have to have a constant rate of change.

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3 years ago

Each side of a square calendar is 19 inches long. What is the calendar's perimeter?

liberstina [14]

Answer:

a square has 4 sides each of those sides is 19in long perimeter is all around the square so you would add 19+19+19+19=79in

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3 years ago

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Pythagorean theorem pls help

Zarrin [17]

Answer:

a²+b²=c²

Step-by-step explanation:

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2 years ago

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A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

morpeh [17]

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

$x^2 +(x+7)^2=(x+9)^2\\\\$

Expand the terms in brackets

$x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81$

collect like terms

$x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0$

solve for x in the quadratic equation by factorization

$x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8$

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

6 0

3 years ago