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4 years ago

Show how to solve the following; answer must be with fractions and pi

Mathematics

1 answer:

Bess [88]4 years ago

3 0

Answer:

3pi/4 and -pi/4

Step-by-step explanation:

We can simplify -6/6 to -1.

Therefore, this function can be simplified to arctan(-1).

Recall that the meaning of arctan is to find a value that will get the value inside the parenthesis when taken the tangent of it. In other words, tan(x) = -1.

Recall that tan(x) = sin(x)/cos(x). Now recall that sin(pi/4) and cos(pi/4) are both sqrt(2)/2, meaning that tan(pi/4) is 1. To make it -1, we can either make sin(x) -1 while keeping cos(x) 1, or the other way around.

If x is -pi/4, cos(x) will still be 1, but sin(x) will be -1, so tan(-pi/4) will be -1.

If x is 3pi/4, cos(x) will be -1, but sin(x) will still be 1, so tan(3pi/4) will be -1.

Side note: there are still infinite more answers. You can attain them by adding or subtracting 2pi as many times as you want from 3pi/4 or -pi/4 and still get an arctan of -1.

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Verizon [17]

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It must be WAY down there where the sun don't shine.

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3 years ago

Find the sum of the geometric series. a b c d

Musya8 [376]

Answer:

B. $4\sqrt{3}-6$

Step-by-step explanation:

We have,

The first term of the series, $a=\sqrt{3}$ .

The common difference is given by, $r=\frac{\frac{-3}{2}}{\sqrt{3}}$ i.e. $r=\frac{-\sqrt{3}}{2}$ .

Since, the given series is an infinite series, then,

Sum of an infinite series = $\frac{a}{1-r}$

i.e. Sum the series = $\frac{\sqrt{3}}{1+\frac{\sqrt{3}}{2}}$

i.e. Sum the series = $\frac{2\sqrt{3}}{2+\sqrt{3}}$

i.e. Sum the series = $\frac{2\sqrt{3}}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}$

i.e. Sum the series = $\frac{2\sqrt{3}\times (2-\sqrt{3})}{4-3}$

i.e. Sum the series = $4\sqrt{3}-6$

Thus, the sum of the series is $4\sqrt{3}-6$ .

8 0

3 years ago

Please assist with this problem.

Flura [38]

Answer:

The answer to your question is:

Step-by-step explanation:

If the line is rotated, we get the perpendicular of the initial line.

See the attachment, the blue line is the original and the red one is the new line.

Process

new slope = 2/5

Point ( 0, 4)

(y - y1) = m (x - x1)

( y - 4) = 2/5 (x - 0)

y - 4 = 2/5 x

y = 2/5 x + 4 New line

8 0

3 years ago

A heptagon has unequal sides that are in a pattern. Each side is 2 more than twice the side of the smaller one before it. Write

bixtya [17]

Heptagon has unequal sides and each side is 2 more than twice the side of the smaller one before it.

Heptagon is a 2 dimensional geometric shape that has got 7 sides.

Lets say the length of smallest side is 'x' units.

Length of the second side will be 2 more than twice the smaller side so the side length will be:

$2\times x+2=2x+2$

Now the length of the third side will be 2 more than twice the second side that is:

$2(2 \times x+2)+2=2(2x+2)+2=4x+4+2=4x+6$

Similarly, length of the fourth side will be:

$2(4x+6)+2=8x+12+2=8x+14$

Similarly, length of the fifth side will be:

$2(8x+14)+2=16x+28+2=16x+30$

Again, length of the sixth side will be

$2(16x+30)+2=32x+60+2=32x+62$

And the length of the seventh side will be

$2(32x+62)+2=64x+124+2=64x+126$

Now, perimeter of any geometric shape is the sum of the lengths of the sides:

Adding all the sides we get:

$x+(2x+2)+(4x+6)+(8x+14)+(16x+30)+(32x+62)+(64x+126)$

$=x+2x+2+4x+6+8x+14+16x+30+32x+62+64x+126$

$=127x+240$

Therefore, the expression for the perimeter of the required heptagon is $127x+240$ .

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3 years ago

What is the slope of line k?

wlad13 [49]

Answer: Slope: 2/3

Step-by-step explanation:

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3 years ago