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Usimov [2.4K]
3 years ago
13

An angle t is drawn from the center of the unit circle. Find a formula in terms of t for the straight line distance d between th

e points where the two radii meet the unit circle. Hint: By rotating the picture, you may assume that one of the radii meets the circle at the point (1,0)

Mathematics
1 answer:
Doss [256]3 years ago
5 0

Answer:

d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}

Step-by-step explanation:

Let suppose that one of the radii meets the circle at the point (1,0). The straight line distance formula is:

d = \sqrt{(\cos t - 1)^{2}+(\sin t - 1)^{2}}

d = \sqrt{(\cos^{2}t - 2\cdot \cos t + 1)+(\sin^{2}t - 2\cdot \sin t + 1)}

d = \sqrt{2-2\cdot (\cos t + \sin t )}

d = \sqrt{2}\cdot \sqrt {1-\cos t - \sin t}

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-3(x - 2) - 2x + 4x^2
Fantom [35]

Answer:

-6x+6+4x^2

Step-by-step explanation:

Distribute the -3

-3(x-2)= -3x+6

Combine like terms

<u>-3x</u>+6<u>-2x</u>+4x^2

-6x+6+4x^2

8 0
3 years ago
How many ways can 6 people sit on a bench if 3 of them have to sit side by side
pickupchik [31]

Answer:

144 ways

Step-by-step explanation:

Let's think of the 3 persons sitting together as "one". So essentially we have 3 + "1" = "4" persons to arrange.

THey can be arranged in 4! ways, which is:

4! = 4 * 3 * 2 * 1 = 24 ways

Now, the 3 persons themselves can be arranged in 3! ways, which is:

3! = 3 * 2 * 1 = 6 ways

Total ways = 4! * 3! = 24 * 6 = 144 ways

4 0
3 years ago
X = 0.19
Luda [366]

Step-by-step explanation:

.19 = 19/100

.864 = 86.4/100

.5348 = 53.48 /100

I multiplied the decimal by 100 to get what it was before which is the same as moving two decimal places to the right and divided by 100

if any confusion ask

4 0
3 years ago
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The distance along a line is considered an undefinable term in mathematics. which situation provides an example of why distance
madam [21]
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3 years ago
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Joshua sells a pack of pens for $3.15, which is 5 percent more than he pays for them. Which equation will help find x, the amoun
nikdorinn [45]

Answer:

x+0.05x=3.15 which has one solution

Step-by-step explanation:

Complete question below:

Joshua sells a pack of pens for 3.15 which is 5 percent more than he pays for them. which equation will help find x, the amount he pays for a pack of pens? how many solutions will this equation have? x+0.05x=3.15, which has infinitely many solutions x+0.5x=3.15, which has one solution x+0.05×=3.15 which has one solution 0.05×=3.15, which has no solution

Let

x= the amount Joshua pays for a pack of pen

5% of x more than he paid for them

=0.05x more

Buying price=0.05x + x

Selling price=3.15

Equate buying and selling price

0.05x + x = 3.15

1.05x=3.15

Divide both sides by 1.05

1.05x / 1.05 = 3.15/1.05

x=3

The equation is 0.05x+x=3.15

The answer is:

x+0.05x=3.15 which has one solution

3 0
4 years ago
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