Answer: U' = (0, 1)
<u>Step-by-step explanation:</u>
U = (3, -5)
rotate 90° counterclockwise means (x, y) = (-y, x)
new U = (5, 3)
down 2 units means subtract 2 from the y-coordinate
newer U = (5, 1)
left 5 units means subtract 5 from the x-coordinate
U' = (0, 1)
To solve this problem, we need to know that
arc length = r θ where θ is the central angle in radians.
We're given
r = 6 (units)
length of minor arc AB = 4pi
so we need to calculate the central angle, θ
Rearrange equation at the beginning,
θ = (arc length) / r = 4pi / 6 = 2pi /3
Answer: the central angle is 2pi/3 radians, or (2pi/3)*(180/pi) degrees = 120 degrees
Considering that the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.
<h3>What are the signs of the sine and of the cosine in each quadrant?</h3>
- Quadrant 1: Both positive.
- Quadrant 2: Sine positive, cosine negative.
- Quadrant 3: Both negative.
- Quadrant 4: Sine negative, cosine positive.
Hence, since the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.
More can be learned about quadrants at brainly.com/question/28021191
#SPJ1
You did not provide us with equations to select.
Find the slope m.
m = (1 - 2)/(3 - (-1))
m = -1/(3 + 1)
m = -1/4
Use the slope and one of the points and plug into the point-slope formula.
y - 1 = (-1/4)(x - 3)
Isolate y.
y - 1 = (-1/4)x + (3/4)
y = (-1/4)x + (3/4) + 1
y = (-1/4)x + (7/4)
Did you follow?
1). Multiply (5400 inches) by (1 foot / 12 inch) then by (1 mile / 5280 foot).
(See explanation at the bottom)
= (5400 inch) x (1 foot / 12 inch) x (1 mile / 5280 foot)
= (5400 x 1 x 1 / 12 x 5280) (inch - foot - mile / inch - foot)
= 0.0852 mile
2). Multiply (16 week) by (7 day/week) then by (24 hour/day)
then by (60 minute/hour) then by (60 sec/minute).
3). Multiply (54 yards) by (3 foot/yard) then by (1 meter/3.28 foot)
and then by (1000 mm/meter)
4). Multiply (36 cm/second) by (3600 second/hour) then by (1 meter/100 cm)
then by (1 mile/1609.3 meter).
5). Look up how many grams in a pound ('P')
Look up how many mL in a gallon ('G')
Multiply (1.09 g/mL) by ( 1 pound/ P gram) then by (1 gallon/ G mL)
6). Multiply (32 foot/sec) by (1 meter / 3.28 foot) then by (60 sec/minute).
Each time I told you to multiply by something, it was always a fraction
where the numerator and denominator are equal, like (60 seconds/minute)
or (1 foot / 12 inch). Since the top and bottom of the fraction are equal, the
value of the fraction is ' 1 ' , and multiplying by it doesn't change the value,
it only changes the units ... that's what this whole exercise is about.
When you multiply, KEEP the units in the product, and then, after you multiply, you can 'cancel' units out of the top and bottom of the product.
Like if you have 'feet' on top and bottom, just cross them out. When you're done, if you did it correctly, the last unit you end up with will be the one you want.
