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svetoff [14.1K]
3 years ago
7

In which quadrant does θ lie if the following statements are true: cos⁡θ>0 and sin⁡θ>0

Mathematics
1 answer:
Papessa [141]3 years ago
6 0

Answer:

First quadrant

Step-by-step explanation:

cosθ > 0 in first/ fourth quadrants

sinθ > 0 in the first/ second quadrants

sinθ and cosθ are both > 0 in the first quadrant

Then θ lies in the first quadrant

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Write the equation of a line passing through (6,-2) and perpendicular to -2x + 3y= -6
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Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.


-2x+3y=-6                 Add 2x in both sides
3y=2x-6                    Divide by 3 in both sides to isolate y
y=2/3x-6/3


The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.

y=mx+b                 Substitute the given point and the previous slope found
-2=(-3/2)(6)+b       Combine like terms
-2=-9+b                 Add 9 in both sides to isolate b
7=b

The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.


4 0
3 years ago
How do I do this Cp geometry
ryzh [129]
Whats your geometry problem? i dont understand the question
5 0
3 years ago
Use Euler's formula to find the missing number.
frez [133]
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3 0
3 years ago
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A northbound bus and a southbound bus are at a bus stop at the same time. The northbound bus returns to the bus stop every 20 mi
gulaghasi [49]

The question is essentially asking for the least common multiple of 20 and 25. There are several ways you can find the LCM. One easy way is to divide the product by the GCD (greatest common divisor).

GCD(20, 25) = 5 . . . . . see below for a way to find this, if you don't already know

LCM(20, 25) = 20×25/GCD(20, 25)

... = 500/5 = 100

The buses will be there together again after ...

... B. 100 minutes

_____

You can also look at the factors of the numbers:

... 20 = 2²×5

... 25 = 5²

The least common multiple must have factors that include all of these*, so must be ...

... 2²×5² = 100

___

* you can describe the LCM as the product of the unique factors to their highest powers. 20 has 2 raised to the 2nd power. 25 has 5 raised to the 2nd power, which is a higher power of 5 than is present in the factorization of 20. Hence the LCM must have 2² and 5² as factors.

_____

You can also look at the factorization of 20 and 25 to see that 5 is the only factor they have in common. That is the GCD, sometimes called the GCF (greatest common factor).

4 0
3 years ago
Read 2 more answers
URGENT:
scoray [572]
I would say the answer would be B

8 0
3 years ago
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