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3 years ago

Point D is at (-4,-2) on a coordinate plane, what would be the ordered pair if

Mathematics

1 answer:

poizon [28]3 years ago

8 0

Answer:

As such, in first quadrant, both the coordinates (x and y) are positive and both are negative in third quadrant. In second quadrant, y is positive and x is negative, while in fourth quadrant x is positive and y is negative, As (-4, -2) has both x and y coordinates negative, it will be found in third quadrant

Step-by-step explanation:

You might be interested in

Is there a transformation that maps shape 1 onto shape 4?

Llana [10]

Answer:

1 place to the left and 2 places down

Step-by-step explanation:

(+1,-2)

5 0

3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

2 years ago

at an amusement park a person spends $30 on admission and food and then goes on r number of rides that cost $2 each

stepladder [879]

The question is find the equation, in the function and standard notations, that represent the amount spent in the range of 0 to 5 rides.

Constant cost: $30
Independent variable, number of rides: r
Variable cost: $2r

Total spend, s(r): 30 + 2r

Function: s(r) = 30 + 2r, for 0 ≤r ≤ 5 ----- this is the function notation

Standard form: s(r) is the dependent variable = s

s = 30 + 2r => s - 2r = 30 =>

s + (-2)r = 30, for 0 ≤ r ≤ 5 ------ this is the standard form

5 0

3 years ago

Joanna joins a CD club. She pays $7 per month plus $10 for each CD that she orders. Write an inequality to find how many CDs she

pantera1 [17]

7m + 10c (is less than or equal to) 100.
m stands for months and c stands for CDs.

I hope this helps! :)

3 0

3 years ago

7/8 of a rectangle is colored red. Damien cuts this red part into a number of pieces so that each piece is 1/24 of the whole rec

Viktor [21]

Answer: 21

Step-by-step explanation: All he did was took the amount of red and gave it a ratio of 7:1 meaning that he will increase the amount of red and make it 21 because the number 8 increased by 3 so 7 must increase by 3 as well.

6 0

3 years ago