Answer:
(x - 1)² + (y + 1/2)² = 65/4
Step-by-step explanation:
Given: the endpoints of the diameter are (3, 3) and (-1, -4). a( To determine the center of this circle, find the midpoint of the line segment connecting these two points:
3 - 1
x = -----------
2
and
-1
y = ----------
2
The center is at x = 1 and y = -1/2: (1, -1/2).
b) The radius is half the diameter. The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):
diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,
radius = (1/2)√65.
square of the radius = r² = 65/4
The general equation of a circle with center at (h, k) and radius r is
(x - h)² + (y - k)² = r². In this case, the equation is:
(x - 1)² + (y + 1/2)² = 65/4
Answer:
(1, 3 )
Step-by-step explanation:
To find a solution choose a value for x, substitute into the equation and solve for y.
let x = 1 , then
- 7(1) + 3y = 2 , that is
- 7 + 3y = 2 ( add 7 to both sides )
3y = 9 ( divide both sides by 3 )
y = 3
One possible solution is therefore (1, 3 )
Answer:
(About) 20043.46 after 14 years
Step-by-step explanation:
~ Let us apply a compound interest formula not through substituting values, but through a similar way of following this formula ~
1. First let us assign the values:
interest ⇒ 6.5 percent ( % ), principle number - start value ⇒ $ 8300, time ⇒ 14 years
2. Now let us convert interest ⇒ decimal form: 0.065
3. Add 1 to this value 0.065 ⇒ 1 + 0.065 = 1.065
4. Now let us take 1.065 exponentially to the power of itself 14 times, or in other words to the power of time ( 14 years ): 1.065^ 14 = 2.414874185.......
5. Multiply this infinite number by the principle number P, or most commonly known as the start value: 2.414874185....... * 8300 ⇒
(About) 20043.46 after 14 years
First, we need to calculate how much money is the discount. We do that by multiplying 20% with 65$ = 20% * 65$ = 0,2 * 65$ = 13$
When we know how much money is the discount, we will subtract it from original value, and we will get the sale price of the tennis racket :
65$ - 13$ = 52$
Answer:
or
Step-by-step explanation:
Find the magnitude of :
Find the direction angle of :
Since is our reference angle, we determine our direction angle by verifying our angle is in Quadrant IV, which is where the vector is located. Therefore,
To represent a vector's magnitude and direction in trigonometric form, we use the form or .
In conclusion, the trigonometric form of the vector is:
or