What are the Cartesian coordinates of a point with polar coordinates (17, 60 degrees)?

Mathematics

1 answer:

nirvana33 [79]3 years ago

8 0

Answer:

C. (8.5, 14.72)

Step-by-step explanation:

You can translate the coordinates using ...

(x, y) = (r·cos(θ), r·sin(θ))

Filling in the given polar coordinates, (r, θ) = (17, 60°), we have ...

(x, y) = (17·cos(60°), 17·sin(60°)

(x, y) = (8.5, 14.72)

If you sketch the vector, you realize that the short side of the triangle (the x-coordinate) is half the length of the hypotenuse (17). This is because you recognize the side-length relationships in a 30°-60°-90° triangle. Only one answer choice shows that value.

You might be interested in

NO LINKS!!!!!

8090 [49]

9514 1404 393

Answer:

5x^2 +10x = -5

Step-by-step explanation:

The equation will have one solution when the discriminant is zero.

In standard form, the equation is ...

ax^2 +10x -c = 0

The discriminant of the equation ax^2+bx+c=0 is ...

b^2 -4ac

so the discriminant of your equation is ...

10^2 -4a(-c) = 100 +4ac

We want that to be zero, so we require ...

100 +4ac = 0

25 +ac = 0

ac = -25

Any pair of values of 'a' and 'c' that have a product of -25 will satisfy the requirement. As you state, one possible pair is a = 5 and c = -5. Putting these values into the given equation makes it ...

5x^2 +10x = -5 . . . . . the equation with a=5, c=-5

_____

Additional comment

Your problem statement does not require that 'a' be non-zero. If a=0, then the equation will have one real solution for any value of c.

If you restrict the solutions to integers, then possibilities include ...

(a, c) = (1, -25), (5, -5), (25, -1), (-25, 1), (-5, 5), (-1, 25)

6 0

2 years ago

In a school auditorium, the number of chairs in a row is the same as the number of rows of chairs. There are 7033 students in th

mafiozo [28]

Same number of rows to chairs in a row would form a square.

Use the total number of students as the area