Answer:
0.49 radians or 28.07 degrees
Step-by-step explanation:
Please recall that the definition of the tangent of an angle is "the ratio of the length of the side opposite the angle to the length of the adjacent side, of a right triangle."
Here, opposite side length 8
tan x = ------------------------------------- = ---------
length of adjacent side 15
We use the inverse tangent function to determine the angle x from the given information:
arctan 8/15 = x
Using a calculator, we find that x = 0.49 radians.
The measure of this angle, in degrees, is found by multiplying 0.49 radians by the conversion factor
180 degrees
--------------------
pi radians
which, in this case, works out to 28.07 degrees.
Do you have a calculator? you can solve it by substituting x.
y=16x^2
0: y = 16(0)^2 = 16(0) = 0
(x = 0 , y = 0)
0.5: y = 16(0.5)^2 = 16(0.25) = 4
(x = 0.5 , y = 4)
1: y = 16(1)^2 = 16(1) = 16
(x = 1 , y = 16)
1.5: y = 16(1.5)^2 = 16(2.25) = 36
(x = 1.5 , y = 36)
2: y = 16(2)^2 = 16(4) = 64
(x = 2 , y = 64)
2.5: y = 16(2.5)^2 = 16(6.25) = 100
(x = 2.5 , y = 100)
3 : y = 16(3)^2 = 16(9) = 144
(x = 3 , y = 144)
4: y = 16(4)^2 = 16(16) = 256
(x = 4 , y = 256)
if you multiply a negative number by itself, it will become positive. So, -4, -3, -2.5, -2, -1.5, -1, -0.5 will be the same as the positive 4, 3, 2.5, 2, 1.5, 1, 0.5.
I'm not sure about the pattern, but if you graph it, it'll be symmetrical across the y-axis.
Slope point form:
We need the slope "m" and a point (x₀,y₀)
y-y₀=m(x-x₀)
1)
we calculate the slope "m".
Given two points:
(x₁,y₁)
(x₂,y₂)
the slope "m" is:
m=(y₂-y₁) / (x₂-x₁)
In this case:
(4,10)
(6,11)
m=(11-10) / (6-4)=1/2
Now, we calculate the solpe point form.
(4,10)
m=1/2
y-y₀=m(x-x₀)
y-10=(1/2)(x-4)
we make the standard form
y-10=x/2 - 2
Lowest common multiple=2
2y-20=x-4
-x+2y=-4+20
-x+2y=16
Answer: -x+2y=16
9514 1404 393
Answer:
(x +3)² +(y -4)² = 145
Step-by-step explanation:
The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...
A = (P +Q)/2
A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2
A = (-3, 4)
The equation of the circle for some radius r is ...
(x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle
The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...
(6 +3)² +(12 -4)² = r² = 9² +8²
r² = 81 +64 = 145
Then the equation of the circle is ...
(x +3)² +(y -4)² = 145
