Answer:
The Proof is given below.
Step-by-step explanation:
Given:
P is the center of Circle
∠ONE ≅ ∠TEN
To Prove:
∠5 ≅ ∠6
Proof:
Exterior Angle Theorem:
Exterior Angle Property of a Triangle states that measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles.
STATEMENT REASON
1. So In ΔONE,
1. Exterior Angle Property of a Triangle.
2. Similarly In ΔTEN,
2. Exterior Angle Property of a Triangle.
3. But , ∠ONE ≅ ∠TEN 3. Given
4. And P is the center of circle So
4.radius of same circle
5. ΔPEN is an Isosceles triangle,
∴ ∠ 1 ≅ ∠ 2 5. Isosceles triangle property
6. ∴ ∠5 ≅ ∠6 6. From 3 and 5 Transitive Property.........Proved
Separate the variables:
y' = dy/dx = xy ⇒ 1/y dy = x dx
Integrate both sides:
∫ 1/y dy = ∫ x dx
ln|y| = 1/2 x² + C
Given that y(0) = 1, we have
ln|1| = 1/2 • 0² + C ⇒ C = 0
so that the particular solution is
ln|y| = 1/2 x²
Solving for y gives
y = exp(1/2 x²)
Answer:
Yes
Step-by-step explanation:
24²+24²=x², x = 33.94
33.94²+14²=x², x = 36.71 inches
1 yard is about 36 inches, so it should just fit.
Answer:
x = 14
Step-by-step explanation:
As the triangle was dilated, all its sides increased by the same ratio.
So, as one side was 3 and then increased to 9, the ratio is:
ratio = 9 / 3 = 3
So, using this same ratio for the other side given, we can find the value of x.
The larger side of length x+1 is 3 times greater than the small side of length 5:
x + 1 = 3 * 5
x + 1 = 15
x = 14
2x - 3(9-x) = -12
2x-27+3x=-12
5x-27=-12
5x=15
x=3
y=9-x
y=9-3
y=6
x=3
y=6
