Answer:
BCD is the outer angle of triangle ABC
=> BCD = ABC + BAC
<=> 150⁰ = ABC + 118⁰
=> ABC = 150⁰ - 118⁰
<=> ABC = 32⁰
48 stamps because 29-5=24 , 24x2=48
The unknown angles are in a ratio of 7 to 13.
Let 7x represent the smaller measure.Then, 13x represents the larger measure.
7x + 13x + 140 = 180
20x + 140 = 180
20x = 40
x = 2
7x = 7 * 2 = 14
13x = 13 * 2 = 26
The measures are 14 degree and 26 degrees.
Answer:
HJ
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
so
The slope of the line that is parallel to a line that has a slope of 3 is equal to 3
Verify the slope of the blue and red line , because their slopes are positive
<em>Blue line</em>
we have
C(-3,0),D(3,2)
The slope m is equal to
m=(2-0)/(3+3)
m=2/6
m=1/3
<em>Red line</em>
we have
H(-1,-4),J(1,2)
The slope m is equal to
m=(2+4)/(1+1)
m=6/2
m=3
therefore
The answer is the red line HJ
If you project S onto the (x,y)-plane, it casts a "shadow" corresponding to the trapezoidal region
T = {(x,y) : 0 ≤ x ≤ 10 - y and -4 ≤ y ≤ 4}
Let z = f(x, y) = √(16 - y²) and z = g(x, y) = -√(16 - y²), each referring to one half of the cylinder to either side of the plane z = 0.
The surface element for the "positive" half is
dS = √(1 + (∂f/∂x)² + (∂f/dy)²) dx dy
dS = √(1 + 0 + 4y²/(16 - y²)) dx dy
dS = √((16 + 3y²)/(16 - y²)) dx dy
The the surface integral along this half is
You'll find that the integral over the "negative" half has the same value, but multiplied by -1. Then the overall surface integral is 0.
