For given problem:
Put midpoint of ellipse, (0,0) at epicenter of bridge at
ground level.
Specified length of vertical major axis = 70=2a
a=35
a^2=1225
Equation of ellipse:
x^2/b^2+y^2=1
plug in coordinates of given point on ellipse(25, 10)
25^2/b^2 + 10^2/a^2 = 1
625/b^2 + 100/1225=1
625/b^2 = 1 - 100/ 1225 = .918
b^2 = 625/.918 ≈ 681
b ≈ 26.09
length of minor axis = 2b = 2(26.09) ≈ 52.16 ft
Span of bridge ≈ 52.16 ft
Answer:
Step-by-step explanation:
Angles 1 and 5 are in corresponding positions, so since A and B are parallel to each other, angles 1 and 5 are also congruent. If they are congruent, then that have the exact same measure. That means that if the sum of them is 100, each one has a measure of 50 degrees.
Angle 4 is vertical to angle 1, so that means that angles 1 and 4 are congruent. If angle 1 measures 50, then so does angle 4.
The sum of the angles of a triangle must equal 180.
A + B + C = 180
50 + B + C = 180
B + C = 180 - 50
B + C = 130
If B and C are equal to each other, we can just divide 130 by 2 to find the other two angles.
130 / 2 = 65
Angles B and C are both 65 degrees
Answer:
Yes, (0,4) is a solution
Step-by-step explanation:
We have to plug in 0 in x and 4 in y IN BOTH THE INEQUALITIES.
IF BOTH ARE TRUE, then the system of inequalities is TRUE.
<u>Let's check:</u>
y ≤ -3x+4
4 ≤ -3(0)+4
4 ≤ 4
Is 4 less than OR equal to 4? Yes. THis is satisfied.
<u>Now, checking 2nd one:</u>
y > x^2 + 3x - 2
4 > (0)^2 + 3(0) - 2
4 > -2
Is 4 greater than -2? Yes, it is. So this is satisfied as well.
Hence, (0,4) is a solution to the system of inequalities shown.
