20^2 = 16^2 +x^2
400= 256+ x^2
x^2 = 400 -256
x = 144^1/2
=12
b. yes
The nth term of the geometric sequence is:
an=ar^(n-1)
where
a=first term
r=common ratio
n=nth term
from the question:
120=ar(3-1)
120=ar^2
a=120/(r^2)....i
also:
76.8=ar^(5-1)
76.8=ar^4
a=76.8/r^4.....i
thus from i and ii
120/r^2=76.8/r^4
from above we can have:
120=76.8/r²
120r²=76.8
r²=76.8/120
r²=0.64
r=√0.64
r=0.8
hence:
a=120/(0.64)=187.5
therefore the formula for the series will be:
an=187.5r^0.8
Area of the shaded sector = (120/360) * pi * 10^2
= 104.72 square units
Area of the other sector = 2 * 104.72 = 209.44 sq units
Answer:
x = 8
y = -7
Step-by-step explanation:
This is a system of equations called simultaneous equations. We shall solve it by elimination method Step 1We shall label the equations (1) and (2)−3y−4x=−11.....(1)3y−5x=−61......(2)Step 2Multiply each term in equation (1) by 1 to give equation (3)1(-3y-4x=-11).....(1)-3y-4x=-11....(3)Step 3Multiply each term in equation 2 by -1 to give equation (4)-1(3y−5x=−61)......(2)-3y+5x=61.....(4)Step 4-3y-4x=-11....(3)-3y+5x=61.....(4)Subtract each term in equation (3) from each term in equation (4)-3y-(-3y)+5x-(-4x)=61-(-11)-3y+3y+5x+4x=61+110+9x=729x=72Step 5Divide both sides of the equation by 9, the coefficient of the unknown variable x to find the value of x 9x/9 = 72/9x = 8Step 6Put in x = 8 into equation (2)3y−5x=−61......(2)3y-5(8)=-613y-40=-61Collect like terms by adding 40 to both sides of the equation 3y-40+40=-61+403y=-21Divide both sides by 3, the coefficient of y to find the value of y 3y/3=-21/3y=-7Therefore, the values of x and y that satisfy the equations are 8 and -7 respectively
