Answer:
x = 2
y = 5
Step-by-step explanation:
3x + y = 11 equation (1)
-x + y = 3 multiply this equation by -1
x - y = -3 equation (2)
by adding 2 equations
4x = 8
x = 2
by sub. in Equation (2)
2 - y = -3
y = 2+3
y = 5
Answer:
61 m^3
Step-by-step explanation:
The difference in volume is (5 m)^3 - (4 m)^3, or (125 - 64) m^3, or
61 m^3
Answer:
The portion of the volume of the cup that is filled with water is 
Step-by-step explanation:
step 1
Find the volume of the paper water cup
The volume of the cone is equal to

we have


substitute


step 2
If the cup is filled with water to half its height, find out what portion of the volume of the cup is filled with water
Remember that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
In this problem the similar cone has half the height of the complete cone
so
The scale factor is equal to 1/2
therefore
The volume of the cup that is filled with water is equal to the volume of the complete cup by the scale factor elevated to the cube

therefore
The portion of the volume of the cup that is filled with water is

This should be easy because we just have to use substitution method. Substitute the value of x from the second equation into the x of the first equation.
-4(2y) + 11y = 15
-8y + 11y = 15
3y = 15 ; y = 5
Substitute this value of y to either the first or second equation.
x = 2(5) = 10
The ordered pair is therefore (10,5).
Area = pi*r^2
Circumference = 2pi*r
Step 1: find the radius from area
81pi=pi*r^2
81=r^2
9=r
Step 2: plug in radius to the circumference equation
Circumference = 2pi*r
18pi is the answer, otherwise know as 56.52 as well.