Given:
radius of a cylindrical construction pipe is 3 ft
lenghtis 25ft long
Required:
what is it’s volume
Explanation:
volume of cylinder:
Required answer:
Answer:
canvas $3
tube of paint $5
paint brush $4
Step-by-step explanation:
We need to choose variables for the prices of the different items, translate the sentences into equations, and solve a system of equations.
1. Define variables
Let c = price of 1 canvas, t = price of 1 tube of paint, and b = price of 1 brush.
2. Translate sentences into equations
"Jermaine bought 2 canvases, 4 tubes of paint, and 2 paint brushes for $34."
2c + 4t + 2b = 34
"Keira spent $22 on 1 canvas, 3 tubes of paint, and 1 paint brush."
c + 3t + b = 22
"Leon already has plenty of paint, so he bought 3 canvases and 2 paint brushes for $17."
3c + 2b = 17
The system of equations is
2c + 4t + 2b = 34 Eq. 1
c + 3t + b = 22 Eq. 2
3c + 2b = 17 Eq. 3
Since the third equation has only the variables c and b, we use the first equations to eliminate variable t and give us an equation in only c and b.
3 * Eq. 1 - 4 * Eq. 2
2c + 2b = 14
c + b = 7 Eq. 4
Eq. 3 and Eq. 4 form a system of equations in two variables.
3c + 2b = 17 Eq. 3
c + b = 7 Eq. 4
Solve Eq. 4 for b.
b = 7 - c Eq. 5
Substitute into Eq. 3.
3c + 2(7 - c) = 17
3c + 14 - 2c = 17
c = 3
Plug in c = 3 into Eq. 5.
b = 7 - 3
b = 4
Plug in c = 3 and b = 3 into Eq. 2.
c + 3t + b = 22 Eq. 2
3 + 3t + 4 = 22
3t + 7 = 22
3t = 15
t = 5
Answer:
canvas $3
tube of paint $5
paint brush $4
Answer:
Step-by-step explanation:
Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.
When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.
Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?
What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!
Putting all of this together gives us:
z = |mag|*(cos(angle) + isin(angle))
= 2*cos(270°) + isin(270°)).
To verify, let's consider what cos(270°) and sin(270°) are.
If you graph cos(x) and look at 270°, you get 0.
If you graph sin(x) and look at 270°, you get -1.
So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.
Answer:
The width would be 86cm
Step-by-step explanation:
Perimeter is (Width*2) +(Length*2)
Length is 96, multiply by 2 : 96*2 = 192
Subtract this from the total perimeter (364-192 = 172)
Divide this by 2 to get 1 width value (172/2 = 86)
86 cm
