The volume of cube and rectangular prism are same. Option B.
Step-by-step explanation:
Given,
The length of the edge of the cube (a) = 5 cm
The dimension of rectangular prism (l×b×h) = 5 cm×25 cm×1 cm
To find the relation between the volume of cube and rectangular prism.
Formula
The volume of a cube = a³ cube cm
The volume of rectangular prism = l×b×h cube cm
Now,
The volume of a cube = 5³ cube cm = 125 cube cm
The volume of rectangular prism = 5×25×1 cube cm = 125 cube cm
Hence,
The volume of cube and rectangular prism are same.
<span>x² +y² -4x -6y +8=0
(x² -4x) +(y² -6y) = -8
We are going to complete square for x and y,
it should look like a²+2ab+b² = (a +b)², or </span>a²-2ab+b² = (a -b)²,
<span>
(x²-2*2x+2²) -2² + (y²-2*3y +3²)-3²=- 8
(x-2)²+(y-3)²-4-9=-8
</span>(x-2)²+(y-3)²=-8+13
(x-2)²+(y-3)²=5
<span>
Formula a circle (x-h)²+(y-k)²=R², where vertex has coordinates (h, k)
So , for our circle vertex (2,3) and radius = </span>√5<span>
</span>
<span>If you would like to know in which step did the student first make
an error, you can find this using the following steps:
y = 4 - 2z
4y = 2 - 4z
________________
-4(y) = -4(4 - 2z)
</span>4y = 2 - 4z<span>
________________
-4y = -16 + 8z ... Step 2
</span><span>4y = 2 - 4z</span><span>
________________
0 = -16 + 8z + 2 - 4z</span>
<span>16 - 2 = 4z</span>
<span>14 = 4z</span>
<span>z = 14/4 = 7/2</span>
<span>
The correct result would be: Student made an error in Step 2.</span>
Answer:
-28
Step-by-step explanation:
2xy=2(7)(-2)=14(-2)=-28
Answer:
2000π in³/s
or 6283.2 in³/s
Step-by-step explanation:
dr/dt = 5
volume of sphere is given as
v = (4/3)(π)r³
differentitate wrt r
dv/dr = 3×4/3 ×π×r²
dv/dr = 4πr²
put r = 10
dv/dr = 4π(10)²
dv/dr = 400π
by chain rule
dv/dt = dv/dr ×dr/dt
dv/dt = 400π× 5
dv/dt = 2000π in³/s
or dv/dt =6283.2 in³/s
