Length×base×height
1.5×0.4×3
1.8 meter cube
Answer:
V=25088π vu
Step-by-step explanation:
Because the curves are a function of "y" it is decided to take the axis of rotation as y
, according to the graph 1 the cutoff points of f(y)₁ and f(y)₂ are ±2
f(y)₁ = 7y²-28; f(y)₂=28-7y²
y=0; x=28-0 ⇒ x=28
x=0; 0 = 7y²-28 ⇒ 7y²=28 ⇒ y²= 28/7 =4 ⇒ y=√4 =±2
Knowing that the volume of a solid of revolution V=πR²h, where R²=(r₁-r₂) and h=dy then:
dV=π(7y²-28-(28-7y²))²dy ⇒dV=π(7y²-28-28+7y²)²dy = 4π(7y²-28)²dy
dV=4π(49y⁴-392y²+784)dy integrating on both sides
∫dV=4π∫(49y⁴-392y²+784)dy ⇒ solving ∫(49y⁴-392y²+784)dy
49∫y⁴dy-392∫y²dy+784∫dy =
V=4π( 
) evaluated -2≤y≤2, or 2(0≤y≤2), also
⇒ V=25088π vu
Answer:
NM = 8
Step-by-step explanation:
Given rectangle JKLM
JN = x + 3 and JL = 3x + 1
JN = 1/2JL as diagonals bisect each other and N is the midpoint of JL.
Substitute and solve for x:
x + 3 = 1/2(3x + 1)
2x + 6 = 3x + 1
3x - 2x = 6 - 1
x = 5
Find JN
JN = 5 + 3 = 8
Looking at the options, we see that
NM = JN = 8
Correct option is A
I'm pretty sure it's no...
You need to solve this "system of linear equations." In other words, find a point (x,y) that satisfies both 4x-3y=17 and 2x-5y=-11.
Try solution by elimination. Multiply the 2nd equation by -2 to obtain -4x+5y=22. Add this result to the 1st equation. I'd suggest you write this out to see what is happening.
4x-3y=17
-4x+10y=22
----------------
7y=39. Solving for y, we get y=39/7 (a rather awkward fraction).
Now find x. To do this, substitute 39/7 for y in either of the given equations. Solve the resulting equation for x.
Write your solution in the form (x, y): ( ? , 39/7).
