The answer is: False, because, by definition, the distance (which is a scalar quantity) is the absolute value of the displacement. This means that the distance cannot be negative, but the displacement (which is define as a vector quantity can be positive or negative.

6 0

4 years ago

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating

natulia [17]

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( $49\frac{y^{5} }{5}-392\frac{y^{3}}{3}+784y$ ) evaluated -2≤y≤2, or 2(0≤y≤2), also

$V=8\pi(49\frac{2^{5} }{5}-392\frac{2^{3} }{3}+784.2)$ ⇒ V=25088π vu

8 0

3 years ago

ABCD is a rectangle Ac=3x+4 and BD=5x-50 what is the value of x

rosijanka [135]

The value of x is 27

Explanation:

5x-50=3x+4

5x-3x=4+50

2x=54

x=27

8 0

3 years ago