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3 years ago

10

The length of the radius of a bicycle wheel is 13 in. Which of the following is closest to the distance the wheel will travel in

three revolutions

1 answer:

chubhunter [2.5K]3 years ago

4 0

Answer:

Step-by-step explanation:

r=13in

Perimeter of a circle is 2πr

P=2×22/7×13

P=81.71in.

If it will make 3 revolution then it will have move 3 times it perimeter

3×81.71

245.14in

The distance the wheel will traveled is 245.14in

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Abbie is 5 years older than Cathy.

nlexa [21]

14 because 14 times 2 is 28 which is less than 30

5 0

2 years ago

If triangle DEF is an isosceles triangle with DE is congruent to EF, find x and the measure of each side

Rudik [331]

Step-by-step explanation:

Given that,

DE = 8x - 13

EF = 5x + 17

DF = x + 21

Also,

DE = EF

which means that,

8x - 13 = 5x + 17

8x - 5x = 17 + 13

3x = 30

x = 30/3

x = 10

Now,

DE = 8x - 13 = 8×10 - 13 = 80 - 13 = 67cm

EF = 5x + 17 = 5×10 + 17 = 50 + 17 = 67cm

DF = x + 21 = 10 + 21 = 31cm

3 0

2 years ago

Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a fun

WITCHER [35]

Answer:

Required solution (a) $f(x,y,z)=xyz+3z^2+C$ (b) 40.

Step-by-step explanation:

Given,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k$

(a) Let,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}$

Then,

$f_x=yz,f_y=xz,f_z=xy+6z$

Integrating $f_x$ we get,

$f(x,y,z)=xyz+g(y,z)$

Differentiate this with respect to y we get,

$f_y=xz+g'(y,z)$

compairinfg with $f_y=xz$ of the given function we get,

$g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)$

Then,

$f(x,y,z)=xyz+h(z)$

Again differentiate with respect to z we get,

$f_z=xy+h'(z)=xy+6z$

on compairing we get,

$h'(z)=6z\implies h(z)=3z^2+C$ (By integrating h'(z)) where C is integration constant. Hence,

$f(x,y,z)=xyz+3z^2+C$

(b) Next, to find the itegration,

$\int_C \vec{F}.dr=\int_C \nabla f. d\vec{r}=f(5,4,2)-f(2,0,-2)=(52+C)-(12+C)=40$

3 0

3 years ago

How do you find a volume of a cone?

Dennis_Churaev [7]

Answer:

V = (1/3)πr²h

Step-by-step explanation:

The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

Cylinder Volume = πr²h

Cone Volume = (1/3)πr²h

where r is the radius (of the base), and h is the height perpendicular to the circular base.

_____

<em>Comment on area and volume in general</em>

You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...

V = Bh . . . . . for an object with congruent parallel "bases"

V = (1/3)Bh . . . . . for a pointed object with base area B.

This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)

Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)

__

* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.

4 0

2 years ago

I don't know how to find angle 1

Ronch [10]

I think it's 150! Hope this helps :)

7 0

3 years ago