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Vikentia [17]
3 years ago
13

Joe walked 4/9 mile in 4/5 of an hour what is his unit per mile

Mathematics
2 answers:
erastovalidia [21]3 years ago
8 0
Find common denominators and move from there
Marta_Voda [28]3 years ago
6 0
(4/9) mile in (4/5) hr
we want x mile in (5/5) hr
Set up a proportion.
(4/9) / (4/5) = x / (5/5)
(4/5)x = (4/9)(5/5)
(4/9)x = (4/5)(5/5)
(4/9)x = (4/5)
Multiply both sides by (9/4) to clear the fraction
x = (4/5)(9/4)
x = 9/5 hr per mile
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5 0
3 years ago
Find the slope of the tangent line to the given polar curve at the point specified by the value of θ
MariettaO [177]

The given curve has equation

<em>r(θ)</em> = 9 + 8 cos(<em>θ</em>)

and its derivative is

d<em>r</em>/d<em>θ</em> = -8 sin(<em>θ</em>)

When <em>θ</em> = <em>π</em>/3, we have <em>r</em> (<em>π</em>/3) = 13, and d<em>r</em>/d<em>θ</em> (<em>π</em>/3) = -4√3.

Differentiate these with respect to <em>θ</em> :

d<em>y</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)

d<em>x</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ</em>) sin(<em>θ</em>)

In polar coordinates, we have

<em>y(θ)</em> = <em>r(θ)</em> sin(<em>θ</em>)

<em>x(θ)</em> = <em>r(θ)</em> cos(<em>θ</em>)

and when <em>θ</em> = <em>π</em>/3, we have <em>y</em> (<em>π</em>/3) = 13√3/2 and <em>x</em> (<em>π</em>/3) = 13/2.

The slope of the tangent line to the curve is d<em>y</em>/d<em>x</em>. By the chain rule,

d<em>y</em>/d<em>x</em> = d<em>y</em>/d<em>θ</em> • d<em>θ</em>/d<em>x</em> = (d<em>y</em>/d<em>θ</em>) / (d<em>x</em>/d<em>θ</em>)

d<em>y</em>/d<em>x</em> = (d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)) / (d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ</em>) sin(<em>θ</em>))

When <em>θ</em> = <em>π</em>/3, the slope is

d<em>y</em>/d<em>x</em> = (-4√3 sin(<em>π</em>/3) + 13 cos(<em>π</em>/3)) / (-4√3 cos(<em>π</em>/3) - 13 sin(<em>π</em>/3))

d<em>y</em>/d<em>x</em> = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))

d<em>y</em>/d<em>x</em> = - 1/(17√3)

So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is

<em>y</em> - 13√3/2 = -1/(17√3) (<em>x</em> - 13/2)

<em>y</em> = -(<em>x</em> - 338)/(17√3)

4 0
2 years ago
What does this equal?
guajiro [1.7K]
It equals 4..........
6 0
3 years ago
If two cylinders are similar and the ratio between the lengths of their edges is 2:5 what is the ratio of their volumes
Hunter-Best [27]
We know that
[scale factor] is equal to the ratio <span>between the lengths of their edges
so
scale factor=2/5

volume smaller cylinder/volume larger cylinder=[scale factor]</span>³
volume smaller cylinder/volume larger cylinder=[2/5]³---> 8/125

the answer is
8/125
7 0
2 years ago
Read 2 more answers
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