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2 years ago

What are these fractions in simplest form?

1 answer:

8 0

$\frac{16y^{3}}{20y^{4}} = \frac{4}{5y}$
$\frac{6xy}{16y} = \frac{3x}{8}$
$\frac{abc}{10abc} = \frac{1}{10}$
$\frac{mn^{2}}{pm^{5}n} = \frac{n}{pm^{4}}$
$\frac{12h^{3}k}{16h^{2}k^{2}} = \frac{3h}{4k}$
$\frac{8x}{10y} = \frac{4x}{5y}$
$\frac{24n^{2}}{28n} = \frac{6n}{7}$
$\frac{30hxy}{54kxy} = \frac{5h}{9k}$
$\frac{5jh}{15jh^{3}} = \frac{1}{3h^{2}}$
$\frac{20s^{2}t^{3}}{16st^{5}} = \frac{5s}{4t^{2}}$

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The quantities xxx and yyy are proportional. xxx yyy 888 222 161616 444 323232 888 Find the constant of proportionality (r)(r)le

Tcecarenko [31]

Answer:

Step-by-step explanation:

1/4

4 0

2 years ago

A rectangular tank that is 5324 ft cubed with a square base and open top is to be constructed of sheet steel of a given thicknes

marishachu [46]

Answer:

Side of 22 and height of 11

Step-by-step explanation:

Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:

$V = s^2h = 5324$

$h = 5324 / s^2$

As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank

Base area with open top $s^2$

Side area 4sh

Total surface area $A = s^2 + 4sh$

We can substitute $h = 5324 / s^2$

$A = s^2 + 4s\frac{5324}{s^2}$

$A = s^2 + 21296/s$

To find the minimum of this function, we can take the first derivative, and set it to 0

$A' = 2s - 21296/s^2 = 0$

$2s = 21296/s^2$

$s^3 = 10648$

$s = \sqrt[3]{10648} = 22$

$h = 5324 / s^2 = 5324 / 22^2 = 11$

4 0

2 years ago

PROBLEM SOLVING You are participating in an orienteering competition. The diagram shows the position of a river that cuts throug

Wewaii [24]

Answer:

The shortest distance is 2.2 miles

Step-by-step explanation:

we know that

The shortest distance you must travel to reach the river is the perpendicular distance to the river

step 1

Find the slope of the line perpendicular to the river

we have

$y=3x+2$

The slope of the river is m=3

Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)

therefore

The slope of the line perpendicular to the river is

$m=-1/3$

step 2

Find the equation of the line into point slope form

$y-y1=m(x-x1)$

we have

$m=-1/3$

$point(2,1)$

substitute

$y-1=-(1/3)(x-2)$

step 3

Find the intersection point of the river and the line perpendicular to the river

we have

$y=3x+2$ ------> equation A

$y-1=-(1/3)(x-2)$ -----> equation B

Solve the system by graphing

The intersection point is (-0.1,1,7)

see the attached figure

step 3

Find the distance between the points (2,1) and (-0,1,1.7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$d=\sqrt{(1.7-1)^{2}+(-0.1-2)^{2}}$

$d=\sqrt{(0.7)^{2}+(-2.1)^{2}}$

$d=2.2\ miles$

6 0

2 years ago

The dot plot represents the amount of rain recorded by rain gauges in different locations around a city. A number line going fro

adell [148]

Answer:

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all of A?

Mrac [35]

A = {1, 2, 5, 6, 8}
{1} U {2, 5, 6, 8}
{2} U {1, 5, 6, 8}
{5} U {1, 2, 6, 8}
{6} U {1, 2, 5, 8}
{8} U {1, 2, 5, 6}
{1, 2} U {5, 6, 8}
{1, 5} U {2, 6, 8}
{1, 6} U {2, 5, 8}
{1, 8} U {2, 5, 6}
{1, 2, 5} U {6, 8}
{1, 2, 6} U {5, 8}
{1, 2, 8} U {5, 6}
{1, 5, 6} U {2, 8}
{1, 5, 8} U {2, 6}
{1, 6, 8} U {2, 5}
The answer is 15 distinct pairs of disjoint non-empty subsets.

5 0

2 years ago