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3 years ago

Categorize each of the following equations as a linear equation in one variable or not.

Mathematics

1 answer:

prohojiy [21]3 years ago

6 0

2x + 6 = 5
5x – 9 = 8x – 4
5x = 2y – 8
6b + 4 = 2
6 + 4 = 10

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Gravel is being dumped from a conveyor belt at a rate of 20 ft3 /min and its coarseness is such that it forms a pile in the shap

pantera1 [17]

Answer:

The height of the pile is increasing at the rate of $\mathbf{ \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

Step-by-step explanation:

Given that :

Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min

i.e $\dfrac{dV}{dt}= 20 \ ft^3/min$

we know that radius r is always twice the diameter d

i.e d = 2r

Given that :

the shape of a cone whose base diameter and height are always equal.

then d = h = 2r

h = 2r

r = h/2

The volume of a cone can be given by the formula:

$V = \dfrac{\pi r^2 h}{3}$

$V = \dfrac{\pi (h/2)^2 h}{3}$

$V = \dfrac{1}{12} \pi h^3$

$V = \dfrac{ \pi h^3}{12}$

Taking the differentiation of volume V with respect to time t; we have:

$\dfrac{dV}{dt }= (\dfrac{d}{dh}(\dfrac{\pi h^3}{12})) \times \dfrac{dh}{dt}$

$\dfrac{dV}{dt }= (\dfrac{\pi h^2}{4} ) \times \dfrac{dh}{dt}$

we know that:

$\dfrac{dV}{dt}= 20 \ ft^3/min$

So;we have:

$20= (\dfrac{\pi (15)^2}{4} ) \times \dfrac{dh}{dt}$

$20= 56.25 \pi \times \dfrac{dh}{dt}$

$\mathbf{\dfrac{dh}{dt}= \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

The height of the pile is increasing at the rate of $\mathbf{ \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

8 0

3 years ago

a fisherman travels 9mi downstream with the current in the same time he travels 3 mi upstream against the current. if the speed

netineya [11]

Answer:

10 mph

Step-by-step explanation:

speed of boat in still water = x

speed of current = 5

speed of boat with current (downstream) = x + 5

speed of boat against current (upstream) = x - 5

distance downstream = 9

distance upstream = 3

time = t

speed = distance/time

distance = speed × time

downstream:

9 = (x + 5)t

upstream:

3 = (x - 5)t

9 = xt + 5t

3 = xt - 5t

9 = xt + 5t

-3 = -xt + 5t

-----------------

6 = 10t

t = 0.6

9 = (x + 5)0.6

15 = x + 5

x = 10

5 0

1 year ago

Rewrite 1 / 6 barrels over 2 over 5 hours as a unit rate

Akimi4 [234]

Answer:

5/12 barrel/hour

Step-by-step explanation:

Type this as a fraction:

(1/6) barrel

--------------------

(2/5) hours

Division by 2/5 is equivalent to multiplication by 5/2:

1 5

--- barrel * -------------- = 5/12 barrel/hour

6 2 hours

Alternatively, this problem could be done using decimal fractions:

0.1667 barrel

-------------------- = 0.416666 barrel/hour = 5/12 barrel/hour

0.4 hours

5 0

3 years ago

About 786,700,000 passengers traveled by plane in the United States in 2010. What is

Schach [20]

Answer: 7.867 x 10^8

Step-by-step explanation:

(the “^8” is an exponent of 8)

4 0

3 years ago

A student timed his drive to work each day for three days. The times are shown below:

cupoosta [38]

Answer:

20 minutes

Step-by-step explanation:

The mean, or average of a data set can be found by adding all the values together, and dividing by the number of values.

The data set is: 20 minutes, 22 minutes and 18 minutes

1. Add the values together

Add all the numbers in the set together.

Data set: 20, 22, 18

Add them: 20+22+18

2. Divide by the number of values

Count how many numbers are in the set.

In this set, there are 3 numbers.

Divide 60 by 3

60/3 =20

20 minutes

His mean time is 20 minutes.

8 0

3 years ago

Read 2 more answers