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4 years ago

How do you change the equation 10q−5r=30 so that r is the independent variable?

Mathematics

1 answer:

Schach [20]4 years ago

8 0

Answer:

r=2q-6

Step-by-step explanation:

10q-5r=30

Subtract 10q from both sides:

-5r=30-10q

Divide both sides by -5:

r=2q-6

Hope this helps!

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-10 + 15xy = 20 Direct and inverse variation. constant of variation (k)

lozanna [386]

Answer:

This is an inverse variation, and the constant of variation is k = 2.

Step-by-step explanation:

Direct variation is something like:

y = k*x

Where k is the constant of variation.

So as x increases also increases y.

Inverse variation is something like:

y = k/x

k is the constant of variation.

In this case, if x increases, y decreases.

Now let's look at the equation:

-10 + 15*x*y = 20

Let's isolate y in one side of the equation:

15*x*y = 20 + 10 = 30

15*x*y = 30

y = 30/(15*x) = (30/15)/x = 2/x

y = 2/x

Then we can conclude that this is an inverse variation, with a constant of variation equal to 2.

4 0

3 years ago

Suppose that when your friend was born, your friend's parents deposited $9000 in an account paying

MaRussiya [10]

Answer: $ 23,132.14

Step-by-step explanation:

A=P(1+r/n)^nt

A=9000(1+.068/4)^4x14

7 0

3 years ago

approximately 31000 citizens of a country dies in automobile accidents in 2015 express this toll in depths per day

Gelneren [198K]

84 is the asnwer you are looking for

8 0

3 years ago

For ΔABC, ∠A = 8x - 10, ∠B = 10x - 40, and ∠C = 3x + 20. If ΔABC undergoes a dilation by a scale factor of 1 2 to create ΔA'B'C'

Sholpan [36]

Answer: It does not confirm that ΔABC∼ΔA'B'C by the AA criterion as the measure of angle B is negative which is not possible.

Step-by-step explanation:

Since we have given that

In ΔABC,

∠A = 8x - 10, ∠B = 10x - 40, and ∠C = 3x + 20

In ΔA'B'C',

∠A' = 6x + 10, ∠B' = 70 - x, and ∠C' = 10x 2

Since ΔABC gets a dilation by a scale factor of $\dfrac{1}{2}$

So, it becomes,

$\dfrac{\angle A}{\angle A'}=\dfrac{1}{2}\\\\\dfrac{8x-10}{6x+10}=\dfrac{1}{2}\\\\2(8x-10)=6x+10\\\\16x-20=6x+10\\\\16x-6x=10+20\\\\10x=30\\\\x=\dfrac{30}{10}=3$

Now, put the value of

$\angle B=10(3)-40=30-40=-10\\\\and \angle B'=70-30=40$

It does not confirm that ΔABC∼ΔA'B'C by the AA criterion as the measure of angle B is negative which is not possible.

8 0

3 years ago

g Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the sh

Maslowich

Answer:

0.3537 feet per minute.

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=10$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

If the Base Diameter = Height of the Cone

The radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=10$

We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.

$When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute$

When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.

7 0

4 years ago