Mathematics, 19.09.2019 16:40 walkereddie580

Monte performs an experiment using 2 identical graduated cylinders with a radius of 2 cm. the volume of the liquid in the first graduated cylinder is 188.4 cm3. the volume of the liquid in the second graduated cylinder is 314 cm3.
what is the difference in the height of the liquid in the two cylinders?
use 3.14 to approximate pi.

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Answer from: davelezow72301

The difference of height is 10 cm

Step-by-step explanation:

Monte performs an experiment using 2 identical graduated cylinders with a radius of 2 cm.

The volume of the liquid in the first graduated cylinder is 188.4 cm³

The volume of the liquid in the second graduated cylinder is 314 cm³

Let height of first graduated cylinder be h₁ and radius (r) = 2 cm

Let height of second graduated cylinder be h₂ and radius (r) = 2 cm

Formula:

$\text{Volume of cylinder}=\pi r^2h$

$\text{Volume of 1st cylinder}=\pi\cdot 2^2h_1$

$188.4=3.14\cdot 2^2\cdot h_1$

h_1=15 cm

$\text{Volume of 2nd cylinder}=\pi\cdot 2^2h_2$

$314=3.14\cdot 2^2\cdot h_2$

h_2=25 cm

The difference in the height of the liquid in two cylinder,

$\Rightarrow h_2-h_1$

$\Rightarrow 25-15$

$\Rightarrow 10$ cm

Hence, The difference of height is 10 cm

Answer from: Quest

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

$y\propto x$

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

Answer from: Quest

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

$\tan\left(x\right)=\frac{\left[altitude\right]}{\left[base\right]}=\frac{p}{r}$

$\tan\left(x\right)=\frac{p}{r}$

$\frac{p}{r}=tan(x)$

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).

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