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3 years ago

Find the area of the large six sided figure with a perimeter of 36ft

1 answer:

wel3 years ago

6 0

The area of a hexagon is rad(3)/2 x a^2
Since the perimeter is 36ft, then one side is a= 36/6 = 6ft
So the area is rad(3)/2 x 36 = 93.53 square feet

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Find the length of the missing side of the right triangle given the area of the two triangles find the length of the sides of th

irina [24]

From here, it looks like all three sides of the right triangle are missing. I don't see any of them in the question.

3 0

3 years ago

Find the lcd. Add or subtract the fractions. Simplify if needed. (- 3/16) + (- 5/2)

Solnce55 [7]

Answer:

$\boxed{-\frac{43}{16}}$

Step-by-step explanation:

$-\frac{3}{16} + (-\frac{5}{2} )$

$= -\frac{3}{16} - \frac{5}{2}$

$= \frac{-3 - 5(8)}{16}$

$= \frac{-3 - 40}{16}$

$= -\frac{43}{16}$

8 0

3 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

4 years ago

If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in cm/min) at which the diameter d

grin007 [14]

Answer:

The diameter decreases at a rate of 0.053 cm/min.

Step-by-step explanation:

Surface area of an snowball

The surface area of an snowball has the following equation:

$S_{a} = \pi d^2$

In which d is the diameter.

Implicit differentiation:

To solve this question, we differentiate the equation for the surface area implictly, in function of t. So

$\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}$

Surface area decreases at a rate of 3 cm2/min

This means that $\frac{dS_{a}}{dt} = -3$

Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.

This is $\frac{dd}{dt}$ when $d = 9$ . So

$\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}$

$-3 = 2*9\pi\frac{dd}{dt}$

$\frac{dd}{dt} = -\frac{3}{18\pi}$

$\frac{dd}{dt} = -0.053$

The diameter decreases at a rate of 0.053 cm/min.

7 0

3 years ago

Using the formula below or Excel, find the correlation coefficient, r, for this set of scores. Answer choices are rounded to the

RideAnS [48]

The correlation coefficient measures the relationship between the two variables

The correlation coefficient is 0.234

<h3>How to determine the correlation coefficient</h3>

The formula of correlation coefficient is:

$r = \frac{1}{n - 1} * \sum{(\frac{x - \bar x}{\sigma_x})*(\frac{y - \bar y}{\sigma_y})$

Using the dataset from the complete question, we have:

$r = \frac{1}{5 - 1} * 0.9375$

Evaluate the difference

$r = \frac{1}{4} * 0.9375$

Evaluate the quotient

$r = 0.234375$

Approximate

$r = 0.234$

Hence, the correlation coefficient is 0.234

Read more about correlation coefficient at:

brainly.com/question/4219149

3 0

2 years ago