What is the discriminant of the quadratic equation 0 = _x2 + 4x

The hopper bin in the picture below is modeled by the two-dimensional figure beside it. The hopper bin is

Zepler [3.9K]

The volume of the hopper bin is the amount of feed in it

The volume of the hopper bin is 35974 cubic feet
The carnival tent can be filled to 85% of its volume and not exceed the weight limit

<h3>The volume of the hopper bin</h3>

The given parameters are:

Height of cylinder, H = 20 ft
Diameter of cylinder, D = 36 feet
Angle, θ = 52°

Start by calculating the radius (r) of the cones.

r = D/2 -------- because the cones and the cylinder have equal diameters.

So, we have:

r = 36/2 = 18

The height (h) of the cones is:

tan(θ) = h/r

This gives

tan(52) = h/18

Make h the subject

h = 18 * tan(52)

Evaluate

h = 23.04

The volume is then calculated as:

Volume = Volume of cylinder + 2 * Volume of cone

This gives

Volume = πr^2H + 2 * 1/3πr^2h

Volume = πr^2H + 2/3πr^2h

Factor out πr^2

Volume = πr^2(H + 2/3h)

Substitute known values

Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)

Evaluate

Volume = 35973.85 cubic feet

Hence, the volume of the hopper bin is 35974 cubic feet

<h3>The weight limit of the hopper bin</h3>

The given parameters are:

Maximum weight = 500000 pounds
Feed weight = 22 pounds per cubic feet

For a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:

Weight = 22 * 35974 pounds

Weight = 791428 pounds

At 85% full, the weight wuld be:

Weight = 85% * 791428 pounds

Weight = 672713.8 pounds

672713.8 pounds is greater than the weight limit of 500000 pounds.

Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit

Read more about volumes at:

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4 0

2 years ago

Help ill give u 25 points

atroni [7]

Answer:

I need points

Step-by-step explanation:

I'm so so sorry

3 0

3 years ago

Suppose that many large samples are taken from a population and that the

Eddi Din [679]

Answer:

99.7% of the sample proportions will fall between 0.133 and 0.307.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 0.22

Standard deviation = 0.029

99.7% of the sample proportions will fall within which of the following intervals?

Within 3 standard deviations of the mean.

Lower end: 0.22 - 3*0.029 = 0.133

Upper end: 0.22 + 3*0.029 = 0.307

99.7% of the sample proportions will fall between 0.133 and 0.307.

7 0

2 years ago

Mia is calculating the volume of the cylinder below using the following work. A cylinder with height of 47 meters and diameter o

inn [45]

Mia’s first error was " she forgot to multiply π by (17.5)²(47) "

Step-by-step explanation:

The formula of the volume of a cylinder is V = π r² h, where

r is the radius of the base of the cylinder
h is the height of the cylinder

∵ The diameter of the base of the cylinder is 35 meters

∵ The radius = $\frac{1}{2}$ × diameter

∴ The radius = $\frac{1}{2}$ × 35 = 17.5 meters

∴ r = 17.5

∵ The height of the cylinder = 47 meters

∴ h = 47

- Substitute r and h in the formula of the volume

∴ V = π (17.5)²(47)

∵ Mai's first step is V = (17.5)²(47)

- She forgot to put π

∴ Her first error is she forgot to multiply π by (17.5)²(47)

Mia’s first error was " she forgot to multiply π by (17.5)²(47) "

Learn more:

You can learn more about the volume in brainly.com/question/6443737

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3 0

3 years ago

Read 2 more answers

Factor out the greatest common factor

saveliy_v [14]

Answer:

B

$5x(2x - 3)$

Step-by-step explanation:

The common factor of the expression is 5x

4 0

3 years ago

What is the discriminant of the quadratic equation 0 = _x2 + 4x – 2?