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Xelga [282]
3 years ago
6

A construction company can remove 3/5 tons of dirt from a construction site each hour. How long will it take them to remove 30 t

ons of dirt from the site?
Mathematics
1 answer:
baherus [9]3 years ago
5 0

Answer:

It will take them 50 hours

Step-by-step explanation:

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Write the number 270 as a sum of three numbers so that the sum of the products taken two at a time is a maximum. (Enter the thre
iren [92.7K]

Answer:

x=y=z=90.

Step-by-step explanation:

let the 3 numbers be x,y,z.

let s be sum

s=x+y+z

we need to maximize xy+yz+zx

or , xy + y(270-(x+y))+x(270-(x+y)) = P(x)

Use Lagrange's Multipliers

⇒ΔP= λΔS

⇒\frac{x+y}{x+z} =1

⇒y=x

⇒\frac{x+z}{x+y} =1

⇒z=y

⇒x=y=z

⇒3x = 270

⇒x= 90

hence, x=y=z=90.

3 0
2 years ago
Find the range of the quadratic function. (y=2x^2-20x+53)
Anit [1.1K]

Answer: The range is y ≥ 3.

Step-by-step explanation:

When we have an equation:

y = f(x)

The range is the set of the possible values of y.

In this case, we have:

y = f(x) = 2*x^2 - 20*x + 53

This is a quadratic equation, and the leading coefficient is positive. This means that the arms of the graph will open upwards.

Then the minimum value of y will be the vale at the vertex.

We know that for a quadratic equation of the form:

a*x^2 + b*x + c

The vertex is at:

x = -b/2a

Then in this case, the vertex will be at:

x = -(-20)/(2*2) = 20/4 = 5

Then the smallest value of this function will be:

f(5) = 2*5^2 - 20*5 + 53 = 3

This is the smallest value that y can take, and y can take any value greater than 3.

Then the range can be written as:

y ≥ 3.

4 0
2 years ago
Why is it necessary to choose a single frame of reference when measuring motion?
Fantom [35]
It is necessary to choose a single frame of reference when measuring motion because c<span>hoosing a meaningful frame of reference allows you to describe the motion in a clear and relevant manner. 

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
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6 0
3 years ago
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the come to the volum
Nimfa-mama [501]

Answer:

\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}

Step-by-step explanation:

\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}

\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}

5 0
2 years ago
The sum of 3 consecutive even numbers is 48. What are the smallest of these numbers
goldenfox [79]

Answer:

The smallest is 14.

Step-by-step explanation:

Let the numbers be x, x+2 and x+4, then:

x + x + 2 + x + 4 = 48

3x + 6 = 48

3x = 42

x = 14.

So the 3 numbers are 14, 16 and 18.

7 0
3 years ago
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