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3 years ago

Last night 30cm of snow fell in 6 hours. If it continues snowing at the

Mathematics

1 answer:

mafiozo [28]3 years ago

5 0

Answer: 9 hrs for 45cm of snow to fall

Step-by-step

If 30cm = 6 hrs

Then divide 30/6 to get the unit rate of the amount of snow per hr

Which is 5/1

So 5cm per hr

Then add 30+5+5+5 to get 45

And since we know 5cm equal 1 hr

Add the original amount of hours which is 6 plus 3 ones

Which is 6+1+1+1

In total, it will take 9 hrs for 45cm of snow to fall.

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A fountain shoots water into the air. The graph shows a water droplet's height y in feet x seconds after it is shot from the fou

katrin2010 [14]

Answer:

A water droplet reaches it's maximum height after 6 s

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

Dada la ecuacion 25x2 + 4y2 = 100, determina las coordenadas de los vertices, focos, las longitudes de los respectivos ejes mayo

Likurg_2 [28]

Answer:

The given equation is

$25x^{2} +4y^{2}=100$

Which represents an elipse.

To find its elements, we need to divide the equation by 100

$\frac{25x^{2} +4y^{2} }{100} =\frac{100}{100} \\\frac{x^{2} }{4} +\frac{y^{2} }{25} =1$

Where $a^{2} =25$ and $b^{2}=4$ . Remember that the greatest denominator is $a$ , and the least is $b$ . So, we extract the square root on each equation.

$a=5$ and $b=2$ .

In a elipse, we have a major axis and a minor axis. In this case, the major axis is vertical and the minor axis is horizontal, that means this is a vertical elipse.

The length of the major axis is $2a=2(5)=10$ .

The length of the minor axis is $2b=2(2)=4$ .

The vertices are $(0,5);(0,-5)$ and $(2,0);(-2,0)$ .

Now, the main parameters of an elipse are related by

$a^{2}=b^{2} +c^{2}$ , which we are gonna use to find $c$ , the parameter of the focus.

$c=\sqrt{a^{2}-b^{2} }=\sqrt{25-4}=\sqrt{21}$

So, the coordinates of each focus are $(0,\sqrt{21})$ and $(0,-\sqrt{21})$

The eccentricity of a elipse is defined

$e=\frac{c}{a}=\frac{\sqrt{21} }{5} \approx 0.92$

The latus rectum is defined

$L=\frac{2b^{2} }{a}=\frac{2(4)}{5} =\frac{8}{5} \approx 1.6$

Finally, the graph of the elipse is attached.

7 0

3 years ago

an open box is to be made from a two-foot by three-foot rectangular piece of metal by cutting equal squares from the corners and

tensa zangetsu [6.8K]

The volume for the largest box will be 1.056 foot³. This can find out by application of differentiation.

What is AOD?

AOD is nothing but application of differentiation. It implies scopes where we can use differentiation to make our calculations easy.

Here, given

Length and breadth = 2,3 foot

Let us consider length of side of square = x

So, after cutting squares left sides of rectangular sheet = 2-2x , 3-2x

So, volume = (2-2x)*(3-2x)*x

v = 4x³ - 10x² + 6x

To find largest volume , $\frac{dv}{dx}$ = 0

$\frac{dv}{dx}$ = 12x² - 20x + 6

12x² - 20x + 6 = 0

x = 0.4 , 1.3

But, for 1.3 volume will be negative i.e. not possible.

So, volume = 2.2*1.2*0.4

= 1.056 foot³

Learn more about differentiation from given link:

brainly.com/question/954654

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1 year ago

How is completing the square beneficial ? Edge 2020 key words

MariettaO [177]

Allows you to factor a function that was previously not able to be factored

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3 years ago

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A bank loaned out $14000, part of it at the rate of 9% per year and the rest at 17% per year. If the interest received in one ye

WINSTONCH [101]

Using simple interest, it is found that $13,872 was loaned at 9%.

<h3>Simple Interest</h3>

The amount of money after t years in simple interest is modeled by:

$A(t) = P(1 + rt)$

In which:

P is the initial amount.

r is the interest rate, as a decimal.

The interest earned is:

$I(t) = Prt$

A bank loaned out $14000, in two parts, hence:

$P_2 = 14000 - P_1$

Part of it at the rate of 9% per year and the rest at 17% per year, hence:

$r_1 = 0.09, r_2 = 0.17$

The interest received in one year totaled $2000, hence:

$I_2 = 2000 - I_1$

Then:

$I_1 = 0.09P_1$

$I_2 = 0.17I_2$

$14000 - P_1 = 0.17(2000 - I_1)$

Isolating $I_1$ as a function of $P_1$ , then we can replace on the equation for the first interest.

$14000 - P_1 = 340 - 0.17I_1$

$0.17I_1 = -13660 + P_1$

$I_1 = \frac{P_1 - 13660}{0.17}$

Then:

$I_1 = 0.09P_1$

$\frac{P_1 - 13660}{0.17} = 0.09P_1$

$P_1 - 13660 = 0.0153P_1$

$0.9847P_1 = 13660$

$P_1 = \frac{13660}{0.9847}$

$P_1 = 13872$

$13,872 was loaned at 9%.

To learn more about simple interest, you can take a look at brainly.com/question/25296782

3 0

2 years ago