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2 years ago

Prove that there exists a pair of consecutive integers such that one of these integers is a perfect square

Mathematics

1 answer:

mr Goodwill [35]2 years ago

7 0

Horrible wording but I'll say 0 squared and 1 squared

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Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown. The height is S

Lubov Fominskaja [6]

<h2>Explanation:</h2><h2></h2>

We know that the volume of a prism is defined by:

$V=lwh \\ \\ \\ Where: \\ \\ l:length \\ \\ w:width \\ \\ h:height \\ \\ \\ l=\frac{d-2}{3d-9} \\ \\ w=\frac{4}{d-4} \\ \\ h=\frac{2d-6}{2d-4}$

Substituting values:

$V=\left(\frac{d-2}{3d-9}\right)\left(\frac{4}{d-4}\right)\left(\frac{2d-6}{2d-4}\right) \\ \\ \\ Simplifying: \\ \\ V=\frac{d-2}{3d-9}\cdot \frac{4}{d-4}\cdot \frac{d-3}{d-2} \\ \\ V=\frac{\left(d-2\right)\cdot \:4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)\left(d-2\right)} \\ \\ V=\frac{4\left(d-3\right)}{\left(3d-9\right)\left(d-4\right)} \\ \\ V=\frac{4\left(d-3\right)}{3\left(d-3\right)\left(d-4\right)}$

$Finally: \\ \\ \boxed{V=\frac{4}{3\left(d-4\right)}}$

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2 years ago

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A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variabl

dusya [7]

Answer:

i think its D. C. or E. I'm not that great in math im kind of struggling thru it

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1 year ago

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Mrs. Varner deposited q dollars in a bank account that has been earning annual interest. The total value of the account is based

Ray Of Light [21]

The answer is f(x) = q * 1.025<span>x + 5, do you have that?

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2 years ago

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The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randoml

PIT_PIT [208]

Answer:

Provided in the picture below.

Step-by-step explanation:

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2 years ago

Two boats leave port at noon. Boat 1 sails due east at 12 knots. Boat 2 sails due south at 8 knots. At 2 pm the wind diminishes

Ivan

Answer:

14.86 knots.

Step-by-step explanation:

<em>Given that:</em>

The boats leave the port at noon.

Speed of boat 1 = 12 knots due east

Speed of boat 2 = 8 knots due south

At 2 pm:

Distance traveled by boat 1 = 24 units due east

Distance traveled by boat 2 = 16 units due south

Now, speed of boat 1 changes to 9 knots:

At 3 pm:

Distance traveled by boat 1 = 24 + 9= 33 units due east

Distance traveled by boat 2 = 16+8 = 24 units due south

Now, speed of boat 1 changes to 8+7 = 15 knots

At 5 pm:

Distance traveled by boat 1 = 33 + 2 $\times$ 9= 51 units due east

Distance traveled by boat 2 = 24 + 2 $\times$ 15 = 54 units due south

Now, the situation of distance traveled can be seen by the attached right angled $\triangle AOB$ .

O is the port and A is the location of boat 1

B is the location of boat 2.

Using pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units$

so, the total distance between the two boats is 74.28 units.

Change in distance per hour = $\dfrac{Total\ distance}{Total\ time}$

$\Rightarrow \dfrac{74.28}{5} = 14.86\ knots$

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2 years ago