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Andru [333]
3 years ago
8

Henry and his family are eating at a rotating restaurant at the top of a tower. The restaurant rotates clockwise 90° every 15 mi

nutes. When the family sat down, their table was located at (-4, 4) in relation to the center of the restaurant. Where is their table located 30 minutes later, in relation to the center of the restaurant? Use complete sentences to justify your answer.
Mathematics
1 answer:
frutty [35]3 years ago
4 0

Answer:

The table of Henry's family will be at (4, -4)

Step-by-step explanation:

The problem states that the initial coordinates of Henry's family is at the coordinates (-4, 4). Each 15 minutes the restaurant will rotate 90° every 15 minutes. If we follow the Cartesian plane and the center of the restaurant being at (0, 0) we know that the table will be situated at the (4, 4) coordinates of the restaurant after the first rotation. After the 30 minute mark, the restaurant rotates one more time and moves the table of Henry's family at the (4, -4) coordinates of the restaurant as the center of the restaurant will never move.

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Find the area of the rhombus.
Goshia [24]

Step-by-step explanation:

as the graphic shows, we are dealing with a special rhombus : a square.

this is proven by the fact that the angle on one side of the diagonal at the corner is 45°. so, the other side must be 45° too, and so we have 90° angles at the corners.

what is not clear to me is : what is 6 cm long ? a half-diameter, or the whole diameter ?

I assume the half-diameter.

what the graphic is trying to suggest is that we have 4 little right-angled triangles that are also isoceles triangles (their legs are equally long).

every leg is 6 cm long (based on my assumption above).

because they are right-angled, the area of each of these little triangles is leg×leg/2

6×6/2 = 18 cm²

we have 4 triangles, so the total area is

4×18 = 72 cm²

if 6 cm stands for the whole diagonal after all, then the only change is the length of the legs, which would be then 6/2 = 3 cm.

then we would have

3×3/2 = 4.5 cm² for a single triangle

and

4×4.5 = 18 cm² for the whole area.

6 0
3 years ago
3√x -2/x^2<br><br>please show step by step of differentiation before combining the terms. ​
EastWind [94]

Answer:

Step-by-step explanation:

Before we differentiate, let us assign a variable to the function. Let y be equal to the function i.e let y = 3√x -2/x²

In differentiation if y = ax^{n}, then \frac{dy}{dx} = nax^{n-1} where n is a constant and dy/dx means we are differentiating the function y with respect to x.

Applying the formula o the question given;

y= 3\sqrt{x}  -2/x^2\\y = 3{x}^\frac{1}{2}  - 2x^{-2} \\\\

On differentiating the resulting function;

\frac{dy}{dx} = \frac{1}{2}*3x^{\frac{1}{2}-1 }   - (-2)x^{-2-1} \\\\\frac{dy}{dx} = \frac{1}{2}*3x^{-\frac{1}{2}} + 2x^{-3}\\ \\\frac{dy}{dx} = \frac{1}{2}*{\frac{3}{x^{\frac{1}{2} } }} + \frac{2}{x^{3} } \\\\\frac{dy}{dx} = {\frac{3}{2x^{\frac{1}{2} } }} + \frac{2}{x^{3} }\\\\\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }

To combine the terms, we will add up by finding their LCM.

\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }\\\frac{dy}{dx}  = \frac{3x^3+4\sqrt{x} }{2x^{3} \sqrt{x}}

3 0
4 years ago
What is the geometric shape of a satellite or planetary orbit?
sasho [114]
An ellipse (by Kepler in 16th century) 
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3 years ago
What does "nth term" mean?
In-s [12.5K]

Answer:

Step-by-step explanation:

nth term means an expression which allows us to find the term that is in the nth position in the sequence.

Hope this helps

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5 0
3 years ago
JPJ Corp has sales of $1.34 million, accounts receivable of $52,000, total assets of $4.99million(of which $2.79 million are fix
Alex Ar [27]

Answer:

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Total Asset Turnover : 0.27 times

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Step-by-step explanation:

1) Account Receivable days is calculated as : (Account Receivable/Revenue) * Number of days in a year. Hence the answer is calculated as = (52000/134

0000) * 365 = 14.16.

2) Fixed Assets Turnover is calculated as : Net Sales/Fixed Assets. Hence the answer is calculated as 1340000/2790000 = 0.48.

3) Total Asset turnover is calculated as : Nets Sales/Total Assets. Hence the answer is = 1340000/4990000 = 0.28.

4) Inventory Turnover is calculated as : COGS/Average Inventory. Hence the answer is = 601000/151000 = 3.98.

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