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ololo11 [35]
3 years ago
11

The standard form of the equation of a circle is (x−5)2+(y−6)2=1.

Mathematics
1 answer:
Crank3 years ago
3 0

Answer:

(A)x^2+y^2-10x-12y+60=0

Step-by-step explanation:

The standard form of the equation of a circle is given as:

(x-5)^2+(y-6)^2=1

Simplifying the above given equation, we get

x^2+25-10x+y^2+36-12y=1

x^2+y^2-10x-12y+36+25=1

x^2+y^2-10x-12y+61=1

x^2+y^2-10x-12y+60=0

which is the required general form of the equation.

Hence, option A is correct.

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Set up and solve the following using dimensional analysis.
Softa [21]
1).  Multiply (5400 inches) by (1 foot / 12 inch) then by (1 mile / 5280 foot).

      (See explanation at the bottom)

         =      (5400 inch) x (1 foot / 12 inch) x (1 mile / 5280 foot)

         =      (5400 x 1 x 1 / 12 x 5280)  (inch - foot - mile / inch - foot) 

         =          0.0852  mile  


2).  Multiply (16 week) by (7 day/week) then by (24 hour/day)
       then by (60 minute/hour) then by (60 sec/minute).

3).  Multiply (54 yards) by (3 foot/yard) then by (1 meter/3.28 foot)
       and then by (1000 mm/meter)

4).  Multiply (36 cm/second) by (3600 second/hour) then by (1 meter/100 cm)
      then by (1 mile/1609.3 meter).

5).  Look up how many grams in a pound  ('P')
       Look up how many mL in a gallon       ('G')

      Multiply (1.09 g/mL) by ( 1 pound/ P gram) then by (1 gallon/ G mL)

6).  Multiply (32 foot/sec) by (1 meter / 3.28 foot) then by (60 sec/minute).


Each time I told you to multiply by something, it was always a fraction
where the numerator and denominator are equal, like (60 seconds/minute)
or (1 foot / 12 inch).  Since the top and bottom of the fraction are equal, the
value of the fraction is ' 1 ' , and multiplying by it doesn't change the value,
it only changes the units ... that's what this whole exercise is about.
When you multiply, KEEP the units in the product, and then, after you multiply, you can 'cancel' units out of the top and bottom of the product.
Like if you have 'feet' on top and bottom, just cross them out.  When you're done, if you did it correctly, the last unit you end up with will be the one you want.      
4 0
3 years ago
If a cube has a volume of 9 feet and a shelf has a height of 27 inches, can the cube fit in the shelf?
rusak2 [61]

Answer:

Yes the cube will fit.

Step-by-step explanation:

If we don't take into account of how wide of long the cube is and just focus on the height, the edge of a cube with a volume of 9 feet is roughly 2.08 feet. That totals to less than 27 inches, therefore the cube will fit on the shelf.

4 0
2 years ago
Read 2 more answers
In △ABC, point D∈ AB with AD:DB=5:3, point E∈ BC so that BE:EC=1:4. If AABC=40 in2, find AADC, ABDC, and ACDE.
DIA [1.3K]

Answer: Using the proportions between the segments, the area of the triangles are:

1. Area of triangle ADC is 25 in^2.

2. Area of triangle BDC is 15 in^2.

3. Area of triangle CDE is 12 in^2.


Please, see the attached files.

Thanks.

8 0
3 years ago
Suppose that the mean water hardness of lakes in Kansas is 425 mg/L and these values tend to follow a normal distribution. A lim
tino4ka555 [31]

Answer:

The mean water hardness of lakes in Kansas is 425 mg/L or greater.

Step-by-step explanation:

We are given the following data set:

346, 496, 352, 378, 315, 420, 485, 446, 479, 422, 494, 289, 436, 516, 615, 491, 360, 385, 500, 558, 381, 303, 434, 562, 496

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{10959}{25} =438.36

Sum of squares of differences = 175413.76

S.D = \sqrt{\dfrac{175413.76}{24}} = 85.49

Population mean, μ = 425 mg/L

Sample mean, \bar{x} = 438.36

Sample size, n = 25

Alpha, α = 0.05

Sample standard deviation, s = 85.49

First, we design the null and the alternate hypothesis

H_{0}: \mu \geq 425\text{ mg per Litre}\\H_A: \mu < 425\text{ mg per Litre}

We use one-tailed t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{438.36 - 425}{\frac{85.49}{\sqrt{25}} } = 0.7813

Now, t_{critical} \text{ at 0.05 level of significance, 24 degree of freedom } = -1.7108

Since,                        

The calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis and accept it.

Thus, the mean water hardness of lakes in Kansas is 425 mg/L or greater.

6 0
3 years ago
How do you construct a hexagon?
horrorfan [7]
A hexagon has 6 even corners that are connected evenly as shown.

5 0
3 years ago
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