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Aneli [31]
4 years ago
14

Use implicit differentiation to find the points where the circle defined by x^2+y^2−6x−4y=-4 has horizontal and vertical tangent

lines. List your answers as points in the form (a,b).
Mathematics
1 answer:
Inga [223]4 years ago
8 0
Implicit differentiation: 2x+2ydy/dx-6-4dy/dx=0. When dy/dx=0, we have a horizontal tangent.
So 2x-6=0 and x=3. To find y we solve 9+y²-18-4y=-4, y²-4y-5=0=(y-5)(y+1), so the points are (3,5) and (3,-1).
2xdx/dy+2y-6dx/dy-4=0. When dx/dy=0 we have a vertical tangent, so 2y=4, y=2, and x²+4-6x-8=-4, x²-6x=0, x=0 and 6.
The points are (0,2) and (6,2).
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Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them up to $400 by paying th
Cerrena [4.2K]

Answer:

I think it would be 25m + 10b = 400

6 0
3 years ago
Every prime number greater than 10 has a digit in the ones place that is include in wich set of numbers A- 1,3,7,9 B-1,3,5,9 D-1
marta [7]

That's very interesting.  I had never thought about it before.
Let's look through all of the ten possible digits in that place,
and see what we can tell:

-- 0:
   A number greater than 10 with a 0 in the units place is a multiple of
   either 5 or 10, so it's not a prime number.

-- 1:
    A number greater than 10 with a 1 in the units place could be
    a prime (11, 31 etc.) but it doesn't have to be (21, 51).

-- 2:
   A number greater than 10 with a 2 in the units place has 2 as a factor
   (it's an even number), so it's not a prime number.

-- 3:
   A number greater than 10 with a 3 in the units place could be
   a prime (13, 23 etc.) but it doesn't have to be (33, 63) .

-- 4: 
   A number greater than 10 with a 4 in the units place is an even
   number, and has 2 as a factor, so it's not a prime number.

-- 5:
   A number greater than 10 with a 5 in the units place is a multiple
   of either 5 or 10, so it's not a prime number.

-- 6:
   A number greater than 10 with a 6 in the units place is an even
   number, and has 2 as a factor, so it's not a prime number.

-- 7:
   A number greater than 10 with a 7 in the units place could be
   a prime (17, 37 etc.) but it doesn't have to be (27, 57) .

-- 8:
   A number greater than 10 with a 8 in the units place is an even
   number, and has 2 as a factor, so it's not a prime number.

-- 9:
   A number greater than 10 with a 9 in the units place could be
   a prime (19, 29 etc.) but it doesn't have to be (39, 69) .

So a number greater than 10 that IS a prime number COULD have
any of the digits  1,  3,  7,  or  9  in its units place.

It CAN't have a  0,  2,  4,  5,  6,  or  8 .

The only choice that includes all of the possibilities is  'A' .

4 0
3 years ago
50 POINTS!!!!!
Makovka662 [10]

We can adjust the data by adding 4 to everything before we calculate the statistics.  Or we can calculate the statistics on the given data and just add 4 to everything at the end.  We'll get the same answer either way.

Let's sort the seven data points:  5 5 5 7 7 9 10

Those add up to 48 so the mean is 48/7 = 6.9

The one in the middle is 7 so the median = 7

The mode is the most common one, mode = 5

The range is the difference between max and min, so range = 10 - 5 = 5

In the second week we add four to everything.  Since that adds four to the min and max, the range doesn't change.

Answer: mean=10.9, median=11, mode=9, range=5

7 0
4 years ago
In the division problem, 0.08 ÷ 2 = 0.04, is 0.08 <br> quotient dividend divisor <br> Choose...
cupoosta [38]

Answer:

Dividen

Step-by-step explanation:

The amount that you want to divide up. dividend ÷ divisor = quotient. Example: in 12 ÷ 3 = 4, 12 is the dividend.

A divisor is the number that the dividen is being divided by

12÷3=4 3 IS THE DIVISOR

3 0
3 years ago
The table below shows the functions to represent the sale f(t), in thousands, of four companies in t years: Company A B C D Sale
bazaltina [42]

1) Company A and C

2)Your answer is f(t) = 180(0.5)^t This is because the number is cut in half for every hour.

3)C 0 ≤ x ≤ 50 is the right answer because the starting time 9:05 is considered as zero and the 9:55 is the ending point which is considered as 50.Or simply the difference of both the times is the domain of the function.



5 0
3 years ago
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