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lbvjy [14]
3 years ago
12

33. What values of the constants a, b, and c make the ellipse

Mathematics
1 answer:
posledela3 years ago
6 0

Answer:

a=0  and  b= -4   and  c=0

Step-by-step explanation:

the ellipse : color red and purple

the tangent : color bleue

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Cual es la derivada de ()=√x sin
fgiga [73]

Answer:

f(x) =\sqrt{x} sin (x)

And on this case we can use the product rule for a derivate given by:

\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)

Where f(x) =\sqrt{x} and g(x) =sin (x)

And replacing we have this:

f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)

Step-by-step explanation:

We assume that the function of interest is:

f(x) =\sqrt{x} sin (x)

And on this case we can use the product rule for a derivate given by:

\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)

Where f(x) =\sqrt{x} and g(x) =sin (x)

And replacing we have this:

f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)

3 0
3 years ago
Write the expanded form of the decimal 0.082¯ using powers of 10
Softa [21]

Answer:

0.082 = 8.2× 10^-2

Step-by-step explanation:

Given the decimal number 0.082, the expanded form using the power of 10 can be gotten by writing the decimal number in standard format(writing as a multiple of 10).

To do that we will shift the decimal point to the front up to the front of digit 8. This shows that the decimal point will be shifted 2times to the front. Since of is shifted 2times to the front, our power of 10 will be -2.

0.082 = 8.2× 10^-2

This gives the required answer.

Note that, the power of 10 is positive when decimals are shifted to the back and negative when shifted to the front(in this case).

3 0
3 years ago
Use the limit theorem and the properties of limits to find the limit.<br> Picture provided below
sashaice [31]

Answer:

b. 1/2

Step-by-step explanation:

lim        (x -3)(x +2)

x-->-∞    ---------------

              2x^2 + x +1

= lim        (x^2 -3x +2x - 6)

x-->-∞    -----------------------

              2x^2 + x +1

= lim        (x^2 -x - 6)

x-->-∞    -----------------------

              2x^2 + x +1

When we plug in x = -∞, we get indeterminate form.

Now we have to use the L'hospital rule.

d/dx (x^2 - x - 6) = 2x -1

d/dx (2x^2 + x + 1) = 4x + 1

Now apply the limit

lim            (2x - 1) / (4x + 1)

x--->-∞

Here we have to degree of the numerator and the denominator of the same. In this case, if x --> -∞, we get the result as the coefficient of the leading term as the result.

According to the rule, we get

= 2/4

Which can simplified as 1/2

The answer is 1/2

Hope this will helpful.

Thank you.

3 0
3 years ago
Read 2 more answers
A supermarket finds that the number of boxes of a new cereal sold increases each week. in the first week, only 16 boxes of the c
vaieri [72.5K]
For this case, the arithmetic sequence is given by:
 an = 17n-1
 Let's check it:
 First week:
 n = 1:
 a1 = 17 (1) -1
 a1 = 17-1
 a1 = 16
 Second week:
 n = 2:
 a2 = 17 (2) -1
 a2 = 34-1
 a2 = 33
 Third week:
 n = 3:
 a3 = 17 (3) -1
 a3 = 51-1
 a3 = 50
 Answer:
 
the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n is:
 
an = 17n-1
6 0
3 years ago
4+xThe function g is defined by g(x) =5 + 3xFind g(5n).
Nikolay [14]

The function g is defined by:

g(x) = (4 + x) / (5 + 3x) ...(1)

Now, we need to find g(5n); that is, we make: x = 5n

Replacing this into equation (1):

g(5n) = (4 + 5n) / (5 + 3*(5n)) = (4 + 5n) / (5 + 15n)

So, the final answer is:

g(5n) = (4 + 5n) / (5 + 15n)

8 0
1 year ago
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