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Kay [80]
3 years ago
6

3√16-5= please help asap

Mathematics
1 answer:
IRISSAK [1]3 years ago
3 0

Answer:

\large\boxed{3\sqrt{16}-5=7}

Step-by-step explanation:

3\sqrt{16}-5=3(4)-5=12-5=7\\\\\sqrt{16}=4\ \text{because}\ 4^2=16

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The graphs of the quadratic functions f(x) = 6 – 10x2 and g(x) = 8 – (x – 2)2 are provided below. Observe there are TWO lines si
natta225 [31]

Answer:

a) y = 7.74*x + 7.5

b)  y = 1.148*x + 6.036

Step-by-step explanation:

Given:

                                  f(x) = 6 - 10*x^2

                                  g(x) = 8 - (x-2)^2

Find:

(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation

(b) The other line simultaneously tangent to both graphs has equation,

Solution:

- Find the derivatives of the two functions given:

                                f'(x) = -20*x

                                g'(x) = -2*(x-2)

- Since, the derivative of both function depends on the x coordinate. We will choose a point x_o which is common for both the functions f(x) and g(x). Point: ( x_o , g(x_o)) Hence,

                                g'(x_o) = -2*(x_o -2)

- Now compute the gradient of a line tangent to both graphs at point (x_o , g(x_o) ) on g(x) graph and point ( x , f(x) ) on function f(x):

                                m = (g(x_o) - f(x)) / (x_o - x)

                                m = (8 - (x_o-2)^2 - 6 + 10*x^2) / (x_o - x)

                                m = (8 - (x_o^2 - 4*x_o + 4) - 6 + 10*x^2)/(x_o - x)

                                m = ( 8 - x_o^2 + 4*x_o -4 -6 +10*x^2) /(x_o - x)

                                m = ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x)

- Now the gradient of the line computed from a point on each graph m must be equal to the derivatives computed earlier for each function:

                                m = f'(x) = g'(x_o)

- We will develop the first expression:

                                m = f'(x)

                                ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

Eq 1.                          (-2 - x_o^2 + 4*x_o + 10*x^2) = -20*x*x_o + 20*x^2

And,

                              m = g'(x_o)

                              ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

                              -2 - x_o^2 + 4*x_o + 10*x^2 = -2(x_o - 2)(x_o - x)

Eq 2                       -2 - x_o^2 + 4*x_o+ 10*x^2 = -2(x_o^2 - x_o*(x + 2) + 2*x)

- Now subtract the two equations (Eq 1 - Eq 2):

                              -20*x*x_o + 20*x^2 + 2*x_o^2 - 2*x_o*(x + 2) + 4*x = 0

                              -22*x*x_o + 20*x^2 + 2*x_o^2 - 4*x_o + 4*x = 0

- Form factors:       20*x^2 - 20*x*x_o - 2*x*x_o + 2*x_o^2 - 4*x_o + 4*x = 0

                              20*x*(x - x_o) - 2*x_o*(x - x_o) + 4*(x - x_o) = 0

                               (x - x_o)(20*x - 2*x_o + 4) = 0  

                               x = x_o   ,     x_o = 10x + 2    

- For x_o = 10x + 2  ,

                               (g(10*x + 2) - f(x))/(10*x + 2 - x) = -20*x

                                (8 - 100*x^2 - 6 + 10*x^2)/(9*x + 2) = -20*x

                                (-90*x^2 + 2) = -180*x^2 - 40*x

                                90*x^2 + 40*x + 2 = 0  

- Solve the quadratic equation above:

                                 x = -0.0574, -0.387      

- Largest slope is at x = -0.387 where equation of line is:

                                  y - 4.502 = -20*(-0.387)*(x + 0.387)

                                  y = 7.74*x + 7.5          

- Other tangent line:

                                  y - 5.97 = 1.148*(x + 0.0574)

                                  y = 1.148*x + 6.036

6 0
2 years ago
Perform the indicated operations:<br> 2/x-2+x/x+9-x+20/x2+7x-18
Gnoma [55]

Answer: The answer is B

6 0
2 years ago
Find the total surface area of the figure below.
Morgarella [4.7K]

Answer:

240

Step-by-step explanation:

You have to find the area of each indivigual side and then add all the areas together. So like 9x5 is 45 so you take 45 and multiply it by 4 since there are 4 sides identical to that side and then you get 180. Then you multiply 6x5 and that gives you 30 which you then multiply by 60, so then all you gotta do is 60+180=240.

3 0
2 years ago
14.89 divided by 0.02
Aneli [31]

Answer:

744.5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
0.6 + 15b + 4 = 25.6 all equivelant
Mila [183]

Answer:

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

Step-by-step explanation:

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

0.6 + 15b + 4 = 25.6 all equivelant

3 0
2 years ago
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