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Georgia [21]
3 years ago
9

Solve this:/ 2m - 5 - 5 = -3m + 15

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
5 0
2m-5-5= -3m +15
2m -10= -3m+15
2m+3m= 15+10
5m= 25
m= 25/5
m=5
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Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x)= 6x^1/3 + 3x^4/3. You must justify
irina [24]

Answer:

x-coordinates of relative extrema = \frac{-1}{2}

x-coordinates of the inflexion points are 0, 1

Step-by-step explanation:

f(x)=6x^{\frac{1}{3}}+3x^{\frac{4}{3}}

Differentiate with respect to x

f'(x)=6\left ( \frac{1}{3} \right )x^{\frac{-2}{3}}+3\left ( \frac{4}{3} \right )x^{\frac{1}{3}}=\frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}

f'(x)=0\Rightarrow \frac{2}{x^{\frac{2}{3}}}+4x^{\frac{1}{3}}=0\Rightarrow x=\frac{-1}{2}

Differentiate f'(x) with respect to x

f''(x)=2\left ( \frac{-2}{3} \right )x^{\frac{-5}{3}}+\frac{4}{3}x^{\frac{-2}{3}}=\frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}\\f''(x)=0\Rightarrow \frac{-4x^{\frac{2}{3}}+4x^{\frac{5}{3}}}{3x^{\frac{2}{3}}x^{\frac{5}{3}}}=0\Rightarrow x=1

At x = \frac{-1}{2},

f''\left ( \frac{-1}{2} \right )=\frac{4\left ( -1+4\left ( \frac{-1}{2} \right ) \right )}{3\left ( \frac{-1}{2} \right )^{\frac{5}{3}}}>0

We know that if f''(a)>0 then x = a is a point of minima.

So, x=\frac{-1}{2} is a point of minima.

For inflexion points:

Inflexion points are the points at which f''(x) = 0 or f''(x) is not defined.

So, x-coordinates of the inflexion points are 0, 1

7 0
3 years ago
ΔABC has vertices A(0,10), B(4,10), and C(-2,4).
laiz [17]

A simple diagram will show you the intersection of altitudes is in the 2nd quadrant. It must have x-coordinate -2, as the altitude to the "base" y=10 must be the vertical line through (-2, 4).

The appropriate choice is ...

... C: (-2, 12)

8 0
3 years ago
Suppose that a cell phone monthly rate plan costs the user 5 cents per minute beyond a fixed monthly fee of $20. This implies th
Gala2k [10]

Answer:

y= .05x + 20

Step-by-step explanation:

3 0
3 years ago
Find the slope (3,6)<br> (3,-3) need in 5 minutes
avanturin [10]

Answer: The slope is undefined.

Step-by-step explanation:

Using the formula given, find the difference in the y coordinates of the points and divide it by the x coordinates.

(3,6)

(3,-3)  

y coordinates:  6 - (-3) =  9

x coordinates:   3- 3 = 0  

9/0 =  undefined.

Any number being divided by 0  is undefined because you can't divide something by anything.  

Also remember that if a line is vertical through any of the x coordinate, the slope will always be undefined and the equation of line is x = 3

4 0
2 years ago
3(d-8) - 5 = 9(d+2) + 1
attashe74 [19]

Answer:

d = - 8

Step-by-step explanation:

3(d-8) - 5 = 9(d+2) + 1

3d-24 - 5 = 9d+18 + 1

3d - 29 = 9d + 19

9d - 3d = -29 - 19

6d = - 48

6d / 6 = -48/6

d = -8

7 0
2 years ago
Read 2 more answers
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