MATHEMATICS HIGH SCHOOL

On what intervals is the graph of f(x)=x^3-2x^2+5x+1 increasing?On what intervals is the graph of f(x)=0.5x^2-6 decreasing?

On what intervals is the graph of f(x)=(x+1)/(x-1) increasing?

Answers

Answer 1
Answer: f(x)=x^3-2x^2+5x+1\n f'(x)=3x^2-4x+5\n3x^2-4x+5=0\n\Delta=(-4)^2-4\cdot3\cdot5=16-60=-44
\Delta<0 \wedge a>0 \Rightarrow the graph of the parabola is above the x-axis, so the derivative is always positive and therefore the initial function is increasing in its whole domain.

f(x)=0.5x^2-6\nf'(x)=x
The function is decreasing when its first derivative is negative. The first derivative of this function is negative for x<0 so for x\in(-\infty,0) the function is decreasing.

f(x)=(x+1)/(x-1)\qquad(x\not=1)\nf'(x)=(x-1-(x+1))/((x-1)^2)=-(2)/((x-1)^2)
The function is increasing when its first derivative is positive. The first derivative of this function is always negative therefore this function is never increasing.

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What 30.000 divided by 500?

Answers

30.000 is just 30


30/500
=
0.06

A 12-foot flagpole casts a nine-foot shadow. What is the measure from the top of the shadow to the top of the flag pole?

Answers

Here is the answer OwO:

A 12-foot flagpole casts a nine-foot shadow. The measure from the top of the shadow to the top of the flag pole is 15.

Here is the explanation/work OwO:

Switch sides.

c^2=12^2+9^2

12^2=144

c^2=144+9^2

9^2=81

c^2=144+81

Add the numbers: 144 + 81 = 225

c^2=225

For x^2 = f(a) the solution is √f(a)

c = 15

Therefore, your answer will be 15.

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Sorry if I am late. Hope this helps!! ^^

Answer:

The answer is 15 ^-^

Step-by-step explanation:

Write the improper fraction 33/10 as a mixed number

Answers

the answer is 3 3/10

hope this helps
Answer = 3 3/10

there’s 33 take away the ones that go to ten.

10 10 and 10 is 30. Therefore it’s 3 and 3/10

Can someone help me with this please ?

Answers


If the triangle is a right triangle, then

       (3x)² + x² = (10)² .

         9x² + x² = 100

             10x²  = 100

                 x²  =  10

                 x  =  √10  =  approx. 3.1622...

If ' x ' is anything less than √10 , then the short sides are too short
to make a right angle at the top, and the angle where they meet
is obtuse.

' x ' has to be greater than  2.5 ... otherwise the two short sides
can't stretch far enough to reach both ends of the long side (10) .

So, if    2.5  <  x  <  √10 , then there is a triangle, and it's obtuse.

A line is drawn through (-4,3) and (4,3). Which describes whether or not the line represents a direct variation

Answers

If the resultant line is a straight line,it represents a direct variation.

A line in the Cartesian plane passes through the points (–2, 4) and (2, –1). What are the rise and the run of the line

Answers

Rise (-1) - 4 = -5 
Run  2 - (-2) = 4

Answer:

The rise is -5, the run is 4.
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