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riadik2000 [5.3K]

3 years ago

t\limits^2_1 {x^{2}-8x+8 } \, dx" alt="\int\limits^2_1 {x^{2}-8x+8 } \, dx" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

12345 [234]3 years ago

4 0

Answer:

${ \underline{ \sf{\int\limits^2_1 {x^{2}-8x+8 } \, dx} \: = \: - 1}}$

Step-by-step explanation:

${ \tt{\int\limits^2_1 {x^{2}-8x+8 } \, dx}} \\ \\ = { \tt{[ \frac{ {x}^{3} }{3} - 4 {x}^{2} + 8x ] {}^{2} _{1}}}$

Substitute x with the limits:

$= { \tt{( \frac{ {2}^{3} }{3} - 4( {2)}^{2} + 8(2)) - ( \frac{ {1}^{3} }{3} - 4( {1)}^{2} + 8(1)) }} \\ = { \tt{( \frac{8}{3} - \frac{11}{3} )}} \\ \\ = { \tt{ - 1}}$

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If using the method of completing the square to solve the quadratic equation x2 + 3x - 17 = 0, which number would have to be add

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Step-by-step explanation:

To solve using completing square, we need to write the equation as x2+3x=17.

The next step is to add a number such that the square can be completed. The number must be equal to (b/2a)^2, so here it will be (3/2)^2 = 9/4

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2 years ago

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Alexandra [31]

Answer: y-axis.

Explanation:

The equation r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.

The logical way is to graph in polar coordinates. I did it using a graphing software and obtained the attached graph.

Also, I attached the graph in cartesian coordinates.

Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).

 θ (rad) r = 3 - 4 sin θ 

0 3 
π/8 2.61731657 
 π/4 2.29289322 
3π/8 2.07612047
 π/2 2
 5π/8 2.07612047 
3π/4 2.29289322 
7π/8 2.61731657 
π 3 
9π/8 3.38268343 
5π/4 3.70710678 
11π/8 3.92387953 
3π/2 4 
13π/8 3.92387953 
7π/4 3.70710678 
15π/8 3.38268343 
2π 3 

In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.

Therefore, the graph is symmetric about the y-axis.