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Nonamiya [84]
3 years ago
11

What is wrong with this "proof"? "Theorem" For every positive integer n,n i =1 i = (n + 1 2 ) 2 /2. Basis Step: The formula is t

rue for n = 1. Inductive Step: Suppose thatn i=1 i = (n + 1 2 ) 2 /2. Then n+1 i=1 i = ( n i=1 i) + (n + 1). By the induc-tive hypothesis, n+1 i=1 i = (n + 1 2 ) 2 /2 + n + 1 = (n 2 + n + 1 4 )/2 + n + 1 = (n 2 + 3n + 9 4 )/2 = (n + 3 2 ) 2 /2 =[ (n + 1) + 1 2 ] 2 /2, completing the induc-tive step.
Mathematics
1 answer:
creativ13 [48]3 years ago
7 0

Answer:

The basis step is not even true.

Step-by-step explanation:

The basis step would be for     n = 1.

If the basis step was true then you would have that.

\sum\limits_{i=1}^{1} i  =  \frac{(1+1/2)^2}{2}

Now. When you say

                                            \sum\limits_{i=1}^{1}  i            

That's just a fancy way of writing    1.  

On the other hand    

\frac{(1+1/2)^2}{2}  = \frac{9}{4} = 2.25

Therefore  

  1 \neq 2.25

And the basis hypothesis is false.

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Help!<br> Central Angles and arc measures
enot [183]

Answer:

  x = 11

Step-by-step explanation:

The sum of arcs of a semicircle is 180°. That fact can be used with the given angle relations to find the value of x.

<h3>Setup</h3>

The measure of an arc is the same as the measure of the central angle it subtends.

  DC +CG +GF = 180

The angle bisector CH ensures that angles CHD and CHG are congruent. That means arcs CD and CG are congruent, and we have ...

  DC +DC +GF = 180 . . . . . . . . . use DC for CG

  2(7x -1) +(2x +6) = 180 . . . . . . . use the given expressions

<h3>Solution</h3>

This equation can be solved for x.

  16x +4 = 180 . . . . . . . . . . . . simplify

  16x = 176 . . . . . . . . . . . . subtract 4

  x = 11 . . . . . . . . . . . . . divide by 16

6 0
2 years ago
Find the slope and y-intercept of the line that is
iragen [17]

Answer:

slope= 3/2

y-intercept= -1/2

Step-by-step explanation:

y =  -  \frac{2}{3} x + 5

The product of the gradients of 2 perpendicular lines is -1.

( -  \frac{2}{3} )(gradient \: of \: line) =  - 1 \\ gradient \: of \: line \\  =  - 1 \div ( -  \frac{2}{3} ) \\  =  - 1 \times ( -  \frac{3}{2} ) \\  =  \frac{3}{2}

y =  \frac{3}{2} x + c

Substitute a coordinate into the equation.

When y=7, x=5,

7 =  \frac{3}{2} (5) + c \\ 7 =  \frac{15}{2}  + c \\ c =7 -   \frac{15}{2}  \\ c =  -  \frac{1}{2}

8 0
3 years ago
Find the image of (-1,3) obtained by translating 2 units down, followed by a rotation of 270 degrees counterclockwise about the
slamgirl [31]

Answer:

[1, 1]

Step-by-step explanation:

Translation → [-1, 3] moves down to [-1, 1]

Now, a <em>90°-clockwise rotation</em> is the exact same as a <em>270°-counterclockwise rotation</em>, and according to the <em>270°-counterclockwise rotation</em> [<em>90°-clockwise rotation</em>] <em>rule</em>, you take the y-coordinate, bring it over to your new x-coordinate, and take the OPPOSITE of the x-coordinate and set it as your new y-coordinate:

<u>Extended Rotation Rules</u>

  • 270°-clockwise rotation [90°-counterclockwise rotation] >> (<em>x, y</em>) → (<em>-y, x</em>)
  • 270°-counterclockwise rotation [90°-clockwise rotation] >> (<em>x, y</em>) → (<em>y, -x</em>)
  • 180°-rotation >> (<em>x, y</em>) → (<em>-x, -y</em>)

Then, you perform your rotation:

270°-counterclockwise rotation [90°-clockwise rotation] → [-1, 1] moves to [1, 1]

I am joyous to assist you anytime.

7 0
3 years ago
HELP !!! (will mark brainliest)
Rasek [7]

Answer:

I think it's A. (6^{4})^{-5}

3 0
3 years ago
Read 2 more answers
Madelyn and her children went into a movie theater and she bought $39 worth of bags of popcorn and pretzels. Each bag of popcorn
Serjik [45]

Answer:

the answer to this question is

Step-by-step explanation:

<em>She bought 6 bags of popcorn and 24 pretzels </em>

<em> </em>

<em>Step-by-step explanation: </em>

<em> </em>

<em>6 bags of popcorn = $39 </em>

<em> </em>

<em>24 pretzels = $78</em>

5 0
3 years ago
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