All categories

3 years ago

On a sheet of paper, you have 100 statements written down.

Mathematics

1 answer:

serg [7]3 years ago

5 0

Answer:

Step-by-step explanation:

If the first statement its true (At most 0 of the statements are true), there are not true statements in the paper. So, the first statement its false.

Now, if the first statement its false, this mean there must be at least 1 true statement in the paper.

Now, if the second statement its true ( at most 1 of the statements are true) this implies that the third statement its true (if "at most 1" its true, then "as most 2" must be true).

If any statement (besides the first) its true, then all the statement that follows it must be true.

The first non false statement, then, must be the statement made by the person 51: "At most 50 statements are true"

And the 49 statements that follows are true as well.

You might be interested in

The graph of function g(x) is a transformation of the graph of function f(x) = x2.g(x) =

mariarad [96]

Given:

The graph of function g(x) is a transformation of the graph of function f(x) = x²

As shown: the graph of g(x) is open down

So, we will reflect f(x) over the x-axis, the function will be ⇒ -x²

And there is horizontal compression so, the factor of compression will be > 1

So, the function will be ⇒ -2x²

Finally, there is a vertical shift down 3 units

So,

$g(x)=-2x^2-3$

6 0

1 year ago

A boat is 122 meters from the base of a lighthouse. The lighthouse is 34 meters tall. The angle formed with the lighthouse and s

mojhsa [17]

Answer:

about 16°

Step-by-step explanation:

Make sure your calculator is in degree mode.

Drawing the right triangle, we see that the shorter leg is 34 meters, and the longer leg is 122 meters. So the angle of elevation is:

$\tan( \alpha ) = \frac{34}{122}$

$\alpha = { \tan }^{ - 1} \frac{34}{122} = 15.57$

3 0

2 years ago

Subtract: (x^2 - 8x + 5)-(-3x^2 + 5x-9)

Marianna [84]

Answer: 4x^2 -13x + 14

Step-by-step explanation:

(x^2 - 8x + 5)-(-3x^2 + 5x-9)

Subtract -3x^2 from x^2

(4x^2 - 8x + 5)-(5x-9)

Subtract 5x from -8x

(4x^2 -13x + 5)-(-9)

Subtract 9 from 5

4x^2 -13x + 14

7 0

3 years ago

The general solution to the second-order differential equation y′′+10y=0 is in the form y(x)=c1cosβx+c2sinβx. Find the value of

allsm [11]

Answer:β=√10 or 3.16 (rounded to 2 decimal places)

Step-by-step explanation:

To find the value of β :

we will differentiate the y(x) equation twice to get a second order differential equation.
We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β

y(x)=c1cosβx+c2sinβx

we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.

Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate βx in each case and multiply with the differential of c1cosx and c2sinx respectively.

lastly the differential of sinx= cosx and for cosx = -sinx.

Knowing all these we can proceed to solving the problem.

y=c1cosβx+c2sinβx

y'= β×c1×-sinβx+β×c2×cosβx

y'=-c1βsinβx+c2βcosβx

y''=β×-c1β×cosβx + (β×c2β×-sinβx)

y''= -c1β²cosβx -c2β²sinβx

factorize -β²

y''= -β²(c1cosβx +c2sinβx)

y(x)=c1cosβx+c2sinβx

therefore y'' = -β²y

y''+β²y=0

now we compare this with the second order D.E provided in the question

y''+10y=0

this means that β²y=10y

β²=10

B=√10 or 3.16(2 d.p)

5 0

3 years ago

A) Factorise 2x² - 9x - 5 (x-5)(2x+1) (2) b) Hence, simplify fully 2x^2- 9x - 5 3x – 15x (2)

Lyrx [107]

Answer:

Step-by-step explanation:

b).

2x² - 9x - 5 = ( x - 5 )( 2x + 1 )

3x² - 15x = 3x ( x - 5 )

$\frac{(x-5)(2x+1)}{3x(x-5)}$ = $\frac{2x+1}{3x}$

8 0

2 years ago