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3 years ago

Can someone please help me with this!!!

Mathematics

1 answer:

Volgvan3 years ago

4 0

Step-by-step explanation:

I am not fully sure what your teacher is aiming for. it friends very much on what you were just discussing in class (which I don't know).

but the first thing coming to mind is a minus sign ("-"). squaring a negative number removed the minus and makes the result equal to squaring the same positive number.

just for the undoing the 1/2 :

that is, because a fraction as exponent specifies in its denominator the root to be calculated for the basic value or expression.

so, 1/2 means square root. and yes, square is the inverse function of a square root, and it "undoes" the square root.

in exponent calculation it just means that for exponent 1 to the power of exponent 2 we simply multiply both exponents. and so, 1/2 × 2 = 1

FYI - the numerator still represents an original "to the power of" operation.

so, e.g. 3/2 would mean put the basis to the power of 3 and then do the square root of that result. or the other way around. these operations are commutative (the sequence does not matter).

You might be interested in

Solve the given initial-value problem. x^2y'' + xy' + y = 0, y(1) = 1, y'(1) = 8

Kitty [74]

Substitute $z=\ln x$ , so that

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dz}\cdot\dfrac{\mathrm dz}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}$

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)$

Then the ODE becomes

$x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}+x\dfrac{\mathrm dy}{\mathrm dx}+y=0\implies\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)+\dfrac{\mathrm dy}{\mathrm dz}+y=0$
$\implies\dfrac{\mathrm d^2y}{\mathrm dz^2}+y=0$

which has the characteristic equation $r^2+1=0$ with roots at $r=\pm i$ . This means the characteristic solution for $y(z)$ is

$y_C(z)=C_1\cos z+C_2\sin z$

and in terms of $y(x)$ , this is

$y_C(x)=C_1\cos(\ln x)+C_2\sin(\ln x)$

From the given initial conditions, we find

$y(1)=1\implies 1=C_1\cos0+C_2\sin0\implies C_1=1$
$y'(1)=8\implies 8=-C_1\dfrac{\sin0}1+C_2\dfrac{\cos0}1\implies C_2=8$

so the particular solution to the IVP is

$y(x)=\cos(\ln x)+8\sin(\ln x)$

4 0

3 years ago

Tic-tac-toe: In the game of tic-tac-toe, if all moves are performed randomly the probability that the game will end in a draw is

Natasha2012 [34]

Answer:

$P(X \geq 1) = 1-P(X$

And if we find the individual probability we got:

$P(X=0)=(7C0)(0.127)^0 (1-0.127)^{7-0}=0.3865$

And replacing we got:

$P(X \geq 1) = 1-P(X$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=7, p=0.127)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X \geq 1)$

And we can use the complement rule and we got:

$P(X \geq 1) = 1-P(X$

And if we find the individual probability we got:

$P(X=0)=(7C0)(0.127)^0 (1-0.127)^{7-0}=0.3865$

And replacing we got:

$P(X \geq 1) = 1-P(X$

6 0

3 years ago

Read 2 more answers

The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, ... where the first and second terms are 1 and each term after that is the

noname [10]

Answer:

44,278,106,022,432,739,384.375 = 1/8 of ((1+√5)/2)^100/√5

Step-by-step explanation:

We separate the x10^21 number into 2 so that becomes x10^8 number with decimal of .75 when it is a x10^21 split into 2 large parts and a small subtraction creates the third step. we have found 1/4 then we half.

354224848179261915075 / 4

= 000000000000065478768.75

354224 848179000000000/4

-88556212044.8

= 354 has become a 12 digit number temporary starting with 885 the decimal .8 is simply put in front

3542248481 79- so it has become a x10^20 number. 885562120448,65478768.75

We arrange the comma's

88,556,212,044,865,478,768.75

88,556,212,044,865,478,768.75 is division by 4

=354224848179261915075

88,556,212,044,865,478,768.75 /2

= 44278106022 (/2) 432739384.375(/2) in two part.

= 44278106022,432739384.375 replace /2 with comma

= 44,278,106,022,432,739,384.375 replace all other comma.

4 0

3 years ago

Trina ran 2 1/2 miles of Friday, 2 3/4 miles on Saturday and 3 mies on SUnday. The next week she ran the same amount. How far in

vodka [1.7K]

Answer:

16 $\frac{1}{2}$ miles

Step-by-step explanation:

2 $\frac{2}{4}$ + 2 $\frac{3}{4}$ = 4 $\frac{5}{4}$ which equals 4 + 1 $\frac{1}{4}$ or 5 $\frac{1}{4}$

5 $\frac{1}{4}$ + 3 = 8 $\frac{1}{4}$

she ran 8 and one-quarter miles in the first week and if she ran the same amount the second week then we can add to get the answer:

8 $\frac{1}{4}$ + 8 $\frac{1}{4}$ = 16 $\frac{2}{4}$ or 16 $\frac{1}{2}$

5 0

2 years ago

He product of ten and a number is greater than the difference of four times the number and two.

Debora [2.8K]

Answer:

You can use 1 as a solution.

Step-by-step explanation:

10 + 1 = 11

1 * 4 = 4

4 - 2 = 2

11 > 2

4 0

3 years ago