1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fed [463]
3 years ago
6

I solved it myself and my result is (n+1)/n. Why is that 1/2 there? An explanation would be great if possible. Thanks!

Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Answer:

The product of (k + 1) series starts with 3 (because k = 2) and you need 2 to be multiplied to this in order to get (n + 1)!

Therefore you need to multiply 2 and 1/2 to make it right. 2 completes the factorial and 1/2 remains.

Hope it was clear explanation.

You might be interested in
Identifying the equivalent expression
iragen [17]

Answer:

\large\boxed{\sqrt{x+3}=(x+3)^\frac{1}{2}}

Step-by-step explanation:

\text{Use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\sqrt{x+3}=\sqrt[2]{x+3}=(x+3)^\frac{1}{2}

6 0
3 years ago
NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+121t
Alenkasestr [34]

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by

h(t)=-4.9t^2+121t+283

The sea level is represented by h = 0, therefore, to find the corresponding time when h splashes into the ocean we have to solve for t the following equation:

h(t)=0\implies-4.9t^2+121t+283=0

Using the quadratic formula, the solution for our problem is

\begin{gathered} t=\frac{-(121)\pm\sqrt{(121)^2-4(-4.9)(283)}}{2(-4.9)} \\ =\frac{121\pm142.083778...}{9.8} \\ =\frac{121+142.083778...}{9.8} \\ =26.8452834694... \end{gathered}

The rocket splashes after 26.845 seconds.

The maximum of this function happens at the root of the derivative. Differentiating our function, we have

h^{\prime}(t)=-9.8t+121

The root is

-9.8t+121=0\implies t=\frac{121}{9.8}=12.347

Then, the maximum height is

h(12.347)=1029.99

1029.99 meters above sea level.

6 0
1 year ago
If the outliers are not included, what is the mean of the data set?
Aleksandr-060686 [28]
The mean of the data without the outliers will be B 65.
6 0
3 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s
wolverine [178]

Answer:

x^4 - 14x^2 - 40x - 75.

Step-by-step explanation:

As complex roots exist in conjugate pairs the other zero is -1 - 2i.

So in factor form we have the polynomial function:

(x - 5)(x + 3)(x - (-1 + 2i))(x - (-1 - 2i)

= (x - 5)(x + 3)( x + 1 - 2i)(x +1 + 2i)

The first 2 factors  = x^2 - 2x - 15 and

( x + 1 - 2i)(x +1 + 2i) = x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i - 4 i^2

=  x^2 + 2x + 1 + 4

= x^2 + 2x + 5.

So in standard form we have:

(x^2 - 2x - 15 )(x^2 + 2x + 5)

= x^4  + 2x^3 + 5x^2 - 2x^3 - 4x^2 - 10x - 15x^2 - 30x - 75

= x^4 - 14x^2 - 40x - 75.

7 0
3 years ago
I've been having problems with this for a while...
Rina8888 [55]
Like all problems that involve images within the question, we should definitely try to draw this out. In the picture above, I have done this.

Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:

20 ............2.5
-------- = ---------
...x ............. 2

where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:

20×2 = 2.5 × x

Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).

We would then have:

20×2
------- = x
2.5

Which then simplifies to:

x = 16

Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)

3 0
3 years ago
Other questions:
  • Find the perimeter of the polygon. Assume that lines which appear to be tangent are tangent. Round to the nearest tenth if neces
    9·1 answer
  • How do I solve this<br> Y= -8x+56<br> 2x+2y=56
    9·1 answer
  • Find the simple interest earned in a savings account that pays 5% interest if $500 is deposited for 4 years.
    11·1 answer
  • X-2y=4. -3x+5y=-3. solving linear systems using multiplication and addition show your work
    11·1 answer
  • What is the missing term?
    15·1 answer
  • John makes a mistake when he inputs the number 1,205. He inputs
    12·1 answer
  • The original price of a bicycle was $100.00. In March, a bicycle went on sale for 10% off. In April, the sale price was raised b
    5·1 answer
  • What is the area of this figure?
    13·1 answer
  • Which is the fraction for 33%
    8·2 answers
  • A principal of $4,570 is placed in an account that earns 4. 5% interest. If the interest is compounded annually, how much money
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!