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3 years ago

Consider the equation x^2=6x+1 rewrite the equation by completing the square

Mathematics

2 answers:

Lynna [10]3 years ago

8 0

Answer:

The answer is x-3=+/- sqrt10

Step-by-step explanation:

astraxan [27]3 years ago

4 0

Answer:

$(x-3)^{2} =10x=3 +/- \sqrt{10}$

Khan Academy

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The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

How many permutations are there of the letters in the words (a) TRISKAIDEKAPHOBIA (fear of the number 13)? (b) FLOCCINAUCINIHILI

zubka84 [21]

Answer: Hello!

Let's start with the word TRISKAIDEKAPHOBIA wich has 17 letters (some of them repeat, but it does not matter in this problem)

We want to know how many permutations we can do with 17 letters: then think this way, Lets compose a word. The first letter of this word has 17 options, the second letter of the word has 16 options (you already took one of the set) the third letter of the word has 15 options, and so on.

The total number of permutations is the product of the number of options that you have for each letter, this is:

17*16*15*14*....*3*2*1 = 17! = 3.6e+14

(b) FLOCCINAUCINIHILIPILIFICATION now we have 30 letters in total, using the same reasoning as before, here we have 30! permutations; this is

30! = 2.65e+32

then P = 47! = 2.59e+59

(d) DERMATOGLYPHICS: here are 18 letters, then:

p = 18! = 6.4e+15

6 0

3 years ago

Jaylon makes twice as much an hour as Sam. Sam makes x dollars an hour. Write an expression describing how much Jaylon makes an

Xelga [282]

Answer:

2+x

Step-by-step explanation:

6 0

3 years ago

2 7/12 x 7 multiply enter the product in the simplest form

allochka39001 [22]

Answer:

18 1/12

Step-by-step explanation:

Hope this helps

5 0

3 years ago

What is the median of the data set?<br> 9 3 10 12 4 5 12 2

kramer

The key is to cross 1 number from both sides till you get to the middle last number so the answer is 4

5 0

2 years ago

Read 2 more answers