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2 years ago

Identify the value of p. p = 11 p = 10 p = 12 p = 13

Mathematics

2 answers:

andrezito [222]2 years ago

8 0

Answer:

Step-by-step explanation:

5^2 + p^2 = (p+1)^2

25 + p^2 = p^2 + 2p + 1

25 = 2p + 1

24 = 2p

12 = p

Korolek [52]2 years ago

5 0

Answer:

Step-by-step explanation:

You may recall that (5, 12, 13) is a Pythagorean triple. That would tell you ...

p = 12

If you have not memorized a few useful Pythagorean triples, you can use the Pythagorean theorem to solve for p. The sum of squares of the sides is the square of the hypotenuse:

5² +p² = (p+1)²

p² +25 = p² +2p +1

24 = 2p . . . . . . . . subtract p²+1 from both sides

p = 12 . . . . . . divide by 2

_____

<em>Additional comment</em>

Some of the Pythagorean triples commonly seen in algebra and geometry problems are ...

(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)

Of course, multiples of these are used, too. For example, (6, 8. 10) is a multiple of the (3, 4, 5) triple.

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A particular type of cell increases by 75% in number every hour. Find the number of cells present at the end of 12 hours if ther

prisoha [69]

We have been given that a particular type of cell increases by 75% in number every hour. We are asked to find the number of cells present at the end of 12 hours if there are initially 4 of these cells.

We will use exponential growth formula to solve our given problem.

$y=a\cdot (1+r)^x$ , where,

y = Final amount,

a = Initial amount,

r = Growth rate in decimal form,

x = Time.

$75\%=\frac{75}{100}=0.75$

Upon substituting initial value $a=4$ and $x=12$ in above formula, we will get:

$y=4\cdot (1+0.75)^{12}$

$y=4\cdot (1.75)^{12}$

$y=4\cdot 825.0050068497657776$

$y=3300.020027$

$y\approx 3300$

Therefore, there will be approximately 3300 cells at the end of 12 hours.

5 0

3 years ago

George wants to invest $20,000 One investment pays interest at a rate of 18 2/3% while another pays interest at a rate of 0.1872

xz_007 [3.2K]

Answer:

Investment with interest rate 0.1872 is better

Step-by-step explanation:

Given as :

George investment principal = $20,000

The Rate of interest (R1) = 18 $\frac{2}{3}$ % = $\frac{56}{3}$ %

I.e R1 = 18.67 %

Again The The Rate of interest (R2) = 0.1872 = 18.72 %

Let the time period for both rate of interest = 1 years

Now from compound interest method

Amount = Principal × $(1 + \frac{Rate}{100})^{Time}$

Or, A 1 = $ 20 , 000 × $(1 + \frac{18.67}{100})^{1}$

Or, A 1 = $ 20 ,000 × 1.1867

∴ A 1 = $ 23,734

And A 2 = $ 20 , 000 × $(1 + \frac{18.72}{100})^{1}$

Or, A 2 = $ 20 ,000 × 1.1872

∴ A 2 = $ 23,744

Hence From the calculation of both amount it is clear that , investment with interest rate 0.1872 is better . Answer

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3 years ago

a. Find symmetric equations for the line that passes through the point (4, −4, 8) and is parallel to the vector −1, 4, −3b. Find

daser333 [38]

The line has equation

$\vec r(t)=(4,-4,8)+(-1,4,-3)t$

where $t$ is any real number. $(-1,4,-3)t$ is the line containing all scalar multiples of the vector (-1, 4, -3); we add (4, -4, 8) to shift the line so that it passes through this point while remaining parallel to the the line.