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Nataly [62]
2 years ago
13

Find the value of 'p' ,if 5^p-3 * 3^2p-8=225

Mathematics
1 answer:
Stells [14]2 years ago
6 0

Answer:   p = 5

<u>Step-by-step explanation:</u>

5^{p-3}\cdot3^{2p-8}=225\\\\5^{p-3}\cdot3^{2p-8}=15^2\\\\5^{p-3}\cdot3^{2p-8}=5^2\cdot 3^2\\\\5^{p-3}=5^2\quad and\quad 3^{2p-8}=3^2\\\\p-3=2\quad and\quad 2p-8=2\\p=5\qquad and \qquad 2p=10\rightarrow p=5

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Natali5045456 [20]

Answer:

17 ± sqrt(337)

 -----------------------

     2

Step-by-step explanation:

Let a = shorter leg

b= longer leg = a+7

c = hypotenuse = 2a-5

We can use the Pythagorean theorem

a^2+b^2 = c^2

a^2 + (a+7)^2 = (2a-5)^2

(a+7)^2 = a^2 +7a +7a+49 = a^2 +14a +49

(2a-5)^2 = 2a*2a -10a -10a +25 = 4a^2 -20a +25

Substituting these into the equation

a^2 + (a^2 +14a +49) = (4a^2 -20a +25)

Combine like terms

2a^2 +14a +49 = 4a^2 -20a +25

Subtracting 2a^2 from each side

2a^2 -2a^2 +14a +49 = 4a^2-2a^2 -20a +25

+14a +49 = 2a^2 -20a +25

Subtract 14a from each side

-14a+14a +49 = 2a^2 -20a -14a+25

+49 = 2a^2 -34a +25

Subtract 49 from each side

49-49 = 2a^2 -34a +25-49

0 =  2a^2 -34a -24

Divide each side by 2

0/2 =  2/2a^2 -34/2a -24/2

0 = a^2 -17a -12

Using the quadratic formula

a=1  b= -17  c = -12

17 ±sqrt( (-17)^2 - 4(1)(-12))

----------------------------------

2(1)

 17 ± sqrt(337)

 -----------------------

     2

4 0
2 years ago
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