What is the answer to this question?

Mathematics

1 answer:

Shalnov [3]3 years ago

4 0

The answer is (3+5i)-(2+i)

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Solve 5^3x+1 = 4^x-5 for x

tensa zangetsu [6.8K]

For the equation $5^{3x+1}=4^{x-5}$ take the $\log$ from both sides:

$\log 5^{3x+1}=\log 4^{x-5},\\ \\(3x+1)\log 5=(x-5)\log 4.$

Find x:

$3x\log 5+\log 5=x\log 4-5\log 4,\\ \\3x\log 5-x\log 4=-5\log 4-\log 5,\\ \\x(3\log 5-\log 4)=-5\log 4-\log 5,\\ \\x=\dfrac{-5\log 4-\log 5}{3\log 5-\log 4}=\dfrac{5\log 4+\log 5}{\log 4-3\log 5}.$

Answer: correct choice is D

7 0

3 years ago

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The incline of a roller coaster is 2 times as long as its elevation, and the horizontal length of the roller coaster is 11 m mor

Gelneren [198K]

Let
x-------> the horizontal length of the roller coaster
y------> the elevation of the roller coaster
c------> the incline of a roller coaster

we know that
applying the Pythagoras theorem
c²=x²+y²-----> equation 1
c=2y-----> equation 2
x=11+y----> equation 3

substitute equation 2 and equation 3 in equation 1
[2y]²=(11+y)²+y²
4y²=11²+22y+y²+y²
2y²-22y-121=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
y=15.026 m

c=2*y-----> c=2*15.026----> c=30.052 m

the answer is
30.05 m