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sineoko [7]
2 years ago
6

Find 2^x=4x, find x ​

Mathematics
1 answer:
Sav [38]2 years ago
7 0

Whatever... I'll try to solve the first two problems.

2^x=4x\\4x=e^{\ln 2^x}\\4x=e^{x\ln 2}\\\dfrac{1}{4x}=e^{-x \ln 2}\\-\dfrac{\ln 2}{4}=-x\ln 2e^{-x \ln 2}\\-x\ln 2=W\left(-\dfrac{\ln 2}{4}\right)\\x=-\dfrac{W\left(-\dfrac{\ln 2}{4}\right)}{\ln 2}

1.

x=\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}\qquad\left( x\geq0\right)\\\\x=\sqrt{13+\sqrt{5+x}}\\\\x^2=13+\sqrt{5+x}\\\sqrt{5+x}=x^2-13\\\\D:5+x\geq0 \wedge x^2-13\geq 0\wedge x\geq 0\\D:x\geq-5 \wedge x^2\geq13\wedge x\geq 0\\D:x\geq \sqrt{13} \vee x\leq-\sqrt{13}\wedge x\geq0 \\D:x\in[\sqrt{13},\infty)\\\\ 5+x=x^4-26x^2+169\\x^4-26x^2-x+164=0\\\vdots\\(x - 4) (x^3 + 4 x^2 - 10 x - 41) = 0\\x-4=0\\x=4

One solution is x=4, and 4\in D, therefore\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}=4.

We can ignore other possible solutions of the polynomial equation, because the expression can not be equal to two different values simultaneously.

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PLEASE HELPP!!
Rasek [7]

Answer:

Given:

Two trail maps:

Trail on the first map = 8 cm

Trail on the second map = 6 cm

Scale on first map = 1 cm : 2 km

A) What is the scale factor from the map to the actual trail?

For the first map, the scale factor is 1 cm: 2km. Therefore the actual trail is 8 centimeters * 2 kilometers = 16 km.

The scale factor of the second map is 16 km / 6 cm = 2.67 km : 1 cm

B) The length of the actual trail is 16 kilometers.

Step-by-step explanation:

3 0
3 years ago
Write an<br> explicit formula for<br> then<br> th<br> an.<br> term of the sequence 45, 15,5. ....
7nadin3 [17]

Answer:

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u(n) = a {r}^{n - 1}

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From the question

a = 45

r = 15 / 45

The explicit formula for the sequence is

U(n) = 45(1/3)^n-1

Hope this helps you

7 0
3 years ago
What’s the ratio for 40 and 64
NARA [144]

Answer:

5/8, 5:8, or 5 to 8

Step-by-step explanation:

you have to simplify the ratio so you have to figure out what 40 and 64 have in common. tho right away you can assume that they both have 2 in common bcz they are both even so you can divide them both by two and get 20/32, and then you can do it again bcz they are both even again and get 10/16, and then you can do it again bcz they are also both even and get 5/8. now 5 is a prime number so you cant divide it any further so you stop it there. and i put three answers bcz there are three ways to write a ratio

6 0
3 years ago
Factor the equation.
Kryger [21]
Hi!

The fully factored form of this equation is (3x+2)²
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3 years ago
Given F(x) =x^2, choose whether the graph moves up down left or right.
malfutka [58]

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8 0
3 years ago
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