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3 years ago

How much more money will i need to get to 50 if i have 20

Mathematics

1 answer:

vaieri [72.5K]3 years ago

5 0

Answer:

2 plus 3 equals 5 and add the zeros and you have 50

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I used Cauchy-Schwarz inequality but it took too much time to finish. Is there any way faster?

ExtremeBDS [4]

Answer:

x = 1, x = -1

Step-by-step explanation:

Given $4(2^{2x}+2^{-2x})-4(2^x+2^{-x})-7=0$

Use substitution

$t=2^x+2^{-x}$

Square previous equality:

$t^2=(2^x+2^{-x})^2\\ \\t^2=(2^{x})^2+2\cdot 2^x\cdot 2^{-x}+(2^{-x})^2\\ \\t^2=2^{2x}+2\cdot 2^{x-x}+2^{-2x}\\ \\t^2=2^{2x}+2\cdot 2^0+2^{-2x}\\ \\t^2=2^{2x}+2\cdot 1+2^{-2x}\\ \\t^2=2^{2x}+2+2^{-2x}\\ \\2^{2x}+2^{-2x}=t^2-2$

Substitute it into the equation:

$4(t^2-2)-4t-7=0\\ \\4t^2-8-4t-7=0\\ \\4t^2-4t-15=0$

Solve this quadratic equation:

$D=(-4)^2-4\cdot 4\cdot (-15)=16+16\cdot 15=16(1+15)=16\cdot 16\\ \\\sqrt{D}=16\\ \\t_{1,2}=\dfrac{-(-4)\pm 16}{2\cdot 4}=\dfrac{4\pm 16}{8}=\dfrac{5}{2},\ -\dfrac{3}{2}$

Note that

$2^x>0\\ \\2^{-x}>0,$

then

$t=2^x+2^{-x}>0,$

$2^x+2^{-x}=\dfrac{5}{2}$

Solve this equation using substitution

$2^x=u\\ \\2^{-x}=\dfrac{1}{2^x}=\dfrac{1}{u}$

Thus,

$u+\dfrac{1}{u}=\dfrac{5}{2}\\ \\2u^2+2=5u\ \ [\text{Multiplied by 2u}]\\ \\2u^2-5u+2=0\\ \\D=(-5)^2-4\cdot 2\cdot 2=25-16=9\\ \\\sqrt{D}=3\\ \\u_{1,2}=\dfrac{-(-5)\pm 3}{2\cdot 2}=\dfrac{5\pm 3}{4}=2,\ \dfrac{1}{2}$

Now,

$u=2\Rightarrow 2^x=2,\ x=1\\ \\2^x=\dfrac{1}{2}\Rightarrow 2^x=\dfrac{1}{2}=2^{-1},\ x=-1$

7 0

3 years ago

I need help, WILL GIVE BRAINLIEST IF RIGHT. i need it in percents

atroni [7]

Answer:

2.) 33.33%

3.) 50%

Step-by-step explanation:

There is only one 5 and only one 2. There are 6 sides. The fraction is 2/6, and as a percent it's 33.33%.

There are 3 even numbers and three odd numbers. The chance of getting an even then an odd would be 3/6, or 50%.

8 0

3 years ago

How many unit cubes will fit in the rectangular prism?

Fantom [35]

I don’t see a picture but to length x width x height :)

5 0

3 years ago

Read 2 more answers

Which of the following represents the polynomial 5x + 3x^4 + 15 − 7x3 in standard form, the degree of the polynomial, and the nu

kkurt [141]

A polynomial is written correctly when the exponents are listed in order from highest to lowest. The highest exponent then dictates the degree of the whole polynomial. The first choice above is written in standard form from highest degree to lowest. Doesn't matter that we might skip the x-squared term or any other x-term, as long as they're in order from highest to lowest. The degree on that first polynomial, the one you're after, is 4 because that's the highest exponent, and there are 4 terms there. Terms are "bunches" of numbers and variables stuck together by multiplication and separated by + or - signs.

6 0

3 years ago

Read 2 more answers

1/3x=5/12 show your work

insens350 [35]

Answer:

4/5 or 0.8

Step-by-step explanation:

1/3x = 5/12

cross multiply

(12×1) = (5×3x)

divide through by 15

x = 12/15

x = 4/5 or 0.8

3 0

3 years ago

How much more money will i need to get to 50 if i have 20​

How much more money will i need to get to 50 if i have 20