Can you solve this? :-)

Please help me answer this question genius

kolbaska11 [484]

Answer:

x ∈ {-0.465, 1.014}

Step-by-step explanation:

The equation can be cast in the form f(x) = 0, and solved easily using a graphing calculator. That shows x ≈ -0.465 and x ≈ 1.014. The same calculator can iterate the roots to full calculator precision.

__

The equation can be made a quadratic by the substitution ...

z = e^(2x)

Then we have ...

$2\cosh(2x)-\sinh(2x)=4\\\\2\cdot\dfrac{e^{2x}+e^{-2x}}{2}-\dfrac{e^{2x}-e^{-2x}}{2}-4=0\qquad\text{use exponential identities}\\\\2z+2z^{-1}-z+z^{-1}-8=0\qquad\text{multiply by 2, substitute z}\\\\z^2 -8z+3=0\qquad\text{multiply by z}\\\\z=\dfrac{8\pm\sqrt{(-8)^2-4(1)(3)}}{2(1)}=4\pm\sqrt{13}\\\\x=\dfrac{\ln(z)}{2}=\dfrac{\ln(4\pm\sqrt{13})}{2}\approx\{-0465133,1.014439\}$

7 0

2 years ago

. Mr. Wayne has a 3-year contract for his cell phone service. He pays $124.65 each month to cover everyone in his family. How mu

telo118 [61]

Answer:

$4,523.40

Step-by-step explanation:

The cell phone cost is $124.65 per month. With 12 months in a year, we multiply $124.65 x 12 to get the answer $1,507.80. Since one year equals $1,507.80, we multiply this answer by 3 for 3 years to get $4,523.40. Thus three years of service with $124.65 a month would equal $4,523.40.

8 0

4 years ago

An urn contains 7 red marbles and 3 white marbles. three marbles are drawn from the urn one after the other. find the probabilit

vaieri [72.5K]

7+3 = 10 total marbles

1st pick = 7/10 for a red one

2nd pick = 6/9 reduces to 2/3 for a red one

3rd pick = 3/8 for a white one

7/10 x 2/3 =14/30 reduces to 7/15

7/15 x 3/8 = 21/120 reduces to 7/40

probability = 7/40

5 0

3 years ago

at a parade, 1/4 of the participants have red hair, 1/6 of them have brown hair and the rest of them have black hair. which frac

netineya [11]

$\frac{1}{1}-\ all\ participants\\\\
\frac{1}{4}-\ participants\ with\ red\ hair\\\\ \frac{1}{6}-\ participants\ with\ brown\ hair\\\\
participants\ ith\ black\ hair=1-\frac{1}{4}-\frac{1}{6}\ \ \ | mu;tiply\ by\ 12\\\\
12participants\ ith\ black\ hair=12-3-2\\\\
12participants\ ith\ black\ hair=7\ \ \ \ | divide\ by\ 12\\\\
participants\ ith\ black\ hair=\frac{7}{12}$

6 0

4 years ago

What are the coordinates of R’, the image of R(-4,3) after a reflection in the line y=x?

navik [9.2K]

Answer:

R'(3,-4)

Step-by-step explanation:

we know that

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places

so

The rule of the reflection across the line y=x is equal to

(x,y) ------> (y,x)

we have

R(-4,3) ------> R'(3,-4)

6 0

3 years ago