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zheka24 [161]
3 years ago
14

A one-year membership to Metro Gym costs $460. There is a fee of $40 when you join, and the rest is paid monthly. Write an equat

ion to represent what you will pay monthly for the yearlong membership. Write an equation that would help members find how much they pay per month.
Mathematics
1 answer:
Masteriza [31]3 years ago
4 0

Answer: See explanation

Step-by-step explanation:

Let the amount of money to be paid per month be represented by x. The information given in the question can then be formed into an equation as:

$40 + 12x = $460

From the equation, the amount that'll be paid monthly will be:

$40 + 12x = $460

12x = $460 - $40

12x = $420

x = $420/12

x = $35

The amount paid monthly is $35

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Sin(x)^4+ cos(x)^4=1/2
posledela
I'll assume that what was meant was \sin ^4 x + \cos ^4 x = \dfrac{1}{2}.

The exponent in the funny place is just an abbreviation:   \sin ^4 x = (\sin x)^4.

I hope that's what you meant. Let me know if I'm wrong.

Let's start from the old saw

\cos^2 x + \sin ^2x = 1

Squaring both sides,

(\cos^2 x + \sin ^2x)^2 = 1^2

\cos^4 x + 2 \cos ^2 x \sin ^2x +\sin ^4x = 1

\cos^4 x + \sin ^4x = 1 - 2 \cos ^2 x \sin ^2x

So now the original question 

\sin ^4 x + \cos ^4 x = \dfrac{1}{2}

becomes
1 - 2 \cos ^2 x \sin ^2x = \dfrac{1}{2}

4 \cos ^2 x \sin ^2x = 1

Now we use the sine double angle formula

\sin 2x = 2 \sin x \cos x

We square it to see

\sin^2 2x = 4\sin^2 x \cos^2 x = 1

Taking the square root,

\sin 2x = \pm 1

Not sure how you want it; we'll do it in degrees. 

When we know the sine of an angle, there's usually two angles on the unit circle that have that sine.  They're supplementary angles which add to 180^\circ.  But when the sine is 1 or -1 like it is here, we're looking at 90^\circ and -90^\circ, which are essentially their own supplements, slightly less messy. 

That means we have two equations:

\sin 2x = 1 = \sin 90^\circ

2x = 90^\circ + 360^\circ k \quad integer k

x = 45^\circ + 180^\circ k

or 


\sin 2x = -1 = \sin -90^\circ

2x = -90^\circ+ 360^\circ k

x = - 45^\circ + 180^\circ k

We can combine those for a final answer,

x = \pm 45^\circ + 180^\circ k \quad integer k

Check.  Let's just check one, how about

x=-45^\circ + 180^\circ = 135^\circ

\sin(135)= 1/\sqrt{2}

\sin ^4(135)=(1/\sqrt{2})^4 = 1/4

\cos ^4(135)=(-1/\sqrt{2})^4 = 1/4

\sin ^4(135^\circ) +\cos ^4(135^\circ) = 1/2 \quad\checkmark


6 0
3 years ago
The table below shows how much it costs per gallon to fill a gas tank with premium
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47.50/10 = 4.75

57/12 = 4.75

76/16 = 4.75

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6 0
3 years ago
What is an equation of the line that passes through the point (-2,-8) and has the slope of 3
NeTakaya

Answer:

y = 3x - 2

Step-by-step explanation:

y +8 = 3 (x + 2)

y + 8 = 3x + 6

y = 3x - 2

3 0
3 years ago
Solve the inequality <br><br> -5x &lt; 35
Marianna [84]
<span>-5x < 35
5x > -35
x > -35/5
x > -7</span>
7 0
4 years ago
Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height<br><br>pls help​
mafiozo [28]

Answer:

8% out of 175 = ( 8 ÷ 100 ) × 175 = 14

175 cm - 14 = 161 cm

...............

7 0
3 years ago
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