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Leno4ka [110]
3 years ago
12

A movie rental store, Frank's Movies, offers customers two choices. Customers can pay a yearly membership of $45 and then rent e

ach movie for $2, or they can choose not to pay the membership fee and rent each movie for $3.50. How many movies would you have to rent before membership becomes the cheaper option?
Mathematics
1 answer:
STALIN [3.7K]3 years ago
3 0

Answer:

13

Step-by-step explanation:

$45=3.50x

divide both sides by 3.50

13 movies (rounded to nearest whole number)

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(X^4)-(45x^2)+324 what are the zeroes? And how many turning points?
dmitriy555 [2]

Zeroes:

We must solve

x^4-45x^2+324=0

To do so, we define the auxiliary variable t=x^2. The equation becomes

t^2-45t+324=0

The quadratic formula yields the solutions

t=9,\quad t=36

Substituting back t=x^2 gives

x^2=9 \iff x=\pm 3,\quad x^2=36 \iff x=\pm 6

So, the zeroes are -6, -3, 3, 6.

Turning points:

Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.

We have

f(x)=x^4-45x^2+324 \implies f'(x)=4x^3-90x

If we set the derivative to be zero, we have

4x^3-90x=0 \iff x(4x^2-90)=0

So, the derivative is zero if x=0 or

4x^2=90 \iff 2x^2=45 \iff x^2=\dfrac{45}{2}\iff x=\pm\sqrt{\dfrac{45}{2}}

6 0
3 years ago
D + 4/3 = -1/3<br> find d.
vovangra [49]

Answer:

d= -5/3

Step-by-step explanation:

d + 4/3 = -1/3

d= -4/3 -1/3

d= -5/3

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Answer:

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