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sammy [17]
3 years ago
15

I HAVE 5 MINUTES (15 points)

Mathematics
1 answer:
boyakko [2]3 years ago
6 0

Answer:

c

Step-by-step explanation:

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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
Please help.. Please. Is this a positive trend or negative trend or no trend ​
Eva8 [605]

Answer:

it's a no trend cause its literally nothing but dots

3 0
3 years ago
If f(x)= 0, what is x?
crimeas [40]

Answer:

X is the input to the function ... it appears that it is unrestricted...

it can be anything from -∞ to + ∞ (the domain) ..

in every case the output (range) is "0"

Step-by-step explanation:

7 0
3 years ago
What is the following product?<br> (4x√5x^2+2x^2√6)2<br><br><br> please help!!
ryzh [129]

Answer:

c

Step-by-step explanation:

6 0
3 years ago
The map of a walking trail is drawn on a coordinate grid with three points of interest.
rewona [7]

Answer:

12 units

Step-by-step explanation:

Given the points :

R(−3, 2) - - - > S(2, 2) - - - - > T(2, −5).

Distance between R and S

Distance between two points is obtained thus :

D = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Distance between R and S

x1 = - 3 ; y1= 2 ; x2 = 2 ; y2 = 2

D1 = sqrt((2 - (-3))^2 + (2 - 2)^2)

D1 = sqrt((5^2 + 0^2))

D1 = sqrt(25)

D1 = 5

Distance between S and T

x1 = 2 ; y1= 2 ; x2 = 2 ; y2 = - 5

D2 = sqrt((2 - 2)^2 + (-5 - 2)^2)

D2 = sqrt((0^2 + (-7)^2))

D2 = sqrt(49)

D2 = 7

Hence, total length = D1 + D2 = 5 + 7 = 12 units

6 0
3 years ago
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