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sineoko [7]
3 years ago
7

Which is the ending behavior of the graph of the polynomial function F(x)=3x^6+30x^5+75x^4

Mathematics
2 answers:
hodyreva [135]3 years ago
7 0

Answer:

D

Step-by-step explanation:

Verdich [7]3 years ago
6 0
A good way to find the end behaviors is to look at the number of the longest exponent in the equation. If it's even, then both ends go the same direction. If it's odd, then the ends go in two different directions. The highest exponent is even, so both ends go the same direction. Since the base of that highest exponent is a positive number, the effects aren't reversed, so the answer to this would be:
As <em>x=</em><em>-</em>∞, y=∞; As x=∞, y=∞
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Limit question: lim x--&gt;pi ((e^sinx)-1)/(x-pi)
aleksandr82 [10.1K]
\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}

Notice that if f(x)=e^{\sin x}, then f(\pi)=e^{\sin\pi}=e^0=1. Recall the definition of the derivative of a function f(x) at a point x=c:

f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}

So the value of this limit is exactly the value of the derivative of f(x)=e^{\sin x} at x=\pi.

You have

f'(x)=\cos x\,e^{\sin x}\implies f'(\pi)=\cos\pi\,e^{\sin\pi}=-1
4 0
3 years ago
The number of salmon swimming upstream to spawn is approximated by the following function:
umka2103 [35]

Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

Step-by-step explanation:

Let S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965, for 6 \leq x \leq 20. x represents the temperature of the water, measured in degrees Celsius, and S is the number of salmon swimming upstream to spawn, dimensionless.

We compute the first and second derivatives of the function:

S'(x) = -3\cdot x^{2}+4\cdot x +405 (Eq. 1)

S''(x) = -6\cdot x +4 (Eq. 2)

Then we equalize (Eq. 1) to zero and solve for x:

-3\cdot x^{2}+4\cdot x +405 = 0

And all roots are found by Quadratic Formula:

x_{1} \approx 12.305\,^{\circ}C, x_{2}\approx -10.971\,^{\circ}C

Only the first root is inside the given interval of the function. Hence, the correct answer is:

x \approx 12.305\,^{\circ}C

Now we evaluate the second derivative at given result. That is:

S''(12.305) = -6\cdot (12.305)+4

S''(12.305) = -69.83

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

5 0
3 years ago
In triangle ΔABC, ∠C is a right angle and CD is the height to AB . Find the angles in ΔCBD and ΔCAD if: Chapter Reference a m∠A
Strike441 [17]

Answer:

Given A triangle ABC in which

 ∠C =90°,∠A=20° and CD ⊥ AB.

In Δ ABC

⇒∠A + ∠B +∠C=180° [ Angle sum property of triangle]

⇒20° + ∠B + 90°=180°

⇒∠B+110° =180°

∠B =180° -110°

∠B = 70°

In Δ B DC

∠BDC =90°,∠B =70°,∠BC D=?

∠BDC +,∠B+∠BC D=180°[ angle sum property of triangle]

90° + 70°+∠BC D =180°

∠BC D=180°- 160°

∠BC D = 20°

In Δ AC D

∠A=20°, ∠ADC=90°,∠AC D=?

∠A +  ∠ADC +∠AC D=180° [angle sum property of triangle]

20°+90°+∠AC D=180°

110° +∠AC D=180°

∠AC D=180°-110°

∠AC D=70°

So solution are, ∠AC D=70°,∠ BC D=20°,∠DB C=70°





5 0
3 years ago
One third plus four sixths plus six eighteenths equals blank
ss7ja [257]

Answer:

1 1/3

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Please help me with this math question
Arturiano [62]

Answer:

145

Step-by-step explanation:

168-23 = 145

    i hope this helps :)

5 0
1 year ago
Read 2 more answers
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