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2 years ago

If a1=6 and a5=12, what does a3=?

Mathematics

1 answer:

sveticcg [70]2 years ago

4 0

a3=9

assuming the pattern is constant, a3 is right in the middle of a1 and a5 so the answer would be right in the middle of 6 and 12. the average of 6 and 12 is 9, so a3=9.

hope this helps!

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The tangent of the graph of y=<img src="https://tex.z-dn.net/?f=e%5E%7Bax%7D" id="TexFormula1" title="e^{ax}" alt="e^{ax}" align

bearhunter [10]

a) The tangent to $y=e^{ax}$ at $x=p$ has slope

$y' = ae^{ax} \implies y'(p) = ae^{ap}$

and $y=e^{ap}$ at this point. It passes through the origin, so its equation is

$y - 0 = ae^{ap} (x - 0) \implies y = ae^{ap} x$

It also passes through the point $(p,e^{ap})$ on the curve, so

$y - e^{ap} = ae^{ap} (x - p) \implies y = e^{ap} + ae^{ap} x - ape^{ap}$

By substitution,

$ae^{ap} x = e^{ap} + ae^{ap} x - ape^{ap} \implies e^{ap} = ape^{ap} \implies ap=1 \\\\ \implies \boxed{p=\dfrac1a}$

b) The normal to $y=e^{ax}$ at $x=2p$ has slope

$-\dfrac1{y'(2p)} = -\dfrac1{ae^{2ap}} = -1 \implies ae^{2ap} = 1$

It follows that

$ae^{2ap} = ae^2 = 1 \implies \boxed{a = \dfrac1{e^2} \text{ and } p = e^2}$

c) The tangent line equation is then

$y = \dfrac1{e^2} e^1 x \implies \boxed{y = \dfrac xe}$

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2 years ago

F(x)=22xplus 33 and g(x)=x2−44x−55, find (g◦f)(88)

Law Incorporation [45]

F(x) = 22x + 33
g(x) = x² - 44x - 55
(g о f)(88) = (22(88) + 33)² - 44(22(88) + 33) - 55
(g о f)(88) = (1936 + 33)² - 44(1936 + 33) - 55
(g о f)(88) = (1969)² - 44(1969) - 55
(g о f)(88) = 3,876,961 - 86,636 - 55
(g о f)(88) = 2,790,325 - 55
(g о f)(88) = 3,790,270

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4 years ago

A helicopter is hovering 100 meters above the ocean. Directly below it, a submarine is at a depth of 200 meters.

sp2606 [1]

Answer:

100

2. Above,

3. -200−200 ,

4. Below

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3 years ago

Find c to complete the perfect trinomial<br><br> x2 + 4x + c

sladkih [1.3K]

Answer:

Step-by-step explanation:

I assume that is supposed to be x squared. A perfect trinomial is the product of a perfect square, (x times a number) squared. With these trinomials, you can look at them as: ax squared times bx + c. When a is 1, the fastest way to get c to make a perfect square is to divide b by 2. In this case, it's 4/2 = 2. The last step is to square that number. 2 squared = 4.

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3 years ago

M is between L and N. If LN = 91 and LM = 23, find MN.

Tasya [4]

Answer:

MN = 68

Step-by-step explanation:

LN = 91

LM = 23

Points L, M, and N are collinear, therefore, according to the segment addition postulate, the following can be deduced:

LM + MN = LN

23 + MN = 91 (Substitution)

Subtract 23 from both sides

23 + MN - 23 = 91 - 23

MN = 68

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3 years ago