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Lostsunrise [7]
3 years ago
12

What is the y-intercept for all graphs of the form y=ab^x (where b is not 0)

Mathematics
1 answer:
erastova [34]3 years ago
4 0
The y-intercept is the value of y when x=0.  Anything raised to the power of zero equals one so:

y=ab^0 is equal to:

y=a

So the y-intercept will be a for any equation of the form y=ab^x, or if you prefer it will always be the point (0,a)
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Hi, I am new to this website :) I'm currently taking an online trig class on De Moivre's theorem and I don't understand it at al
Vladimir [108]
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.

For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes

[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))] 

it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.

For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)

[2^6(cos(40*6))+isin(40*6)],

[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)

And the answer is -32 -32 √3 i

Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i

7 0
3 years ago
Please help!! 15 points
zlopas [31]

Answer:

? = 125°

Step-by-step explanation:

The central angle is equal to the measure of the arc that subtends it, thus

? = 125°

3 0
3 years ago
If x = y, then x + 2 =
yawa3891 [41]

Answer:

As far as i can tell it would just be y+2?

4 0
2 years ago
The ratio of Tv commercial mins to scheduled show time mins is 6 to 24 how many mins of commercial time will be seen during a 2
vodomira [7]
Well first set up the first ratio as 6/24. That is commercial mins over show time mins. Then to keep the units the same convert 2 hours into minutes which would be 120 minutes. Then set up your next ratio as x/120 since you’re trying to find the commercial minutes. Then cross multiply so that it’s 24x=720 and then x=30 and that’s the amount of commercial minutes for 2 hours.
3 0
3 years ago
Every set of three points must be collinear.
maria [59]

Answer:

I suppose you're trying to make a triangle of some sort on a plane! So, in this case, yes the three points would reside all on the same plane. Making all three of them collinear.

3 0
3 years ago
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