The area of the circle is equal to the area of the polygon
It would be 76 degrees because it’s a vertical angle
Answer:
x ≈ -4.419
Step-by-step explanation:
Separate the constants from the exponentials and write the two exponentials as one. (This puts x in one place.) Then use logarithms.
0 = 2^(x-1) -3^(x+1)
3^(x+1) = 2^(x-1) . . . . . add 3^(x+1)
3×3^x = (1/2)2^x . . . . .factor out the constants
(3/2)^x = (1/2)/3 . . . . . divide by 3×2^x
Take the log:
x·log(3/2) = log(1/6)
x = log(1/6)/log(3/2) . . . . . divide by the coefficient of x
x ≈ -4.419
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A graphing calculator is another tool that can be used to solve this. I find it the quickest and easiest.
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<em>Comment on alternate solution</em>
Once you get the exponential terms on opposite sides of the equal sign, you can take logs at that point, if you like. Then solve the resulting linear equation for x.
(x+1)log(3) = (x-1)log(2)
x=(log(2)+log(3))/(log(2)-log(3))
Answer:
The main reason to know the multiplication table is so you can more easily multiply larger numbers. For example, suppose you want to multiply 53 x 7. Start by stacking these numbers on top of another, aligning the ones place. Draw a line underneath, and then multiply 3 by 7. Because 3 x 7 = 21, write down the ones digit (1) and carry the tens digit (2) to the tens column:
Next, multiply 5 by 7. This time, 5 x 7 = 35. But you also need to add the 2 that you carried over, which makes the result 37. Because 5 and 7 are the last numbers to multiply, you don’t have to carry, so write down the 37 — you find that 53 x 7 = 371:
When multiplying larger numbers, the idea is similar. For example, suppose you want to multiply 53 by 47. Be sure to align the stacked numbers by the ones place. (The first few steps — multiplying by the 7 in 47 — are the same, so pick up the next step.) Now you’re ready to multiply by the 4 in 47. But remember that this 4 is in the tens column, so it really means 40. So to begin, put a 0 directly under the 1 in 371:
This 0 acts as a placeholder so that this row is aligned properly.
When multiplying by larger numbers with two digits or more, use one placeholding zero when multiplying by the tens digit, two placeholding zeros when multiplying by the hundreds digit
Answer:
The distance between Albany and Buffalo along the I90 is 288.8 mi.
The speed of Fabio is 62 mph.
After 1.5 hours, he is 221 miles from Albany.
Things we can calculate here:
Using the relation:
Distance = time*speed.
We can calculate the number of miles that he moved in that 1.5 hours.
D = 62mph*1.5h = 93mi.
If after 1.5 hours, he was 221 miles Albany, then before that he was 93 miles closer to Albany.
His initial position was:
221 - 93 = 128 miles away from Albany.
Now we also can calculate the time left to arrive at Buffalo.
We know that the distance between Albany and Buffalo is 288.8 mi
And he is 221 mi away from Albany.
Then the distance left to Buffalo is:
288.8mi - 221mi = 67.8mi
And the time left will be:
Distance/speed = time
67.8mi/62mph = 1.1 hours.
He needs to drive for another 1.1 hours to get to Buffalo.
