Answer:
- x = log(y/4)/log(1.0256)
- your answer for y=12 is correct
Step-by-step explanation:
The question is asking you to solve ...
y = f(x)
for x. (In other words, find the inverse function.)
You already did this using a constant for y. Do the same thing with y instead of the constant.
y = 4(1.0256^x)
y/4 = 1.0256^x . . . . . . . divide by 4
log(y/4) = x·log(1.0256) . . . . . take logs
log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x
Now, you have a model for x in terms of y, which is what the question is asking for.
x = log(y/4)/log(1.0256) . . . . . . . exact expression
When y=12, this is ...
x = log(12/4)/log(1.0256) ≈ 43.46 . . . . weeks
_____
This is a linear equation in log(y), so can be written as such:
x = 91.0912·log(y) -54.8424 . . . . . approximate expression
Answer:
The statement is false
Step-by-step explanation:
we know that
The tangent function will be positive when the sine function and the cosine function have the same sign
so
In the first quadrant the tangent function is positive
In the third quadrant the tangent function is positive
so
The statement is false
That would be :
4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substitute for y)
PROOF: y + 5x = x²<span> + 10
</span> (4x - 10) + 5x = x² + 10
4x - 10 = x² -5x + 10
<span>
</span>0 = x2 – 9x + 20<span> (liked terms are grouped and simplified)
PROOF: </span> 4x - 10 = x² -5x + 10
4x = x² -5x + 10 + 10
0 = x² -5x -4x + 20
0 = x² - 9x + 20
Solving:
x² - 9x + 20 = 0
x² - 5x - 4x + 20 = 0
(x - 5) (x - 4) = 0
⇒ x = 4 (as question says) OR x = 5
<h3>Given</h3>
A(-3, 1), B(4, 5)
<h3>Find</h3>
coordinates of P on AB such that AP/PB = 5/2
<h3>Solution</h3>
AP/PB = 5/2 . . . . . desired result
2AP = 5PB . . . . . . multiply by 2PB
2(P-A) = 5(B-P) . . . meaning of the above
2P -2A = 5B -5P . . eliminate parentheses
7P = 2A +5B . . . . . collect P terms
P = (2A +5B)/7 . . . .divide by the coefficient of P
P = (2(-3, 1) +5(4, 5))/7 . . . . substitute the given points
P = (-6+20, 2+25)/7 . . . . . . simplify
P = (2, 3 6/7)
Answer:
4/3
Step-by-step explanation:
7x + 4 = 10x
4 = 3x
x = 4/3
