The point (4,y) has a known x coordinate of x = 4. The y coordinate is unknown right now so we'll just call it y.
Draw a vertical line (see side note below) through 4 on the x axis. I've done so in red (see attached image). The red line crosses the graph at the point (4,1) so this tells us that
y = 1Answer: y = 1
Side Note: you don't have to draw a vertical red line but it's handy to see how it works out. After you get used to these types of problems, you can visually be able to see the answer without these extra lines.
One A
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444
y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line =
y' = e^1*ln(1) + e^1/1
y' = e*0+e = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)
e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e
line equation and answer.
y = e*x - e
Answer:
0.12
Step-by-step explanation:
Independent events are when probability of one event happening doesn't affect the probability of the other event happening.
Also,
In probability "AND" means "multiplication" and "OR" means "addition".
The question asks for probability that Nick oversleeps "AND" has pop quiz. So we need to multiply the individual probabilities (since independent, they have no affect on each other).
P(Nick oversleeps) = 0.48
P(pop quiz) = 0.25
Thus,
P(Nick oversleeps AND pop quiz) = 0.48 * 0.25 = 0.12
Answer:
Area:
Step-by-step explanation:
Area of the blue area:
Perimeter of blue area:unsure as no numbers are given for the slanted side if the triangle.
Answer:
Yes and no nor
Step-by-step explanation:
