Answer:
Perimeter = √40 + 6 + 4√2 + √28
Step-by-step explanation:
As we know that the perimeter of a triangle is the sum of the length of sides.
<em>Perimeter = 4√2 + x + 6 + y</em>
Now for x and y-
<u>I. By Pythagorean theorem in left side right angle triangle-</u>
( 4√2)² = 2² + x²
32 - 4 = x²
x² = 28
x = √28
<u>II. By Pythagorean theorem in Right angle triangle-</u>
y² = 2² + 6²
y² = 4 + 36
y² = 40
y = √40
Hence Perimeter = 4√2 + x + 6 + y
P = 4√2 + √28 + 6 + √40
∴ P = √40 + 6 + 4√2 + √28
95% of red lights last between 2.5 and 3.5 minutes.
<u>Step-by-step explanation:</u>
In this case,
- The mean M is 3 and
- The standard deviation SD is given as 0.25
Assume the bell shaped graph of normal distribution,
The center of the graph is mean which is 3 minutes.
We move one space to the right side of mean ⇒ M + SD
⇒ 3+0.25 = 3.25 minutes.
Again we move one more space to the right of mean ⇒ M + 2SD
⇒ 3 + (0.25×2) = 3.5 minutes.
Similarly,
Move one space to the left side of mean ⇒ M - SD
⇒ 3-0.25 = 2.75 minutes.
Again we move one more space to the left of mean ⇒ M - 2SD
⇒ 3 - (0.25×2) =2.5 minutes.
The questions asks to approximately what percent of red lights last between 2.5 and 3.5 minutes.
Notice 2.5 and 3.5 fall within 2 standard deviations, and that 95% of the data is within 2 standard deviations. (Refer to bell-shaped graph)
Therefore, the percent of red lights that last between 2.5 and 3.5 minutes is 95%
Answer:
Step-by-step explanation:
Here you go mate
Step 1
8m+4n+7m-2n Equation/Question
Step 2
8m+4n+7m-2n Simplify
8m+4n+7m-2n
Step 3
8m+4n+7m-2n Combine terms
(8m+7m)+(4n+-2n)
Step 4
(8m+7m)+(4n+-2n) Add them
answer
15m+2n
Hope this helps
Answer:
-1
Step-by-step explanation:
The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.
d(log(x))/dx = 1/(x·ln(10))
d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))
Then the ratio of these derivatives is ...
lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x
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At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.
d(-sin(x)cos(x))/dx = -cos(2x)
dx/dx = 1
so the limit is ...
lim = -cos(2x)/1
lim = -1 when evaluated at x=0.
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I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.
