Rewrite the limand as
(1 - sin(x)) / cot²(x) = (1 - sin(x)) / (cos²(x) / sin²(x))
… = ((1 - sin(x)) sin²(x)) / cos²(x)
Recall the Pythagorean identity,
sin²(x) + cos²(x) = 1
Then
(1 - sin(x)) / cot²(x) = ((1 - sin(x)) sin²(x)) / (1 - sin²(x))
Factorize the denominator; it's a difference of squares, so
1 - sin²(x) = (1 - sin(x)) (1 + sin(x))
Cancel the common factor of 1 - sin(x) in the numerator and denominator:
(1 - sin(x)) / cot²(x) = sin²(x) / (1 + sin(x))
Now the limand is continuous at x = π/2, so
[tex]\displaystyle\lim_{x\to\frac\pi2}\frac{1-\sin(x)}{\cot^2(x)}=\lim_{x\to\frac\pi2}\frac{\sin^2(x)}{1+\sin(x)}=\frac{\sin^2\left(\frac\pi2\right)}{1+\sin\left(\frac\pi2\right)}=\boxed{\frac12}[/tex]
There are 20 pieces of fruit in a bowl and 8 of them are bananas. What percentage of the pieces of fruit in the bowl are bananas?
**choose your answer from the choices on Slide 5, but you must show how you got your answer on the chart, blank drawing space below, or explain in words**
How do I find the volume of a solid by rotating the region bounded by the given curves about a specified line?
Step-by-step explanation:
if a region is bounded by two curves y=f(x) and y=g(x) on an internal a,b where 0<g(x)< f(x) then the volume of the solid obtained by the rotating region about the Y-axis is expressed by the integral of the difference of two functions: v= 2πbfax(x)jdx
A line passes through the points (1, 7) and (0, 3). What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:1. you can compute the slope, m
2. point (0,3) is the y-intercept; b=33
3. y = mx + b, so put the numerical values in for m & b. DON
Step-by-step explanation:
What is the answer
a3-c + b, when a=3,b=6, c=8
Answer:
The answer is 25
Step-by-step explanation:
simplify the expression -2d + -2d - 9 + -9
Answer:
-4d-18
Step-by-step explanation:
Combine like terms:
-2d and -2d can combine since they have the same variable of d creating the term of -4d and -9 and -9 can combine to create -18. Put those together and you get the answer above.
Answer:
-4d-18
Step-by-step explanation:
solve for x. x+53=99 A.36 B.46 C.47 D.152
Answer:
Hii, the answer B. 46
Step-by-step explanation:
x+ 53 = 99
So to find what x equals we just do simple subtraction
99 - 53 = 46
so x = 46
Hope this helps!
Simplify by combining like terms: 9xy-3y-y-2xy+3
Answer:
7xy -4y + 3
Step-by-step explanation:
combine 9xy and -2xy (7xy - 3y -y +3)
combine -3y and -y (7xy - 4y + 3)
all done yay
If the number 45 is multiplied by 100, In what place value will the 4 be?
thousands
tens
ones
hundreds
Answer:
thousands
Step-by-step explanation:
the number would be 4,500
Which of the following is equivalent?
Compare the graphs of the functions listed below.
Function 1: y = 0.25x2
Function 2: y = 4x2
Function 3: y = -½x2
Function 4: y = -16x2
The graph of is the widest.
Answer:
The graph of FUNCTION 1 is the widest.
Step-by-step explanation:
So sorry lolll. But this is definitely right
Round 1231.50432 to the nearest tenth
Answer:
1231.5
Step-by-step explanation:
I hope this help.
Negative nine minus negative ten?
Answer:
-9 - 10 = -19
Step-by-step explanation:
If both numbers are a negative, then add them together but keep the negative or minus sign
Hope this Helps!!!
i need to find the equations for these solutions
Answer:
hope these answers helps u out
Step-by-step explanation:
PLZZ MARK ME AS BRAINLIEST
Y - 5= - (5 - y)
Does it have a solution?
Answer:
infanite
Step-by-step explanation:
2/5 > 1/2 or 2/5 <1/2
Answer:
It's 2/5 <1/2.
Jennifer sets her binoculars to enlarge objects 10 times their actual size. If the length of an ant is 0.52 inches, what is its length as seen through her binoculars?
Answer:
The length as seen through her binoculars is of 5.2 inches.
Step-by-step explanation:
The length of an ant is 0.52 inches, what is its length as seen through her binoculars?
The binocular is set to enlarge the object 10 times their actual size.
We have that the actual length is 0.52 inches.
0.52*10 = 5.2 inches
The length as seen through her binoculars is of 5.2 inches.
Brandon has a points card for a movie theater. He receives 70 rewards points just for signing up. He earns 12.5 points for each visit to the movie theater. He needs 145 points for a free movie ticket. How many visits must Brandon make to earn a free movie ticket?
Answer: x=6
Step-by-step explanation:
Answer:
placeholder going to the bathroom brb
Step-by-step explanation:
What is the sum of the largest and smallest recorded capacity?
Which improper fraction is equivalent to 15 3/7
Answer:
108/7
Step-by-step explanation:
15*7 is 105+3 is 108/7
Consider the angle 0.
What is the value of the ratio opposite/adjacent
Answer:
Step-by-step explanation:
12/5
as a mixed fraction 2 2/5
or as decimal 2.4
5. Choose the likelihood of a probability of 50 percent.
Event: November 25th will fall on a Monday
Certain
Highly likely
Less likely
Impossible
Answer:
well, highly likely. it will always fall on a monday,
Step-by-step explanation:
if you look at all of the years it has fallen on since 2010 you will see it has always fallen on monday.
how do u solve 5/2x-7=3/4x+14
Answer:
x=12
Hope this help :)
Helpppp PLZ 20 POINTS
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
combine like terms
(10f -5f)
(8 + 4)
(6g)
Bianca makes an error when she tries to write an expression equivalent to
12 + 15(3 - y) - 10y. What is the error? Fix Bianca's error.
I NEED HELP ASAPPPPPP!!!
Answer:
57 - 25y
Step-by-step explanation:
when 15 was distributed it should be '45 - 15y' instead of '45 + 15y'
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The correct expression is
12 + 15(3 - y) - 10y
12 + 15 x 3 - 15y - 10y
12 + 45 - 15y - 10y
57 - 20y
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Step 1:
12 + 15(3 - y) - 10y
Step 2:
12 + 15 x 3 - 15y - 10y
Step 3:
12 + 45 - 15y - 10y
Step 4:
57 - 20y
Now,
We see that,
There was an error in step 2 where instead of -15y, +15y was written.
Thus,
The correct expression is
12 + 15(3 - y) - 10y
12 + 15 x 3 - 15y - 10y
12 + 45 - 15y - 10y
57 - 20y
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
David has 54 marbles, 24 of which are black, 18 are red, and 12 are blue. What fraction represents the ratio of black marbles to blue marbles?
What is bigger 4.62 or 4.24
Answer: 4.62 is bigger than 4.24
Step-by-step explanation:
please help fr i don’t understand this
Answer:
A.
Hope that helps!
Step-by-step explanation:
Answer:
the answer is A I believe good luck
This banana 8 inches How many 0.4 inch slices of banana can be cut from this banana?
Answer:
20 banna slices can be cut from a banna
Step-by-step explanation:
8 divided by 0.4 equals 20
Who can answer this
Answer:
Check pdf
Step-by-step explanation:
can someone help me with this