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]
You deposit $200 in an account earning 3.5% simple interest. How many years will it take for the balance of the account to be $221
Please help me I wanna go to sleep
What is true about this sequence?
8000, 4000, 2000, 1000, ...
Answer:
B
Step-by-step explanation:
each consecutive term is divided by 2
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
radioactive dating of rocks
What type of number is v5?
Choose all answers that apply:
1. Whole number
2. Integer
3. Rational
4. Irrational
PLEASE HELP ME ILL GIVE 10 POINTS
What is the average rate of change for f(x) = 2 ^ x + 10 over the interval 2 <= x <= 4
Rex's house is located at point (2,-5) on a coordinate plane. The location of Terrell's house is the reflection of the location of Rex's house across the X-axis.In what quadrant is Terrell's house?
Answer:
When you reflect a point of the x-axis you can apply:
(x,y) -> (x,-y)
Using this:
(2,-5) -> (2,5)
Since both the x and y places are positive, it is in quadrant 1.
Hope this helps!
Step-by-step explanation:
Scale factor from A to B is 4:5.
Help
Answer:
24
Step-by-step explanation:
4/5 = x/30, then (4×30)/5 =24
The missing value is 24.
We have,
From the figure,
We can write an expression as:
4:5 = x : 30
This can be written as,
4/5 = x/30
Now,
Cross multiply.
x = 4 x 30 / 5
x = 4 x 6
x = 24
Thus,
The missing value is 24.
Learn more about expressions here:
https://brainly.com/question/3118662
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How do you write 60/100 and 40/100 as decimal expressions?
Answer:
60/100=0.6 , 40/100=0.4
Step-by-step explanation:
60/100=6/10
6/10=0.6
40/100=4/10
4/10=0.4
Can somebody help and show work
Answer:
( x +1 ) ( x + 3 )
PLEASE HELP ITS DONE IN 16 HOURSSS!!!
question: A substance with 12 negatively charged atoms combined with a substance that has 10 positively charge atoms. What is the total charge of the substance when the atoms are combined?
answer options:
+22
-22
+2
-2
If I have six eggs I crack two I cooked two and I eat two how many eggs do I have left
Answer:
4
Step-by-step explanation:
you cracked, cooked, and ate the same two eggs
If f(x) = 5x2 – 6x + 13 and g(x) = 6 – 4(x – 1) which is an equivalent form of f(x) + g(x)?
Answer:
61-4-2. (3t-a)(at+1) f. 6x2 - 17x+10. 16x-5X(x-2) e x-2x*-*+2 x2{x-2)-1(x-2). (x-2)(x2_1). (x-2)x+1)(x-) hi ** +5x2 +6 ... Leave your answers in simplest radical form if needed. ... 4. Let 'n(x)=x2-Ox and g(x)=2x-7. Find all values of x, for which h(x) = g(x) ... p=2 4p=8. (x+6*=8(y+3) x+6X+36=8Y+24. X*+6x +12= By gx+x+1=Y. 13.
Step-by-step explanation:
What is 3-2y+(-8y)+8.4 as a simplified expression
Answer:
-10y + 11.4
I hope this helps you out
Answer:
-10y+11.4
Step-by-step explanation:
you combine -2y with -8y to get negative -10y. Then you combine 3 and 8.4 to get 11. Variables usually come first in equations, I don't think it matters, but you might want to put them first anyway.
After a discount of 40%, the sale price of a ride pass at a fun park is $30. What is the original
price?
Answer:
30 divided by 0.40 = 75
The original price was $75
Step-by-step explanation:
30 divided by 0.40 = 75
The original price was $75
Highlight all of the Like Terms on questions 1-2 please!! (any color) (due in 5 minutes)
Answer:
1. 8,13,8,3,g
2. 8,13,3,g (Like term pair 1) and 8 (Like term pair 2)
Step-by-step explanation:
Hey guys can someone help me out?
Answer: yes with what
Step-by-step explanation:
3-gallon container of disinfectant costs $52.80. What is the price per cup?
In 2004, an art collector paid $62,817,000 for a particular painting. The same painting sold for $31,000 in 1950. Complete parts (a) through (d).
For part c, estimate the rate of change of the painting's value in 2026 but I want to know how to obtain the answer to the problem. Thanks!
Answer:
WeIIcome
Step-by-step explanation:
PLEASE HELP
determine the intercepts of the line
x intercept (__ , __)
y intercept (__ , __)
Answer:
i think y=2 and x=-7
Step-by-step explanation:
What is the distance between - 10
and 2 on the number line?
12 units
-8 units
5 units
8 units
Answer:
12 units
Step-by-step explanation:
Draw a number line and mark x = -10 and x = 2. You can readily see that the distance from -10 to the origin is 10 units, and from the origin to 2 is 2 units, in both cases measured from left to right. Adding these two positive quantities together, we get 10 + 2, or 12.
The distance from -10 to 2 on the number line is 12 units.
HEY can You help me with this work pls i need help don't put random. if u don't know it pls guys.
1️⃣Remove parentheses
6a+6+3x-2+2a+4
2️⃣Collect like terms
(6a+2a)+(6-2+4)+3x
3️⃣Simplify
8a+8+3x
Answer: 8a+8+3x
QUESTION 21️⃣Remove parentheses.
-2z-3+4c+6y+y+3c
2️⃣Collect like terms.
-2z-3+(4c+3c)+(6y+y)
3️⃣Simplify
-2z-3+7c+7y
Answer: -2z-3+7c+7y
QUESTION 31️⃣Subtracting (7.8 - 5.1t) from (2.8 - 3.2t)
(2.8 - 3.2t) - (7.8 - 5.1t)
2️⃣Remove the parentheses.
2.8 - 3.2t - 7.8 + 5.1t
= 5.1t - 3.2t + 2.8 - 7.8 (we have now shown the difference in another way)
3️⃣Subtracting the like terms, will give:
1.9t - 5
4️⃣Recall
(2.8 - 3.2t) - (7.8 - 5.1t).
(-3.2t + 2.8) - (-5.1t + 7.8)
Answer:
a. (-3.2t + 2.8) - (-5.1t + 7.8)
b. 1.9t - 5
c. (-3.2t + 2.8) - (-5.1t + 7.8)
QUESTION 41️⃣Simplify
1/2p-(1/4p-4)
2️⃣Simplify
p2-(p/4-4)
3️⃣Simplify
p2-p/4+4
4️⃣Combine Terms
(p/2-p/4)+4
5️⃣Combine Terms
p/4+4
Answer: p/4+4
Done ✔
At an Auto Repair shop, 4 of the 16 cars received oil changes. What percent of the cars received oil changes?
Answer:
its 25 percent
Step-by-step explanation:
want an explanation cuz im happy to give you 1
If a point on a coordinate plane is placed 5 lines to the right and 3 lines up, what would the ordered pair be?
Answer:
(5,3)
Step-by-step explanation:
what is the value of the 1 in 56.123
Answer:
The value of 1 is tens =) i hope i help u
Multiple Choice
Use the diagram below to answer questions 1–3.
Which angle is congruent to angle 1?
A. angle2
B. angle5
C. angle6
D. angle7
The sum of half of a number and 49 is 2 1/4 of the number. Find the number
Answer:
x = 28
Step-by-step explanation:
given, x/2 + 49 = 21/4
x/2 + 49 = 9x/4
2x +196 = 9x
7x = 196
x = 28
I hope this helps a little bit.
12(-5z - 4)
please help me
Answer:
-60z - 48
Step-by-step explanation:
Is your expression.
Matematicas Aprendizaje
Step-by-step explanation:
jejdjdhxbdhhdhdjsjsjsjsjsjjsjs
y=3x-4 slope intercept form
Answer:the slope is 3 and the y intercept is -4
Step-by-step explanation:
Factorise 3x⁴-4y⁴ completely
Answer:
Step-by-step explanation:
[tex]3x^4-4y^4\\=(\sqrt{3}x^2)^2-(2y^2)^2)\\=(\sqrt{3}x^2+2y^2)(\sqrt{3}x^2-2y^2)\\=(\sqrt{3} x^{2} +2y^{2} )((3^{\frac{1}{4} } x)^2-(\sqrt{2} y)^{2} )\\=(\sqrt{3} x^{2} +2y^{2} )(3^{\frac{1}{4} } x+\sqrt{2} y)(3^{\frac{1}{4} } x-\sqrt{2} y)[/tex]