[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{ - 1} t \: dt}[/tex]
Answers
Use L'Hopital's rule twice:
[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \lim_{x\to0^+} \frac1{\sin^2(x)} \left(\int_0^x \sin^{-1}(t) \, dt - \int_0^{\frac x2} \sin^{-1}(t) \, dt\right) \\\\ = \lim_{x\to0^+} \frac{\sin^{-1}(x) - \frac12 \sin^{-1}\left(\frac x2\right)}{2\sin(x)\cos(x)} ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{2\sin^{-1}(x) - \sin^{-1}\left(\frac x2\right)}{2\sin(2x)} \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{2\sqrt{1-\frac{x^2}4}}}{4\cos(2x)} ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{\sqrt{4-x^2}}}{4\cos(2x)}[/tex]
The remaining limand is continuous at x = 0, and the limit is
[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \frac{2-\frac12}4 = \boxed{\frac38}[/tex]
![[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/Oc1eIaAqjbs8KCnGaLZZVKUhnF5QHact.jpeg)
![[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/LvBteEcmZIJaQI3hpKLwM4parnGiRnu8.jpeg)
![[tex] \displaystyle\red{ \sf\lim_{x \to {0}^{ + } }\frac{1}{ {sin}^{2}x } \int _{ \frac{x}{2} }^{x} {sin}^{](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/leifCbR0Yn68TY0MVRLAYZE7TAQAJCTL.jpeg)
Related Questions
i need help please
Answers
Answer:
The answer is 35 degrees
Step-by-step explanation:
Subtract 105 degrees and 40 degrees from 180 degrees
So just 180 - 105 - 40 =35
Answer:
35 degrees
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
UW = 97 cm
Step-by-step explanation:
UW is congruent to VX and VX is 97 cm so UW would be 97 cm
Answer:
97
Step-by-step explanation:
As you can see, the marks on that trapezoid show that those 2 sides are equal in length, so both of those sides are equal.
Hope This Helps! :) Please Mark as Brainliest!
can someone help with this?
Answers
Answer:
4) r = 10 yd
d = 20 yd
5) r = 7 in
d = 14 in
6) r = 15 ft
d = 30 ft
7) r = 23 in
d = 46 in
8) r = 16 yd
d = 8 yd
9) r = 21 ft
d = 42 ft
Step-by-step explanation:
Diameter = 2 x radius
*diameter (d)*
*radius (r)*
Check
Find the area of the given triangle.
feet
The base (6) of the triangle is
feet
1
1
The height (h) of the triangle is
25 feet
1
1
The area of the triangle is
square feet
115 feet
10 feet
Dono
Answers
Height = 15
A= 1/2bh
10x15 is 150.
150x1/2 is 75, so the area is 75.
How many congruent faces does the square pyramid below have?
A.
5
B.
6
C.
4
D.
2
Answers
Answer:
C. 4
Step-by-step explanation:
Each side of the Square pyramid is congruent
Answer: c which is 4 sides
Step-by-step explanation: the square pyramid has 4 sides which are having equal sides so they are congruent . Hope it helps . Please give brainliest .
A basket contains 40 mangoes out of which 8 are rotten. Find the percentage of the mangoes that are in good condition
Answers
So 32/40 are good
32/40 as a percentage is 80%
There are 80% of mangoes which are good condition.
What is percentage?Percentage is a relative value indicating hundredth parts of any quantity.
Given that, A basket contains 40 mangoes out of which 8 are rotten.
Mangoes in total = 40
Number of mangoes which are rotten = 8
Mangoes which are good condition = 40-8 = 32
Percentage of good mangoes = 32/40x100 = 80%
Hence, 80% of mangoes are not rotten.
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in how many years will 600$ double itself at 10% simple interest?
Answers
Answer:
10years
Step-by-step explanation:
100%+100%=double
100/10=10 years to reach 100% so after ten years you will have 200%/double
[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]
[tex] \\ \large \purple{ \sf{Given→}} \\ [/tex]
P (Principal) → 600$R (the annual rate) → 10% ,0.1nd
Time → years let be x[tex] \sf{A = 2P} \\ \sf{A = 2 \times 600} \\ \sf{ A =\:1200} \\ \sf{cuz \: future \: value \: since \: the \: 600 \: will \: double \: itself}[/tex]
[tex]\blue{\rule{70mm}{2.2pt}}[/tex]
[tex] \\ \large \purple { \sf{Formula \: used→}} \\ \\ \rm{A = P(1 + r \times t)}[/tex]
[tex]\blue{\rule{70mm}{2.2pt}}[/tex]
→Substituting values
[tex]\rm{1200 = 600(1 + 0.1 \times x)} \\ \\ \rm{600(1 + 0.1 \times x) = 1200} \\ \\ \rm{1 + 0.1 \times x = \frac{1200}{600} } \\ \\ \rm{ 1 + 0.1 \times x = \cancel \frac{1200}{600} } \\ \\ \rm{1 + 0.1 \times x = 2} \\ \\ \rm{0.1 \times x = 2 - 1} \\ \\ \rm{x = 1 \times \frac{10}{1} } \\ \\ \rm{x =10 } [/tex]
[tex]\underline{\underline{\rule{70mm}{2.2pt}}}[/tex][tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]
How would you write 8^5 as a multiplication expression?
OA 8x5
ОВ.8x8x8x8x8
OC. 5x5x5x5x5x5x5x5
Answers
Answer:
The answer is B
Step-by-step explanation:
Because the exponent shows how many times you multiply that number
Example: 8^2 would be 8x8 because it is to the second power
Hopefully this helps
Answer:
Step-by-step explanation:
8•8•8•8•8 is the correct answer
work out 7 1/2 x 3 2/3
give your answers as a mixed number
Answers
Answer:
27½
Step-by-step explanation:
7½×3⅔=((7×2+1)/2) × ((3×3+2)÷3)
= (15×11)÷6=165/6
165/6= 27½
The expression [tex]7\frac{1}{2} - 3\frac{2}{3}[/tex] simplifies to [tex]3\frac{5}{6}[/tex].
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
The expression [tex]7\frac{1}{2} - 3\frac{2}{3}[/tex] is 15/2 - 11/3.
Now, LCM of 2 and 3 is 6.
∴ (45 - 22)/6.
= 23/6.
= [tex]3\frac{5}{6}[/tex]
learn more about fractions here :
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A bakery sells cupcakes by the dozen. Last week they sold 258 dozen cupcakes. How many cupcakes did they sell?
Answers
Work out the value of 5^8 x 5^-2/5^4
Answers
Answer:
This is how i arrived at an answer 25
Find 13x2/5
Please answer this in 5 min
Answers
Answer:
5.2 I hope this helps. Im not the best at math...
Answer:
the answer should be like 5.2 or something close to that.
Step-by-step explanation:
i tried doing the math no promises that its right..
A scale drawing of an American flag is 6 inches tall. The actual flag is 3 feet tall. What is the scale of the drawing?
Answers
If the figure is a net of a square pyramid, drag it to the “Nets of Square Pyramids” column.
If the figure is not a net of a square pyramid, drag it to the “Not Nets of Square Pyramids” column.
Answers
Answer:
Step-by-step explanation:
1st is a net of a square pyramid.
2nd is a net of a square pyramid.
3rd is not a net of a square pyramid.
4th is not a net of a square pyramid.
5th is a net of a square pyramid.
6th is not a net of a square pyramid.
Answer:
see attached
Step-by-step explanation:
A net of a square pyramid will have four triangle shapes representing the lateral faces, and one square shape representing the base. The vertices of the triangles that are opposite the base edge will meet at a single point.
__
Figures 3 and 4 must be rejected because they have 3 and 5 triangles, respecively.
Figure 6 must be rejected because the figure cannot be folded to form a square pyramid. (The two left-side triangles will overlap.)
Krista Kellman has an opportunity to purchase a government security that will pay $200,000 in 5 years.
Answers
A triangle with exactly two sides of the same length is called
Answers
Answer:
isosceles
Step-by-step explanation:
isosceles
What was her speed?
0.1 mile per minute
0.5 mile per minute
5 miles per minute
10 miles per minute
Answers
Answer:
0.1 mile per minute
( option A )
5. You get a car loan for $13,000 to buy a used car. The car dealer who gives you the loan charges
8.4% interest, compounded monthly, for 4 years.
(a) What's the total amount you will have to pay back for this loan?
(b) What is your monthly payment for this loan?
Answers
Answer:
Total = $15,351.10
Monthly = $319.81
Spencer deposited $10 in an account earning 5% interest compounded annually.
To the nearest cent, how much will he have in 3 years?
Answers
Answer:
I (interest) = $1.58
Step-by-step explanation:
A = $11.58
A = P + I where
P (principal) = $10.00
I (interest) = $1.58
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 10.00(1 + 0.05/1)^(1)(3)
A = 10.00(1 + 0.05)^(3)
A = $11.58
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $10.00 at a rate of 5% per year compounded 1 times per year over 3 years is $11.58
Which of the following data sets are NOT likely to be normally distributed?
The day of the month on which randomly selected students were born
The day of the month on which randomly selected students were born
The final exam scores of all students taking the same class and given the same final exam in a large school district
The final exam scores of all students taking the same class and given the same final exam in a large school district
The number of wheels on the next 100 vehicles that pass by a point along a highway
The number of wheels on the next 100 vehicles that pass by a point along a highway
The heights of tenth-grade male students at a large high school
The heights of tenth-grade male students at a large high school
The IQs of the students at a large high school
Answers
Answer:
Which group's distribution of race times would most likely have the largest standard deviation? The group competing in the open competitions is most likely to have a higher standard deviation than the group competing in the qualified competitions .
Step-by-step explanation:
What is the surface area of this rectangular prism?
SA =
ft2
Answers
Answer:1,504
Step-by-step explanation:
20x16=320
20x12=240
16x12=192
16x20=320
12x16=192
12x20=240
add them all the answer will be 1,504
No spammers pls and also giving brainliest to correct answer
Answers
Answer:
C. (5 , 6)
Step-by-step explanation:
a dilation of center O(0,0) and 3 as a scale factor :
Transform point (x , y) to point (3x , 3y)
Then it transforms R(1 , 2) to R’(3 , 6)
Now ,we translate R’(3 , 6) by the translation (x , y) ——-> (x+2 , y)
So , R’(3 , 6) ————> R’’(3+2 , 6)
A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 51.6 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answers
Tthe total weight of the liquid in the tank, to the nearest full pound is 13,514 pounds.
What is the total weight of the liquid in the tank?The first step is to determine the volume of the tank.
Volume of a hemisphere = Volume of a hemisphere = (2/3) x (π) x (r³)
π = 22/7r = radius2/3 x 5³ x 22/7 = 261.91 ft³
Weight = 261.91 ft³ x 51.6 = 13,514 punds
To learn more about the volume of a hemisphere, please check: https://brainly.com/question/26840364
Solve 3x+1=15 for using the change base formula
Answers
Answer:
Step-by-step explanation: X = 4/3 or X= 1.3
3x + 1 = 5
3x = 5 - 1
3x = 4
X= 4/3 or X= 1.3
Help picture below problem 18
Answers
Answer:
X⁶
Step-by-step explanation:
x⁹/x³
= x⁹-³
= x⁶ is the answer
Answer:
E. [tex]x^{6}[/tex]
Step-by-step explanation:
To divide two fractions we subtract the power of second expression from the first one:
[tex]x^{(9-3)} = x^{6}[/tex]
Find the measure of ∠b.
A. 110∘
B. 102∘
C. 111∘
D. 121∘
Answers
Answer:
110 :)
Step-by-step explanation:
Triangle total angle measurement: 180
Now lets solve!
28 + 42 + ? = 180
70 + ? = 180
Now we have to subtract!!
180 - 70 = 110
Have an amazing day!!
Please rate and mark brainliest!!
28 + 42 + ∠b = 180
70 + ∠b = 180
∠b = 180 - 70
∠b = 110
Evaluate F ( 3 ) :
F ( 3 ) =
X =
Answers
Answer:
f(3) = 1
x = 2
Step-by-step explanation:
f(2) = 3 then x = 2
Please ,Check the illustration I provided.
HELP PLS
WORTH 1 POINT
GIVING 10
WHAT DID I DO WRONG?
Answers
supplementary angles form a straight line (together 180°) and the ones that you indicated didn't.
Help picture below problem 18 will give brainlest
Answers
Answer:
c²=a²+b².
Step-by-step explanation:
28²=17²+b² 766=289+b². -b²=289-766. b²=√475
please help! (math)
Which expression is equivalent to the one below?
-1/2(10+1/4)
Answers
Answer:
B
Step-by-step explanation:
-½(10+¼)
-½*10 + -½*¼
-5 + -⅛
-5-⅛
Don't forget a positive and negative makes a negative
