By applying the exponential and logarithmic functions, we have
[tex]x^{\sin(x)} = \exp \left(\ln \left(x^{\sin(x)}\right)\right)[/tex]
Then in the limit,
[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \lim_{x\to0} \exp \left(\ln \left(x^{\sin(x)}\right)\right)[/tex]
[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \ln \left(x^{\sin(x)}\right)\right)[/tex]
[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \sin(x) \ln(x) \right)[/tex]
[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \frac{\ln(x)}{\csc(x)} \right)[/tex]
As x approaches 0 (from the right), both ln(x) and csc(x) approach infinity (ignoring sign). Applying L'Hopitâl's rule gives
[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp \left( \lim_{x\to0} \frac{\frac1x}{-\csc(x)\cot(x)} \right) = \exp \left( -\lim_{x\to0} \frac{\sin^2(x)}{x\cos(x)} \right)[/tex]
Recall that
[tex]\displaystyle \lim_{x\to0} \frac{\sin(x)}{x} = 1[/tex]
Then
[tex]\displaystyle \lim_{x\to0} \frac{\sin^2(x)}{x\cos(x)} = \lim_{x\to0} \frac{\sin(x)}{\cos(x)} = \lim_{x\to0} \tan(x) = 0[/tex]
So, our limit is
[tex]\displaystyle \lim_{x\to0} x^{\sin(x)} = \exp(0) = \boxed{1}[/tex]
2p+5+3=180 HELPPPPPP
Answer:
this one is actually not that hard. the answer is around 2p = 125
Step-by-step explanation:
Answer:
p = 35
Step-by-step explanation:
2p + 5 + 3p = 180 (Linear Pair)
=> 5p + 5 = 180
=> 5p = 180 - 5
=> 5p = 175
=> p = 175/5
=> p = 35
There are 25 students in math class. Yesterday, 6 students were absent. What percent of students were absent?
Answer:
1.5 out of 25
Step-by-step explanation:
1. Mrs. Shelley's class is reading The Lion, the Witch,
and the Wardrobe. If they read 16 pages every week,
how many pages can they read in 5 weeks?
Answer:
80 weeks
Step-by-step explanation:
We can use proportions to figure out the answer to this problem:
[tex]\frac{16}{1} = \frac{x}{5}[/tex]
16 pages every week, and some amount of pages every 5 weeks. Notice that if we can multiply 1 by 5 to get 5, we should be able to multiply 16 by 5 to get the value of x. 16 times 5 is 80, and this is the answer to our problem.
If you have any questions, let me know!
If you selected two of these stocks at random, what is the probability that both the stocks in your selection had yields of 3.25% or more
Using the binomial distribution, it is found that there is a 0.04 = 4% probability that both the stocks in your selection had yields of 3.25% or more.
For each stock, there are only two possible outcomes, either it yields 3.25% of more, or it does not. The probability of an stock yielding 3.25% or more is independent of any other stock, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
There are 2 stocks, hence [tex]n = 2[/tex]We suppose that 20% of them yield 3.25% of more, hence [tex]p = 0.2[/tex].The probability of both is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.2)^{2}.(0.8)^{0} = 0.04[/tex]
0.04 = 4% probability that both the stocks in your selection had yields of 3.25% or more.
A similar problem is given at https://brainly.com/question/24863377
In the triangle below, which of the following is equivalent to the tangent of
62 ?
25
62
16
24
O A. 21
B.
7
25
C.
24
25
O D.
7
7
24
The tangent of 62 degree is 24/7 because tan is the ratio of side opposite to the angle to side adjacent to the angle option (A) is correct.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a right angle triangle shown in the picture with side length.
As we know the tan is the ratio of side opposite to the angle to side adjacent to the angle.
tan62 = 24/7
Thus, the tangent of 62 degree is 24/7 because tan is the ratio of side opposite to the angle to side adjacent to the angle option (A) is correct.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ1
PLS HELP ME UNDERSTAND THIS!!
Answer:
88.25
Step-by-step explanation:
An animal pen is in the shape of a triangle. One of the interior angle of the triangle is 60 degrees. The measures of the other interior angles are 2x and x. What are the measures of the other interior angles?
Answer:
2x=80º
x=40º
Step-by-step explanation:
180-60=3x
120=3x
40=x
Using the graph as your guide, complete the following statement.
The discriminant of the function is ____
Step-by-step explanation:
Graph is not intersecting with Line X, so D < 0
Discriminant is negative
Option → A
Answer:
A. Negative
Step-by-step explanation:
A rectangular area is to be enclosed and divided into thirds. The family has $880 to spend for the fencing material. The outside fence costs $10 per foot installed, and the dividers cost $20 per foot installed. What are the dimensions that will maximize the area enclosed
Answer:
\W = Width
L = Length
Draw rectangle W x L
Divde rectangle into thirds with two lines parallel with width.
Outside fance perimeter = 2 W + 2 L
Inside fance length = 2 W
Total cost :
( 2 W + 2 L ) * 10 $ + 2 W * 20 $ = 400 $
( 2 W + 2 L ) * 10 + 2 W * 20 = 400
20 W + 20 L + 40 W = 400
60 W + 20 L = 400 Divide both sides by 20
60 W / 20 + 20 L / 20 = 400 / 20
3 W + L = 20 Subtract 3 W to both sides
3 W + L - 3 W = 20 - 3 W
L = 20 - 3W
Area :
A = W * L =
W * ( 20 - 3W ) =
20 W - 3 W ^ 2
First derivation :
dA / dW = 20 - 3 * 2 * W = 20 - 6 W
If first derivation = 0 a function has a local maximum or a local minimum.
dA / dW = 0
20 - 6 W = 0 Add 6 W to both sides
20 - 6 W + 6 W = 0 + 6 W
20 = 6 W Divide both sides by 6
20 / 6 = 6 W / 6
20 / 6 = W
2 * 10 / ( 2 * 3 ) = W
10 / 3 = W
W = 10 / 3 ft
If second derivative < 0 then function has a maximum.
If second derivative > 0 then function has a mimum.
In this case second derivative = - 6
Second derivative < 0 so function has a maximum.
For W = 10 / 3 ft
L = 20 - 3W = 20 - 3 * 10 / 3 = 20 - 10 = 10 ft
Amax = W * L = 10 / 3 * 10 = 100 / 3 ft ^2
HEY. YES, YOU. PLEASE HELP
Answer:
B: 1 years
Step-by-step explanation:
thats what the 1+ means
Susan's art class is 8 hours long. How long is her class in minutes?
Answer:
480
Step-by-step explanation:
Grandma Rose planted tomatoes in 3/8 of her vegetable garden.
What percentage is equivalent to the fraction of the vegetable garden that is tomatoes
A) 42%
B) 40%
C) 37.5%
D) 38%
Answer:C
Step-by-step explanation:
Answer:
c trust me
Step-by-step explanation:
WILL GIVE BRAINLIEST PLEASE HELP !!!!!
Answer: sorry but i am not in collage just in 8 grade
Step-by-step explanation:
Two objects are congruent if they are the same size and shape. ... There are three main types of congruence transformations: reflections (flips), rotations (turns), and translations (slides). These congruence transformations can be used to obtain congruent shapes or to verify that two shapes are congruent.
given m|| n, find the value of x.
Step-by-step explanation:
7x - 7 = 6x + 11
7x - 6x = 11 + 7
x = 18
Solution → x = 18
What is the value of y in the triangle shown below?
Answer:
Step-by-step explanation:
sinθ = opp/hyp
ssin30 = 17 / y
y = 17 / sin30 = 17 /0.5 = 34
find the perimeter of an isosceles triangle having a base of 4 feet and the congruent sides equal to 3 feet 9 inches
Answer:
11 1/2 feet
Step-by-step explanation:
4ft + 3ft 9 in(2)= 11 1/2 Feet
possible answers: 1.5 × 108 km
1.5 × 10−8 km
Answer:
b
Step-by-step explanation:
pls help I need for tomorrow
Answer:
This was hard to answer, ugh. Does this help :(
Step-by-step explanation:
----------1---2 3/10-------2----------3
----------1-----2 2/5-----2----------3
Which function is negative for the interval [1, 1]?
100+100+100+100+100=
Answer:
500
Step-by-step explanation:
hope it's help you.......
HELP ASAP!! WILL MARK BRAINLIEST
Tomi’s band has won twice as many awards as Ali’s band. Write an algebraic expression for the number of awards Tomi’s band has won. Be sure to indicate what the variable in your expression represents.
Answer:
Step-by-step explanation:
Well find out how many rewards ali one them time that by 2 too see what answer you get you have to first figure out what
a reward ali one
Answer:
t = 2 * a
Step-by-step explanation:
Awards won by Tomi's band is t
Awards won by Ali's band is a
Equation for t
t = 2 * a
Solve the following quadratic by
completing the square.
y = x2 - 6x + 7
Answer:
x = 5 or x = 1
Step-by-step explanation:
x² - 6x + 7 = 0
x² - 6x = -7
x² - 6x + 9 = -7 + 9 1/2 of the x term than square it and add it the both sides.
(x - 3)(x - 3) = 2
( x -3)² = 2
[tex]\sqrt{(x - 3)^2[/tex] = [tex]\sqrt{2}[/tex]
(x - 3) = ± 2
x - 3 = 2 or x - 3 = -2
x = 5 or x = 1
Please hurry, will mark brainliest if you answer correctly
Answer:
0
Step-by-step explanation:
25/5=5, 5+7=12, 4*3=12, 12-12=0
Answer:
The answer is 0
Step-by-step explanation:
The order of the operations is:
ParenthesisExponentsMultiplication and divisionAddition and subtractionSo first multiply [tex]4 \cdot 3 = 12[/tex] and after divide [tex]\frac{25}{5} = 5[/tex] and sum this result to 7 for substract to -12.
I need this TODAY or I’m so unbelievably screwed i need to know how to do these kind of table graphs really quickly i have a test tomorrow and its worth 90 percent of my grade also If you could tell me how to get slope that would make my day and night.
Thank you. And if you can tell me how to find slope that would be great.
Answer: Hey, getting slope is actually really easy!
Step-by-step explanation: So, if you’re given 2 sets of number such as (2,5) or (-7,3) then you just take them and you have to realize that 2 is x and 5 is y. also that -7 is x2 and 3 is y2. so then you use this formula (y2-y1 / x2-x1) this will give you the slope!! here’s an example using the points i said earlier: 3-5 / -7-2. so it would be 2/-9 for the slope! also i’d they only give you one point and the y intercept then you can just use the one point and then make the y intercept have a 0. so id the y intercept is 9 then the ordered pair would be (0,9) Good Luck! and let me know if you need to know how to graph the slope:)
Write a rational function that matches the given statement:
A rational function whose graph would have a horizontal asymptote at y=15
y
=
15
and a vertical asymptote at x=−6
Answer:
i put a graph in there
Step-by-step explanation:
________
[tex] \: [/tex]
Step by step :A.) y = 15
B.) x = -6
Soo, graph in the picture!
7+3 (2x - 5) = 3x +7
Which could be a step in solving the equation?
A. 10 (2x - 5) = 3x +7
B. 10 (2x + 2) = 3x + 7
O c. 7+ 6x - 15 = 3x + 7
OD. 7+ 5x – 2 = 3x + 7
Help help help help help
The answer is 0.2 because the answer to the division would be 0.20125 and when it's rounded it gives you 0.2.
HELPPPPPPPPPPPPPP PLSSSSSSSSSSSSSSSSSSS
Answer:
B
Step-by-step explanation:
3 + f = 14 [tex]\frac{2}{7}[/tex] ← change to improper fraction
3 + f = [tex]\frac{100}{7}[/tex] ( multiply through by 7 to clear the fraction )
21 + 7f = 100 ( subtract 21 from both sides )
7f = 79 ( divide both sides by 7 )
f = [tex]\frac{79}{7}[/tex] = 11 [tex]\frac{2}{7}[/tex] → B
Answer:
B. [tex]f=11\frac{2}{7}[/tex]
Step-by-step explanation:
We have the equation 3 + f = 14 2/7
We need to get f alone, doing so is subtracting three from both sides:
3 + f = 14 2/7
-3 = -3
14 2/7 - 3 = [11 2/7]
Leaving us with f = 11 2/7
This is B.
I get so confused on these things, how do I do them?
Answer:
Confusion get the best of us. May I ask what are you confused on. I may be able to help
HELLLLP
Erika calculated that she would spend $115 on school supplies this year. She actually spent $82.50 on school supplies. What is Erika’s percent of error?
A) 28.3%
B)2.8%
C) 39.4%
D) 32.5%
Answer:
c hope it helps
Step-by-step explanation:
