1
Step-by-step explanation:
[tex]\displaystyle \lim_{x \to 0}\dfrac{\sin x}{x}[/tex]
Let
[tex]f(x)= \sin x[/tex]
[tex]g(x)=x[/tex]
We are going to use L'Hopital's Rule here that states
[tex]\displaystyle \lim_{x \to c}\dfrac{f(x)}{g(x)}=\lim_{x \to c}\dfrac{f'(x)}{g'(x)}[/tex]
We know that
[tex]f'(x) = \cos x[/tex] and [tex]g'(x)=1[/tex]
so
[tex]\displaystyle \lim_{x \to 0}\dfrac{\sin x}{x}=\lim_{x \to 0}\dfrac{\cos x}{1}=1[/tex]
Evaluate the integral.
∫ 17/ (x^3 − 27) dx
Answer:
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Anita had $400 in her savings account when she went to college. Her parents will add $200 to her account each month.
Miguel had $25 in his savings account. His parents will double the amount in his account each month.
If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.
Answer:
Miguel's account
Step-by-step explanation:
Miguel's account savings are doubled every month. Hence, they will eventually surpass the savings of Anita, even though Anita's account has more money atm.
Answer:
Miguel's account
Step-by-step explanation:
Even though Anita had more money at first compared to Miguel, Miguel savings will double each month while Anita will get only $200 each month. As a result, Miguel's account will grow faster compared to Anita's.
Which expression is equivalent to xy^2/9?
Answer:
[tex]xy^\frac{2}{9} = x*\sqrt[9]{y^2}[/tex]
Step-by-step explanation:
Given
[tex]xy^\frac{2}{9}[/tex]
Required
The equivalent expression (see attachment)
We have:
[tex]xy^\frac{2}{9}[/tex]
Split
[tex]xy^\frac{2}{9} = x*y^\frac{2}{9}[/tex]
Apply the following laws of indices
[tex]y^\frac{m}{n} = \sqrt[n]{y^m}[/tex]
So, we have:
[tex]xy^\frac{2}{9} = x*\sqrt[9]{y^2}[/tex]
Hence (d) is correct
Answer:
Its D.
Step-by-step explanation:
Just took the quiz on EDGE2022
Pencils cost x cents and erasers cost y cents each. Mary buys 7 pencils and 3 erasers. Write down the total cost in cents, in terms of x and y.
Answer:
7x + 3y.
Step-by-step explanation:
7 pencils cost 7x cents and 3 erasures cost 3y cents.
3 points If you have the following experimental running times in seconds for some program, mark the one word hypothesis on the order of growth of the running time that best explains the given experimental evidence
Answer:
LogarithmiclinearithmiclinearAnswer:
express the following equation as two statement each using the word varies and proportional i) v(rl=4/3
Use the calculator to evaluate each expression. Round your answers to the nearest hundredth.(GIVING BRAINLEST TO BEST ANSWER)
Answer:
tan 43 =.93
cos 67=.39
sin 39=.63
Step-by-step explanation:
tan 43 = .932515086=.93
cos 67=.390731128=.39
sin 39=.629320391=.63
a solid wooden cube has 4.35cm long.calculate the volume of the cube
Answer:
82.31
Step-by-step explanation:
I believe this is correct, if it isn't feel free to let me know and I will fix it. I'm sorry in advance if this is incorrect.
At : a.m. the angle of elevation of the sun for one city is . If the height of a monument is approximately , what is the length of the shadow it will cast at that time? Round to the nearest foot.
This question is incomplete, the complete question;
At 11:30 a.m. the angle of elevation of the sun for one city is 55.7°. If the height of a monument is approximately 555 ft, what is the length of the shadow it will cast at that time? Round to the nearest foot.
Answer:
the length of the shadow will be 379 ft
Step-by-step explanation:
Given the data in the question and as represented in the diagram below;
height of monument = 555 ft
angle of elevation = 55.7°
From the image below, this makes a right angled triangle
we know that the some of the interior angles of a triangle is 180
so
∠ABC + ∠BCA + ∠CAB = 180°
90° + 55.7° + ∠CAB = 180°
∠CAB = 180° - 145.7°
∠CAB = 34.3°
Now, using sine rule;
BC / sinA = AB / sinC
so we substitute
BC / sin( 34.3°) = 555 / sin( 55.7° )
BC / 0.563526 = 555 / 0.826098
we cross multiply
BC × 0.826098 = 0.563526 × 555
BC × 0.826098 = 312.75693
BC = 312.75693 / 0.826098
BC = 378.595 ≈ 379 ft
Therefore, the length of the shadow will be 379 ft
WILL MARK YOU IF YOU HELP ME !!!!
Answer:
Perpendicular bisector
Answer:
perpendicular bisector
2. Tricky Flips sells a coin that promises to land on heads 3 out of every 4 times. If the coin is
flipped 20 times, which of the following is the number of times you should expect it to land
on head
Answer:
15
Step-by-step explanation:
Because 3/4 of 20 or 75% of 20 is 15
One hundred forty-eight ten thousandth is
Help!!
f is a quadratic function where f(2) = 0, f(-2) = 0, and f(0) = -0.12. Find an algebraic equation for
f(u).
Answer:
bad gvkvkgcnhvvjzadhljang
v
gjddkfzutwdjtabkf
Will mark Brainlest hellpppp
[tex]h(-3) - h( - 2) = - \frac{5}{ 8} \\ \\ [/tex]
Step-by-step explanation:
[tex]\boxed{h(x) = \frac{2 {x}^{2} - x + 1}{3x - 2}}[/tex]
[tex]h(2) = \frac{2 {(2)}^{2} - (2) + 1}{3(2) - 2} [/tex]
[tex]h(2) = \frac{2 {(4)} - 2 + 1}{6 - 2} [/tex]
[tex]h(2) = \frac{ 8 - 1}{4} [/tex]
[tex]h(2) = \frac{7}{4}[/tex]
[tex]h( - 3) = \frac{2 {( - 3)}^{2} - ( - 3) + 1}{3( - 3) - 2} \\ h( - 3) = \frac{2 (9) + 3 + 1}{ - 9- 2} \\ h( - 3) = \frac{18 + 4}{ - 11} \\ h( - 3) = \frac{22}{ - 11} \\ h(-3) = -2[/tex]
[tex]h( - 2) = \frac{2 {( - 2)}^{2} - ( - 2) + 1}{3( - 2) - 2} \\ h( - 2) = \frac{2 (4) + 2+ 1}{- 6 - 2} \\ h( - 2) = \frac{8 + 3}{- 8} \\ h( - 2) = \frac{11}{- 8} [/tex]
[tex]h(3) - h( - 2) = -2 - \frac{11}{- 8} \\ h(3) - h( - 2) =-2 + \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-2}{1}+ \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-16}{8} + \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-16+11}{8} \\ h(3) - h( - 2) = \frac{-5}{8} \\ - \frac{5}{ 8} [/tex]
SOMONE HELP WITH MATH
Answer:
x = 28
Step-by-step explanation:
HFG = EFI
6x - 4 = 164
6x = 164 + 4
6x = 168
x = 168/6
x = 28
Find the value of x if x/3-2=6
Step-by-step explanation:
hope it is helpful to you
stay safe happy and healthy
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x}{3}-2=6}[/tex]
[tex]\mathsf{= \dfrac{1}{3}x - 2 = 6}[/tex]
[tex]\textsf{ADD 2 BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{1}{3}x - 2 + 2 = 6 + 2}[/tex]
[tex]\textsf{CANCEL out: -2 + 2 because that gives you 1}[/tex]
[tex]\textsf{KEEP: 6 + 2 because that helps solve for x}[/tex]
[tex]\mathsf{6 + 2 = \boxed{\bf 8}}[/tex]
[tex]\mathsf{NEW \ EQUATION: \dfrac{1}{3}x = 8}[/tex]
[tex]\textsf{MULTIPLY 8 to BOTH SIDES}[/tex]
[tex]\mathsf{3\times\dfrac{1}{3}x=3\times8}[/tex]
[tex]\mathsf{CANCEL\ out: \ 3 \times \dfrac{1}{3} \ because \ that \ gives \ you \ 1}[/tex]
[tex]\mathsf{KEEP: \ 3 \times 8 \ because \ that\ gives \ you \ the \ value \ of \ x}[/tex]
[tex]\mathsf{\boxed{\bf x}= 3\times8}[/tex]
[tex]\mathsf{3\times8 = \boxed{\bf x}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf x = 24}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Pls Help I will give Brainliest!
Answer:
Step-by-step explanation:
Borrows £10,000 over 5 years simple interest rate of 15%
Answer:
[tex]{ \tt{simple \: interest = p \times r \times t}} \\ = 10000 \times 15\% \times 5 \\ = £7500[/tex]
What is the length of each leg of the triangle below?
459
22
90°
45
O A. 11.12
B. 1
C. 15
D. 11
ET
F. 22
Answer:
option A
Step-by-step explanation:
since the given triangle is an isosceles triangle it's two remaining sides are equal
let the length of missing side be x
using pythagoras theorem
a^2 + b^2 = c^2
x^2 + x^2 = 22^2
2x^2 = 484
x^2 = 484/2
x = [tex]\sqrt{242}[/tex]
x = [tex]11\sqrt{2}[/tex]
HELP ME PLSSS!
The graph below have a same shape what is the equation of the red graph?
A) g(x)=(3-x)2
B) g(x)=3-x2
C) g(x)=2-x2
D) g(x)=(2-x)2
============================================================
Explanation:
The y intercept of the blue curve f(x) is (0,5)
The y intercept of the red curve g(x) is (0,2)
We see that the y intercept has been shifted down 3 units when going from f(x) to g(x). Overall, the entire f(x) curve has been shifted down 3 units to get the g(x) curve.
Based on that, we would say
g(x) = f(x) - 3
g(x) = (5-x^2) - 3
g(x) = -x^2 + (5 - 3)
g(x) = -x^2 + 2
g(x) = 2 - x^2 ..... answer is choice C
Answer:
2-x^2
Step-by-step explanation:
Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule. ∆ARE ≅ ∆_____ by _____
Answer:
add a picture so i can see .
Step-by-step explanation:
in order for the parallelogram to be a rhombus x=
Answer:
17
Step-by-step explanation:
Properties used:-
All sides of rhombus are equal therefore in the triangles
EQUAL SIDE OPPOSITE TO ANGLES, ANGLES BECOME EQUAL
then we use alternate interior angles
Then we get,
3x-11=x+23
2x=34
x=17
Do you think a friend would steal a led light controller after sleeping over cause I cannot find it?
Answer:
maybe u missplaced it somehow and it also would depend if you trust that person or not. some times that 'friend' can turn out to be fake but i don't mean it about ur friend. for now, u should just ask, there's no harm in that.
approximate 10.54 to the nearest ten
Answer:
11 because <.5 is rounded to the next ten
If 12 muffins cost $27, how much would 2 muffins cost?
How does this post work?
HELP WITH MY MATH PLEASEEE
Answer:
x = 18
Step-by-step explanation:
JM = LM
8x - 3 = 141
8x = 141 + 3
8x = 144
x = 144/8
x = 18
Answer:
since its a square each side is equal so
8x-3=141
8x=144
x=18
so
A: x=18
Hope This Helps!!!
What is the volume of the solid figure?
help pls
Answer:
B, 4x6x7 and 1x3x3.
Step-by-step explanation:
First, remember the formula: V=LWH (Volume equals length times width times height). Lastly, find the equations that match that formula, therefor B, 4x6x7 and 1x3x3 matches the formula, so B is your correct answer.
Find the sum of the first 5 terms of the following geometric series.
512 - 256 + 128 +...
Answer:
352
Step-by-step explanation:
512 - 256 + 128 - 64 + 32 = 352
A statistics teacher found that the average quiz score in her class is 86%, and the average test score in her class is 81%.
Which of the following is the best way to represent this data?
A. using a bar graph where one has a length of 86 units and one bar has a length of 81 units
B. using a square with a side length of 86 units and a square with a side length of 81 units
C. using a pie chart with one section labeled 86% and one section labeled 81%
D. using a cube with a side length of 86 units and a cube with a side length of 81 units
Answer:
A. using a bar graph where one has a length of 86 units and one bar has a length of 81 units
Step-by-step explanation:
Took the quiz. The usual.
The optimal method to represent this data is with a "bar graph", with one bar 86 units long and the other 81 units long. which is the correct answer that would be an option (A).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The best way to represent this data is using a "bar graph" where one bar has a length of 86 units and one bar has a length of 81 units.
This is because a bar graph is used to compare the sizes of different data points, and the length of each bar represents the value of the data point.
In this case, the average quiz score is 86% and the average test score is 81%, so the length of the bar representing the quiz score would be longer than the length of the bar representing the test score.
Thus, Option A correctly describes the use of a bar graph to represent the data, so it is the correct answer.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ2
Work out the following, giving your answers in their simplest form:
b) 5/9 ÷ 5
Answer:
5/9÷55/9×1/51/9Hope it helps youAnswer:
Since i m not sure of the equation i have dont both possible ways :)
Step-by-step explanation:
b)
(5/9) ÷ 5
[tex]= \frac{5}{9} \div 5\\\\=\frac{\frac{5}{9}}{5}\\\\=\frac{5}{9 \times 5}\\\\=\frac{1}{9}[/tex]
5/(9÷5)
[tex]=\frac{5}{9 \div5}\\\\= \frac{5}{\frac{9}{5}}\\\\=\frac{5 \times 5}{9}\\\\=\frac{25}{9}[/tex]
