Answers
Answer: [tex]\frac{-m^2+n^2}{2}[/tex]
If the font is too small, it says (-m^2+n^2)/2
==============================================
Explanation:
If you plug x = 0 into the original expression, then you'll get the indeterminant form 0/0 after simplifying.
Recall that cos(0) = 1
So we use L'Hospitals rule to derive the numerator and denominator separately (don't use the quotient rule)
[tex]\displaystyle \lim_{x\to0} \frac{\cos(mx)-\cos(nx)}{x^2}\\\\\\\displaystyle \lim_{x\to0} \frac{-m\sin(mx)+n\sin(nx)}{2x}\\\\\\[/tex]
Plug x = 0 into this new expression. You should get 0/0 again here as well, which means you'll have to do another round of L'Hospital
[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\[/tex]
Now plugging in x = 0 leads to something that isn't indeterminant
Evaluating the limit gets us
[tex]\displaystyle \lim_{x\to0} \frac{-m^2\cos(mx)+n^2\cos(nx)}{2}\\\\\\=\frac{-m^2\cos(m*0)+n^2\cos(n*0)}{2}\\\\\\= \frac{-m^2+n^2}{2}\\\\\\[/tex]
Related Questions
36/40 to lowest term
Answers
Answer:
9/10
Step-by-step explanation:
36/4=9
40/4=10
IM IN A BIG BIG RUSH HELP PLEASE
Answers
Answer:
Perimeter = 10
Step-by-step explanation:
Horizontally 3 units; vertically 2 units.
If h is horizontal measure, and v is vertical measure, then perimeter is 2(h+v) and area is hv.
[4] The Perimeter of the rectangle is how many units?
Perimeter formula ; 2(h+v)
2(3+2) = 10
~Learn with Lenvy~
Please help this is Math
Answers
Answer:
I cant see the reference image so I dont have enough info to help. Srry :(
Step-by-step explanation:
What is the period of the function f(x) shown in the graph?
Answers
Answer:
[tex]\dfrac{\pi }{2}[/tex]
Step-by-step explanation:
The period of the function is from one peak to the next (or from one trough to the next).
[tex]\sf \implies period=\dfrac{\pi }{2}[/tex]
**see attached for the measurement of the period for this function**
Solve the inequality. And show work please
5
-- y = 12
6
Answers
Answer:
y= [tex]\frac{72}{5}[/tex] or 14.4
Step-by-step explanation:
[tex]\frac{5}{6}y = 12\\[/tex]
Multiply both sides by 6/5, the reciprocal of 5/6.
[tex]y = 12 * (\frac{6}{5} )[/tex]
Express 12 x (6/5) as a single fraction.
[tex]y = \frac{12 * 6}{5}[/tex]
Multiply 12 and 6 to get 72.
[tex]y = \frac{72}{5}[/tex]
Step by step:
1) x6 on both sides = 5y=72
2)divide both sides by 5= y=14.4
ABCD is a parallelogram. Find z.
Answers
Step-by-step explanation:
here is the answer Step-by-step for you
I hope you understand...
Which equation represents a line that passes through (-2,4) and has a slope of 2/5?
Answers
Answer:
A
Step-by-step explanation:
The slope is 2/5. Plug in the points and slope into the slope- intercept form y-y1=m(x-x1).
It would be...
y-4=2/5(x+2)
please help me with both of these
Answers
Answer:
1. Square is a box shape so you can tell her it can be shaped like an package
2.Tell Alex any real numbers a and b, if ab = 0, then that means a equals zero, or b equals zero, but sometimes both a and b equal zero
Step-by-step explanation:
I hope this helps!
IMHO I think Alex will be really confused
three green socks, four red socks, and five blue socks are in a drawer, and 2 socks are withdrawn at random. Find the probability of one blue sock and one red sock
Answers
Step-by-step explanation:
Number of socks: 3+4+5= 12
Number of red socks= 4
Red socks/other socks= 4/12
Simplify: fraction: 1/3
percentage: 33.33%
decimal: 0.3333
If you place a 37 ft ladder against the top of a 12 ft building how many ft will the bottom of the ladder be from the bottom of the the building
Answers
Answer: 25 feet
Step-by-step explanation:
If you place a 37 foot ladder against the top of a 12 food building, since 37 is greater than 12 the ladder will keep going past the building.
37-12=25
the ladder will be 25 feet from the bottom of the building
hope this helped :)
At 12:00 AM (hour 0 of the day) the tide at a certain beach was at its lowest level of the day: 1.0 feet. At 6:00PM (hour 18 of the day) the tide at a certain beach was at its highest level of the day: 2.0 feet. Assuming that this tide follows a sinusoidal model, about how high would you expect the tide to be at noon?
Answers
Answer:
At noon the tide will be at the lowest point which is 1 ftStep-by-step explanation:
please see attached a sketch of the solution for your reference
What is a sinusoidal wave?
Alternatively called a sine wave is a type of wave that shows a repetitive pattern or oscillation, it normally starts from a low point moves to the next point which is usually higher than the previous and repeats itself as the whole process continues
A , B and C form a triangle where ∠ B A C = 90 ∘ . A B = 0.5 mm and B C = 15.4 mm. Find the length of A C , giving your answer rounded to 1 decimal place.
Answers
Answer:
15•4 mm
Step-by-step explanation:
using sine rule
a÷ sinA=c ÷sinC
15•4÷sin90=0•5÷sinC
sinC =0•5 × sin90 ÷ 15•4
C =1•9°
A+B+C= 180
90+B+1•9=180
B= 88•2°
b÷sinB = a÷sinA
b÷sin88•2= 15•4÷sin90
b=sin88•2 ×15•4 ÷sin90
b =15•39
to 1 dp
b =15•4 mm
Please look at the image.
Answers
Answer: C or 6/5
Step-by-step explanation: the question is 4/5 plus 2/5 so 6/5
Twice a number, decreased by 58 is less than 112
Answers
Answer:
2x-58<112
Step-by-step explanation:
A car travels at a constant speed, as shown on the double number line. How far does the car travel in 14 hours?
Time (hours) 1 2 3
Distance (kilometers) 70 140 210 (for 3)
How far does the car travel in 14 hours? Explain or show your reasoning
Answers
Answer:
980km
Step-by-step explanation:
Multiply 14 by 70
double u, divide v by the result, then add t to what you have
Answers
do u want me to solve it to??
HELP PLEASE! 40 POINTS AND WILL MARK BRAINLIEST.
The number 97 is a term of the sequence defined by the explicit rule f(n)=4n-3. Which term in the sequence in 97? Justify your answer.
Answers
Answer:
The 25th term is 97
Step-by-step explanation:
The explicit rule is f(n)=4n-3
Let f(n) = 97
97 = 4n-3
Add 3 to each side
97+3 = 4n-3+3
100 = 4n
Divide by 4
100/4 = 4n/4
25 = n
A dilation has center (0,0). Find the image of the point A(-5,5) for the scale factor 1.2.
Answers
Step-by-step explanation:
Since the dilation is centered at the origin, you can multiply each of the coordinates by the scale factor. This means the image is A'(-6, -6)
Which statement best explains the value of 12-(-4)??
Answers
Answer:
16................
Step-by-step explanation:
Above
Answer:
The answer is 16.
Step-by-step explanation:
Negatives can be tricky, but once you get the hang of it, it will be much easier! The rule to remember here is:
"Anything 'minus a negative' just means plus, because the negatives cancel each other out."
a. For example, 4 -(-1) is the same thing as 4+1, which equals 5.
b. In this problem, 12-(-4) is the same thing as 12+4, which equals 16.
I hope this helps! Feel free to give me Brainliest if you feel this helped. :)
Please help me with find the slope
Answers
Answer: Finding the slope
Step-by-step explanation:
I'm sorry but the pic is a but blurry so basically you pick two points and use the equation 2y-y1/2x-1x then simplify if you can find a better picture I would love to help.
Answer my question please on my page :)
How can you determine the difference between square root and cube functions?
Answers
Test Prep There are 80 marbles in a bag. If 30% of the marbles are green, how many marbles are not green
Answers
Hey there!
Step 1: Calculate percentage
Since 30% of the marbles are green
=> 80 × 30/100
=> 8 × 30/10
=> 240/10
=> 24
So, 24 of the marbles are green
Step 2: Substract 24 from 80
=> 80 - 24
=> 56
Therefore, 56 marbles are not green
Select all of the names that apply to -24
Answers
Answer:
I need an image to help you.
Step-by-step explanation:
Answer:
Integer, rational number, and real number
Step-by-step explanation:
Integer is a number that can be either positive or negative, but can't be a fraction or irrational number such as pi. It's also a subset of rational numbers, which is a subset of real numbers.
if you brought 20 stamps for 0.45 each and 15 stamps for 0.32 each how much money did you spend on stamps
Answers
Answer:
$13.8
Step-by-step explanation:
20(0.45)+15(0.32)
= 13.8
John 3 miles on Monday, 2 miles on Tuesday. He ran 4 more miles on Wednesday then he did on Monday. How many miles did John run Monday through Wednesday?
Answers
Answer: John ran 10 miles through Monday and Wednesday.
Step-by-step explanation: He ran for miles on 4 but 4 more than Monday and he ran 3 miles on Monday, so you add 4 + 3 which = 7 then you add 3 to 7 because he ran 3 miles on Monday then you get 10.
Kofi sliced a watermelon into 9 equal parts .If each part had 87 seeds,how many seeds did each watermelon have?
Answers
The watermelon has 783 seeds
Answer:
783 seeds in each watermelon
Step-by-step explanation:
bc if each watermelon has 87 seeds u just multiply
Hi, so I think I got this right but do you have to put a negative symbol anywhere or just leave it how it is? number 12 (sorry is blurry my back camera is broken)
Answers
Answer:
Just leave it how it is, you don't have to do anything with the negative symbol.
Could I please have BRAINLIEST?PLEASE HELP The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentage
If their wage went from $6.80 to $10.19 in 7 years what is the doubling time?
Answers
Answer:
1928374.193 %
thats my answer
brainiest to who ever answers first
Answers
Answer:
18/24 for the first one
Step-by-step explanation:
Please help on this practice paper my parents couldn’t solve this either
Answers
We are given that ,
[tex]{:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}=a+b\sqrt{2}}[/tex]
Consider LHS;
[tex]{:\implies \quad \sf \dfrac{12+\sqrt{128}}{1-\sqrt{2}}}[/tex]
Can be further written as ;
[tex]{:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}}[/tex]
Rationalizing the denominator we have ;
[tex]{:\implies \quad \sf \dfrac{12+8\sqrt{2}}{1-\sqrt{2}}\times \dfrac{1+\sqrt{2}}{1+\sqrt{2}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{(12+8\sqrt{2})(1+\sqrt{2})}{(1-\sqrt{2})(1+\sqrt{2})}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12(1+\sqrt{2})+8\sqrt{2}(1+\sqrt{2})}{1-2}}[/tex]
[tex]{:\implies \quad \sf \dfrac{12+12\sqrt{2}+8\sqrt{2}+16}{-1}}[/tex]
[tex]{:\implies \quad \sf \dfrac{28+20\sqrt{2}}{-1}}[/tex]
[tex]{:\implies \quad \sf -28-20\sqrt{2}}[/tex]
Hence, we can conclude that ;
[tex]{\bf a=-28}[/tex] [tex]{\bf b=-20}[/tex]