Answer:
The derivative of the function is:
[tex]f'(x)=1-\frac{1}{x^{2}}[/tex]
Step-by-step explanation:
The first principle is given by:
[tex]f'(x)=\frac{dy}{dx}=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]
The function here is:
[tex]f(x)=x+\frac{1}{x}[/tex]
Now, using the first principle we have:
[tex]f'(x)=lim_{h\rightarrow 0}\frac{(x+h)+\frac{1}{(x+h)}-x-\frac{1}{x}}{h}[/tex]
[tex]=lim_{h\rightarrow 0}\frac{h+\frac{1}{(x+h)}-\frac{1}{x}}{h}[/tex]
[tex]=lim_{h\rightarrow 0}\frac{h-\frac{h}{x(x+h)}}{h}[/tex]
[tex]=lim_{h\rightarrow 0}\frac{h(1-\frac{1}{x(x+h)})}{h}[/tex]
[tex]=lim_{h\rightarrow 0}1-\frac{1}{x(x+h)}[/tex]
[tex]=1-\frac{1}{x^{2}}[/tex]
Therefore, the derivative of the function is:
[tex]f'(x)=1-\frac{1}{x^{2}}[/tex]
I hope it helps you!
How to make a data set with only 5 numbers. And so the mean is 7, the median is 7, and the mode is 5?
Answer:
5,5,7,8,10
Step-by-step explanation:
mode=5 so that would appear the most so start with 5,5
median=7 that would be the middle number so 7 would be next
when you add 5+5+7=17 now just choose any number to add to 17 and I choose 10 which makes 17+10=27.
mean=7 so that means the total has to be divided by how many numbers you have, which is 5. So the total divided by 5 should equal 7. Since have 27, the number divided by 5 to get 7 is 35. So, add to 27 to get 35 which would be 8.
27+8=35 that is your total. Now divide by 5 to get the mean of 7.
The length of a rectangle is shown below: If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (5 points) Question 8 options: 1) C(−2, −1), D(1, −1) 2) C(−2, −4), D(1, −4) 3) C(−2, −2), D(1, −2) 4) C(−2, −5), D(1, −5)
what is 6 divided by 1164
Answer:
[tex] \blue{ \boxed{ \boxed{ \sf{6 + 1164 = 0.00515463917}}}}[/tex]
[tex] \sf \pink{ = = = > \: jazmine}[/tex]
Which points reflected of each other across both exes PLEASE HELP ASAP
Answer:
I am pretty sure it is (-2,8) and (2,-8)
Step-by-step explanation:
I think my answer is correct because it goes from Quadrant 1 into 4. Other answers are just I quadrant away.
What is the volume of a cone with a diameter of 12 inches and a height of 4
inches? *
Answer:
48 cubic inches
Step-by-step explanation:
Answer:
192π
and or [tex]603in^{3}[/tex]
Step-by-step explanation:
Identify the time being asked.
Given
12-hour
24-hour
1.) Half past midnight
2.) 2 hours to 9:00 p.m.
3.) 5 to 23:00 H
4.) Quarter after 00:00 H
5.) 3 hours and 2 minutes before 8:40 a.m.
Answer:
honestly,I also really didn't know the ans so I took it from internet. hope you won't mind
Answer:
1.) 12:30am
2.) 7:00pm
3.) 22:55 or 10:55pm
4.) 12:15am
5.) 5:38am
Step-by-step explanation:
Not me having to turn the clock on my phone to military time to make sure my answers were right XD
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Help me solve all my math problems and I will mark you ask a brainly thing
What is the surface area of the cylinder with height 5 mi and radius 3 mi? Round your answer to the nearest thousandth.
Answer:
659.82m^3
Step-by-step explanation:
Given data
Height= 5 m
Radius= 3m
The expression for the surface area is given as
SA= 2πr^2+2πrh
SA= 2*31.42*3^2+ 2*3.142*3*5
SA= 2*31.42*9+ 2*3.142*3*5
SA= 565.56+ 94.26
SA= 659.82m^3
Hence the volume of the 659.82m^3
A Cylinder with
a volume of 27π
in 3 and a height
of 3 in. What is
the radius?
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Surface Areas and Volume.
==> Volume of Cylinder = πr^2h
==> 27π = πr^2(3)
==> 27 = r^2 (3)
==> r^2 = 9
==> r = 3 inch
hence the radius is 3 inches.
Solve for x.
..................................
Answer: For 7x-11 is There are no like terms.
I don’t know if you want me to solve because I did “Answer: There are no like terms.” or how you want it because the picture you show it confusing
For 4x-2 is Factor 4x−2
4x−2
=2(2x−1)
Answer:2(2x−1)
Step-by-step explanation: Hope this help :D
What is the volume of the Cube?
132 cubic inches
726 cubic inches
1331 cubic inches
33 cubic inches
Answer:
1331 cubic inches
Step-by-step explanation:
volume = 11×11×11 = 1,331 in³
An isosceles triangle has base length 18 cm and height 4cm what is the approximate length of the two other sides
Answer:
The approximate length of the two other sides is 10cm
Step-by-step explanation:
Given
[tex]Base\ Length = 18[/tex]
[tex]Height = 4[/tex]
Required
The length of the two other sides
Divide the triangle to 2 (See attachment)
Considering one of the triangles, we have:
[tex]l^2 = 4^2 + 9^2[/tex]
[tex]l^2 = 16 + 81[/tex]
[tex]l^2 = 97[/tex]
Take square roots
[tex]l = \sqrt{97[/tex]
[tex]l = 9.8488[/tex]
[tex]l = 10[/tex] --- approximated
20 points.
Round off x to the nearest tenth.
Answer:
[tex]x=15.3[/tex]
Step-by-step explanation:
In right triangles only:
The sine of an angle is equal to its opposite side divided by the hypotenuse. (o/h)
The cosine of an angle is equal to its adjacent side divided by the hypotenuse. (a/h)
The tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)
Therefore, we have the following equation:
[tex]\sin 58^{\circ}=\frac{x}{18},\\x=18\sin 58^{\circ}\approx \boxed{15.3}[/tex]
Alternative:
[tex]\cos 32^{\circ}=\frac{x}{18},\\x=18\cos32^{\circ}\approx \boxed{15.3}[/tex]
Help please!
Thanks.
Answer:
6a is the answer I believe.
If i'm wrong correct me in comments.
137°
X-25
Find the value of X
Quadrilateral JKLM has side lengths of JK = 2y + 3, KL = 8x – 10, LM = 5y – 6, and JM = 3x + 20. Find the values of x and y that make quadrilateral JKLM a parallelogram. A. X = 6, y = 6 B. X = 6, y = 3 C. X = 13, y = 3 D. X = 2, y = 1
Answer:
(6, 3)
Step-by-step explanation:
Note that the opposite side of parallelogram are congruent, hence;
Jk = LM
2y + 3 = 5y - 6
2y - 5y =-6 - 3
-3y = -9
y = 9/3
y = 3
Similarly;
KL = JM
8x – 10 = 3x+20
8x - 3x = 20 + 10
5x = 30
x = 30/5
x = 6
Hence (x,y) is (6, 3)
Answer:
B.
Step-by-step explanation:
Which measure of variation is found by placing the data in ascending order and subtracting the lowest value from the highest value?
Answer:
Range
Step-by-step explanation:
The range of a given set of data is the difference between the largest value and the smallest value in the data. For convenience and ease in the calculation, it is advisable to place the data in ascending order.
For example, given the following set of data:
4,9,5,6,2
To find the range;
=> First arrange the data in ascending order
2,4,5,6,9
=> Find the smallest and largest numbers and then find their difference.
Since the data has been arranged, it is obvious to see that the smallest number is 2 and the largest number is 9.
Therefore the;
range = 9 -2 = 7
Solve the inequality and describe the solution set.
y–6≥12
Answer:
y ≥ 18
All numbers greater than or equal to 18
Step-by-step explanation:
y – 6≥ 12
Add 6 to both sides
y ≥ 18
All numbers greater than or equal to 18
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help
Answer:
38°
Step-by-step explanation:
The measure of angle NPM is 38°.
➠ ∠MPJ + ∠LPM = 180°
➠ ∠MPJ + 90° = 180°
➠ ∠MPJ = 180° – 90°
➠ ∠MPJ = 90°
∠NPM = ∠MPJ – ∠JPN
➠ ∠NPM = 90° – 52°
➠ ∠NPM = 38°
∴ Required answer :∠NPM = 38°
Find sin(B) in the triangle.
a- 4/3
b- 3/5
c- 4/5
D- 3/4
Which of the following expressions is equivalent to -6?
A: -9 + 15
B: 9 - (-15)
C:-9 - 15
D: 9 + (-15)
Amy bakes x cakes.
Barry bakes four times as many cakes as Amy.
Ceri bakes 12 more cakes than Amy.
They bake a total of T cakes.
Find a formula, in terms of x, for the total number of cakes.
Give your formula in its simplest form
Answer:
6x+12=T
Step-by-step explanation:
Amy bakes x cakes.
Barry bakes 4x.
Ceri bakes x+12
So the total is 6x+12=T
Marianne sold 3 times as many T-shirts as Brayan. Marianne sold 36 T-shirts. Write and solve
an equation to find how many T-shirts Brayan sold.
Mariah borrowed $1200 to buy a new computer system. She paid the simple interest loan off in 24 monthly payments of $56 each. What was the interest rate of this loan? a.2%
b.6%
c.4.4%
d.7%
Answer:
B. 6%
Step-by-step explanation:
Answer:
6%
Step-by-step explanation:
Her 24 monthly payments total 24 x $56 = $1344
That means that $1344 - $1200 = $144 is just interest. What percent is this of her loan amount? Divide to find out:
144 / 2400 = 0.06 = 6%
Aileen is decorating for the grand opening of the town's new courthouse. The entrance is marked by two stone columns that each stand 4.5
meters tall and a semicircular arch above the columns. She has a hung a 2-meter-long welcome banner between the two columns, and she
wants to line the entrance with a garland.
WELCOME!
2 m
4.5 m
If the garland will cover the inside edge of the entrance, from the bottom of the columns to the top of the arch, how many meters of
garland will Aileen need?
Answer:
I am not sure but I think it is 11
Step-by-step explanation:
I am so very sorry if im wrong :/
Need ALL of the RIGHT answers for this math quiz pls. ASAP
Answer:
1.54cm 2. 112m 3. 576cm 4. 52ft
Step-by-step explanation:
Brainliest!! The following two-way table describes student's
after school activities. Find the probability that a
randomly selected student is in sports.
Total number of sports students = 65
Total number of music/drama students = 25
Total number of work students = 10
Total number of students = 65 + 25+ 10 = 100
Probability = Total number of favourable outcomes/Total number of outcomes
Probability of picking a sports student = 65/100 = 13/20
Therefore, probability of picking a sports student is 13/20
Help me no wrong answer and answer ASAP please help me!!!!
Answer:
You probably already answered, but the first option would be correct <3
If you want an explanation tell me!
Which expression is equivalent to 14 x minus 21 over 7 ?
Answer:
-42
Step-by-step explanation:
Which expression is equivalent to 14 x minus 21 over 7 ?
Mathematically this expression is written as:
= (14 × -21)÷ 7
= (14 × -21)/7
= - 294/7
= -42
Therefore, the equivalent of the above expression is calculated as -42