Answer: $80
Step-by-step explanation:
Given:
The laptop consumes 40 watts/hour
The operating cost is $0.20 per kilowatt - hour
So,
The cost for 1 hour of consumption = 40 * 0.20 = $8
The cost for 10 hours of consumption = $8 * 10 hours = $80
Which are the foci of the hyperbola represented by 5y2 – 4x2 – 80 = 0?
(–6, 0) and (6, 0)
(0, –6) and (0, 6)
(0, –5) and (0, 5)
(–5, 0) and (5, 0)
The foci of the hyperbola represented by (0, –6) and (0, 6). Then the correct option is B.
What is a hyperbola?The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
The equation of the parabola is given below.
5y² – 4x² – 80 = 0
Then the equation can be written as
y² / 4 – x² / 5 – 4 = 0
y² / 16 – x² / 20 = 1
Then the value of eccentricity will be
a² = 16 and b² = 20
Then we have
e = √[1 + (b² / a²)]
e = √[1 + (20 / 16)]
e = 1.5
Then the focus of the parabola will be
⇒ (0, ±ae)
⇒ (0, ± 4 x 1.5)
⇒ (0, ±6)
⇒ (0, –6) and (0, 6)
Then the correct option is B.
More about the hyperbola link is given below.
https://brainly.com/question/12919612
#SPJ1
sub to oiVJDF NvlC Nvlkjxdv Nlkj;zsdn
Theresa uses a unique box in the shape of a trapezoidal prism for her specialty candles. The area of the bas
of the box for the smaller candle is 125 cm² and the box is 12 cm tall. The box used for the larger candle has
a base whose area is 160% that of the smaller box, and it is 6 centimeters taller.
What percent of the volume of the smaller box is the volume of the larger box?
Pls explain ur Answer<3
Answer:
eyyyyyyyyyy wassupppppppp
Answer:
240%
Step-by-step explanation:
Volume of a prism is Bh (area of the base * height)
Let's start with the small prism.
B=125
h=12
Volume = 125*12 = 1500 cubic cm
Bigger prism base are is 160% of 125. 1.6 * 125 = 200
Height is 6 cm more = 12+6 = 18
V = 200 * 18 = 3600
To find the percentage, divide 3600 by 1500. You get 2.4, which is 240%
Tim has 9 pencils in his book bag. Jaime has 3 more pencils than Tim. Which of the following equations would describe n, the number of pencils that Jaime has in her book bag?
There are 120 students in Year 11 at a school.
Each student studies one language, either French, Spanish, German or Welsh.
21 of the 40 students studying Welsh are male.
18 males and 9 females study French.
12 of the 17 students studying Spanish are female.
Twice as many females study German than males.
How many students in Year 11 are female?
Answer:
80 students are female
Step-by-step explanation:
21 are male meaning 19 are female
9 are female in French
12 are female in Spanish
total = 40
2x + 40 = 120
2x = 80
x = 40
females' = 80
total = 80
A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure.
x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1
y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1
What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.
(11.4, 14.2)
(7.6, 8.8)
(5.7, 7.5)
(10.2, 12.6)
Using proportions, it is found that the coordinates of the treasure as given as follows: (7.6, 8.8).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Researching the problem on the internet, the coordinates are as follows:
Rock (3,2).Treasure (x,y).Tree (16,21).The treasure is buried between a rock and a tree in a 5:9 ratio, hence the expression is:
[tex]Ts - R = \frac{5}{14}(Tr - R)[/tex]
Hence, for the x-coordinate:
[tex]x - 3 = \frac{5}{14}(16 - 3)[/tex]
x - 3 = 5 x 13/14
x = 7.6.
For the y-coordinate:
[tex]y - 2 = \frac{5}{14}(21 - 2)[/tex]
y - 2 = 5 x 19/14
y = 8.8.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Answer: the answer is b
Step-by-step explanation:
Write this number in standard form: 5,000,000 + 200,000+ 8,000 + 400+60+9
Answer:
5,208,469
Step-by-step explanation:
5,000,000 + 200,000+ 8,000 + 400+60+9
5,000,000
200,000
00,000
8,000
400
60
9
5,208,469
I need help, I need to find the volume of this
Answer:
396 Km³to the nearest hundred400 Km³Step-by-step explanation:
volume of a cuboid = Length × Width × Height Cubic units
6 × 11 × 6 =
66 * 6 =
396 Km³
to the nearest hundred
400 Km³
Please help me answer this question
Step-by-step explanation:
look at the attachment above
Answer:
[tex]\textsf{1)} \quad -\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}[/tex]
[tex]\textsf{2)} \quad - \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]
Step-by-step explanation:
Question 1
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration of $e^{ax}$} \\\\$\displaystyle \int e^{ax}\:\text{d}x=\dfrac{1}{a}e^{ax}+\text{C}$\\\\for $a\neq 0$\\\end{minipage}}[/tex]
Given integral:
[tex]\displaystyle \int xe^{-4x}\:\text{d}x[/tex]
Using Integration by parts:
[tex]\textsf{Let }\:u=x \implies \dfrac{\text{d}u}{\text{d}x}=1[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=e^{-4x} \implies v=-\dfrac{1}{4}e^{-4x}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x & =uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x\\\\\implies \displaystyle \int xe^{-4x}\:\text{d}x & =-\dfrac{1}{4}xe^{-4x}-\int -\dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}+\int \dfrac{1}{4}e^{-4x}\: \text{d}x\\\\& =-\dfrac{1}{4}xe^{-4x}-\dfrac{1}{16}e^{-4x}+\text{C}\\\\& =-\dfrac{1}{16}e^{-4x}\left(4x+1\right)+\text{C}\end{aligned}[/tex]
Question 2
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\\ \end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]
Rewrite the given integral:
[tex]\begin{aligned}\displaystyle \int \sin^5 x \: \text{d}x & =\int (\sin x)^4 \cdot \sin x \: \text{d}x\\& =\int (\sin^2 x)^2 \cdot \sin x \: \text{d}x\end{aligned}[/tex]
Use the trig identity [tex]\sin^2x+\cos^2x \equiv 1[/tex] to rewrite [tex]\sin^2x[/tex] :
[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x = \int (1-\cos^2 x)^2 \cdot \sin x \: \text{d}x[/tex]
Integration by substitution
[tex]\textsf{Let }\:u=\cos x \implies \dfrac{\text{d}u}{\text{d}x}=-\sin x \implies \text{d}x=-\dfrac{1}{\sin x}\: \text{d}u[/tex]
Therefore:
[tex]\begin{aligned}\implies \displaystyle \int \sin^5 x \: \text{d}x & = \int (1-u^2)^2 \cdot \sin x \cdot -\dfrac{1}{\sin x}\: \text{d}u\\& = \int -(1-u^2)^2 \: \text{d}u\\ & =\int -1+2u^2-u^4 \: \text{d}u\\& =-u+\dfrac{2}{3}u^3-\dfrac{1}{5}u^5+\text{C}\end{aligned}[/tex]
Finally, substitute [tex]u = \cos x[/tex] back in:
[tex]\implies \displaystyle \int \sin^5 x \: \text{d}x=- \cos x+\dfrac{2}{3} \cos^3 x - \dfrac{1}{5} \cos^5 x +\text{C}[/tex]
Find the reciprocal of 8 2/5
[tex]\huge\underline\red{Answer -}[/tex]
[tex]\bold{8 \frac{2}{5} }\: \\\\ \implies \: \frac{5 × 8 + 2}{5} \: \\ \\ \implies \: \frac{ 40 + 2}{5} \\\\ \implies \frac{42}{5} \\\\ \rightarrow \:\boxed {reciprocal \: = \frac{5}{42} } \\ \\[/tex]
hope helpful ~
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8 \dfrac{2}{5}}\\\\\mathsf{= \dfrac{8\times5+2}{5}}\\\\\mathsf{= \dfrac{40 + 2}{5}}\\\\\mathsf{= \dfrac{42}{5}}\\\\\mathsf{=\dfrac{5}{42}}\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{\dfrac{5}{42}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Given the following functions, find and simplify (f+g)(-2).
Do not include "(f+g)(-2)=" in your answer.
f(x) = -3x² - 2x
g(x) = -2x +3
Answer:
43
Step-by-step explanation:
because if you add it up thats how you get that
Graph the equation by plotting three points. If all three are correct, the line will appear. -3y=2x-7 ....... 20 POINTS
First lets simplify to slope intercept (y=mx+b)
y=[tex](2x-7)/-3[/tex]
y=-2/3x+7/3
Point 1: (0,7/3) as when x is 0, y=7/3.
Point 2: lets plug x in as 3 to cross cancel.
[tex]\frac{-2}{3} *\frac{3}{1} = \frac{-2}{1}[/tex]
So (3,-2).
Lets do point 3: plug in -3.
[tex]\frac{-2}{3} *\frac{-3}{1} = \frac{2}{1} = 2[/tex]
So (-3,2).
Your three points are (0,2.33 repeat) or (0,7/3), (3,-2) and (-3,2)
Hopefully this helps you out, heart if it was helpful and please do not hesitate to ask any questions. I have also attached an image of the line
#learnwithbrainly
For the graph y=41 find the slope
Answer:
m=0 , b=41
Step-by-step explanation:
y=41y=0x+41, y=mx +by=0x+41, m=0, b=41therefore m=0, b=41The vertices of a trapezoid are points (0,x), (0,0), (y,0), and (z,x). Find the area in terms of x, y, and z.
I put 1/2x (y+z), I just want to make sure! thank you.
Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)
We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.
Hence the area is
[tex]\dfrac{x(y+z)}2[/tex]
(which is identical to what you have).
Item 6
A set of books sits on a shelf at a store. This line plot shows the thickness of each book. Juan buys one of the thickest books on the shelf. Min buys the third thinnest book on the shelf.
How much thicker is Juan’s book than Min’s book?
Answer:
There is no line plot
Step-by-step explanation:
Use the graph to Write an equation of the line(3,165)(1,55)
Answer:
y=55x
Step-by-step explanation:
(y1-y2)/(x1-x2)=(165-55)/(3-1)=55
55 is the slope
To find y-intercept:
y=55x+b
substitute 1 for x and 55 for y
55=55(1)+b
b=0
So y= 55x
the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x. To write the equation of the line that passes through the points (3, 165) and (1, 55), you can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)
where (x₁, y₁) is one of the points on the line, m is the slope of the line.
First, calculate the slope (m) using the given points (3, 165) and (1, 55):
m = (y₂ - y₁) / (x₂ - x₁) = (55 - 165) / (1 - 3) = (-110) / (-2) = 55
Now that you have the slope (m = 55) and one of the points (let's use (3, 165)), you can plug them into the point-slope form:
y - 165 = 55(x - 3)
Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):
y - 165 = 55x - 165
To isolate y, add 165 to both sides:
y = 55x
So, the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x.
to know more about equation:
https://brainly.com/question/32543980
#SPJ3
Megan bought 3 tickets to the ballet for $57.50. How much would it cost for her to buy 15 tickets?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction
What are the measures of Angles a, b, and c? Show your work and explain your
answers. (10 points)
Answer:
a= 30
b=60
c=105
Step-by-step explanation:
A forms a vertical angle with another angle that measures 30 degrees, therefore,
a= 30 degrees.
Since a is 30 degrees and a and b are in the same triangle with a 90-degree angle and all interior angles in a triangle equal 180 degrees.
Then, 30+90+b=180
120+b=180
b=60
Angle c and an angle that equals 75 degrees are supplementary. meaning that they add up to 180 degrees.
180-75=c
105=c
1. Solve the given linear equations for 'x':
i ) 3(2x - 3) = 4(2x + 4)
ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
2. Solve : 3x /4 - 7 /4 = 5x + 12 =
3. Show that x = 4 is a solution for the equation x +7 - 8x/3 = 17/6 - 5x/8
4. Three consecutive integers are as such they are taken in increasing order and multiplied by 2, 3, and 4, respectively, they add up to 56. Find these numbers.
5 . Jane is 6 years older than her younger sister. After 10 years, the sum of their ages will be 50 years. Find their present ages.
6. The perimeter of a rectangular swimming pool is 154 meters. Its length is 2m more than twice its breadth. What are the length and the breadth of the pool?
7. The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.
8. A steamer goes downstream and covers the distance between two ports in 4 hours while it covers same distance upstream in 5 hours .If the speed of the stream is 2km per hour find the speed of the streamer of still water.
9 .Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4,00,000. How many notes of each denomination does she have?
10. The age of a man is 24 years more than his son. In two years, the father's age will be twice that of his son. Find the present age of his son.
Pls tell all answers with rought work
i ) 3(2x - 3) = 4(2x + 4)
[tex]6x - 9 = 8x +1 6 \\ \\ 6x - 8x = 16 + 9 \\ \\ - 2x = 25 \\ \\ x = - \frac{25}{2} .[/tex]
ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
[tex]2x + 4 + 5x + 25 = 4x - 32 + 2x - 4 \\ \\ 7x + 29 = 6x - 36 \\ \\ 7x - 6x = - 36 - 29 \\ \\ x = - 65.[/tex]
----------------------2. 3x /4 - 7 /4 = 5x + 12
[tex] \frac{3x}{4} - \frac{7}{4} = 5x + 12 \\ \\ \frac{3x}{4} - 5x = 12 + \frac{7}{4} \\ \\ \frac{3x - 20x}{4} = \frac{48 + 7}{4} \\ \\ \frac{ - 17x}{4} = \frac{55}{4} [/tex]
cancel 4 from both sides
[tex] - 17x = 55 \\ \\ x = \frac{ - 17}{55} .[/tex]
-------------------3. x +7 - 8x/3 = 17/6 - 5x/8
[tex]x + 7 - \frac{8x}{3} = \frac{17}{6} - \frac{5x}{8} [/tex]
put x = 4
[tex]4 + 7 - \frac{ 8\times 4}{3} = \frac{17}{6} - \frac{5 \times 4}{8} \\ \\ 11 - \frac{32}{3} = \frac{17}{6} - \frac{20}{8} \\ \\ \frac{33 - 32}{3} = \frac{68 - 60}{24} \\ \\ \frac{1}{3} = \frac{8}{24} \\ \\ \frac{1}{3} = \frac{1}{3} .[/tex]
L.H.S. = R.H.S.
--------------------4. Let 3 consecutive integers : x , x+1 , x+2
As per the question : 2x + 3(x+1) + 4(x+2) = 56
9x + 11 = 56
Transpose 11 to RHS
9x = 45
Divide both sides by 9
x = 5 ,
x + 1 = 5 + 1 = 6
x + 2 = 5 + 2 = 7
Numbers are 5 , 6 and 7 .
-----------------------5. Let the age of Jane’s younger sister is x.
Age of Jane will be x + 6
As per the question, after 10 years the sum of their ages will be 50.
After 10 years,
age of Jane = x + 16
age of her younger sister = x + 10
Therefore,
x + 16 + x +10 = 50
2x + 26 = 50
2x = 24
x = 12
Thus, the present age of Jane’s younger sister is 12 years.
And of Jane’s is 12 + 6 = 18 years.
---------------------6. Let the breadth of rectangular swimming pool be x metres.
Then, its length = (2x + 2) metres.
We know that the Perimeter of a rectangle
= 2(Length + Breadth)
= 2(2x + 2 + x) = 6x + 4
According to the given condition, we have
6x + 4 = 154
6x = 154 − 4
6x = 150
[Dividing both sides by 6]
x = 25
Thus, breadth = 25 m and
length = 25 × 2 + 2 = 52 m .
---------------------7. Let the digit in ten's .
Place be x and the digit in the one's place be y.
x − y = 5 ⟶ (i)
Two digit number = 10x + y
Two digit after reversing the digits = 10y + x
According to question ,
10x + y + 10y + x = 99
11x + 11y = 99
x + y = 9 ⟶ (ii)
On adding (i) and (ii),
2x = 14
x = 7
Putting the value of x in equation (i)
x − y = 5
y = 2
Number = 10x + y
=72 .
-----------------------8. Let the speed of the steamer in still water be x km/h.
Then , the speed downstream = (x+2) km/h
and the speed upstream = (x−2) km/h
Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream
4(x + 2) = 5(x − 2)
4x + 8 = 5x − 10
4x − 5x = − 10 − 8
[Transposing 5x to LHS and 8 to RHS]
−x = −18 or x = 18 km/h .
-----------------------9. Let the number of notes of different denomination be x.
∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.
Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x
Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x
Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x
As per the question
Total amount = 400000
200x + 150x + 50x = 400000
400x = 400000 , x = 1000
No of Rs 100 notes = 2x = 2 × 1000 = 2000
No of Rs 50 notes = 3x = 3 × 1000 = 3000
No of Rs 10 notes = 5x = 5 × 1000 = 5000 .
------------------------10. Let the age of the man be x
Then age of his son becomes (x − 24)
2 years later from now,
Age of man will be = x + 2
and age of his son will be = (x − 24 + 2) = x − 22
According to question,
2(x − 22) = x + 2
i.e., 2x − 44 = x + 2
i.e., x = 46
Therefore ,
Present age of man = 46 years
And present age of his son = 46 − 24 = 22 years .
How would you know the answer (important)
Answer:
okay so I can't see the last option on ur sheet but when u graph this equation the point that lies on the curve is (2,-3) so that is the vertex but if I move up this curved line it passes through the Y axis at (0,-1), the Last answer that I can't see it wouldn't happen to be (-1,6) would it
Using the distance formula calculate the distance show me example
Answer:
[tex]4\sqrt{26}[/tex]
Step-by-step explanation:
The distance formula is [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Thus we can plug the numbers in:
[tex]\sqrt{(-2-(-6))^2+(10-(-10))^2}[/tex]
[tex]\sqrt{(4)^2+(20)^2}[/tex]
[tex]\sqrt{16+400}[/tex]
[tex]\sqrt{416}[/tex]
[tex]4\sqrt{26}[/tex]
Pre-Test Active
2 3
5 6
7
9 10
Which formula should be used to find the circumference of a circle?
O C-nd
O C-2nd
0 С-яг
OC-4
Save and Exit
Mark this and return
Next
TIME REMAINING
45:32
Submit
Answer:
C = 2√(πA) units
Step-by-step explanation:
$10,000 is invested for 4 years at an annual simple interest rate of 16%.
Answer:
$16,400
Step-by-step Explanation:
Step 1: We multiply $10,000 by 16%, getting $1,600.
Step 2: We then multiply $1,600 by 4 (which is given). That gives us $6,400.
Step 3: Add that to $10,000. We get $16,400 as the answer!
Please mark me as brainliest! I really need it!!! Thanks!Answer:
Simple interest = P x r x t
= 10,000 x 16/100 x 4
= $6400
Final amount = P (1 +rt)
= 10,000 (1 + 16/100 x 4)
= $16400
(or you can just add the simple interest to the principle amount to get the final amount)
The given equation is either linear or equivalent to a linear equation. Solve the equation. (If there is no solution, enter NO SOLUTION. If all real numbers are solutions, enter REALS.)
(t − 7)2 = (t + 7)2 − 112
t =
Answer:
No solution
Step-by-step explanation:
Which of the numbers below are whole numbers?
A. 6282
B. 650
C. 87
D. 99.8
E. 442.49
F. 1/10
Answer: A B C
Step-by-step explanation:
A whole number is like 1,500 and a nonwhole number is like 33.2 or like 55/100.
And have a good day.
Which of the following expressions are equal to -8/11 - 3/4 - 1/4
In the expressions that we are given, we can note that there is a negative in all of them. This means that we can factor out the negative.
With the negative factored out, it will look like this: [tex]-(\frac{8}{11} + \frac{3}{4} + \frac{1}{4} )[/tex]
The reasoning for this is because you distribute the negative to each term. For example 8/11 is a term, and so is 3/4, and 1/4. So our first answer is D.
Another way we can do this is by combining like terms. We see that in the denominator for -3/4 and -1/4 they both share 4. We can combine it so it becomes -4/4 or -1. It would be E.
The third way we can do this is by rewriting it. Answer A rewrites it so that it is + -, effectively just -. This allows us to treat the equation as if it were the original one.
Hopefully this helps you out, brainliest would help me out.
#GetVerifiedAnswers #LearnWithBrainly
Sampling is used in the situations
A. Cooking rice in an utensil
B. Purchase of food commodity from
C. shopkeeper
D. All the above
E. Blood test of the patients
Answer:
all of the above
Step-by-step explanation:
please mark me as brainliest
Let f(x)=7x^5 ln(x) + 1/3 x^3
f’(x)=
I’m stuck on this calculus problem. If anyone could help me work this out. I would appreciate if you showed all your steps.
Answer:
f'(x) = 7x^4 (5 ln(x) + 1) + x^2
Explanation:
[tex]\sf Let \ f(x)=7x^5 ln(x) + \dfrac{1}{3} x^3[/tex]
Properties used while differentiating:
[tex]i) \quad \sf \dfrac{d}{dx} (ln(x)) = \dfrac{1}{x}[/tex]
[tex]ii) \quad \sf \dfrac{d}{dx} (x^n) = n(x)^{n-1}[/tex]
[tex]iii) \quad \sf \dfrac{d}{dx}(uv)=u \dfrac{dv}{dx}+v \dfrac{du}{dx}[/tex]
Begin solving:
f'(x) =
[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\:+\:\dfrac{1}{3}\:\:x^3\right)[/tex]
[tex]\Longrightarrow \sf \dfrac{d}{dx}\:\left(7x^5\:ln\left(x\right)\right) + \dfrac{d}{dx}\left(\dfrac{1}{3}x^3\right)[/tex]
[tex]\Longrightarrow \sf \dfrac{d}{dx}(7x^5)\:\ \times ln\left(x\right) + \dfrac{d}{dx}(ln(x)) \times \ 7x^5 + \left(3\:\times \dfrac{1}{3}x^{3-1}\right)[/tex]
[tex]\Longrightarrow \sf 5(7x^{5-1})\:\times\ ln(x) + \dfrac{1}{x} \:\times\ 7x^5 \ + x^2[/tex]
[tex]\Longrightarrow \sf 35x^{4} ln(x) + \ 7x^4 \ + x^2[/tex]
[tex]\Longrightarrow \sf 7x^4(5 ln(x) + 1) \ + x^2[/tex]
The inverse of the function f(x) = x + 10 is shown.
==
h(x) = 2x-0
What is the missing value?
01
05
O 10
O 20
Answer:
So, the answer is 20
Step-by-step explanation:
[tex]f(x) = \frac{1}{2} x + 10 = = = > \\ f(x) - 10 = \frac{1}{2} x = = = > \\ 2f(x) - 20 = x = = = > \\ {f}^{ - 1} (y) = 2y - 20 = = = > {f}^{ - 1} (x) = 2x - 20[/tex]
The missing value of the inverse function is 20.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the inverse of a function, we usually replace f(x) with y, then solve for x in terms of y, and finally replace y with the inverse function notation h(x).
So let's do that with the given function:
f(x) = (1/2)x + 10
y = (1/2)x + 10
2y = x + 20 (multiply both sides by 2 to isolate x)
x = 2y - 20 (subtract 20 from both sides)
Now we can replace x with h(x) and y with x to get the inverse function:
h(x) = 2x - 20
Thus,
The missing value is 20.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ5
Refer to the figure to complete the following item.
Given:
If m = 60° and m = 30°, then 3 =
45
15
30
If m VB = 60° and m BS = 30°, then m ∠3 =15°.
What is tangent?A tangent is a line passing by touching the perimeter of the circle, perpendicular to the line joining the center and touch point.
Given, PB tangents PV, PU secants
If m VB = 60° and m BS = 30°, then m ∠3 =
The measurement of the external angles is the semi difference of the arcs it consists.
∠3 = 1/2 (60 - 30)
∠3 = 15°
Thus, If m VB = 60° and m BS = 30°, then m ∠3 =15°.
Learn more about tangent.
https://brainly.com/question/23265136
#SPJ1
