Answer: [tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=\sin(9\ln (x))[/tex]
Using chain rule differentiate w.r.t. x.
[tex]f'(x)=\cos(9\ln (x))\dfrac{d}{dx}(9\ln (x))[/tex] [tex]\left[\because \dfrac{d}{dx}\sin x=\cos x\right][/tex]
[tex]f'(x)=\cos(9\ln (x))\left[9\dfrac{d}{dx}(\ln (x))\right][/tex]
[tex]f'(x)=\cos(9\ln (x))\left[9\times \dfrac{1}{x}\right][/tex] [tex]\left[\because \dfrac{d}{dx}\ln x=\dfrac{1}{x}\right][/tex]
[tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex]
Therefore, [tex]f'(x)=\dfrac{9\cos(9\ln (x))}{x}[/tex].
Choose the rate of change (slope) to match the line.
ТУ
14 2 0
2
O A 2
B
3
D.
celine
Review prog
Math plzzzzz help
Answer:
B. [tex] -\frac{3}{2} [/tex]
Step-by-step explanation:
Rate of change/slope is given as [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinate pairs of any two points on the slope/line.
Let's use the following coordinates pairs:
[tex] (-2, 4) = (x_1, y_1) [/tex]
[tex] (0, 1) = (x_2, y_2)
Plug in the values into the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]:
[tex] m = \frac{1 - 4}{0 - (-2)} [/tex]
[tex] m = \frac{-3}{0 + 2} [/tex]
[tex] m = \frac{-3}{2} [/tex]
[tex] m = -\frac{3}{2} [/tex]
13 + 3y= 37 solve for y
Answer:
y = 8
Step-by-step explanation:
Step 1: Write out equation
13 + 3y = 37
Step 2: Subtract 13 on both sides
3y = 24
Step 3: Divide both sides by 3
y = 8
Answer:
y=8
Step-by-step explanation:
37-13 = 24
3y=24
3/24=8
y=8
parallel to y = 3x – 1 and passes through the point ( – 4, – 11)
You are shopping for dinner for your family in a fast-food restaurant, but you are concerned about fat. An informative menu gives you the following information. Item Hamburger Chicken sandwich Fries Onion rings Grams of fat 24 13 30 25 How much total fat is in an order of hamburgers, chicken sandwich, orders of fries, and orders of onion rings
Answer:
Total amount of fat = 92 grams
Step-by-step explanation:
Given:
Item Amount of fat (in gram)
Hamburger 24
Chicken sandwich 13
Fries 30
Onion rings 25
Find:
Total amount of fat
Computation:
Total amount of fat = [Hamburger + Chicken sandwich + Fries + Onion rings]
Total amount of fat = [24 + 13 + 30 + 25] grams
Total amount of fat = 92 grams
Imagine that city officials in your hometown expect a huge rise in population over the next few years. Which of the following people would be the best person to hire to help prepare the city for the future? A. a meteorologist B. a physical geographer C. an urban planner D. a cartographer Select the best answer from the choices provided please A ?, B ?, C ?, or D ?
Answer: C
Step-by-step explanation:
The best person will be an urban planner to help prepare the city for the future. The correct option is C.
What is the work of an urban planner?
In towns, cities, counties, and metropolitan areas, urban and regional planners construct land use plans and programs that support the development of communities, allow for population increase, and renew physical infrastructure.
Given that the city officials in your hometown expect a huge rise in population over the next few years.
The best person to help in preparing the city for the future will be an urban planner.
Therefore, the best person will be an urban planner to help prepare the city for the future. The correct option is C.
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Solve:||x-3|-2|≤1
Please show work!
Thanks
Answer:
Step-by-step explanation:
Hello,
We know that
[tex]|x|=\begin{cases}x & \text{if } x\geq 0 \\ -x & \text{if } x<0 \end{cases}[/tex]
So we need to take into account two cases
Case 1 - [tex]x-3\geq 0<=> x\geq 3[/tex]
Then, |x-3|=x-3
||x-3|-2|=|x-3-2|=|x-5|
Either x-5 is positive and then |x-5|=x-5 and
[tex]|x-5|\leq 1<=>x-5\leq 1<=>x\leq 6[/tex]
Or x-5 is negative and then, |x-5|=-x+5
[tex]|x-5|\leq 1<=>-x+5\leq 1<=>4\leq x[/tex]
So the solution is [4;6]
Case 2 - [tex]x-3< 0<=> x< 3[/tex]
Then, |x-3|=-x+3
||x-3|-2|=|-x+3-2|=|-x+1|
Either -x+1 is positive and then |-x+1|=-x+1 and
[tex]|-x+1|\leq 1<=>-x+1\leq 1<=>0\leq x[/tex]
Or -x+1 is negative and then, |-x+1|=x-1
[tex]|-x+1|\leq 1<=>x-1\leq 1<=>x\leq 2[/tex]
So the solution is [0;2]
Conclusion
The solution is [0;2]∪[4;6]
Thanks
leave answers as simplified radicals
Answer:
1
Step-by-step explanation:
[tex]\frac{\sqrt{48} }{4\sqrt{3} }=\frac{\sqrt{16} }{4}=\frac{4}{4}=\frac{1}{1}=1[/tex]
When Josh babysits, he chargers a flat fee of $14 plus an hourly rate of $9. How long would Josh need to babysit if he wants to earn $86 in one night?
Answer:
[tex]\frac{36}{7}[/tex]hours
Step-by-step explanation:
First let's get the flat fee of 14 out of the way, because he wants to earn 86 dollars and the 14 dollar fee is the y intercept.
[tex]86-14 = 72[/tex]
We would then divide 72 by the slope (14 per hour) to see how many hours he has to work:
[tex]72/14 \approx5.14285714286[/tex]
I would just simplify because this decimal isn't exact
[tex]72/14 = 36/7[/tex]
So 36/7 hours
Can somebody help me out on this question I would really appreciate it so much . Please and thank you .
Step-by-step explanation:
AB = AC, so mark the two sides with single tick marks.
m∠ACD = 128°, so label the angle 128°.
∠ACB is supplementary to ∠ACD, so:
m∠ACB + m∠ACD = 180°
m∠ACB + 128° = 180°
m∠ACB = 52°
ΔABC is an isosceles triangle, so m∠B = m∠ACB.
m∠B = m∠ACB
m∠B = 52°
Angles of a triangle add up to 180°, so:
m∠A + m∠B + m∠ACB = 180°
m∠A + 52° + 52° = 180°
m∠A = 76°
The perimeter of a rhombus is 40 cm and the length of one of its diagonals is 12 cm then the length of the other diagonal is
Answer:
16 cms.
Step-by-step explanation:
The length of each side = 40 / 4 = 10 cm (as the 4 sides of a rhombus are congruent).
If we draw the other diagonal we form 4 right angled triangles (another property of the rhombus - diagonals bisect each other at tight angles. ).
The side of the rhombus is the hypotenuse of the right triangle.
So if we consider one triangle:
10^2 = 6^2 + x^2 where x is half the length of the other diagonal.
x^2 = 10^2 - 6^2
x^2 = 100 - 36 = 64
x = 8 cm.
So the diagonal is 16 cms long.
what is the reciprocal of 15 1/4
The reciprocal of 15 1/4 is 4/61
Step-by-step explanation:
15 1/4 multiply 15 by 4 and then add 1 it will give you 61/4 then you change into reciprocal which will be 4/61
the inequality 13q<7q-29 and write the solution in fraction formats and interval notations
Answer:(-infinity,-29/6)
Step-by-step explanation:
Interval notation of this problem.
Ms.rider travels 468 miles in 6 hours . how many miles per hour is she driving
Answer:
78
Step-by-step explanation:
She is driving 78 miles per hour because if you take the miles she drove, and the amount of time she drove, and divide them, you get 78 :)
Divide. Express your answer in simplest form. 14 ÷ 2/7
=49
Solution by Formulas
First:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
141÷27
Applying the fractions formula for division,
=14×71×2 =982
Simplifying 98/2, the answer is =49
help me please this means a lot to my grade
Answer:
Step-by-step explanation:
You know that lines PQ and RS are parallel and line XY is a transverse line. This means that XMP and QMN are equal because they are vertical angles. Now set the equations equal to each other because they are.
10x-7=6x+21 and solve for x
4x-7=21
4x=28
x=7 boom
(10-3x2)2 someone solve this
Answer: 8
(10-3x2)2
(10-6)2
4 x 2
8
Answer:
8
Step-by-step explanation:
3×2=6
10-6=4
4x2=8
Your answer is 8
Can someone help me plssssss ;w;
The magnitude of an earthquake depending on the energy it produces can be modeled using the equation M = 0.6666 log x – 3.2. Complete the sentences about the model.
The curve representing the relationship includes the point_______ .
The growth factor is________ .
An earthquake with an energy level of has a magnitude of ________ .
Answer: The curve representing the relationship includes the point (1, -3.2) .
The growth factor is 0.6666 .
An earthquake with an energy level 1 of has a magnitude of -3.2 .
Hello my Alpha.... bows down*
The curve representing the relationship includes the point (1, -3.2).
The growth factor is 0.6666. An earthquake with an energy level of has a magnitude of – 3.2.
It is given that the magnitude of an earthquake depending on the energy .it produces can be modeled using the equation M = 0.6666 log x – 3.2.
It is required to find growth factor, point and magnitude.
The curve representing the relationship includes the point_______ .The growth factor is________ .An earthquake with an energy level of has a magnitude of _______.The amount of energy released is represented as E and an earthquake release the magnitude represented by M which is given in the question. This magnitude is represented as equation using logarithm of the height of the wave that is the scale measured by seismograph.
Thus, The curve representing the relationship includes the point (1, -3.2).
The growth factor is 0.6666 .
An earthquake with an energy level of has a magnitude of – 3.2.
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Find the straight time pay if you earn $7.90 per hour and worked 37 hours.
Answer: $292.30
Step-by-step explanation:
is 2.4444 rational or irrational
Answer:
Rational.
Step-by-step explanation:
Irrational are these.
[tex]\sqrt{2} , \sqrt{5}[/tex] ,π
Yes, the given number is a rational number.
What are rational numbers?Rational numbers are numbers that can be written in the form p/q, where p and q are integers and q≠0.
Given that, a number 2.4444...
Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers.
Hence, 2.4444 is a rational number.
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What is the density of Olivine? Mass = 20g; Volume = 6.15 cubic cm.
Round to TWO decimal places
-4x2 + 2x - 5(1 + 3)
What expression is equivalent to the given expression?
or +
x2 +
Answer:
-4x^2 -3x -5
Step-by-step explanation:
If you eliminate parentheses and collect terms, you get ...
-4x^2 +2x -5(1 +x)
= -4x^2 +2x -5 -5x
= -4x^2 +x(2 -5) -5
= -4x^2 -3x -5
In 1970, a farmer using a two-row combine with a corn head could easily harvest 0.75 ha (1.85 acres) per hour and a typical corn yield was 5000 kg/ha (80 bu/acre). Before 1940, most corn was harvested by hand and a skilled person could harvest 250 kg/h (10 bu/h). Calculate the productivity ratio.
Answer:
The value is [tex]w = 6.7 \%[/tex]
Step-by-step explanation:
Generally the productivity rate is mathematically represented as
[tex]P_r = K * Z[/tex]
Here K is the ha the farmer could harvest in an hour and Z is a typical yield of corn in kg/ha
Now considering 1970
The productivity rate is
[tex]P_r = 0.75 *5000[/tex]
=> [tex]P_r = 3750 \ kg/h [/tex]
Now considering 1940
The productivity rate is given as [tex]P_R = 250 \ kg/h [/tex]
Generally the productivity ratio is mathematically ration is mathematically represented as
[tex]w = \frac{P_R}{P_r} * 100[/tex]
=> [tex]w = \frac{250}{3750} * 100[/tex]
=> [tex]w = 6.7 \%[/tex]
Look at this angle what is the vertex
Answer:
T
Step-by-step explanation:
T is the vertex because vertex is the point from which the arms of any angle form.
2+x^2=18
Help please
Answer:
2+x^2=18 = 2+4^2=18
Step-by-step explanation:
Because when you have the ( ^2) then that means your going to multiply a number by the same number and then 4 times 4 equals 16 and you still have the +2 therefore you add that on the 16 and 16+2 equals 18.
BRAINLIEST!!Felicia had $80 when she went to a music store that charges $18 for each CD. She needs to have no less than $20 in her wallet when she leaves the store so she has enough money to buy gas for the ride home.
Which shows a possible number of CDs she could buy? Select three options.
1
2
3
4
5
Answer:
The possible number of CDs she could buy is 1, 2, and 3.
Step-by-step explanation:
First, you have to make an equation to solve to find the answer(s):
80 - (18 · x) ≥ 2080 is how much money Felicia has; 18 is for the cost of each CD; x is for the number of CDs; ≥ is no less; and 20 is how much money Felicia needs to have left.1.) 80 - (18 · 1) ≥ 20
80 - 18 · 1 ≥ 20
80 - 18 ≥ 20
62 ≥ 20
Since 62 ≥ 20 is always true, there are infinitely many solutions.
2.) 80 - (18 · 2) ≥ 20
80 - 18 · 2 ≥ 20
80 - 36 ≥ 20
44 ≥ 20
Since 44 ≥ 20 is always true, there are infinitely many solutions.
3.) 80 - (18 · 3) ≥ 20
80 - 18 · 3 ≥ 20
80 - 54 ≥ 20
26 ≥ 20
Since 26 ≥ 20 is always true, there are infinitely many solutions.
4.) 80 - (18 · 4) ≥ 20
80 - 18 · 4 ≥ 20
80 - 72 ≥ 20
8 ≥ 20
Since 8 ≥ 20 is false, there is no solution.
5.) 80 - (18 · 5) ≥ 20
80 - 18 · 5 ≥ 20
80 - 90 ≥ 20
- 10 ≥ 20
Since - 10 ≥ 20 is false, there is no solution.
Answer:
1,2,3
Step-by-step explanation:
14
13. MR1 Make Sense and Persevere
Ms. Wilson bought two bags of pet
fish for her twin nieces. Each bag has
g gupples and one tetra. She also
bought one box of fish food that cost d
dollars. Write an algebraic expression to
represent how much she paid in all.
Answer:
67thnhttbny
Step-by-step explanation:
An algebraic expression that represent h how much she paid in all is 2(g+ 1) + d.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The following represents the items bought
Each bag has g gupples and one tetra.
She also bought one box of fish food that cost d dollars.
The expression that represents the items in a bag will be;
bag = g + 1
So, the total spent on fish food is:
2(g + 1)
Fish food
A box costs d dollars.
This means that, the total amount Ms. Wilson spent in the store is 2(g+ 1) + d
An algebraic expression that represent h how much she paid in all is 2(g+ 1) + d.
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Use the number line below, where , , and . a. What is the value of y? b. Find RS and ST. R S T a. What is the value of y? y 4 (Type an integer or a decimal.) b. Find RS and ST. RS 4.2 (Type an integer or a decimal.)
Answer:
y = 4
RS = 35
ST = 26
Step-by-step explanation:
Given:
RS = 8y + 3
ST = 5y + 6
RT = 61
Required:
a. Value of y
b. Numerical lenght of RS and ST
SOLUTION:
a. Points R, S and T are collinear, therefore, based on segment addition postulate, the following equation can be created to find the value of y:
[tex] RS + ST = RT [/tex]
[tex] (8y + 3) + (5y + 6) = 61 [/tex] (substitution)
Solve for y
[tex] 8y + 3 + 5y + 6 = 61 [/tex]
Combine like terms
[tex] 8y + 5y + 3 + 6 = 61 [/tex]
[tex] 13y + 9 = 61 [/tex]
Subtract 9 from both sides
[tex] 13y + 9 - 9 = 61 - 9 [/tex]
[tex] 13y = 52 [/tex]
Divide both sides by 13
[tex] \frac{13y}{13} = \frac{52}{13} [/tex]
[tex] y = 4 [/tex]
b. RS = 8y + 3
Plug in the value of y
RS = 8(4) + 3 = 32 + 3
RS = 35
ST = 5y + 6
Plug in the value of y
ST = 5(4) + 6 = 20 + 6
ST = 26
Answer:
Guy above me is Wrong its 14
Step-by-step explanation:
please help meeeeeeeee
Answer:
2 4/5 and 3 2/3
Step-by-step explanation:
find how many times the denominator can go into the numerator the left over numbers are now your second part of the fraction going with the whole number
1/4 of the total bird population in your town is 200 birds. How many birds are there in your town?
Answer:
800
Step-by-step explanation:
16.2=2.7(h+1) solve for h
Step-by-step explanation:
16.2 = 2.7(h+1)
2.7(h+1) = 16.2
(h+1) = 16.2 ÷ 2.7
h+1 = 6
h = 5
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{h = 5}}}}}[/tex]
Step-by-step explanation:
[tex] \bigstar{ \sf{ \: \: 16. 2 = 2.7( \: h \: + \: 1)}}[/tex]
[tex] \tt{Step \: 1 \: }[/tex] : Swap the sides of the equation
[tex] \longmapsto{ \sf{2.7(h + 1) = 16.2}}[/tex]
[tex] \tt{Step \: 2 \: }[/tex] : Distribute 2.7 through the parentheses
[tex] \longmapsto{ \sf{2.7 \times h + 2.7 \times 1 = 16.2}}[/tex]
[tex] \longmapsto{ \sf{2.7h + 2.7 = 16.2}}[/tex]
[tex] \tt{Step \: 3 \: }[/tex] : Move 2.7 to right hand side and change it's sign
[tex] \longmapsto{ \sf{2.7h = 16.2 - 2.7}}[/tex]
[tex] \tt{Step \: 4 \: }[/tex] : Subtract 2.7 from 16.2
[tex] \longmapsto{ \sf{2.7h = 13.5}}[/tex]
[tex] \tt{Step \: 5 \: }[/tex] : Divide both sides by 2.7
[tex] \longmapsto{ \sf{ \frac{2.7h}{2.7} = \frac{13.5}{2.7}}} [/tex]
[tex] \tt{Step \: 6 \: }[/tex] : Calculate
[tex] \longmapsto{ \sf{h = 5}}[/tex]
The value of h is 5
Hope I helped!
Best regards! :D
~TheAnimeGirl