![If F(x) = Ln [ Sin2(2x)(e-2x+1) ] , Then F(x) Is I Want To Solve ?](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/sLrWcTODxRUYLp3IyCcIbLJ1U2xctWK8.png)
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Here we will write our function in regular form using an identity.
[tex]log(ab)=loga+logb[/tex][tex]log(a/b)=loga-logb[/tex]Therefore, the rule of our function [tex]f(x)[/tex] will be as follows.
[tex]f(x)=ln(sin^2(2x))+ln(e^{-2x}+1)[/tex]The derivative of the natural logarithm [tex]ln(x)[/tex] function is of the following form.
[tex](ln(x))'=\frac{x'}{x}[/tex]It is found by dividing the derivative of the function in [tex]lnx[/tex] by the function in [tex]lnx[/tex].
For example:
[tex](ln(5x))'=\frac{(5x)'}{5x} =\frac{5}{5x} =\frac{1}{x}[/tex]According to this information, let's take the derivative of our function.
[tex]f'(x)=\frac{2sin(4x)}{sin^2(2x)} +\frac{-\frac{2}{e^{2x}} }{e^{-2x}+1}[/tex][tex]f'(x)=4cot(2x)-\frac{2}{1+e^{2x}}[/tex]Rules:[tex]((sin2x)²)'=2.2sin(2x)cos(2x)=2sin(4x)[/tex][tex](e^x)'=x'.e^x[/tex]Related Questions
Robin is saving money to buy a 720$ phone. she has 105$ saved, and each week she adds 30$ to her savings. write an equation to find the number of weeks (w) until she has enough savings to buy the phone.
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Let call w the number of weeks she has been saving.
Then, we can write the expression for her saving in function of the number of weeks as:
[tex]S(w)=105+30\cdot w[/tex]We now have to find the number of weeks it will take for her savings to reach $720.
We can find it by calculating w for S(w)=720:
[tex]\begin{gathered} S(w)-105+30w=720 \\ 105+30w=720 \\ 30w=720-105 \\ 30w=615 \\ w=\frac{615}{30} \\ w=20.5\approx21 \end{gathered}[/tex]Answer: it will take her 21 weeks to have enough savings.
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total. Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs $8. Let R represent the number of additional rolls that Sofia orders.Which inequality described this scenario?What is the least amount of additional money sofia can spend to get the sushi they need?
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Answer:
the least amount Sofia can spend is $608
For which equation would x = 12 not be a solution?96 ÷ x = 89 x - 7 = 101x + 4 = 105 + 4 x = 53
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Notice that:
1)
[tex]\frac{96}{12}=8.[/tex]Therefore x=12 is a solution to
[tex]96\div x=8.[/tex]2)
[tex]9*12-7=108-7=101.[/tex]Therefore x=12 is a solution to:
[tex]9x-7=101.[/tex]3)
[tex]12+4=16\ne10.[/tex]Therefore x=12 is not a solution to:
[tex]x+4=10.[/tex]4)
[tex]5+4*12=5+48=53.[/tex]Therefore x=12 is a solution to:
[tex]5+4x=53.[/tex]Answer: Third option:
[tex]x+4=10.[/tex]Algebra Find the value(s) of the variables in each kite.
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56º,34º
1) A kite is a quadrilateral that according to the following theorem:
2) And examining that picture, we can tell that the angle labeled as 8x is congruent to its opposite counterpart.
3) In addition to this, but not less important that bigger diagonal bisects that the other pair of opposite angles. So we can sketch the following
So we can pick one triangle and write out the following according to the Triangle sum theorem:
[tex]\begin{gathered} 8x+(5x-1)+90=180 \\ 8x+5x-1+90=180 \\ 13x+89=180 \\ 13x=180-89 \\ \frac{13x}{13}=\frac{91}{13} \\ x=7 \end{gathered}[/tex]4) Finally, let's plug into each one the quantity of x and get the measure of those angles:
Hey I need help on this math problem thank you
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Answer:
From the image below we will bring out two coordinates we are going to use to calculate the rate of change of the graph
The coordinates are given below as
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(2,4) \\ (x_2,y_2)\Rightarrow(-2,0) \end{gathered}[/tex]Concept:
The rate of change will be calculated using the formula below
[tex]\begin{gathered} \text{rate of change =}\frac{change\text{ in y}}{\text{change in x}} \\ \text{rate of change}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{rate of change}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change}=\frac{_{}0-4_{}}{-2_{}-2_{}} \\ \text{rate of change}=\frac{-4}{-4} \\ \text{rate of change}=1 \end{gathered}[/tex]Hence,
The rate of change = 1
10. (01.04 LC)
Your first six-month auto insurance premium was $658.00. Based on your driving record, your renewal premium is $756.70. What percent increase did you see in your premium? (1
12%
15%
28%
35%
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There is 15% in the premium.
How take out percentage?From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
First six-month auto insurance = $658
Renewal premium = $756
Change in the insurance = $98
percentage of $98 from $658
= 15%
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Find the measure of angle CDB. Explain your reasoning, including the theorem or postulate you used. (2 pts.) b) Find the measure of angle. (1 pt.)
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The triangle is isosceles, since two of its sides are equal. Besides, the little triangles ABD and CBD are congruent and this can be concluding using the criterion SSS , since they share one side, and the other sides are equal. Then the angles are congruent, and the angles ADB and CDB are congruent and have the same measure. Then
[tex]\begin{gathered} m\angle ADB+m\angle CDB=m\angle ADC \\ 2m\angle CDB=m\angle ADC \\ m\angle CDB=\frac{72}{2} \\ m\angle CDB=32 \end{gathered}[/tex]Then, the measure of angle CDB is 32 degrees.
Apply the product rule to rewrite the product below using a single base and exponent then simplify: 3^2 *3^3 our base is Answerour exponent is Answerthis simplifies to Answer
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Explanation:
[tex]3^2\text{ }\times3^3[/tex][tex]\begin{gathered} \text{The expression has same base.} \\ \text{Base = 3} \\ We\text{ take one base and bring the exponents together} \\ \text{The sign betw}en\text{ them changes from multiplication to addition} \end{gathered}[/tex][tex]\begin{gathered} 3^2\text{ }\times3^3\text{ = }3^{2\text{ + 3}} \\ \text{Exponent = 2 + 3} \\ \text{Exponent = 5} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplifying:} \\ 3^{2+3}=3^5 \\ 3^5\text{ = 243} \end{gathered}[/tex]help I'm practicing
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We have the next formula to find the volume of a triangular prism-
[tex]V=B\times h[/tex]where
B= area of the base
h= height
in our case
B=18 square inches
H= 5 inches
[tex]V=18\times5=90in^3[/tex]the volume of the triangular prism is 90 cubic inches
Approximately how old would you be in the years if you lived 1,000,000 hours? round your answer to the nearest whole number.
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First let's see how many hours are in a year:
[tex]\begin{gathered} 1\text{ year }\rightarrow\text{ 365 days} \\ 1\text{ day }\rightarrow\text{ 24 hours} \\ \Rightarrow1\text{ year }\rightarrow365\cdot24=8760\text{ hours} \end{gathered}[/tex]We found that 1 year has 8769 hours, then if we lived 1,000,000 hours, we have to divide it by 8760 to know the number of years lived:
[tex]\frac{1000000}{8760}=114.15[/tex]therefore, you would have lived 114.15 years
I child drinks 1 1/2 cups of milk twice a day.If a container of milk has 15 cups of milk remaining for the child to drink ,in how many days will the container be empty?
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Data
Milk drank = 1 1/2 twice a day
Volume in a container = 15 cups
Number of days the contaier will be empty = ?
Procedure
To solve this problem just divide the volume of the container by the milk drank by the child.
As the child drinks 1 1/2 twice a day, the total milk drank in a day will be = 2 x 1 1/2 = 3
Division 15/3 = 5
Solution: The container will be empty in 5 days
I'm attempting to solve and linear equation out of ordered pairs in slopes attached
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We know that the equation of a line is given by
y = mx + b,
where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.
In order to find the equation we must find m and b.
In all cases, m is given, so we must find b.
We use the equation to find b:
y = mx + b,
↓ taking mx to the left side
y - mx = b
We use this equation to find b.
1We have that the line passes through
(x, y) = (-10, 8)
and m = -1/2
Using this information we replace in the equation we found:
y - mx = b
↓ replacing x = -10, y = 8 and m = -1/2
[tex]\begin{gathered} 8-(-\frac{1}{2})\mleft(-10\mright)=b \\ \downarrow(-\frac{1}{2})(-10)=5 \\ 8-5=b \\ 3=b \end{gathered}[/tex]Then, the equation of this line is:
y = mx + b,
↓
y = -1/2x + 3
Equation 1: y = -1/2x + 3
2Similarly as before, we have that the line passes through
(x, y) = (-1, -10)
and m = 0
we replace in the equation for b,
y - mx = b
↓ replacing x = -1, y = -10 and m = 0
-10 - 0 · (-1) = b
↓ 0 · (-1) = 0
-10 - 0 = b
-10 = b
Then, the equation of this line is:
y = mx + b,
↓
y = 0x - 10
y = -10
Equation 2: y = -10
3Similarly as before, we have that the line passes through
(x, y) = (-6, -9)
and m = 7/6
we replace in the equation for b,
y - mx = b
↓ replacing x = -6, y = -9 and m = 7/6
[tex]\begin{gathered} -9-\frac{7}{6}(-6)=b \\ \downarrow\frac{7}{6}(-6)=-7 \\ -9-(-7)=b \\ -9+7=b \\ -2=b \end{gathered}[/tex]Then, the equation of this line is:
y = mx + b,
↓
y = 7/6x - 2
Equation 3: y = 7/6x - 2
4The line passes through
(x, y) = (6, -4)
and m = does not exist
When m does not exist it means that the line is vertical, and the equation looks like:
x = c
In this case
(x, y) = (6, -4)
then x = 6
Then
Equation 4: x = 6
5The line passes through
(x, y) = (6, -6)
and m = 1/6
we replace in the equation for b,
y - mx = b
↓ replacing x = 6, y = -6 and m = 1/6
[tex]\begin{gathered} -6-\frac{1}{6}(6)=b \\ \downarrow\frac{1}{6}(6)=1 \\ -6-(1)=b \\ -7=b \end{gathered}[/tex]Then, the equation of this line is:
y = mx + b,
↓
y = 1/6x - 7
Equation 5: y = 1/6x - 7
What is the volume of this triangle right prism 8 cm 15 cm 12 cm
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The volume of a triangle right prism is given by the formula
How can I know how many students scored 5 in their test?
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Based on the given table, consider that the value in the column frequency specifies the number of times that a certain score (first column) is repeated in a given data.
In this case, the value of the frequency for a specific score determines the number of students with such a score in their tests.
As you can notice, for the value of the frequency equal to 3, the corresponding value of the score is 5. It means that 3 student get 5 scores in their tests.
Evaluate h(x) at x = 6, x = 8, and x= 12. h(x)=1.31^×
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Answer : h(6) = 5.054
h(8) = 8.673
h(12) = 25.542
Given that h(x) = 1.31^x
[tex]\begin{gathered} h(x)=1.31^x \\ \text{ find the value of h(6) when x = 6} \\ h(6)=1.31^6 \\ h(6)\text{ = 5.05}4 \\ \text{when x = 8} \\ h(8)=1.31^8 \\ h(8)\text{ = 8.67}3 \\ \text{when x = 12} \\ h(12)=1.31^{12} \\ h(12)\text{ = 25.54}2 \end{gathered}[/tex]Therefore,
h(6) = 5.054
h(8) = 8.673
h(12) = 25.542
Find a polynomial function P(x)with the given zeros.4, 3, 8
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Given the word problem, we can deduce the following information:
The zeroes are: 4, 3, 8
To determine the polynomial function P(x) with the given zeroes, we follow the process as shown below:
[tex]\begin{gathered} (x-4)(x-3)(x-8)=0 \\ \\ \end{gathered}[/tex]We first expand (x-4)(x-3):
[tex](x-4)(x-3)=x^2-7x+12[/tex]Next, we expand (x^2-7x+12)(x-8):
[tex]\begin{gathered} (x^2-7x+12)(x-8)=x^2(x)+x^2(-8)-7x(x)-7x(-8)+12(x)+12(-8) \\ Simplify \\ =x^3-15x^2+68x-96 \end{gathered}[/tex]Hence,
[tex]x^3-15x^2+68x-96=0[/tex]Therefore, the polynomial function is:
[tex]P(x)=x^3-15x^2+68x-96[/tex]find the value or measure. Assume all lines that appear to be tangent are tangent. mPM=
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Segments that crosses around a circle
MN ^2 = OP • ON
mm
then 59° = (
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Select all the equations that are equivalent to the formula PV = nRT.
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The equations that are equivalent to the formula PV = nRT are V = nRT/P, n = PV/RT and R = PVnT. Option B, C and D
How to determine the equationsFrom the information given, we have that;
The Ideal Gas law is represented as;
PV = nRT
Given that;
P is the pressure V is the volumeT is the temperaturen is the amount of gasR is a physical constantSubject of formula is described as the variable expressed in terms of other variables in an equation.
It is made to stand on its own on one end of the equality sign.
Let's make 'V' the subject of formula
Divide both sides by the coefficient of V which is the variable 'P', we have;
V = nRT/P
Making 'R' the subject of formula, we have
R = PV/ nT
Making 'n' the subject of formula, we have;
n = PV/RT
Hence, the equations are options B, C and D
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The complete question:
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Which of the equations below are equivalent to the formula PV = nRT? Select all that apply. A. P = VnRT B. V = nRT/P C. n = PV/RT D. R = PVnT E. T = nR/PV
Answer:Pv=NRT
Step-by-step explanation:
Xandro's Lighting Company purchased a dozen light bulbs for 900 pesos each. This purchased was subject to a trade discount of 25%. What was the total net price?
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Total price of one dozen light bulbs will be equal to
[tex]12\times900=10800[/tex]Total trade discount is equal to (list price x trade discount rate)
[tex]\text{Discount }=10800\times0.25=2700[/tex]So, the net price will be (List price - discount)
[tex]\text{Net price = 10800-2700=}8100[/tex]Therefore, the total net price is 8100 pesos.
find the surface area of the figure and round to the nearest
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The figure in the image is a Hemisphere.
The surface area of a hemisphere is given as:
[tex]3\text{ }\times\text{ }\pi\text{ }\times r^2[/tex]Thus, the surface area is:
[tex]\begin{gathered} 3\text{ }\times\text{ 3.142 }\times8.6^2 \\ 697.15ft^2 \end{gathered}[/tex]Hence, the surface area of the figure, to the nearest whole number is 697 square feet.
10Estimate the solution to the following system of equations by graphingOA (1,7)OB. (-1,1)OC.OD. (-1,-1)
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we have the system of equations
-4x + 5y =8
6x - y = 11
Using a graphing tool
Remember that
the solution is the intersection point of both lines
The answer is the option Awhat is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters? round to the nearest hundred
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Right triangular pyramid
base = 5 meters
altitude = 4 meters
Volume = ?
Step 02:
The volume of a right triangular pyramid
V = 1/3 B * h
B = 1/2 b * h
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\cdot5m\cdot4m \\ B=\text{ }10m^2 \end{gathered}[/tex][tex]V\text{ = }\frac{1}{3}\cdot10m^2\cdot4m=\text{ }13.3333m^3[/tex]The answer is:
The volume of the pyramid is 13.33 m³.
HeyI need help with this, having trouble solvingIt is from my ACT prep guide
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We will determine the height of the building as follows:
First, we determine the height above her window, that is:
[tex]\tan (56)=\frac{h_u}{150ft}\Rightarrow h_u=(150ft)\tan (56)[/tex][tex]\Rightarrow h_u=222.3841453\ldots ft[/tex]Now, we calculate the height below her window:
[tex]\tan (32)=\frac{h_l}{150ft}\Rightarrow h_l=(150ft)\tan (32)[/tex][tex]\Rightarrow h_l=93.73040279\ldots ft[/tex]Then, we will have that:
[tex]h_T=h_l+h_l\Rightarrow h_T=150(\tan (56)+\tan (32))[/tex][tex]\Rightarrow h_T=316.1145581\ldots ft\Rightarrow h_T\approx316.1ft[/tex]So, the height of the building is approximately 316.1 ft tall.
Write a situation for this equation
1.5 < 1.67
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The inequality equation is correct the way it is in the form 1.5 < 1.67 and will continue to be correct if 1.5x < 1.67 where x is
negative numberx less than or equal to 1What are inequalities?Inequalities as used in mathematics refers to the symbol that is used to related the values in the left hand side and the values at the right hand side of the expression
The symbol used in the inequality expression are
less than or equal togreater than or equal toless thangreater thanThe given expression is less than and read as 1.5 is less than 1.67
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Which of the following are a qualitative catecorical variables
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A qualitative variable, also called a categorical variable, is a variable that isn’t numerical. It describes data that fits into categories.
From the given options below, the arrival status of a train ( early, on time, late, canceled) and a person's blood type are the only qualitative variables.
Hence, Option 3 and Option 5 are the correct answers.
find the coordinates of the midpoint of the line joining the points and show your work.
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formula of midpoint
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]the we replace (7,1) and (-1,3)
[tex](\frac{7+(-1)}{2},\frac{1+3}{2})[/tex]simplify to solve
[tex]\begin{gathered} (\frac{7+1}{2},\frac{4}{2}) \\ \\ (\frac{8}{2},\frac{4}{2}) \\ \\ (4,2) \end{gathered}[/tex]Midpoint is (4,2)
Graph
geometry extra credit- 25 questions
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Given that the triangles are similar, then their corresponding sides are in proportion, that is,
[tex]\frac{AB}{JK}=\frac{BX}{KY}[/tex]Substituting with data and solving for BX:
[tex]\begin{gathered} \frac{32}{10}=\frac{BX}{6} \\ 3.2=\frac{BX}{6} \\ \text{3}.2\cdot6=BX \\ 19.2=BX \end{gathered}[/tex]solve the equation 3x^2 - 5x + 1 = 0 expressing your answer correct to two decimal places
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You have th following equation;
[tex]3x^2-5x+1=0[/tex]In order to find the solution to the previous equation, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, a = 3, b = -5 and c = 1. By replacing these values into the quadratic formula, you obtain:
[tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(3)(1)}}{2(1)} \\ x=\frac{5\pm\sqrt[]{25-12}}{2}=\frac{5\pm\sqrt[]{13}}{2} \\ x=\frac{5\pm3.60}{2}=2.5\pm1.80 \end{gathered}[/tex]Hence, the solutions are:
x = 2.5 + 1.80 = 4.30
x = 2.5 - 1.80 = 0.70
Express your answer as a polynomial in standard form.f(x) = x^2 + 6x +7g(x) = x + 2Find: g(f(x)
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1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):
[tex]\begin{gathered} g(f(x))=(x^2+6x+7)+2 \\ g(f(x))=x^{2}+6x+9 \end{gathered}[/tex]2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.
[tex]y=x^2+6x+9[/tex]Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
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We need to find the distance between the two points given. Use the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replace using P1(3,-9) and P2(-2,4):
[tex]d=\sqrt[]{((-2)_{}-3_{})^2+(4_{}-(-9)_{})^2}[/tex][tex]d=\sqrt[]{(-5)^2+(13)^2}[/tex][tex]d=13.9283[/tex]Rounded to the hundredths:
[tex]d=13.93[/tex]