Answer:
[tex]y = x \ln 2 +\left(\ln 2 \right)^2-2 \ln 2[/tex]
Step-by-step explanation:
Differentiation is an algebraic process that finds the gradient of a curve.
At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\If $y=f(u)$ and $u=g(x)$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}u}\times\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Differentiating $x^n$}\\\\If $y=x^n$, then $\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Differentiating $\ln x$}\\\\If $y=\ln x$, then $\dfrac{\text{d}y}{\text{d}x}=\dfrac{1}{x}$\\\end{minipage}}[/tex]
Differentiate the given function using the chain rule:
[tex]\begin{aligned}f(x) & = \left(\ln x\right)^2\\\implies f'(x)& = 2\left(\ln x\right)^{2-1} \cdot \dfrac{\text{d}}{\text{d}x} \ln x\\& = 2\left(\ln x\right)^{1} \cdot \dfrac{1}{x}\\& = \dfrac{2}{x} \ln x \end{aligned}[/tex]
To find the gradient of the function at x = 2, substitute x = 2 into the differentiated function:
[tex]\implies f'(2) = \dfrac{2}{2} \ln 2 = \ln 2[/tex]
Therefore, the gradient of the function at x = 2 is ln(2).
Substitute x = 2 into the function to find the y-value of the point on the curve when x = 2:
[tex]\implies f(2)= \left( \ln 2\right)^2[/tex]
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Substitute the point (2, (ln 2)²) and the found gradient into the slope-intercept formula and solve for b:
[tex]\begin{aligned} y & = mx+b\\\implies \left(\ln 2 \right)^2 & = \ln 2 \cdot 2 + b\\\left(\ln 2 \right)^2 & =2\ln 2 +b\\b & = \left(\ln 2 \right)^2-2 \ln 2\end{aligned}[/tex]
Therefore, the tangent has the equation:
[tex]y = x \ln 2 +\left(\ln 2 \right)^2-2 \ln 2[/tex]
help please!!
What are the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE ??
Answer:
When we rotate a figure of 90 degrees clockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.
Step-by-step explanation:
I THINK IT HELPS YOU
Select the reason that best supports Statement 3 in the given proof
The correct is option A which is definition of bisector
What is bisect?
The term bisect refers to dividing into two equal parts. In mathematics, the term is used mostly in geometry, when a line intersects another line, say line A intersects line B, when the point of intersection is the mid point of line A. Then it can be said that line B is the bisector of line A. If the point of intersection is also the mid point of line B then line A also is the bisector of line B. Bisector then refers to the line that bisects the other.
The terms bisect and bisector is not used for lines alone it can be used in many other circumstances for instance say angle. An angle may be bisected into two equal parts two. An example is angle 180 degrees can be bisected to get angle 90 degrees. Angle 90 degrees can be further bisected to give angle 45 degrees.
Hence we can say that line DF which is 96 is bisected by line EG to get two equal parts of 48 each, This means that line EG intersects line DF at the midpoint
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Solve 9(x+7)-6(x-3)=99 . What is the value of x ?
The given equation;9(x+7)-6(x-3)=99 then the value of x in the given equation is 6.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
For a solution , it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point
WE need to Solve the given equation;
9(x+7)-6(x-3)=99 .
Open the bracket;
9(x+7)-6(x-3)=99
9x + 63 - 6x + 18 = 99
Collect the like terms then solve it;
9x + 63 - 6x + 18 = 99
9x - 6x + 63+ 18 - 99 = 0
3x - 18 = 0
3x = 18
Divide by 3 on both sides the n we get;
x = 6
Therefore, the value of x in the given equation is 6.
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Write an equation of each line in standard form with integer coefficients. y=1/2 x-2
The equation of the given line y=1/2 x-2 in standard form is x - 2y - 4 = 0
Equation of a line in standard form can be expressed as:
Ax + By + C = 0
Where:
A and B are called coefficients.
x and y are called variables of degree 1 or linear variables.
C is called a constant.
In the above equation, the values of A, B, and C should be integers, not fractions or decimals. Furthermore, "A" needs to be a positive number.
The given equation is:
y = 1/2 x - 2
Notice that the coefficient of x is not an integer, therefore we need to multiply the equation by 2.
2y = 2 . (1/2)x - 2 . 2
2y = x - 4
Subtract x from both sides
2y - x = x - 4 - x
-x + 2y = -4
Add 4 to both sides
-x + 2y + 4 = -4 + 4
-x + 2y + 4 = 0
Note that the coefficient of x is negative, hence, we need to multiply both sides by (-1).
x - 2y - 4 = 0
This is the standard form of the given line.
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13. 4 people are splitting the
bill at a restaurant. If the
cost was $36.08, how much
will each person owe?
1
Answer:
Each person will owe $9.02
Step-by-step explanation:
Just divide 36.08 by 4
Answer:
$9.02
Step-by-step explanation:
36/4 = 9
8/4 = 2, so 0.08/4 = 0.02
36.08/4 = 9.02
Express the function f(x) = [tex]\frac{x+1}{7}[/tex] in y=mx+b
Answer: f(x)= 1/7 * x + 1/7
Step-by-step explanation:
f(x) = (x+1)/7
f(x) = x/7 + 1/7
f(x)= 1/7 * x + 1/7
The difference of 9 and the quotient of a number f and 6 is 5.
According to the given statement;
The difference of 9 and the quotient of a number f and 6 is 5.
the value of f is = -24
What is Variable?A variable is an alphabet or term that stands in for an unknowable quantity, value, or number. Particularly in the case of algebraic expressions or algebra, the variables are used. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.
The variable is a quantity that can change or is not fixed. Typically, in algebra, we use the terms "x" and "y" to express an unknown number. However, this is not unique, and we are free to use any alphabet.
According to the given value;
9 - (f÷ 6) = 5
Subtract 9 from both sides.
9 - 9 - (f ÷ 6) = 5 - 9
Simplify.
- (f ÷ 6) = -4
Distribute -1 throughout the parenthesis.
-f ÷ -6 = -4
Multiply both sides by -6.
-f ÷ -6 × -6 = -4 × -6
Simplify.
-f = 24
Divide both sides by -1.
-f ÷ -1 = 24 ÷ -1
Simplify.
f = -24
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Can someone help with this math problome.
Answer: c=26
Step-by-step explanation:
x= c
a^2 + b^2 = c^2
24^2 +10^2 = c^2
Take the square root of all the values
c=26
Answer:26
Step-by-step explanation:
pythagorean theorem
c=[tex]\sqrt{a^{2} +b^{2} }[/tex]
a=24,b=10
[tex]24^{2}[/tex]=576, [tex]10^{2}[/tex]=100
576+100=676
[tex]\sqrt{676}[/tex]=26
What is the answer to this problem?
PLEASE SHOW WORK
ALSO DO THE CHECK YOUR WORK BOX
Answer:
Hey there fella!
I can do you the 1st and it will help you do the rest
Step-by-step explanation:
[tex]multiply \: 2 \: with \: x + 4 \\ we \: get \: 2x + 8 \\ put \: the \: rest \: equation \\ 2x + 8 + 3 = 8 \\ 2 x + 11 = 8 \\ take \: the \: 11 \: to \: other \: side \: \\ the \: sign \: will \: change \\ 2x = 8 - 11 \\ 2x = 3 \\ 2 \: is \: getting \: multiplied \: with \: x \: so \: it \: will \: be \: divided \: with \: 3 \\ x = \frac{2}{3} \\ x = 1[/tex]
I hope this is clear to you if not ask me questions I will be sure to help!
Solve each system by elimination.
3x+2y = 6 , 3x+3 = y
By elimination, the solution of the system of equations, 3x + 2y = 6 and 3x + 3 = y, is (0 , 3).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Rearranging equation 2 to standard form,
3x + 3 = y (equation 2)
3x - y = -3
Subtracting the two equations will eliminate the variable x.
3x + 2y = 6 (equation 1)
3x - y = -3 (equation 2)
0x + 3y = 9
y = 3
Substitute the value of y to any of the two equations and solve for x.
3x + 2y = 6 (equation 1)
3x + 2(3) = 6
3x = 6 - 6
3x = 0
x = 0
Hence, the solution of the system of equations is (0 , 3).
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Make a scatter plot and describe the correlation.
(0,11),(2,8),(3,7),(7,2),(8,0)
A scatter plot is a series of points plotted on horizontal and vertical axes. If there is no correlation between variables, the points appear randomly scattered on the coordinate plane. If the correlation is high, the points will be clustered around the straight line. A scatter chart is a data visualization tool that helps show trends.
The scatter plot shows not only the magnitude of the correlation, but also the direction of the correlation.
As the vertical (or Y-axis) variable increases, the correlation is positive as the horizontal (or X-axis) variable increases.
The correlation is negative if the y-axis variable decreases and the x-axis variable increases, or vice versa.
The correlation is zero if none of the above criteria can be established.
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Where I can get additional practice answer keys?
Answer:
What do you mean by that?
Step-by-step explanation:
Answer:
Here, at Brainly!!
Step-by-step explanation:
Here, we can solve any questions or problems that you have! We'll always keep you updated, and make sure that all your questions are answered! If you have any questions, try asking questions, and be ready to receive and answer soon!!!
Thank You,
I really hope this helps
Adriano runs a website that helps writers write better stories. Every month, Adriano receives a subscription fee of \$5$5dollar sign, 5 from each of the subscribers to his website. The website had 200200200 subscribers last month. This month 404040 new members joined the website and 101010 members cancelled their subscription.
How much money will Adriano’s online business earn this month?
The amount Adriano earns this month is $1150.
How much did Adriano earn?The amount Adriano would receive would increase by the number of new subscribers and reduce by the number of subscribers who cancel.
Total amount Adriano earns this month = (number of subscribers x subscription fee) + (number of new subscribers x subscription fee) - (number of people who cancelled x subscription fee)
(200 x $5) + (40 x $5) - (10 x $5)
$1000 + $200 - $50 = $1150
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. Two similar prisms have surface areas of 98 square centimeters and 18 square centimeters. What is the ratio of the height of the large prism to the height of the small prism?
The ratio between the height of the prisms is 7/3.
What are prisms?Prisms are geometric bodies or solids that start from the extrusion of a plane figure, and that is the origin of their name, for example, if the base is square, the prism is quadangular.
What is a numerical ratio?A numerical ratio is a constant value that relates a system of two or more variables, it allows us to know how their variations will be as the values change.
Since prisms are said to be similar, then the ratio of their areas and heights must be proportional, expressed as:
a²/b² = 98/18
a²/b² = 49/9
a/b = 7/3
The ratio between the height of the prisms is 7/3.
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Evaluate the quantity one half raised to the fourth power times one half raised to the zero power end quantity all raised to the second power.
A - one over 32
B - one over 64
C - one over 128
D - one over 256
Answer: Your answer is A one over 32
Answer: 1/64
Step-by-step explanation:You need to multiply 1/2 by the other 1/2 as well not just the exponents.
According to Heron's Formula, if the lengths of the sides of a triangle are a, b and c, and s= (a + b + c)/2,
then the area, A, is given by the formula: A = √s(s-a) (s-b) (s-c). Find the area of a triangle whose
sides are 6ft, 7ft and 11ft.
O A = 21.1 ft²
O A = 18.4 ft²
OA = 19.0 ft²
O A = 20.0 ft²
Answer:
Hello,
answer C: 19.0ft (rounded to 1 digit)
Step-by-step explanation:
[tex]s=\dfrac{6+7+11}{2} =12\\\\A=\sqrt{12*6*5*1} =\sqrt{360}= 18,97366596...\approx{19.0}\ (ft^2)[/tex]
Answer:
19.0 ft^2.
Step-by-step explanation:
s = (6 + 7 + 11)/2
= 12
--> A = √[12(12-6)(12-7)(12-11)]
= √(12 * 6 * 5 * 1)
= √360
= 18.97
how to solve 6x - 2y = 6 for x
Answer:
2x^2
Step-by-step explanation:
x
Please really someone help need to have this done tonight!!!!!!!!
I'd really appreciate it!
125 students have volunteered to be on the prom committee. 2 of those students will be randomly chosen to win free tickets to the prom. How many different ways can the winners be chosen?
Does order matter? Answer
No
This is a Answer
combination
.
How many different ways can winners be chosen?
Answer
125
Answer
C
Answer
2
= Answer
7750
What is the probability that the first two students who signed up will be the winners? P(1st two students who signed up win) = Answer
Using the combination formula, it is found that:
There are 7750 different ways for the winners to be chosen.The probability that the first two students who signed up will be the winners is 1/7750.The order in which the students are chosen is not important, as for example, João and Elisa is the same outcome as Elisa and João, hence the combination formula is used to solve this question;
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
2 students are chosen from a set of 125, hence the number of combinations is:
[tex]C_{125,2} = \frac{125!}{2!123!} = 7750[/tex]
There are 7750 different ways for the winners to be chosen.
The first two students winning is only one outcome, hence:
The probability that the first two students who signed up will be the winners is 1/7750.
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Read each question. Then write the letter of the correct answer on your paper.
What is the common ratio in a geometric series if a₂ = 2/5 and a₅ = 16/135 ?
(A) 2/5
(B) 2/3
(C) 6/65
(D) 8/27
The common ratio of a geometric series with a₂ = 2/5 and a₅ = 16/135 is r = 2/3 (B)
The formula for the nth term of a geometric series is given by:
a(n) = a(1) . rⁿ⁻¹
Where:
a(1) = first term
r = common ratio
Parameters given:
a(2) = 2/5
a(5) = 16/135
Note that:
a(2) = a.r
a(5) = a.r⁴
Divide a(5) by a(2)
a.r⁴ : a.r = 16/135 : 2/5
r³ = 8/27
r = 2/3 (B)
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Refer to ®N . Identify each.
c. a radius
A radius is a segment with endpoints at the center and on the circle. Here, NC, ND, NE or NF is radius.
What is meant by the radius of a circle?In classical geometry, a radius of a circle or sphere is any of the line segments connecting its center to its perimeter; in more modern usage, it is also their length. The term comes from the Latin word radius, which means both ray and spoke of a chariot wheel.
A circle's radius is the distance between its center and any point on its circumference. The letters 'R' or 'r' are commonly used to represent it. In almost all circle-related formulas, this number is significant. The radius of a circle is used to calculate its area and circumference.
A radius is a segment with ends at the circle's center and on the circumference. Radius can be NC, ND, NE, or NF in this case.
The complete question is:
Identify each
c. a radius
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2
Jonathan worked 5 1/2 hours on Monday and 8 3/4 hours on Tuesday. If he made $16 per
hour, how much money did he make in those two days? Show all of your work to arrive at an
answer. * (2 Points)
O $224.00
O $228.00
$88.00
O $140.00
3
Miranda bas $150 22 in her bank account She withdrew $82.50 to buy clothes then
Jonathan made $228 in these two days of working on Monday and Tuesday.
What is fraction?Fractions indicate pieces of a whole or group of objects. A fraction is divided into two pieces. The numerator is the number at the top of the line. It specifies how many equal pieces of the total or collection are taken. The number below the line is referred to as the denominator. It displays the total number of equal portions into which the whole is divided or the total number of the same objects in a collection.
Given that he makes $16 per hour
On Monday he made = 5 1/2 × 16
= $88
On Tuesday he made = 8 3/4 × 16
= $140
Total money he made = 140 + 88
= $228
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A particle moves in a velocity field v(x, y) = x2, x y2 . if it is at position (x, y) = (4, 5) at time t = 6, estimate its location at time t = 6.01.
New location of a particle moves in a velocity field at time 6.01 is given by: (7.49, 2.11).
What is a velocity field?Think about the fluid flow's steady-state velocity vector field, or v. The instantaneous velocity of the fluid particles (atoms or molecules) as they pass through the point (x,y) is measured by the vector v(x,y).
The vector field used to quantitatively characterize the motion of a continuum in continuum mechanics is called the flow velocity in fluid dynamics, macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism. The flow speed is a scalar and is represented by the length of the flow velocity vector.
It is also known as a velocity field, and a velocity profile is what it is known as when it is measured along a line.
Everything about a fluid's motion is efficiently described by its flow velocity.
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The price of a technology stock has dropped to $9.53 today. Yesterday’s price was $9.64. Find the percentage decrease.
Answer:
1%
Step-by-step explanation:
9.64-9.53 = 0.11
0.11/ 9.64 = 0.011 x 100 = 1.1% or basically 1%
Si en la pandemia de 1918 murieron 40 millones ¿Qué porcentaje representa del total de la población mundial de ese año?
La "Gripe Española" de 1.918 acabó con 2.105 por ciento de la población mundial de su tiempo.
¿Cuál es el porcentaje de personas muertas por causa de la "Gripe Española" de 1918?
La "Gripe Española" fue una enfermedad respiratoria emparentada con los virus SARS-COV vistos en las últimas dos décadas que alimentó una pandemia que mató a decenas de millones de personas entre 1.918 y 1.920.
En esta pregunta debemos determinar el porcentaje de personas muertas con respecto a la población mundial de la época. Esto calcula al dividir el número de personas muertas por el número total de pobladores del mundo y multiplicar tal razón por 100.
La población aproximada del mundo en 1.920 fue de casi 1.900 millones de personas, entonces tenemos que el porcentaje de personas muertas es:
x = (40 000 000 / 1 900 000 000) × 100
x = 2.105 %
La "Gripe Española" de 1.918 acabó con 2.105 por ciento de la población mundial de su tiempo.
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Y is between points J and A.
J A = 17 and Y A = 3.
What is J Y?
Enter your answer in the box.
Answer: JY=14
Step-by-step explanation:
JA=JY+YA
17=JY+3
17-3=JY+3-3
JY=17-3
JY=14
can someone help me ???????????????????????????????
Answer:
-83x - 18
Step-by-step explanation:
simplify
7x+9(-10x - 2)
multiply by 9
9(-10x - 2)
-90x -18
7x- 90x -18
-83x -18
(a³b¹²c²) × (a³c²) × (b³c¹) ⁰ =
12.4
O A. a¹5¹24
○ в. a³b¹¹c³
8
O c. a³b¹²4
OD. a¹4b¹5c9
Answer:
Step-by-step explanation:
keep in mind that any number to the power 0 is equal to 1 therefore if you check carefully in the expression you will find that [tex](b^{5} c^{4} )^{0} =1[/tex]And you should be able to know and apply the rules of exponentsbut in this case the only one to be applied is :if you are to are multiplying powers of the same base add the exponents.[tex]=a^{3} *a^{5}* b^{12} *c^{2} *c^{2}\\\\= a^{3+5} *b^{12} *c^{2+2}\\ =a^{8}b^{12} c^{4}[/tex]OPTION C IS the correct answerJeff brown has collected sales data for his cupcake stand. calculate the moving average forecast for period 13 with n = 4. round your answers to 2 decimals.
The moving average forecast for period 13 = 44.55.
What is average forecasting?A statistical technique for predicting long-term trends is the moving average. The method entails shifting the range while averaging a group of numbers from a particular range.The equation is as follows: previous month's sales x velocity = additional sales; subsequent month's anticipated sales are equal to additional sales plus the prior month's rate.You take each of the three periods in our three-period spread and apply a percentage of that period's average to create a weighted average. To get a more precise projection, we might, for instance, pick 15% of period 1, 20% of period 2, and then 35% of period 3.Calculate the moving average forecast for period 13 with n = 4. round your answers to 2 decimals.
The moving average technique averages a number of the most recent actual values in the data given for generating the forecast. When n=4, a four-period moving average is calculated by taking the average of 4 most recent actual values. Here we have to take the average of actual sales values of periods 9,10, 11, and 12.
Hence moving average forecast for period 13= (A9+A10+A11+A12)/4
= (60+48+41.2+29.0)/4
= 44.55
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Find the slope of the line through each pair of points. (-1/2 ,-1/2) and (-3,-4)
The slope of the line with points (-1/2 ,-1/2) and (-3,-4) is 1.4
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
We know that slope, slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (-1/2 ,-1/2) and (-3,-4)
⇒ m = [tex]\frac{-4- (-1/2)}{-3 - (-1/2)}[/tex]
⇒ m = [tex]\frac{-7/2}{-5/2 }[/tex]
⇒ m = 7/5
⇒ m = 1.4
Hence, the slope of the line with points (-1/2 ,-1/2) and (-3,-4) is 1.4
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