By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
How to use logarithmic differentiation
Logarithmic differentiation is a combination of derivative rules and logarithm properties which is useful to derive power, exponential and power-exponential functions:
y = 2ˣ
㏑ y = ㏑ 2ˣ
㏑ y = x ㏑ 2
y' / y = ㏑ 2
y' = y · ㏑ 2
y' = 2ˣ · ㏑ 2
By logarithmic differentiation, the first derivative of y = 2ˣ is y' = 2ˣ · ㏑ 2.
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What is f(-3) for the function f(x)=-3 x+6 ?
The value of f(-3) is 15.
The given function is f(x) = -3x+6. Now, f(-3) = x = -3
Substituting and Evaluating the value of x in the equation f(x) = -3x+6, we get
f(-3) = -3(-3)+6f(−3)=−3(−3)+6
f(-3) = 9+6f(−3)=9+6
f(-3) = 15f(−3)=15
∴ The value of f(-3) for the function f(x) = -3x+6 is equal to 15.
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PLs solveg g g g g g g g g g g g
Answer:
4°=1
g g g g g g g g g g
Step-by-step explanation:
Lee is laying out a design for the tiles of a section of his bathroom floor. he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design. how many of each type of tile will lee use?
If Lee is laying out a design for the tiles of a section of his bathroom floor and he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design then the number of white and black tiles Lee will use is equal to 4 and 24 respectively.
The number of white and black tiles Lee will use can be determined by using an algebraic expression.
As 1 white tile is used for every 6 black tiles, an algebraic expression can be represented as,
x + 6x = 28
By solving the value of x, the number of each type of tile that Lee will use can be calculated,
x + 6x = 28
7x = 28
x = 28 ÷ 7
x = 4
As there is one white tile for every six black tiles,
White tiles = 1(x) = 1(4) = 4
Black tiles = 6(x) = 6(4) = 24
Hence the number of white tiles Lee will use is equal to 4 and the number of black tiles Lee will use is equal to 24.
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Eileen is 3y years old now. Her mother is 4 times as old as her. Find their total age in 7 years' time. Give your answer in terms of y.
Answer:
15y+14
Step-by-step explanation
Answer: 14 + 15y
Step-by-step explanation:
E = Eileen’s age = 3y
M = Mum’s age
Total Age = 14 + 3y + 4(3y)
= 14 + 15y
Total age in 7 years time is their current ages plus 7 years for each (14 years)
Eileen is 3y, and her mum is 4 times that, which is 12y, meaning that their total ages are 3y + 12y, or, 15y.
Total age is then 15y + 14. Since we don’t know what y equals, we cannot add these two terms, and we can just leave them like that!
So, the answer is 14 + 15y.
Peter bought three items at a store. Here are their prices (in dollars):
18.23, 6.39, and 15
What is the total amount Peter paid at the store? Do not round your answer.
$____
Type your numerical answer below.
-
Answer: $39.62
Step-by-step explanation: To get the answer to the cost of Peter's three items, I took the prices of the three and added them together. This amount would be the amount he paid WITHOUT TAX.
Please help with this answer! Thank you so much guys really thanks
Apparently a math question.
Answer:
Since Ian has $75 dollars, it would be enough to buy at least one DVD box set. However, there's not that much information in the statement.
Hope this helps with your question :)
use the figure below to answer the following. What is congruent. Given MN=6x-1 and MP=3x+8
The value of x if the sides are congruent is 3
How to determine the congruent sides?The given parameters are
MN=6x-1 and MP=3x+8
For the sides to be congruent, then the following equation must be true
MN = MP
This gives
6x - 1 = 3x + 8
Collect the like terms
6x - 3x = 1 + 8
Evaluate the like terms
3x = 9
Divide by 3
x = 3
Hence, the value of x if the sides are congruent is 3
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Identify a pattern and find the next three terms in the pattern.
8,9,10,11, . . .
Patterns of the given terms 8,9,10,11,.... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
As given in the question,
Given pattern is 8,9,10,11,...
First term a₁ = 8
Second term a₂ = 9
Third term a₃ = 10
Fourth term a₄ =11
d =aₙ - aₙ₋₁
=a₂ -a₁
=9 -8
=1
8,9,10,11,... represents arithmetic progression
aₙ=8 + (n-1)d
a₅ =8+ 4(1)
=2
a₆ =8 + 5(1)
=13
a₇ =8 + 6(1)
=14
Therefore, patterns of the given terms 8,9,10,11,... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.
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(PLEASE HELP!!)
Solve the following system of equations using either Gaussian elimination or a matrix. Write your answer as a point and explain how you would check your work:
2xy + 4z = 33
x + 2y - 3z = -26
-5x - 3y + 5z = 23
Using Gaussian elimination, the solution to the given system of equations is given as follows:
x = 5, y = -11, z = 3.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the equations are given as follows:
2x - y + 4z = 33.x + 2y - 3z = -26.-5x - 3y + 5z = 23.(I suppose there was a typing mistake on the first equation, as Gaussian elimination can only be applied to solve linear systems).
For Gaussian elimination, the first step is building the matrix of the system, in which:
The first three columns contain the coefficients of x, y and z, respectively.The last column contains the results of the operations.Hence, the matrix of the system is given as follows:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]
Then, we need to make the coefficient of x zero in the second and third rows, hence:
R2 -> 2R2 - R1.R3 -> 5R1 + 2R3.Then the matrix will be given by:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]
Now we need to make the coefficient of y on the third row zero, hence:
R3 -> 11R2 + 5R3.
Then:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]
From the third row, we have that:
40z = 120
z = 120/40
z = 3.
From the second row, we have that:
5y - 10z = -85
5y - 30 = -85
5y = -55
y = -11.
From the first row, we have that:
2x - y + 4z = 33
2x + 11 + 12 = 33
2x = 10
x = 5.
Hence the solution of the system is given by:
x = 5, y = -11, z = 3.
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Please help (show steps too)
Answer:
5
Step-by-step explanation:
[tex]d=\frac{|-3(5)-4(5)+10|}{\sqrt{(-3)^2+(-4)^2}}=5[/tex]
If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (s circle t) (negative 7)? HALP
-439 is the value which is equivalent to (s circle t) (negative 7).
Given,
s(x) = 2 - x²
t(x) = 3x
We have to find the value which is equivalent to (s circle t) (negative 7)
That is,
(s circle t) (negative 7) : This is a notation for compound function.
A function that takes another function as an argument is referred to as a compound function.
s(t(-7)) is the alternative notation for this compound function, which means that the value obtained from the function t(-7) will be used in the function s. (x).
Now, let's calculate the value of t(-7):
That is,
t(x) = 3x
t(-7) = 3 × (-7) = -21
Next, apply the value of t(-7) for s(x)
That is,
s(x) = 2 - x²
s(t(-7)) = s(-21) = 2 - (-21)^2 = 2 - 441 = -439
That is, -439 is the value which is equivalent to (s circle t) (negative 7).
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Question 7 of 10
Given NELR, solve for x.
R
(7x+33)
N
OA. 8
B. 7
O C. 6
O D. 5
(11x+21)
E
For the parallelogram NELR, we get the value of x as 7°.
We are given a parallelogram NELR.
We know that , the adjacent angles of a parallelogram are supplementary.
So, we get that:
∠ N + ∠ E = 180°
Substituting the values, we get that:
7 x + 33 + 11 x + 21 = 180
18 x + 54 = 180
18 x = 180 - 54
18 x = 126
x = 126 / 18
x = 7°
Therefore, for the parallelogram NELR, we get the value of x as 7°.
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Find the sum of each finite series. Σ¹° n = 5 (20-n)
The sum of the given finite series is 75
The given series is:
[tex]\sum\limits^{10}_{n=5} {(20-n)}}[/tex]
To find the sum of this series,
Expand the summation notation by using the properties of sum operator:
Σ(a+b) = Σa + Σb
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
If a is a constant, then Σa = k. a, where k is the number of terms = upper limit - lower limit + 1
Using this property:
[tex]\sum\limits^{10}_{n=5} {20} = (10 - 5+1)\times20=6\times20=120[/tex]
Expand
[tex]\sum\limits^{10}_{n=5} {n}=5+6+7+8+9+10=45[/tex]
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
= 120 - 45 = 75
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Statement about translated figures
If two sides are parallel in the original figure, then those sides may not be parallel in the final figure.
True False
What is the equation of the line that passes through the point (-2,-1)(−2,−1) and has a slope of 5/2
The equation of line having slope of 5/2 is given as 2y -5x = 8.
What is termed as the equation of line in point-slope form?A line's equation written in point slope form is (y - y₁) = m(x – x₁).When the line passing through the origin the equation of a line with slope m is: y - 0 = m(x = 0), i.e. y = mx.where m is the slope and (x₁, y₁) are the coordinates passing point on the line .As, per the given question;
The slope of the line is given as; m = 5/2
The coordinates of the passing points (-2, -1).
Thus, (x₁, y₂) = (-2, -1).
The equation of the becomes.
(y - y₁) = m (x – x₁)
Put the values;
y - (-1) = (5/2)(x - (-2))
Simplifying
y + 1 = (5/2)(x + 2)
2y + 2 = 5x + 10
2y -5x = 8
The equation of line is calculated as 2y - 5x = 8.
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Describe the transformation of the parent function f(x) . h(x)=0.25 f(x)
The transformation applied to the parent function is vertical compression by a factor of 0.25.
In mathematics, functions can be manipulated algebraically to obtain graphs of functions through certain transformations. Such transformations are reflections of the x-axis or the y-axis. To flip a function f(x) on the x-axis, multiply the whole function by a negative value to get -f(x), and to flip a function f(x) on the y axis, f(-x ), specify the x variable with a negative value.
Vertical compression helps shrink features vertically. Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.
It is vertically compressed by a factor of 0.25.
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For any correlation, people often assume that change in one quantity causes change in the second quantity. This is not always true. For each situation, do you think that change in the first quantity causes change in the second quantity? What else may have affected the change in the second quantity?
a person's age and the number of cassette tapes he or she owns
For the given situation, we can clearly say that the change in one quantity will cause a change in the second quantity as well.
Correlation is a relationship between the values of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.
Causality means that one event causes another. Causality can only be determined by well-designed experiments. In such experiments, similar groups receive different treatments, and the results of each group are examined.
From the above information, we concluded that a person's age and the number of cassette tapes he/she owns are correlated more he lives the more he buys the cassette tapes. So we can make relation from this,
Person's Age ∝ Number of Cassette
This clearly states that by increasing/changing one quantity we will increase/change the other quantity as well.
Similarly, now that they have a direct relation if we decrease the Age of the person, the number of Cassette's will also decrease. A positive correlation we can call it.
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A small cylindrical can of tuna has a radius of 4 centimeters and a height of 3.8 centimeters. A larger and similar can of tuna has a radius of 5.2 centimeters.
a. What is the scale factor of the cylinders?
The scale factor of the two similar cylindrical cans of tuna is 13/10.
Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:
height of A / height of B = radius of A / radius of B
Scale factor refers to the ratio of the corresponding dimensions of similar solids.
If the smaller cylindrical can of tuna has a radius of 4 centimeters and the larger and similar can of tuna has a radius of 5.2 centimeters, then the scale factor is:
scale factor = radius of larger can/ radius of smaller can
scale factor = 5.2 cm / 4 cm
scale factor = 13/10
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The low temperature in degrees celsius for some cities on the same days in march are recorded in the dot plots. Decide if each statement is true or false
Answer:
the statement is true.
Step-by-step explanation:
Use the formula for the probability of two dependent events P(A and B) to derive the conditional probability formula for P(B | A) .
The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).
What is said to be dependent events?When the outcome from one event influences the outcome of the other, two events are referred to as dependent.
Dependent events in probability are generally real-life events that depend on another event to occur. Sam, for example, did well on his math test because he prepared; the gym class used to have a football session even though Adam brought a football from home. When you look at these examples, you will realize that one occurrence is dependent on the other.Derivation of conditional probability from two dependent events P(A and B) is-
The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).
This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.
Step 1: Write the multiplication rule down:
P(A and B) = P(A)*P(B|A)
Step 2: P(A) divides both sides of the equation:
P(A and B) / P(A) = P(A)*P(B|A) / / P(A)
Step 3: On the right side of the equation, cancel P(A):
P(A and B) / P(A) = P(B|A)
Step 4: Rewrite the equation as follows:
P(B|A) = P(A and B) / P(A)
Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).
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Find the value of x.
Answer:
43
Step-by-step explanation:
the plane is 180 degrees
subtract 2x4
172
divide by 4
43
BOOM
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
r = x/8,d= ___, C=?
A circle is a curve sketched out by a point moving in a plane. The diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that radius of the circle is x/8 units. Therefore, the diameter and the circumference of the circle can be written as,
Diameter of circle = 2 × (Radius of the circle)
= 2 × (x/8) units
= x/4 units
Circumference of circle = 2 × π × (Radius of the circle)
= 2 × π × (x/8) units
= (x/4)π units
Hence, the diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
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Given two functions
F(x) = 2x+1 and G(X) = x^2-40
Find f(-4) + g(-7)
Answer:
f(-4) = -7
g(-7) = 9
Step-by-step explanation:
f(x) = 2x + 1
f(-4) = 2(-4) + 1 = -8 + 1 = -7
g(x) = x^2 - 40
g(-7) = (-7)^2 - 40 = 49 - 40 = 9
(-8) x (-2/3) =
1/3a = -5
URGENTTT
Answer: -8
Step-by-step explanation:
= 12 * (-2/3)
= -24/3
= -8
(−8) ⋅ (−2/3) = 1/3a = −5
The formula weights=mass of 1 mole of (−8) ⋅ (−2/3) = 1/3a = −5 = 0g
Piecewise defined functions
Part a
[tex]\frac{\pi}{3} > \frac{\pi}{4} \implies f(\pi/3)=\sin(\pi/3)=\boxed{\frac{\sqrt{3}}{2}}[/tex]
Part b
[tex]\frac{\pi}{6} \leq \frac{\pi}{4} \implies f(\pi/6)=2+\cos(\pi/6)=\boxed{2+\frac{\sqrt{3}}{2}}[/tex]
Part c
[tex]\frac{\pi}{4} \leq \frac{\pi}{4} \implies f(\pi/4)=2+\cos(\pi/4)=\boxed{2+\frac{1}{\sqrt{2}}}[/tex]
Hence, or otherwise, express 0.372 as a fraction.
Answer:
93/250
3/8
0,375 has three numbers after a decimal so we will multiply and divide 0,375 by 1000
Write an equation in slope-intercept form for the line.
(-7,2) and (5,8)
The equation in slope-intercept form for the line that passes from the points (-7,2) and (5,8) is y = (1/2)x -3/2.
We know that, the slope intercept form is given by:-
y = mx + b
Where,
(x,y) is the ordered pair of every point on the line
m is the slope of the line
b is the y-intercept of the line
We know that, slope = (8-2)/(5-(-7)) = 6/12 = 1/2
Putting (-7,2) in (x,y) and m = 1/2 in the slope intercept form, we get,
2 = (1/2)(-7) + b
2 = -7/2 + b
b = -3/2
Hence, the slope intercept form of the line is y = (1/2)x -3/2.
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Three divers kept track of the number of crabs they've seen this year.
Diver Crabs observed Dives
Scuba Sam 33 11
Wet Suit Willy 81 18
Deep Diving Dan 104 26
Which diver saw the most crabs per dive?
Choose 1 answer:
The diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
What is an average?An average is a mean or the central value obtained by dividing the sum of all data values by the number of data values.
Data and Calculations:Diver Crabs observed Dives Average Crab per dive
Scuba Sam 33 11 3
Wet Suit Willy 81 18 4.5
Deep Diving Dan 104 26 4
Thus, the diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.
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find the value of x
2x+5=6x-3
Answer:
Step-by-step explanation:
2x+5=6x-3
subtract 6x
2x-6x+5=6x-6x-3
-4x+5=-3
subrtract-5
-4x+5-5= -3-5
-4x=-8
divide-4
-4x÷-4=-8÷-4
x=2
