The derivative of log₇(x) is 1/(xln(7))
To find the derivative of log₇(x), we can use the chain rule and the properties of logarithms.
The chain rule states that if we have a composite function, such as y = f(g(x)), then the derivative of y with respect to x is given by
dy/dx = dy/dg * dg/dx.
In this case, y = log_7(x) and g(x) = x, so
dy/dx = d/dx (log_7(x))
As by logarithmic property log₇x = ln(x)/ ln(7)
dy/dx = d/dx (ln(x)/ln(7))
To find the derivative of ln(x), we can use the property that the derivative of ln(x) is 1/x. This is because the natural logarithm function is the inverse of the exponential function eˣ, and the derivative of eˣ is eˣ. Therefore, the derivative of ln(x) is the reciprocal of x, or 1/x.
The differentiation of log₇(x) is given by:
d/dx (log₇(x)) = (1/x) * (d/dx (x)) * (1/ln(7))
= (1/x) * 1 * (1/ln(7))
= 1/(x ln(7))
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hi pls help math math
The number of teams who took less than 40 minutes to complete the game is 34 teams
How many of the team took less than 40 minutes to complete the game?0 ≤ t < 20 = 6
time greater than or equal to 0 less than 20 minutes
20 ≤ t < 40 = 28
time greater than or equal to 20 minutes less than 40 minutes
40 ≤ t < 60 = 12
time greater than or equal to 40 minutes less than 60 minutes
60 ≤ t < 80 = 7
time greater or equal to 60 minutes less than 80 minutes
The number of the team who took less than 40 minutes to complete the game are;
0 ≤ t < 20 = 6
20 ≤ t < 40 = 28
So,
6 + 28 = 34 teams
Hence, 34 teams took less than 40 minutes to complete the game.
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How many types of log functions are there?.
There are mainly two types of logarithmic functions - common logarithm and natural logarithm.
Common logarithm (log): The logarithm function with base 10, it is represented as log10(x) or simply log(x) if the base is not specified.
Natural logarithm (ln): The logarithm function with base e (approx 2.718), it is represented as ln(x)
These two logarithmic functions are the most commonly used and have many applications in mathematics, physics, engineering, and other sciences. They are inverse functions of the exponential functions (10^x and e^x) respectively.
Additionally, there are other types of logarithms, such as logarithms with bases other than 10 or e, for example log2(x) which is logarithm with base 2, it is used in information theory and computer science.
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1) Which of the following pairs of ratios does NOT form a proportion?
a) 2/7, 8/28
c) 27/9, 12,4
b) 36/30, 7/6
d) 52/13, 4/1
36/30, 7/6 does NOT form a proportion.
What is proportion?A proportion refers to the similarity of the two ratios.Write proportion to help you find equivalent ratios and solve for unknown quantities.A proportion is an equation that equates two ratios.For example, if you have one boy and her three girls, the ratio can be written as:1:3 (for every boy he has 3 girls) 1/4 are boys and 3/4 are girls. 0.25 boys (1 divided by 4)Direct proportionality or direct proportion is the ratio of two quantities where the ratio is equal to a constant value.It is denoted by the proportional sign ∝.In fact, the same symbol is used to represent the inverse proportion, because the difference in magnitude is reversed here.36/30 = 16/15 not equal to 7/6.
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In exploration 4. 1. 1 problem 3, which is the strongest answer on why the equation is or is not an identity?.
The equation is an identity because it is true for all values of the variables within the equation.
The equation is an identity because it is true for all values of the variables within the equation. This means that when the equation is evaluated for any given values of the variables, the left-hand side and the right-hand side of the equation will be equal. This is different from an equation that is not an identity, which will only be true for certain values of the variables. An identity equation is also different from an equation that is not an identity, which may be true for some values of the variables but not for all values. An identity equation is one that is true for all values of the variables, no matter what values are chosen.
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In how many ways can four people be selected from this group of seven
Answer:
a group of 4 people can be selected in 35 ways
What is the displacement for the the following changes in position? -4km to 5km
-9km is the displacement for the changes in position from -4km to 5km.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
We have to find the displacement for the the following changes in position
-4km to 5km.
Displacement is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude.
-4-5
=-9 km is the displacement.
Hence, -9km is the displacement for the changes in position from -4km to 5km.
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1+1=x
if i were trying to find x what would x be
Answer:
X = 2
Because x means our answer and the answer to 1 + 1 is 2!
Answer:
2
Step-by-step explanation:
1+1=2
x=2
How do you translate a log graph?.
Answer:
If h>0 , the graph of the base function shifts to the right. If h<0 , the graph of the base function shifts to the left. The function y=logb(x)+k y = l o g b ( x ) + k is the base function y=logb(x) y = l o g b ( x ) shifted vertically by k .
Step-by-step explanation:
write a multiplication equation that represents the question How many 2/3's are in 9/8
The equation (2/3)x = 9/8 represents the question "How many 2/3's are in 9/8?" because it shows that the unknown number of 2/3's (represented by x) multiplied by 2/3 equals 9/8.
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.
The following equation represents the question "How many 2/3's are in 9/8?" because it shows that the unknown number of 2/3's (represented by x) multiplied by 2/3 equals 9/8.
(2/3)x = 9/8
To find out how many 2/3's are in 9/8, you would need to solve for x by dividing both sides of the equation by 2/3.
⇒ x = (9/8)/(2/3)
⇒ x = (9/8) × (3/2)
⇒ x = 27/16
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solve x^2+3x+2=0
x=
OR
x=
Solve x^2+3x+2=0
[tex]x_{1} = -1\\x_{2} = -2[/tex]
The first is to use the quadratic formula
x= (-b±[tex]\sqrt[{} ]{b^{2} -4ac}[/tex]) ÷ 2a
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
[tex]x^{2} +3x+2 = 0[/tex]
Where,
a = 1
b = 3
c = 2
So,
x = (-b±[tex]\sqrt[{} ]{b^{2} -4ac}[/tex]) ÷ 2a
= (-3±[tex]\sqrt[]{3^{2}-4.1.2 }[/tex]) ÷ 2.1
The next step is to simplify numbers.
x= (-3±1) ÷ 2
The next step is separate it into two equations: one with the plus sign and the other with the minus sign.
x = (-3+1) ÷ 2
and
x = (-3-1) ÷ 2
Then,
[tex]x_{1}[/tex] = (-2)÷2 = -1
Or,
[tex]x_2}[/tex] = (-4)÷2 = -2
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y varies directly with x when y=16 then x=4, find what y will be when x is 5.5?
Answer:
30.25
Step-by-step explanation:
This is because y is the square of x
HOPE IT HELPS YOUPLS RATE AS BRAINLIEST ANSWERIn ΔEFG, g = 8.4 inches,
�
m∠G=79° and
�
m∠E=25°. Find the length of f, to the nearest 10th of an inch.
The image explains it all. First we find the third degree using the sum of angles in a triangle (180), then, using the rule of sines, we find the f and round it to the nearest 10th inch
"Lake superior has roughly 25 times the volume of Lake Erie. If the volume of Lake
Superior is approximately 1.22x10^10 km^3, what is the approximate volume of Lake
Erie?"
Answer:
[tex]\boxed{\sf{30.5 \times 10^{10}\;km^3}}[/tex]
Step-by-step explanation:
Volume of Lake Erie
[tex]\sf {= 25 \times 1.22 \times 10^{10} \\\\= 30.5\times 10^{10} \;km^3}[/tex]
How do you write 21600000 in standard form?.
To write 21600000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point.
21600000 in standard form would be written as 2.16 x 10^7. Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers. To write a number in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point.
The number of places the decimal point is moved is indicated by a power of 10. In the case of 21600000, the decimal point is moved 7 places to the left, giving us 2.16 x 10^7. This notation makes it easy to compare numbers of different magnitudes, and it simplifies calculations involving large or small numbers. It is commonly used in scientific, engineering and mathematical fields. A standard form is a useful tool for expressing numbers in a clear and concise way.
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if do= (6y-17.81) and ro= (3y+10.54) what is the length of hv
If do= (6y-17.81) and ro= (3y+10.54) then the measure of length of hv = 26
What about the length?A measurement that is longer than or longest than another. a dimension or distance that can be measured. Dimensions: 10 ft. Weights and Measures Table, Metric System Table being lengthy is a quality or a state.
In addition to utilising handspan, foot span, and other methods, one can measure length in many units, such as centimetres, inches, metres, and so on. The several types of units used to measure length can be divided into two categories: standard units and non-standard units.
The number of digits in the base-numerical for, as determined by the formula, determines a number's base length.
HF = 10x + 6
VH = 8 x – 14 and
FV = 4x+10
Substitute
8x - 14 + 4x + 10 = 10x +6
12x - 4 = 10x + 6
12x - 10x = 6 + 4
2x = 10
x = 5
Identify the VH's length.
VH = 8x - 14
VH = 8(5) - 14
VH = 26
Consequently, VH is 26 units long.
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The perimeter of AABC equals 12 in. The midpoints of the sides, M, N and K,
are connected consecutively. Find the perimeter of AMNK.
According to the Triangle midline theorem, slicing across a triangle's midline results in a section that is parallel to the base and only half as long. MNK=6 INCH
What is Triangle midline theorem?Theorem of the triangle midline: In a triangle, the midline connecting the midpoints of two sides is parallel to and half as long as the third side.
The midsegment linking the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is half that of the third side, according to the midsegment theorem.
The midpoints of the sides AB, BC, and AC are points M, N, and K. The Triangle Midline Theorem states that
MN=1/2AC
NK=1/2AB
MK=1/2BC
The perimeter of the triangle MNK is
P(MNK)=MN+NK+MK
=1/2AC+1/2AB+1/2BC
=1/2(AC+AB+BC)
=1/2PABC
=1/2.12
=6 inch
Therefore MNK=6 INCH
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What is the end behavior for f(x)=x^5?
The end behavior for f(x)=x^5 is asymptotic growth to positive infinity as x approaches positive infinity and asymptotic growth to negative infinity as x approaches negative infinity.
What is asymptotic growth?Asymptotic growth is a term used to describe the behavior of a function as it approaches a certain value, usually infinity. In mathematics, an asymptotic function is one that grows or shrinks towards a certain point without ever actually reaching it. In other words, it approaches a limit without bound. Asymptotic growth is often used to describe the rate of growth of a function as its input values approach infinity. It is also used to describe the rate at which a function expands or contracts as its argument approaches a certain point. Asymptotic growth is a useful concept in many areas of mathematics, from calculus to number theory.
This is because x^5 becomes increasingly larger as the absolute value of x increases, resulting in an ever-growing value of f(x).
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Express the following ratio in it's simplest form: 8kg:800g:4000g
Answer:
Step-by-step explanation:
8kg = 8000 grams
New Ratio = 8000:800:4000
Reduced = 20:2:10
Reduced even more = 10:1:5
HOPE THIS HELPED!
PROBLEM SOLVING Plutonium-238 is a material that generates steady heat due to decay and is used in power systems for some spacecraft.The function y=a(0.5)t/x represents the amount y of a substance remaining after t years, where a is the initial amount and x is the length of the half-life (in years).
Plutonium- 238, Half-life is approximately 88 years.
a. A scientist is studying a 3-gram sample. Write a function that represents the amount y of plutonium-238 remaining after t years.
Question 2
b. Use the function to estimate the amount of plutonium-238 remaining after 8 years.
Question 3
c. Use the graph of the function to estimate the amount remaining after 12 years.
About grams
The equation is [tex]\rm y = 3 \times \left (0.5 \right)^{t/88}[/tex]. Then the amount remaining after 8 years and 12 years will be 2.8168 grams and 2.729 grams, respectively.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the factor.
The exponent is given as
y = a(b)ˣ
The function is given below.
[tex]\rm y = a \left (0.5 \right)^{t/88}[/tex]
A scientist is studying a 3-gram sample. Then the function is written as,
[tex]\rm y = 3 \times \left (0.5 \right)^{t/88}[/tex]
The amount of plutonium-238 remaining after 8 years will be given as,
[tex]\rm y = 3 \times \left (0.5 \right)^{8/88}[/tex]
y = 3 × 0.9389
y = 2.8168 grams
From the graph, the amount remaining after 12 years will be 2.729 grams.
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.43333333333 as a fraction
Answer:
13/30
Step-by-step explanation:
8.
(6.6) Lizzy is buying oranges and pineapples for an evemt. Oranges cost $3 per pound and
pineapples cost $4 per pound. Lizzy needs to buy at least 16lbs of fruit for her event, but she only
has $60 to spend.
a) Define the variables and write a system of inequalities to represent this situation,
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality.
Explain about the inequalities?
In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.
Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
= Orange she bought 8 kg x 3 = $24
= Pineapple she bought 9KG X 4 = $36
= $24 +36
= $60
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how do u interpret the fraction 12/4
At a real etate agency, an agent old a houe for $342,000. The commiion rate i 4. 5% for the real etate agency and the commiion rate for the agent i 30% of the amount the real etate agency get. How much did the agency make on the houe? How much did the agent earn in commiion?
So, the agency made $15,390 on the sale of the house and the agent earned $4,617 in commission.
First, to find out how much the agency made on the house, you need to calculate the commission they received. The commission rate for the agency is 4.5%, so to find the commission you would multiply the sale price of the house ($342,000) by the commission rate (0.045)
$342,000 x 0.045 = $15,390
The agency made $15,390 on the sale of the house.
To find out how much the agent earned in commission, you need to first find out how much the agency earned in commission ($15,390) and then multiply that by the agent's commission rate (30%).
$15,390 x 0.3 = $4,617
The agent earned $4,617 in commission.
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To calculate the commission, multiply the selling price of the home ($342,000) by the agency's commission rate, which is 4.5%. (0.045)
$342,000 x 0.045 = $15,390
The sale of the property brought in $15,390 for the organization.
To calculate the amount of commission earned by the agent, multiply the amount of commission received by the agency ($15,390) by the agent's commission rate (30%).
$15,390 x 0.3 = $4,617
The dealer received a commission of $4,617.
Which is bigger -1/8 or -2/11
let's put both fractions using the same denominator by multiplying each top and bottom by the other's denominator.
[tex]-\cfrac{1}{8}\cdot \cfrac{11}{11}\implies \boxed{-\cfrac{11}{88}}\hspace{15em}-\cfrac{2}{11}\cdot \cfrac{8}{8}\implies \stackrel{\textit{\LARGE \checkmark}}{\boxed{-\cfrac{16}{88}}}[/tex]
well, let's take a looksie above, on the positive side of the number line, 16/88 is larger than 11/88, however, on the negative side, the closer to "0", the larger, for that matter -1 is a much larger number than -1,000,000.
So, -11/88 is closer to 0 on the negative side, and because of that, is larger than -16/88 that is farther from 0.
Quadrilateral ABCD has vertices A(3, 8), B(6, -8),
C(-6, -6), and D(-3, 4). Using the origin as the
center of dilation, the quadrilateral is horizontally
stretched by scale factor 4/3 then vertically
compressed by scale factor 1/2
Part A
Graph quadrilateral A"B"C"D".
the dilatation of the quadrilateral ABCD, where the vertices' coordinates are [tex]A (x1,y1), B (x2,y2), C (x3,y3),D(x4,y4){}[/tex] is written as: with scale factor k.
What are the vertices of a quadrilateral ABCD?A(,3,8), B(6,-8), C(-6,-6) and D are the vertices of the quadrilateral ABCD (-3,4) Establish the rhombic shape of ABCD.
A polygon with four sides exactly is referred to as a quadrilateral. The fact that a quadrilateral has exactly four vertices and four angles is also implied by this.
Each diagonal is parallel to the other. It is therefore a rhombus. The diagonals of the parallelogram are a rectangle, rhombus, and square since they are congruent and perpendicular to one another. A rhombus is ABCD.
[tex]A(x1,y1){}[/tex]⇒[tex]A'(kx1,ky1){}[/tex]
[tex]B(x2,y2){}[/tex]⇒[tex]B'(kx2,ky2){}[/tex]
[tex]C(x3,y3){}[/tex]⇒[tex]C'(kx3,ky3){}[/tex]
[tex]D(x4,y4){}[/tex]⇒[tex]D'(kx4,ky4){}[/tex]
Therefore, a dilated quadrilateral A'B'C'D"s vertices would have the coordinates [tex]A'(kx1,ky1), B'(kx2,ky2), C'(kx3,ky3), and D(kx4,ky4){}[/tex]
It should be noted that "k" could have an integer, decimal, or fractional value.
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If 92 people attend a concert and ticket for adult cot $3 while ticket for children cot $2. 25 and total receipt for the concert wa $246. 75, how many of each went to the concert?
The people who went to the concert will be 53 Adults and 39 Children respectively.
We will solve this problem with the help of a Binomial equation.
Let the number of adults is X and the number of children is Y.
Our first equation will be =
X + Y = 92
The total cost for adults is $3 and for Children is $2.25.
The total receipt for the concert is $246.75.
Our second equation will be =
3X + 2.25Y = 246.75
From equation 1, we get
X + Y = 92
X = 92-Y
Substitute this in equation second equation, and we get
3(92-Y) + 2.25Y = 246.75
276 - 3Y + 2.25Y = 246.75
-0.75Y = 246.75 - 276
-0.75Y = -29.25
Y = 39
So, our number of Children is 39.
Putting the value of Y in the first equation, we get:
X = 92 - 39 = 53
So, our number of adults is 53.
Therefore 53 Adults and 39 Children went to the concert respectively.
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How do you solve linear systems with linear combinations?.
In mathematics, a linear combination is any expression of the form ax + by, where a and b are constants, that are created from a set of terms by multiplying each term by a constant and adding the results.
The linear equations can be solved through the given steps-
Three methods exist for resolving a linear combination: Utilize the equations as is. A different equation should be used. Both equations should be changed. Use the equations exactly as they are. The two equations can be subtracted from one another to eliminate x because the coefficient of x is 1 in both instances.For example, a linear combination of x and y would be any expression of this form.To learn more about linear equations here
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Use cross products to solve for x. Type your answer as a simplified fraction (Ex. 37/4).
5/x+3 = 4/x
X =
Answer:
x=1/3
Step-by-step explanation:
= 5/x - 4/×=3
= 1/x=3/1
= 1=3×
= x=1/3
ord CB is a diameter and
The Arc AB = (π * r * 38) / 180.
What is central angle?
A central angle is the angle formed when two radii intersect at the center of a circle.
Since chord CB is a diameter of the circle, angle B is a right angle and measures 90 degrees. Arc AB is half the circumference of the circle, so its measure is equal to half the circumference times the ratio of the central angle to the total central angle (360 degrees) of the circle.
Let r be the radius of the circle. Then the circumference is 2 * π * r and the measure of arc AB is:
Arc AB = (1/2) * 2 * π * r * (angle B / 360)
Arc AB = (π * r * angle B) / 180
Arc AB = (π * r * 38) / 180
Therefore, Arc AB would be (π * r * 38) / 180.
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What do you call the expression a2 2ab b2?.
Answer:
perfect square trinomials
Step-by-step explanation:
Comes from (a+b) ^2
