gradient, in mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the partial derivatives of the function with respect to its three variables. The symbol for gradient is ∇.
Electrical potential acting on an ion and driving it in one direction or another is the definition of an electrical gradient..
The migration of particles (solutes) from a region of higher concentration to a region of lower concentration, separated by a membrane, is referred to as a concentration gradient.
An ion can travel across a membrane depending on the concentration of a solute thanks to an electrochemical gradient, which combines an electrical gradient with a concentration gradient.
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5. Let p be "an animal is a puppy" and let q be "it is a dog." Write each statemen
in words. Then decide whether it is true or false.
a. the conditional statement p → q
b. the converse q→ p
c. the inverse -p-9
d. the contrapositive -q→ ~P
a. The conditional statement p → q is true
b. The converse q → p is False.
c. The inverse p → ~q is False
d. The contrapositive -q→ ~p is True
How to Interpret Conditional Statements?
We are given the conditional statement;
Let p be "an animal is a puppy" and let q be "it is a dog."
a) The conditional statement p → q which is "If an animal is a puppy, then it is a dog" is true.
b) The converse statement q → p which is "If an animal is a dog, then it is a puppy" is false.
c) The inverse statement p → ~q which is "If an animal is not a puppy, then it is not a dog" is false.
d) The contrapositive statement: q → ~p which is "If an animal is not a dog, then it is not a puppy" is true.
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what is divide 3/2 and 9/4
Answer:
Step-by-step explanation:
1.5 and 2.25
Which expression is equivalent to 9(15)?
9(10+5)
9 left parentheses 10 plus 5 right parentheses
9(10+50)
9 left parentheses 10 plus 50 right parentheses
9(1+5)
9 left parentheses 1 plus 5 right parentheses
9(1+50)
Answer:
9(10+5)
Step-by-step explanation:
because 10+5 is fifteen so then when you as them together you get the same expression as before
Answer:
9(10+5)
Step-by-step explanation:
because 10+5=15 and it's 9(15)
The distance around track is 400 m if you take 14 more laps how much is total amount of distance
The total distance covered is 6,000 m.
What is distance?Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object had also covered regardless of its starting as well as ending point.
The magnitude as well as size of displacement between two positions is defined as distance. It is important to note that the distance between two points isn't the same as the distance traveled among them. The total length of a path traveled among two points is referred to as the distance traveled. Travel distance isn't a vector.Now, as per the question;
The distance around track is 400 m.
14 more laps has been covered along with the initial one.
Thus the total distance will be;
Total distance = 400 + 400×14
= 400 + 5,600
Total distance = 6,000
Therefore, the total distance covered is 6,000 m.
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Use logarithmic differentiation or an alternative method to find the derivative of the function. y = (sin 7x)ln x
The derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]
Derivative of a function f(x) is defined as the rate of change of that function with respect to x at a point in its domain.
For Example , Derivative of [tex]3x^{2} =6x[/tex].
Product Rule of Differentiation
Let f(x) and g(x) be any two function. The derivative of their will be
F(x)=f(x)*g(x)
[tex]F'(x)=f(x)*g'(x)+g(x)*f'(x)[/tex]
Given y=(sin(7x))ln(x)
[tex]y'=Sin(7x)*\frac{d}{dx} ln(x)+ln(x)*\frac{d}{dx}Sin(7x)[/tex]
[tex]y'=Sin(7x)*\frac{1}{x} +ln(x)*Cos(7x)*7[/tex]
[tex]y'=\frac{Sin(7x)}{x} +7*ln(x)*Cos(x)[/tex]
Therefore , the derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]
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Complete the point-slope equation of the line through (-4,8) (−4,8)
Use exact numbers.
(Point-Slope Equation)
any detailed answer for this??
Answer: y = 8
Step-by-step explanation:
Point-slope form is written as y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ([tex]x_1[/tex] , [tex]y_1[/tex]) are points on the line.
First, we need to find the slope. This can be found with change in y over change in x:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{8-8}{-4--4}=\frac{0}{-4+4}=\frac{0}{0}=[/tex] undefined
Now, we will plug this undefined slope (0) into the equation below. Anything times 0 is 0, so no matter what (x - [tex]x_1[/tex]) is, the right side of the equation will always be 0.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - [tex]y_1[/tex] = (0)(x - [tex]x_1[/tex]) ➜ y - [tex]y_1[/tex] = 0
Lastly, we will take the y-value of 8 and plug it into the equation and simplify.
y - [tex]y_1[/tex] = 0 ➜ y - (8) = 0 ➜ + 8 (y - 8) = (0) + 8
y = 8
See attached for a visual explanation.
Question 4 4.1 Determine the value of c in the diagram. 65% c 4.2 Determine the value in the diagram. x-20° 84° (3) Statement Statement Reason Reason
The value of c is 25° and x is 116°.
From figure 1, we can see hat the entire angle is given to be 90°. This angle is divided into 2 parts, one is 65° and the other is c
This means that-
65 + c = 90
c = 90 - 65
c = 25
Thus, the value of c is 25°.
Now, in the 2nd figure, we can see that both the horizontal lines are parallel and a transversal is drawn between them.
Both the angles thus formed are opposite interior angles and are hence supplementary.
Therefore, (x - 20) + 84 = 180
x - 20 = 180 - 84
x - 20 = 96
x = 96 + 20
x = 116
Thus, the value of x is 116°
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write each quadratic function below in terms of linear factors
f(x)=x^2+81
(x+3i)(x-3i)
A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = √-1 and both a and b are real numbers.
Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.
Using complex numbers,
x²+81 = x² - (-9i)²
= (x²- 9²i²)
= (x+3i)(x-3i)
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1. In a study of how college education costs have changed since 1980,
each year's average cost of tuition is expressed as a percentage of the
1980 cost. Which term refers to the 1980 cost?
(a) Reference value
(c) Rate of inflation
(b) Index number
(d) Price index
Solve for the formula m
e=mc squared
A rectangle garden has a length of 5 less than 2 times the width. the perimeter if 50 meters. what are the side lengths?
The length of the rectangle garden is 15 meters and the width of the rectangle garden is 10 meters.
Perimeter of the rectangle:
Perimeter of the rectangle is defined as the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
The formula for perimeter of the rectangle is,
P = 2 (a + b) units
where
“a” is the length of the rectangle
“b” is the breadth of the rectangle
Given,
A rectangle garden has a length of 5 less than 2 times the width.
The perimeter if 50 meters.
Here we need to find the side lengths of the rectangle garden.
Let w be the width of the garden.
According to the given details, the length is
l =2w - 5
Now apply the values on the perimeter formula,
Then
=> 2 ((2w - 5) + w) = 50
=> 2 (3w - 5) = 50
=> 3w - 5 = 25
=> 3w = 30
=> w = 10 meters.
Apply the value of width on the equation to find the length of the garden.
=> l = (2 x 10) -5
=> l = 20 - 5
=> l = 15 meters.
Therefore, the length of the garden is 15 meters and the width of the garden is 10 meters.
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Write two numbers so that the value of the digit 9 in the second number is 10 times the value of the digit 9 in the first number?
The two numbers with the value of 9 in the first digit being 10 times the value of 9 in the second digit are 98 and 9.
What are the two numbers?The first number will be 9 and the second number will be 98.
In the second number, the 9 is in the tens position which means that it has the value of 90.
In the first number, the value of 9 is simply 9.
90 is 10 times the value of 9 which means that 9 and 98 satisfy the requirements.
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As treasurer of her school's 4H club, Carol wants to buy gifts for all
11 members. She can buy t-shirts for $5 and sweatshirts for $12.
The club has $118 to spend and Carol wants to spend all of the
money. How many of each type of gift should she buy?
Using algebraic expressions and equations, Carol should buy 2 t-shirts and 9 sweatshirts.
We can set up an algebraic expressions and equations to determine how many of each type of gift should Carol buy.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
1. Write an equation for the total number of members.
x + y = 11 (equation 1)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
2. If each t-shirt costs $5 and each sweatshirt costs $12, write an equation for the total amount spent buying the gift.
$5(x) + $12(y) = $118 (equation 2)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
3. Rewrite equation 1 as an equation of y in terms of x.
x + y = 11 (equation 1)
y = 11 - x
4 . Plug in the expression for y in equation 2 and solve for x.
$5(x) + $12(y) = $118 (equation 2)
5x + 12(11 - x) = 118
5x + 132 - 12x = 118
-7x = -14
x = 2
5. Substitute the value of x in either equation 1 or 2 and solve for x.
x + y = 11 (equation 1)
2 + y = 11
y = 11 - 2
y = 9
Hence, Carol should buy 2 t-shirts and 9 sweatshirts.
Checking,
2 + 9 = 11
Each member will receive a gift.
2($5) + 9($12) =$118
Carol will be spending $118 for the gifts.
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Suppose that a system of seven equations with thirteen unknowns corresponds to a matrix in row echelon form. what is the largest possible number of pivots for this matrix?
For a system of seven equations with thirteen unknowns corresponds to a matrix in row echelon form. The largest possible number of pivots for this matrix is 7.
What is row echelon form and pivots?Using a technique known as Gaussian elimination, any matrix can be converted to reduced row echelon form. This is especially useful for solving linear equation systems.
If a matrix has the following properties, it is in Row Echelon form:
The bottom of the matrix contains any row that is entirely made up of zeros.The first non-zero entry in each row which does not encompass entirely zeros is 1. (called a leading 1).The leading 1 in the higher row is even further left than the leading 1 in the lower row for two consecutive (non-zero) rows.Pivoting is the process of transferring the first matrix to the second matrix utilizing row operations similar to equations.
The matrix "A" has three columns. As a result, there can only be three pivots, implying that at least one row of "A" in echelon type must be zero.
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63) Julia has 1/3 many stamps as Robert and also 2/3
as many stamps as
Erin. If Erin has 36 stamps, what is the total number of stamps that
the 3 children have?
Answer: The total number of stamps is 132.
Step-by-step explanation:
We know that Erin has 36 stamps.
Given that information, we can calculate how many stamps Julia has which is 2/3 as many stamps as Erin.
2/3 * 36 = 24
Julia has 24 stamps.
Julia also has 1/3 as many stamps as Robert.
24 = 1/3 * Robert
Robert = 72 stamps
Add the three numbers together to get your final answer
24 + 72 + 36 = 132
**WITH STEPS ASAP
1. If you know that limx→−1 f(x)=−3 and limx→0 g(x)=3, then evaluate the following limit:
limx→0 f(x−1)g(x)=
2. If you know that limx→4 f(x)=3 and limx→0 g(x)=−5, then evaluate the following limit:
limx→0 f(x+4)+g(x)=
Applying it's properties, the limits of the functions are given as follows:
1. 9.
2. -2.
What is a limit?A limit is given by the value of function f(x) as x tends to a value. Algebraically, for continuous functions, we have that:
[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex].
Hence, applying the property above, for item 1, we have that:
limx→0 f(x−1)g(x) = f(0 - 1)g(0) = f(-1)g(0) = -3 x 3 = 9.
For item 2, we have that:
limx→0 f(x+4)+g(x) = limx→4 f(x) + limx→0 g(x) = 3 - 5 = -2.
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3. What is the cardinality number of the set {2, 4, 6, 8, 10, 12}?
a. 2
b. 6
c. 8
d. 10
The cardianality of the set {2, 4, 6, 8, 10, 12} is 6.
According to the given question.
We have a set {2, 4, 6, 8, 10, 12}.
Here, we have to find the cardianality of the set {2, 4, 6, 8, 10, 12}.
As we know that, the cardinality of a set is a measure of the number of elements of the set.
From the given set {2, 4, 6, 8, 10, 12} we can say that the total number of elements in the given set is 6. So, the cardianality of the set is 6.
Hence, the cardianality of the set {2, 4, 6, 8, 10, 12} is 6.
Thus, option b is correct.
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each * represents a missing operation.
23*11*22*11 = 11
how to solve this? please i need the steps not just answers
Which is greater explain the reasoning
Answer:
0.00000057652
Step-by-step explanation:
5.764 × 10^-7 = 0.0000005764 (move the decimal place 7 steps forward)
0.00000057652>0.0000005764 (65>64)
Therefore 0.00000057652 is greater.
Hope this helped! ^^
At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151At a school, the average of the number of boys, girls, male teachers, and female teachers is 117. The average of the number of boys, girls, and male teachers is 151. There are 6 fewer male teachers than there are female teachers. The number of female teachers is 1/16 the number of girls. How many boys are there at the school? boys
Using a system of equations, it is found that there are 204 boys at the school.
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 variables are given as follows, considering the situation described:
Variable x: number of boys in the school.Variable y: number of girls in the school.Variable z: number of male teachers in the school.Variable w: number of female teachers in the school.The average of the number of boys, girls, male teachers, and female teachers is 117, hence:
(x + y + z + w)/4 = 117
x + y + z + w = 468.
The average of the number of boys, girls, and male teachers is 151, hence:
(x + y + z)/3 = 151
x + y + z = 453.
Then:
x + y + z + w = 468.
453 + w = 468
w = 15.
There are 6 fewer male teachers than there are female teachers, hence:
z = w - 6 = 15 - 6 = 9.
So:
x + y + z = 453.
x + y = 444.
The number of female teachers is 1/16 the number of girls, hence:
y = 16w = 16 x 15 = 240.x = 444 - y = 444 - 240 = 204.There are 204 boys at the school.
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Paul's Bikes rents bikes for $11 plus $4 per hour. Amanda paid $31 to rent a bike. For how many hours did she rent the bike?.
As given Paul's Bikes rents bikes for $11 plus $4 per hour and Amanda paid $31 to rent a bike shows she rent the bike for 5hours.
As given in the question,
Let 'h' represents the number of hours
Paul's Bikes rents bikes for $11 plus $4 per hour
Amanda paid $31 to rent a bike
Required equation is:
31 = 11 + 4h
⇒4h = 20
⇒h = 5hours
Therefore, as given Paul's Bikes rents bikes for $11 plus $4 per hour and Amanda paid $31 to rent a bike shows she rent the bike for 5hours.
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evaulate 5m+7 if m=5
Answer:
32
Step-by-step explanation:
[tex]5\cdot \:5+7[/tex]
please help me!! i have no clue
Answer:
Step-by-step explanation:
the following are amounts of total snow falls (in inches) in different midwestern cities in the united states in a certain year: 20 40 31 7 15 29 25 20 17 32 28 12 34 29 20 17 33 23 find the sample mean.
The sample mean of the given data is 24.
What do we mean by mean?In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific set of data, often in order to better understand the overall value (magnitude and sign) of a given data set.The arithmetic mean, also known as "arithmetic average," of a data set is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.To find the mean:
Mean = sum of terms/number of termsMean = 432/18Mean = 24Therefore, the sample mean of the given data is 24.
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Find the sum of the whole numbers from 1 to 680.
The sum of the whole numbers from 1 to 680 is 231540.
What is the sum of the whole numbers from 1 to 680?Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant called the common difference.
The formula for sum of first n numbers can be expressed as;
Sₙ = (n/2)( a₁ + aₙ )
Where n is the number of terms, a₁ is the first term and aₙ is the nth term.
Given that,
The numbers are whole numbers from 1 to 680
Number of terms n = 680First term a₁ = 1680th term a₆₈₀ = 680Sum S₆₈₀ = ?Plug the given values into the equation above.
Sₙ = (n/2)( a₁ + aₙ )
S₆₈₀ = (680/2)( 1 + 680 )
S₆₈₀ = 340( 681 )
S₆₈₀ = 231540
Therefore, the sum of the whole numbers from 1 to 680 is 231540.
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The position of a car is given, for positive t, by x = 9t - 3t3. x is in meters and t is in seconds. when (in seconds) it its velocity zero?
When the velocity of the car is zero. Then the time will be 1 second.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The position of a car is given, for positive t, by x = 9t - 3t³. x is in meters and t is in seconds.
We know that velocity is the rate of change of displacement. Then we have
v = dx / dt
v = 9 - 9t²
When the velocity of the car is zero. Then the time will be
v = 0
9 - 9t² = 0
1 - t² = 0
(1 - t)(1 + t) = 0
t = 1, -1
When the velocity of the car is zero. Then the time will be 1 second.
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The number of cable TV systems recently decreased from 14,100 to 13,920. Find the percent decrease.
The percent decrease was %. (Round to the nearest tenth, if needed.)
Answer:
1.3
Step-by-step explanation:
[tex]\frac{14100-13920}{14100} \times 100 \approx 1.3[/tex]
6-x^2 what is it
please answer correctly to be awarded brainliest
Answer:
i think the question might be incorrect or the question is incomplete
0olve the equation
x/6 -5 = (-13)
Answer:
x=-13
Step-by-step explanation:
[tex]\frac{x}{6-5}=\left(-13\right)[/tex]
[tex]\frac{x}{1}=\left(-13\right)[/tex]
[tex]x=-13[/tex]
Answer: x= -48
Step-by-step explanation:
x/6 -5 = -13 check answer
+5 = +5 (-48)/6 -5 =-13
x/6 = -8 -8 -5 = -13
6(x/6) = (-8)6 -13 = -13
x=-48
What is this called ,
, <--- That is called a comma