In mathematics, differentiation refers to the process of finding the derivative of a function. The basic means of differentiation include:
Limit definition: The derivative of a function is defined as the limit of the difference quotient as the interval over which the quotient is taken approaches zero.
Power rule: The derivative of a function of the form f(x) = xⁿ is given by f'(x) = nx⁽ⁿ⁻¹⁾
Product rule: The derivative of a product of two functions u(x) and v(x) is given by (u × v)'(x) = u'(x) × v(x) + u(x) × v'(x).
Quotient rule: The derivative of a quotient of two functions u(x) and v(x) is given by (u/v)'(x) = [u'(x) × v(x) - u(x) × v'(x)] / v(x)².
Chain rule: The derivative of a composition of functions f(g(x)) is given by f'(g(x)) × g'(x).
These basic means of differentiation are essential tools for analyzing and modeling functions in calculus and related fields.
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Wayne earns 5.3% simple interest for 5 years on $3000. How much interest does he earn on the account? I=prt
*
1 point
$883.86
$795
$3,883.86
$1,795
Answer: I would say it’s D. $1,795
Step-by-step explanation: why not pick D….
Hope this helps^^
The simple interest earned on $3000 after 5 years at 5.3% rate of interest is $795. The correct option is C .
Given,
Principal amount = $3000
Rate of interest = 5.3%
Time = 5 years
Now,
Simple interest = Principal × ROI ×Time/100
Substitute the values ,
Simple interest = 3000 * 5.3 * 5/ 100
Simple interest = 79500/100
Simple interest = $795
Total amount after 5 years = $3000 + $795
= $3795
Hence simple interest earned on $3000 at ROI of 5.3% after 5 years will be $795 .
Therefore option C is correct.
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Select all the equations that are equivalent to this equation
The equations equivalent to the given equation 3x - 4 = 5 are A) 3x = 9, B) 3x - 4 + 4 = 5 + 4 and E) -4 = 5 - 3x.
What is an Equation?An equation is defined as a mathematical statement containing two expressions on either sides which are connected with an equal to sign.
Either sides of an equation are called as left hand side and right hand side.
Given equation is 3x - 4 = 5.
Adding the number 4 on both sides, we get,
3x - 4 + 4 = 5 + 4, which is the equation B.
Simplifying,
3x = 9, which is the equation A.
x = 3
3x - 4 = 5
Subtracting 3x on both sides of the equation,
3x - 4 - 3x = 5 - 3x
-4 = 5 - 3x, which is the equation E.
Hence the equivalent equations are A, B and E.
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Your question is incomplete. Probably the correct question is as follows.
Select ALL the equations that are equivalent to the equation 3x - 4 = 5.
A) 3x = 9
B) 3x - 4 + 4 = 5 + 4
C) x - 4 = 2
D) x = 9
E) -4 = 5 - 3x
In the diagram, ABC = DEF.
6. Find the value of x.
7. Find the value of y.
64.3
A
65°
B
75°
96.6
90.6
40°
C
D(2y-5)°
E 2x + y
The triangles ∆ABC and ∆DEF are similar triangles, and ∆ABC ≅ ∆DEF. The values of x and y are 30.6 and 30° respectively.
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
We have that line AC of the triangle ∆ABC corresponds to line BK of the triangle ∆DEF and also angle A of the triangle ∆ABC corresponds to angle D of the triangle ∆DEF.
We can evaluate for the values of x and y as follows:
2y - 5 = 65
2y = 65 - 5 {subtract 5 from both sides}
2y = 60
y = 60/2 {divide through by 2}
y = 30
2x + y = 90.6
2x + 30 = 90.6
2x = 90.6 - 30 {subtract 30 from both sides}
2x = 60.6
x = 60.6/2 {divide through by 2}
x = 30.3
In conclusion, the triangles ∆ABC and ∆DEF are similar triangles, and ∆ABC ≅ ∆BMK. The values of x and y are 30.6 and 30° respectively.
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half as big as last night’s crowd ( c = size of last night’s crowd )
verbal expression to algebraic expression
Answer: (1/2)c
To write an algebraic expression, convert parts of the verbal expression.
What is an expression?An expression is numbers or variables with operations performed between them. It does not have an equal sign.
OperationsOperations are ways we change numbers, usually to make them bigger or smaller. Examples of operations are multiplication, division, subtraction, addition, and square root.
Write an expressionThe question says: "half as big as last night’s crowd"
last night's crowd = c
'half as big' = 1/2
This is a proper fraction with the top number smaller than the bottom number. When we multiply 'c' with a proper fraction, the answer would get smaller.Therefore, we can represent the problem using the expression [tex]\frac{1}{2}c[/tex].
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A group of 10 Science Club students is on a field trip. That number of students represents
20% of the total number of students in the Science Club. What is the total number
of students in the Science Club?
A
B
D
20
30
50
80
The total number of students in the science club will be 50. The correct option is C.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
If 10 students represent 20% of the total number of students in the Science Club, then 10 / 0.2 = 50 students is the total number.
Therefore, The total number of students in the science club will be 50. Then the correct option is C
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aiden earns 16.00 per hour if he gets a 4% raise, what will be his new hourly wage
Aiden's new hourly wage would be 16.64 per hour.
Solution:
We have been given that Aiden's hourly wage is 16.00 per hour
So, If he gets a 4% raise then his hourly wage will be,
16* (100+ 4) / 100 = 16.64
Therefore, Aiden's new hourly wage will be 16.64 per hour.
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. Use a graph to find x and y values that make both y = x+3 and y = 2x +5 true.
The point (-2, 1) satisfies both equations y = x + 3 and y = 2x + 5 simultaneously.
What is graph of equation?
Write the equation in the form y = mx + b to determine the slope m and y-intercept (0, b). 2) Next, determine the y-intercept. 3) Depending on whether the slope is positive or negative, go up or down and left or right from the y-intercept.
We are looking for the values of x and y that satisfy both equations simultaneously. We can do this by setting the right-hand sides of the two equations equal to each other:
y = x + 3 (equation 1)
y = 2x + 5 (equation 2)
Setting the right-hand sides equal to each other, we get:
x + 3 = 2x + 5
Simplifying this equation, we get:
x = -2
Now that we have the value of x, we can substitute it into either of the two equations to find the corresponding value of y. Let's use equation 1:
y = x + 3
y = -2 + 3
y = 1
So, the values of x and y that make both equations true are:
x = -2
y = 1
Therefore, the point (-2, 1) satisfies both equations y = x + 3 and y = 2x + 5 simultaneously.
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A trip to Washington from Boston will take you 5 3/4 hours. If you have traveled 1/3 of the way how much longer will the trip take
The remaining time of the trip is 3 5/6 hours.
If a trip from Boston to Washington takes 5 3/4 hours and you have traveled 1/3 of the way, the remaining time of the trip can be calculated by subtracting the time traveled from the total time of the trip.
First, we need to convert 5 3/4 hours to a fraction:
5 3/4 = (5 * 4 + 3)/4 = 23/4
Next, we need to calculate the time traveled so far:
23/4 * 1/3 = 23/12
Now we can subtract the time traveled from the total time of the trip:
23/4 - 23/12 = (23 * 3 - 23 * 1)/12 = 46/12 = 3 10/12 = 3 5/6
Therefore, the remaining time of the trip is 3 5/6 hours.
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HELP!!!!!! IM SICK AND IM TRYING TO TEACH MYSELF MATH!!!!!!!!!!!
Fill in each blank with the correct number or variable.
7 (x + 2) = 7 x ___ + 7 x ___
Answer: x,2
Step-by-step explanation:
Answer:
7 x x + 7 x 2
Step-by-step explanation:
7(x + 2)
7x + 7(2)
7x + 14
Seven people are going to share an 84-ounce bottle of soda. How many ounces will each person get to drink? Choose the correct equation and answer for this situation.
7 ÷ 84 =
= 12 ounces
84 ÷ 7 =
= 12 ounces
7 ÷ 84 =
ounces
84 ÷ 7 =
ounces 50 points if answered
Answer:
Each person will receive 12 ounces
Step-by-step explanation:
84 ounces divided by 7 people
84 / 7 = 12
How is matrix multiplication done in MATLAB?
The " * " operator is used in MATLAB to do matrix multiplication. In MATLAB, the matrix multiplication process is based on linear algebraic principles.
So the " * " operator is used in MATLAB to do matrix multiplication. In MATLAB, the matrix multiplication process is based on linear algebraic principles. In MATLAB, the standard syntax for multiplying matrices is:
When the dimensions of A and B satisfy the matrix multiplication rule, the css copy code C = A * B can be used. Particularly, the number of rows in matrix B and the number of columns in matrix A must match.
The resulting matrix C will be the same size in terms of both rows and columns as matrix A and matrix B. Here is an illustration of how matrix multiplication functions in MATLAB:
A = [1 2; 3 4];% Define matrix A B = [5 6; 7 8];% specify matrix.
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Find an expression that represents the difference when (-4x+4) is subtracted from (-9x-7) in simplest terms.
The required simplified expression result of (-4x+4) is subtracted from (-9x-7) is -5x -11.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The expression (-9x-7) - (-4x+4) can be simplified as follows:
First, we'll combine the like terms:
-9x - 7 - (-4x + 4)
Next, we'll use the distributive property to simplify the right side:
-9x - 7 - (-4x) + 4
Combining like terms on the right side:
-9x - 7 + 4x - 4
Combining the remaining terms:
-5x -11
Thus, the requried simplified expression is given as -5x-11.
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3. CONSTRUCTION
The diagram shows an
example of the Pratt truss used in bridge
construction.
Find m/1.
The angle ∠1 is 55 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that diagram shows an example of the Pratt truss used in bridge
construction.
We need to find the angle ∠1.
The given triangle is a right angle triangle which has one angle 90 degrees.
The adjacent angle to 145 degrees be angle 2.
145+∠2=180
∠2=180-145
∠2=35 degrees.
We know that the sum of three angles is 180 degrees
So ∠1+35+90=180
∠1+125=180
Subtract 125 from both sides
∠1=180-125
∠1=55
Hence, the measure ∠1 is 55 degrees.
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Sanjay stacks three boxes in a pile. The heights of the boxes are 25cm 36cm and 47cm. They are all measured correct to the nearest centimetre. What is the greatest possible height of the stack of the three boxes?
Micaela bought a concert ticket online for $76. She used a coupon code to get a 20%
discount. The website also applied a 5% processing fee to the price after the discount.
How much did Micaela pay, in the end? Round to the nearest cent.
Micaela paid the amount of $63.8 in the end for a concert ticket.
How to calculate the percentage discount?Subtract the final price from the original price then Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages.
Reformulate the basic equation to:
% discount = 100 × (original price - discounted price) / original price
To calculate the final price that Micaela paid, we need to apply the discount and the processing fee to the original price of the ticket.
The discount is 20% of the original price of $76, which is:
discount = 0.2 x $76 = $15.20
So Micaela paid:
price after discount = $76 - $15.20 = $60.80
Now we need to apply the processing fee. The processing fee is 5% of the price after the discount, which is:
processing fee = 0.05 x $60.80 = $3.04
So the final price that Micaela paid is:
final price = $60.80 + $3.04 = $63.84
Therefore, she paid $63.8 in the end, rounded to the nearest cent.
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Ayana is
1
1
2
1
2
1
1, start fraction, 1, divided by, 2, end fraction meters tall. Her little sister Chike is
1
1
4
1
4
1
1, start fraction, 1, divided by, 4, end fraction meters tall.
Ayana is 6/5 times as tall as Chike.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Height of Ayana = 1 1/2 meter
And, Height of Chike = 1 1/4 meter
Now, We can simply solve the above problem as follows;
Height of Ayana = 1(1/2) meters
We can also write it as;
= 3/2 meters
And, Height of Chike = 5/4 meters
Hence, To compare the given fractions we will first make the denominator equal by taking the LCM.
LCM of 2 and 4 = 8
Hence, Heights of Ayana can be rewritten as, 12/8 meters
And, Height of Chike can be rewritten as, 10/8
Now, Comparing the height of Ayana and Chike as;
= (12/8) ÷ (10/8)
= 12/10
= 6/5
Hence, Ayana is 6/5 times as tall as Chike.
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Complete question is this,
Ayana is 1(1/2) meters tall. Chike is 1(1/4) meters tall. Complete the comparison.
Ayana is ____ times as tall as chike.
HELP ASAP !!!!!!!PLEASE
The functions y = 2 (1/5)^(x) - 5 and y = 2^x are compared as follows
y = 2 (1/5)^x - 5 y = 2^x
Starting value: 2 1
base function: decay function = 1/5 growth function = 2
Transformation: translation: 5 units down no transformation
What is decay function?A decay function is a mathematical function that models the decrease or diminution of a value over time and is used in many disciplines including physics, engineering, economics, and machine learning.
It is a sort of function that, as time goes on, approaches zero at a pace proportionate to its current value.
The base function for decay functions is an exponential function, is
0 < k < 1
The growth function, which has values greater than 1, is the reverse of the decay function.
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Please help!!!
I will give brainly if it gives me the opportunity
The expression that will help to find the area of the given shaded region is 3x²+27x+51.
What is area?Area is a measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units, such as square inches, square feet, or square meters. The area of a shape can be calculated by multiplying its length by its width, or by using a specific formula for that shape. For example, the area of a rectangle is found by multiplying its length and width, while the area of a circle is found by multiplying the square of its radius by pi (3.14). Area is an important concept in mathematics, and it is used in many real-world applications such as calculating the amount of paint needed to cover a wall, or the amount of land needed to build a house.
Here,
area of rectangle=(x+10)(2x+5)
area of square=(x+1)²
area of shaded region=area of rectangle-area of square
=(x+10)(2x+5)-(x+1)²
=2x²+20x+5x+50+x²+2x+1
=3x²+27x+51
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Linda drove 567 miles in 9 hours.
At the same rate, how long would it take her to drive 693 miles?
The time taken by Linda to cover 693 miles is 11 hours.
What is rate of change?Rate of change is the speed at which the variables changes with respect to time.
In 9 hours Linda drove 567 miles.
Miles travelled in 1 hour is,
[tex]speed=\frac{distance covered}{timetaken}[/tex]------(1)
=[tex]\frac{567}{9}[/tex]
= 63 miles per hour.
Linda drove 63 miles per hour.
She is travel in the same rate from the beginning.
Let t be the time taken by her to travel 693 miles is,
By using (1),
[tex]speed=\frac{distance covered}{timetaken}[/tex]
[tex]t=\frac{693}{63}[/tex]
⇒t=11 hours.
Hence, the time taken by Linda to cover 693 miles is 11 hours.
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What is 168 cm to ft inch ?
From the information given, 168 cm is approximately equal to 5 feet and 6.14 inches (rounded to two decimal places).
To convert centimeters to feet and inches, you can use the following conversion factors:
1 inch = 2.54 cm
1 foot = 12 inches
First, convert the length in centimeters to inches by dividing by 2.54:
168 cm ÷ 2.54 cm/inch = 66.14 inches
Next, convert the total number of inches to feet and inches. To do this, divide the total number of inches by 12 to get the number of whole feet, and then use the remainder as the number of inches.
66.14 inches ÷ 12 inches/foot = 5 feet with a remainder of 6.14 inches
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Edward deposited $7000 into a savings account 3 years ago. The simple interest rate is 2%. How much money did earn in interest?
The amount of money that he earned in interest is given as follows:
$420.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.
r is the interest rate, as a decimal.
The interest accrued is given as follows:
I(t) = Prt.
The parameters for this problem are given as follows:
P = 7000, r = 0.02, t = 3.
Hence the total interest is of:
I(3) = 7000 x 0.02 x 3
I(3) = $420.
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Find a particular solution y, of the following equation using the Method of Undetermined Coefficients. Primes denote the derivatives with respect to x. y'' + 17y=3e^8xA particular solution is y,(x) =
The general solution for the non-homogeneous equation is the sum of the homogeneous solution and the particular solution::
y(x) = c1 * cos(√-17i * x) + c2 * sin(√-17i * x) + (3/64) * e^8x
where c1 and c2 are arbitrary constants.
The method of undetermined coefficients is used to find a particular solution for a non-homogeneous linear ordinary differential equation of the form:
dy/dx + p(x)y = g(x)
where p(x) and g(x) are known functions. To use this method, we first find the general solution of the corresponding homogeneous equation:
dy/dx + p(x)y = 0
The general solution of this homogeneous equation can be written as:
y = c1 * y1(x) + c2 * y2(x)
where c1 and c2 are arbitrary constants and y1(x) and y2(x) are the linearly independent solutions of the homogeneous equation.
Next, we guess a particular solution yp of the non-homogeneous equation of the form:
yp = A * f(x)
where A is an unknown constant and f(x) is a function of x that matches the form of the forcing function g(x).
For the given equation: y'' + 17y = 3e^8x
The corresponding homogeneous equation is: y'' + 17y = 0
The characteristic equation is: r^2 + 17 = 0
The roots are: r = ±√-17i
So the general solution of the homogeneous equation is:
y = c1 * cos(√-17i * x) + c2 * sin(√-17i * x)
where c1 and c2 are arbitrary constants.
For the non-homogeneous equation, we guess a particular solution of the form:
yp = A * e^8x
where A is an unknown constant. Substituting this into the non-homogeneous equation, we have:
yp'' + 17yp = A * 8^2 * e^8x = A * 64e^8x
Comparing the right-hand sides of the two equations, we see that yp'' + 17yp = A * 64e^8x = 3e^8x, so A = 3/64.
Therefore, a particular solution for the non-homogeneous equation is:
y = yp = (3/64) * e^8x
The general solution for the non-homogeneous equation is the sum of the homogeneous solution and the particular solution:
y = c1 * cos(√-17i * x) + c2 * sin(√-17i * x) + (3/64) * e^8x
where c1 and c2 are arbitrary constants.
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Meg paints the whole outside of a 5 x 5 x 5 cube red and then cuts it up into 1 x 1 x 1 cubes.How many cubes have just one red face?
The number of cubes that have just one red face is 25.
What is a cube?A solid three-dimensional shape called a cube contains six square faces, eight vertices, and twelve edges.
Given:
Meg paints the whole outside of a 5 x 5 x 5 cube red and then cuts it up into 1 x 1 x 1 cube.
The surface area of the cube with dimensions 5 x 5 x 5,
= 6 x 5 x 5
= 150 square units.
The surface area of the cube with dimensions 1 x 1 x 1,
= 6 square units.
The number of cubes that have just one red face is,
= 150/6 = 25
Therefore, 25 is the required number.
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-3.5 (2 – 1.5n) – 4.5n
a. -7 – 6n
b. -7 + 0.75n
c. -7 – 9.75n
d. -7 – 9.5n
Answer:B
Step-by-step explanation:
-7+5.25n-4.5n=-7+0.75n
how do i solve -(-8q-8.7)
On solving the expression, we get -> (8q + 8.7).
What are algebraic expressions in mathematics?In mathematics, an expression or mathematical expression is a combination of terms, both constants and variables. For example -
2x + 4y + z
Given is the algebraic expression as -
- (- 8q - 8.7)
The given expression is -
- (- 8q - 8.7)
- (- 8q) - (- 8.7)
8q + 8.7
Therefore, on solving the expression {- (- 8q - 8.7)}, we get -> (8q + 8.7).
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Please work the problem
Answer:
6x-7=3x-29
6x-3x=-29+7
3x=-23
x=-23/3
6x-7=8y+17
6(-23/3)-7=8y+17
-46-7=8y+17
8y+17+53=0
y=70/8
Y=8.75
ANS!!
Multiply. Show all work. 0.12 x 0.4
Answer:
To multiply 0.12 x 0.4, first you need to write the numbers in standard form. 0.12 can be written as 0.120 and 0.4 can be written as 0.400.
Then, multiply the numbers by first multiplying the digits in the ones column, then the digits in the tenths column and finally the digits in the hundredths column.
This is done by multiplying the first digit in the first number (1) with the first digit in the second number (4), then multiplying the second digit (2) with the second digit (0), and finally multiplying the third digit (0) with the third digit (0).
Therefore, the multiplication can be written as:
1 x 4 = 4 2 x 0 = 0 0 x 0 = 0
Adding these three numbers together gives us 0.048, which is the answer to 0.12 x 0.4.
The price p of a sweater was discounted by 10%
The price of the sweater after the discount is 0.72P.
What is Discount?A reduction made from the gross (see gross entry 1 sense 3b) amount or value of something.
Since the price P would represent 100% and the price was discounted by 10%, you can calculate 10% of 100% and subtract that amount, which would be:
100× 10%=10
100-10=90%
The price paid would be 90% of P.
Then, the statement says that the price was discounted by another 20%. Now let us calculate 20% of the price and subtract that amount from the price:
90×20%=18
90-18=72%
Hence, the price of the sweater after the discount is 0.72P.
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The total number of signatures on a petition
doubles each week. In the sixth week, there
are 192 signatures on the petition. How many
signatures were on the petition in the first week?
(PLEASE give me an answer that is different from 192/2 96/2 etc..)
The number of signature on the petition in the first week is 6
What is doubling?A double is a number or an amount that is twice as large as the given number or amount. So, if we multiply a number by 2 or if we add a number to itself, we say that the number is doubled.
Since the signature doubles every week
represent the initial signature by x
p(o) = x
second week =2 x
third week =4 x
fourth week = 8x
fifth week =16 x
sixth week = 32x
32x = 192
x = 192/32
x = 6
therefore the number of signature on the petition in the first week is 6
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