The derivative of the given polynomial equation is 16x³ - 6x + 6.
We are given an equation. The equation represents a polynomial in one variable. The degree of the polynomial is four; hence, it is called biquadratic. We need to find the derivative of the given polynomial. The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
The equation is given below.
y = 4x^4 - 3x² + 6x + 14
dy/dx = (d/dx)(4x^4 - 3x² + 6x + 14)
dy/dx = (d/dx)(4x^4) - (d/dx)(3x²) + (d/dx)(6x) + (d/dx)(14)
dy/dx = [4*4x^(4 - 1)] - [3*2x^(2 - 1)] + [6*1x^(1 - 0)] + [14*0x^(0 - 1)]
dy/dx = 16x³ - 6x + 6
Hence, the derivative of the given polynomial equation is 16x³ - 6x + 6.
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Nigel is selling candy bars for his outdoor club. He is averaging 4 bars every 3 days. If he continues at this rate, how many days will it take to sell his box of 35? Answer in whole number form and round up to the next whole number.
The number of days that it will take to sell his box of 35 is 21 days.
What is a ratio?Ratio simply demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, Nigel is selling candy bars for his outdoor club and he is averaging 4 bars every 3 days.
Let the number of days be x.
This will be:
3/x = 4/35
Cross multiply
4x = 3 × 35
x = (3 × 35)/4
x = 105 / 4
x = 21
It will take 21 days
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two trains leave a station at the same time and travel in opposite directions. one train travels 20 kph faster than the other train. after 3 hours, they are 810 miles apart. what is the speed of each train?
The speed of each train is 125kph and 145kph.
Here it is given that the distance between the two trains is 810 miles after traveling for 3 hours.
The difference in their speed is 20 kph.
Let x be the speed of one train. So by this, we get the speed of the second train that is x + 20.
Formula to calculate speed is:
Speed = Distance / Time
Distance = Speed × Time
Distance covered by first train = x × 3
Distance covered by second train = (x + 20) × 3
Total distance = 810
So we get;
3x + (x + 20)3 = 810
3x + 3x + 60 = 810
6x = 750
x = 125
x + 20 = 125 + 20 = 145
Therefore we get the speed of both trains which is 125kpp and 145 kph.
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The proportional relationship between the cost and weight is given as y = 0.89x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The absolute expense for clothing administration, in dollars, relies upon the heaviness of the clothing, in pounds. This relationship is corresponding, as it costs $22.25 for 25 pounds of clothing and $36.49 for 41 pounds of clothing.
The equations are given below.
22.25 = 25m + c ...1
36.49 = 41m + c ...2
From equations 1 and 2, then we have
41m - 25m = 36.49 - 22.25
16m = 14.24
m = 0.89
Then the value of c will be given as,
22.25 = 25 (0.89) + c
c = 0
The proportional relationship between the cost and weight is given as y = 0.89x.
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The polynomial f(x) = 2x ^ 3 + a * x ^ 2 + bx + 6 is exactly divisible by 2x - 3 and has the remainder -28 when divided by (x + 3) a) find the values of a and b. b) solve the equation f(x) = 0
The polynomial f(x) = 2x³ + ax² + bx + 6 is exactly divisible by 2x - 3. The values of a and b are a = 131/27 and b = -71/9
To solve the problem, use the polynomial remainder theorem. If a polynomial f(x) is divided by a linear function with zero x = a, then the remainder r = f(a).
The given polynomial is:
f(x) = 2x³ + ax² + bx + 6
- The polynomial is exactly divisible by (2x-3) means:
f(3/2) = 0
2. (3/2)³ + a(3/2)² + b(3/2) + 6 = 0
27 + 9a + 6b + 24 = 0
9a + 6b = - 51 (equation 1)
- f(x) divided by (x+3) has remainder -28
f(-3) = -28
2. (-3)³ + a(-3)² + b(-3) + 6 = -28
9a - 3b = 20 (equation 2)
Substract equation 2 from equation 1
9a + 6b = -51
9a - 3b = 20 _
9b = -71
b = -71/9
9a - 3(-71/9) = 20
9a = 131/3
a = 131/27
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In a company, 85% of the workers are women. If 675 people work for the company who aren't women, how many workers are there in all?
Answer:
so there are 3825 worker in total
Step-by-step explanation:
675=15%
women=85%
how much workers are 5%=675/3 =225
225=5%
how many workers is 85%= 85/5=17
85%=225x17=3825
Use the rules of measurement to divide
Answer:
[tex] \frac{ {m}^3{} }{25} [/tex]
Step-by-step explanation:
that is the answer
/what is y-5x=3 solve for Y
Answer:
y=3+5x
Step-by-step explanation:
Add 5x to both sides.
Ester sarai and kurry chose a number esters number is 1/10 of saris kurrys number is 10 times as much as sarais sarais number is 0.09. what number did each person choose?
Ester, Sarai, and Kurry each selected a number: 0.009, 0.09, and 0.9, respectively.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes. For instance, 3+3+3+3+3 can be expressed as 3 5.
the ester's number is equal to one-tenth of the Sarai number.
= 1 / 10 × 0.09 = 0.009
to determine Kurry's number, multiply Sarai's number by 10
= 10 × 0.09 = 0.9
Therefore, it can be inferred that Kurry chose 0.9, Ester chose 0.009, and Sarai chose 0.09.
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Find m∠1 and m∠2. Tell which theorem can be used.
According to the vertical angles theorem, m∠1 = 117°.
Based on the corresponding angles theorem, m∠2 = 117°.
What is the Vertical Angles Theorem?The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.
What is the Corresponding Angles Theorem?When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.
Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.
Therefore:
m∠1 = 117° [vertical angles theorem]
Angles 1 and 2 are corresponding angles. Therefore:
m∠2 = m∠1
Substitute
m∠2 = 117° [corresponding angles theorem]
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Zachary is applying biomechanics to develop a specialized bat for a professional player. What does he compar
the hitter to?
Oa machine
O a computerized model
O another professional player
O a 3-D diagram
Answer:
Another Professional Player
Peni needs $1.20 daily for bus
fares, 50 cents daily to spend at the school canteen and $1.00 per day for newspaper.
Answer:
Peni will need a total of $17.90
Step-by-step explanation:
$1.20 x 7 = $8.40
$0.50 x 5 = $2.50
$1.00 x 7 = $7.00
$8.40 + $2.50 + $7.00 = $17.90
1. which of these variables are discrete and which are continuous random variables? (a) the number of new accounts established by a salesperson in a year. (b) the time between customer arrivals at a bank atm. (c) the number of customers at big nick's barber shop. (d) the amount of fuel in your car's gas tank. (e) the number of minorities on a jury. (f) the outside temperature today.
The discrete and continuous random variables are-
a) Discrete; (b) Continuous; (c) Discrete; (d) Continuous; (e) Discrete; (f) Continuous
Define the term discrete and continuous random variables?Discrete variables are those whose values may be measured through counting. Contrarily, random variables which it reflect something are designated continuous variables.(a) So because number of new accounts is counted, (a) discrete (like, non-negative integers).
(b) Continuous, given that the interval between customer arrivals may have decimal values (like 2.9 minutes or 27.75 seconds).
(c) Because the quantity of clients is counted, (c) discrete (like, non-negative integers).
(d) Continuous, as the fuel consumption can have decimal values (like 15.5 gallons).
(e) Since this number of minorities is counted, (e) discrete (like, non-negative integers).
(f) Continuous since the outdoor temperature can be expressed in decimal degrees (e.g., 7.78 C).
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During the problem disaggregation process, the logic trees should have branches that are?.
During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.
Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.
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The sum of two numbers is 12. The difference of the same two numbers is -4. Wht is the smaller number?
Answer:
The smaller number is 4.
Step-by-step explanation:
X and Y are the two numbers
x+y=12
x-y=-4
Subtract these two equations
(x+y=12)
-(x-y=-4)
—————-
2y=16
y=8
Plug it in to any equation:
x+y=12
x+8=12
x=4
The functions f(x)=−34x+2 and g(x)=(14)x+1 are shown in the graph. What are the solutions to −34x+2=(14)x+1? Select each correct answer. Responses −1 negative 1 0 0 1 1 2 2 3
A solution to −34x+2=(14)x+1 is x = 1/48
In this question, we have been given functions f(x) = -34x + 2 and g(x) =(14)x + 1
We need to find the solutions to −34x + 2 = (14)x + 1
i.e., we need to find the solution to f(x) = g(x)
Consider, f(x) = g(x)
-34x + 2 = (14)x + 1
-34x + 2 - 14x = 14x + 1 - 14x
-48x + 2 = 1
-48x = -1
x = 1/48
Therefore, a solution to −34x+2=(14)x+1 is x = 1/48
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A triangle has an angle that measure 36.6° and a second angle that measures 59.3°. What is the
measure of the third angle?
2 pts
Answer: 82 is the answer
Step-by-step explanation: I just did this question and worked it out and it said it was right
Which statement is true?
This table does not show a probability distribution.
This table shows a probability distribution.
After using the probability distribution table, the given table does not show a probability distribution. The statement 1 is correct.
In the given question, we have to check which statement is correct regarding to the given option.
The given statements are:
(1) This table does not show a probability distribution.
(2) This table shows a probability distribution.
Before checking the statement we learn about a probability distribution table.
In a probability distribution table every result of a statistical experiment is connected to the likelihood that the result will actually occur. An experiment's result is recorded as a random variable, which is typically written with a capital letter.
As we can see that there is given the probability of having the blue, green, yellow and red color.
So the given table does not show a probability distribution.
So the statement 1 is correct.
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Walt Disney Co paid a $1.42 annual dividend on a day it closed at a price of $96 per share.
What was the annual dividend for 500 shares?
The annual dividend for 500 shares was $710.
How is the annual dividend computed?The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.
Dividends are always declared per share with a stated dollar amount or percentage.
Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.
Dividends are a kind of financial reward to stockholders for their investment in the entity.
The dividend per share = $1.42
Market price per share = $96
The number of shares held = 500
The dividend received for the year = $710 ($1.42 x 500)
Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.
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what is the definition of pi
and multiply it to a decimal number
(any equation)[tex]\pi[/tex]
Pi written as 3.l4 and π in mathematics is the ratio for the diameter of a circle to the circumference of that circle. The value is unending
What is Pi?Pi, which is represented by the Greek letter p, or, is a shorthand for the ratio of a circle's diameter to its circumference. No matter how big the circle is, this ratio will always be equal to pi. The value of pi is about 3.14 in decimal notation.
We are to multiply Pi to any equation
let the equation be (20.5 + 3x)[tex]\pi[/tex]
pi is represented in numbers by 3.14
Hence we would have the equation to be of the form
(20.5 + 3x)3.14
multiply through the bracket
64.37 + 9.42x
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Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer: 0.86 pounds of fruit
Step-by-step explanation:
8.3-7.44=0.86
The bids in an online auction are represented by the arithmetic sequence shown below. Write an explicit formula to represent the bids as an arithmetic sequence. What is the twelfth bid?
195, 205, 215, 225,...
A(n) =
A(12) =
(Type an expression using n for the variable.)
(Simplify your answer.)
(a) The nth term of the sequence is given by A(n)=195 + (n - 1)10.
(b) The 12th term of the sequence is A(12) = 305.
What is an arithmetic sequence?One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...
The term "finite arithmetic progression" or "arithmetic progression" refers to a limited segment of an arithmetic progression.
A mathematical sequence has the following structure: a, a+d, a+2d, a+3d, etc., up to n terms. The initial term is a, the shared distinction is d, and n is the total number of words. Find the AP, the first term, the number of terms, and the common difference for the computation using the arithmetic sequence formulae. To determine the nth term, sum, or common difference of a given arithmetic sequence, many formulae related to arithmetic series are utilized.
A(n)=195+(n-1)10
The given arithmetic sequence is 195, 205, 215, 225,.....
The first term a =195
The common difference d= 205-195
d =215-205
d =225-215
So, d = 10
(a) The nth term is given by
A(n)=a+(n-1)d
A(n)=195+(n-1)10
(b) For n=12, the 12th term is given by
A(12)=195+11(10)
A(12)=305
Therefore, A(n)=195+(n-1)10
And A(12)=305
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Corinne and Deanna decide to race from one corner of an open field to the other. The field is rectangular in shape, 60 meters long and 80 meters wide. Since Corinne is older and faster, she's going to run along the outside of the field, and Deanna will take the diagonal route. If Deanna can run at a rate of 5 meters per second, how fast will Corinne have to run to get there at the same time as Deanna?
Answer:
Corinna will have to run at 7 meters per second to get there at the same time as Deanna.
Step-by-step explanation:
So to find the distance of Deanna's route, you can use the Pythagorean theorem.
a^2 + b^2 = c^2
60^2 + 80^2 = 10000
c^2 = 10000
Take the square root of both sides.
c = 100
So Deanna runs 100 meters at 5 meters per second.
100/5 = 20
She runs for 20 seconds.
To find Corinne's distance, we add 60 and 80, which is 140.
To find how fast she need to run to get there in 20 seconds, you divide 140 by 20, which gets 7 (meters per second). You can also think of it like this: to run 140 meters in 20 seconds, she has to run at 140 meters per 20 seconds, which you can simplify (like a fraction) to 7/1, or just 7
y = 1,000x is that a constant proportionality
Trapezoid G is a scaled copy of trapezoid F.
Answer:
yes it is???
Step-by-step explanation:
2 Dora has solved the equation 4(x - 1) = 11
4(x - 1) = 11
4x41 = 11
4x = 52
x = 13
Dora is incorrect. Explain her mistake.
Dora put the x es
and did 4x11
11 and
Find the correct solution to 4(x − 1) = 11
I mark
Dora solved the equation.
She multiplies 4 inside the bracket. But she fails to know that 4× -1 = -4. Instead she multiplied that 4×-1 = -41. This is her first mistake.
In the second step, she shifted -41 to the right side in order to find the value of x. As -41 gets shifted to right side , -41 becomes +41 and added with +11 to get 52. which is totally a wrong method.
Step-by-step explanation:
Here is the exact method of solvation.
[tex]{ \blue{ \bold{4(x - 1) = 11}}}[/tex]
[tex]{ \blue{ \bold{4x - 4 = 11}}}[/tex]
[tex]{ \blue{ \bold{4x = 11 + 4}}}[/tex]
[tex]{ \blue{ \bold{4x = 15}}}[/tex]
[tex]{ \blue{ \boxed{ \red{ \sf{x = \frac{15}{4}}}}}} [/tex]
You're putting 81 feet of molding
along the walls around a rectangular
room that's 12 feet wide; what is the
area of that room (if you subtracted
3 feet for the width of the door)?
Answer:
360 sq feet
Step-by-step explanation:
The width of the room is given in the question, 12 feet.
We don't know the length. Let's call the length x.
x = length
We were also given the perimeter, 81, that's the distance around the sides...
all the sides added up.
Use x for the long wall.
Use x-3 for the wall with the door in it.
x + 12 + x-3 + 12 = 81
combine like terms
2x + 21 = 81
subtract 21
2x = 60
divide by 2
x = 30
The room is 30 feet long by 12 feet wide.
Area =
length × width
= 30 × 12
= 360
The area of the room is 360sq feet.
Please help now asap !!! Due tomorrow
Answer:
Step-by-step explanation:
it help by showinbng thta
Latisha wants to buy pumpkins and autumn squash for a fall display. She has a budget of $117 but wants to buy more than 10 vegetables. The pumpkins are $5. 59 each. The squash are $3. 50 each. List THREE possible combinations of pumpkins and squash that latisha can purchase to represent the situation
(x,y) = (8,20), (6,24), and (10,17).are three alternative combinations of pumpkins and squash that Latisha may buy to depict the circumstance.
Latisha's total wealth is $17.
More than 10 veggies are the number of vegetables that Latisha wants to purchase.
A pumpkin costs $5.50.
An autumn squash costs $3.50.
Let n pumpkins purchased equal x.
Purchased number of autumn squash = y
There are three alternative squash and pumpkin combination that Latisha might buy to symbolize the circumstance.
With x acting as the independent variable, we may identify many y's.
x ( Pumpkin) y(Autumn squash) (integral value)
8 20
6 24
10 17
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the profit y (in dollars) for a business from selling x games is represented by y=33x graph the equation
THIS IS URGENT!!! SOMEONE PLEASE RESPOND!!!!
ty!
Answer: check the image attached
Step-by-step explanation:
Hope this helps
Answer:
Just point the graph on Y=33x+0
Step-by-step explanation:
There's no B or starting point, so you would just plant the point on 0,33
Write an equation of a line that passes through (-1,2) and is parallel to a line with x-intercept (3,0) and y-intercept (0,1).
The Equation of line is y= -1/3x + 5/3
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
x-intercept = (3,0) and y-intercept = (0,1).
slope, m= 0-1/ 3-0= -1/3
so, The slope-intercept form of the equation of a line is
y= mx + b
y= -1/3x +b
Now, the passes through (-1, 2) we get
2= -1/3(-1) + b
2- 1/3= b
b= 5/3
So, the Equation of line is y= -1/3x + 5/3
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