Answers
Answer:
dy = -3
dx
equation of normal=
y=1/3x+1
Step-by-step explanation:
dy/dx=10x-3
=10(0)-3
= -3
equation of normal:
grad=1/3
y-1 =1/3
x-0
3y-3=x
y= 1/3x+1
[tex]\underline{\textbf{First part:}} \\\\\text{Given that,}\\\\~~~~~~y= 5x^2-3x+6\\\\\\\implies \dfrac{dy}{dx} = \dfrac{dy}{dx} (5x^2 -3x +6)\\ \\\\~~~~~~~~~~~=5\dfrac{d}{dx} x^2-3\dfrac{d}{dx} x + \dfrac{d}{dx} (6)\\\\\\~~~~~~~~~~~=5\cdot 2x-3+0\\\\\\~~~~~~~~~~~=10x-3\\\\\text{At (0,1)}\\\\\dfrac{dy}{dx} = 10(0) -3 \\\\~~~~~=0-3\\\\~~~~~=-3[/tex]
[tex]\underline{\textbf{Second part:}}\\\\[/tex]
[tex]\text{Equation of normal,}\\\\~~~~~~y-y_1 = -\dfrac{1}{\tfrac{dy}{dx}} (x-x_1)\\\\\\\implies y - 1 = -\dfrac 1{-3 }(x-0)\\\\\\\implies y-1 = \dfrac 13 x\\\\\\\implies y= \dfrac 13 x +1[/tex]
Related Questions
If for a particular one-to-one function f(2) = 13, what are the corresponding input and output
values for the inverse function?
Answers
Answer:
[tex]f^{-1}(13) = 2[/tex].
Step-by-step explanation:
For function [tex]f[/tex], the notation [tex]f(2) = 13[/tex] means that when the input to the function is [tex]2[/tex], the output would be [tex]13[/tex].
The inverse function of a one-to-one function [tex]f[/tex] is commonly denoted as [tex]\!f^{-1}[/tex].
The inverse function undoes the action of the original function. In this question, [tex]f[/tex] maps [tex]2[/tex] to [tex]13[/tex]. Thus, [tex]f^{-1}[/tex] would need to map [tex]13\![/tex] back to [tex]2\![/tex]. Therefore, [tex]f^{-1}(13) = 2[/tex] should be the corresponding input and output values.
Anyone know what -8x-y=5 ; y=x+4 is using yhe subtraction method? Please explain to! would help greatly
Answers
Answer:
The answer would be x = -1 and y = 3
Step-by-step explanation:
Work is as shown:
1) -8x - y = 5
y = x + 4
2) -8x - (x+4) = 5
3) -8x -x = 9
4) -9x/-9 = 9/-9
5) y = -1 + 4 = 3
If there are any questions or if i didn't answer the question reply with the question please.
What is the range of the following numbers: 2, 5, 5, 8, 4, 3
Answers
Answer: range is 6
Step-by-step explanation:
Smallest number is 2
largest number is 8
8-2=6
Find the mean of each distribution.
Correct answers will be mark as BRAINLIEST and get 50 points
Wrong answers will be reported
Answers
Answer:
See below ~
Step-by-step explanation:
a)
Mean = 3(21) + 1(22) + 2(23) + 5(24) + 1(25) / 12Mean = 63 + 22 + 46 + 120 + 25 / 12Mean = 276/12Mean = 23b)
Mean = 4.3 + 4.8 + 5.1 + 5.1 + 5.2 + 5.5 + 5.7 + 6.6 + 6.9 + 7.3 + 7.4 / 11Mean = 63.9/11Mean = 5.81Answer:
a) 23 °C
b) 5.81 m² (2 dp)
Step-by-step explanation:
Part (a)This set of data is presented as a Dot Plot.
The frequency (how often a data value occurs) is represented by the number of dots above each data value.
For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.
To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.
[tex]\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}[/tex]
Part (b)This set of data is presented as a stem and leaf diagram, where the units and tenths are split. The units column is the 'stem' and the tenths become the 'leaf'.
Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8
To find the mean, sum the data values, then divide by the total frequency.
To find the total frequency, simply count the number of values in the leaf part of the diagram.
Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4
Total frequency = 11
[tex]\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}[/tex]
What is the product of the fraction below (3/x+2) (7/2x)
Answers
Answer:21x^2+14x over 2
Step-by-step explanation:
Which function has the greatest x-intercept?
Et
f(x) = 3x - 9
g(x) = (x + 31)
h(x) = 2x – 16
j(x) = -5(x - 2)2
Answers
Answer:
g(x) = (x + 31)
f(x)= 3x-9
3×x-9= -9+3×x
=-6x
g(x)=(x+31)
1×x+31=32+1×x
=32x
h(x)=2x-16
2×x-16= 16+2×x
=18x
j(x)= -5(x-2)2
(-5x+10)2
-10x+20= 10×x+20
=20-10×x
=10x
Consider the solution to the system of inequalities below
-7x+y≥12.5
v+0.3x2 <-1
Which of the following functions could be added to the system without changing the solution set?
y < –2.1
y > –2.1
y = 2.1
y > 2.1
Answers
Answer:
i just want to try this but i think its y<2.1
Step-by-step explanation:
Can someone help me with this
Answers
Answer:
95% = Within two standard deviations from the mean
99.7% = Within three standard deviations from the mean
68% = Within one standard deviation from the mean
Step-by-step explanation:
I hope this helped! If it did, please click "Thanks" to help me out!
Given x varies inversely as y and x = 6 when y = - 4, find y when x = 8 .
Answers
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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Given that x varies inversely with y, x=6 when y=-4, find y when x=8.
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
If x varies inversely with y, we divide.
So the formula looks as follows:-
[tex]\bold{x=\displaystyle\frac{k}{y} }[/tex]
where k = constant of proportionality
Plug in the values:-
[tex]\bold{6=\displaystyle\frac{k}{-4}}[/tex]
Multiply both sides by -4:-
[tex]\bold{-24=k}[/tex]
Now find y when x=8:-
[tex]\bold{8=\displaystyle\frac{-24}{y}}[/tex]
Multiply both sides by y:-
[tex]\bold{8y=-24}[/tex]
Divide by 8 on both sides:-
[tex]\dashrightarrow\bigstar{\boxed{\boxed{\underline{\bold{y=-3}}}}\dashleftarrow[/tex]
Good luck.
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Can someone help me with this question?
Answers
Answer: CD segment
Step-by-step explanation:
Gravity is one of the four fundemental forces in the universe. Electromagnetism is another one. The Other two are the strong force and the weak force that happen at the subotamic level. Find some information on what role these two forces play inside each atom and why one is considered strong and the other weak
Answers
Answer:
gravity is the force that helps u stay on the earth
Factor the polynomial completely. 2x^2-9x+7
Answers
The polynomial is a quadratic function, and the completely factored expression of 2x^2 - 9x + 7 is (2x -7)(x - 1)
How to factor the polynomial?The polynomial expression is given as:
2x^2 - 9x + 7
Expand
2x^2 - 9x + 7 = 2x^2- 2x - 7x + 7
Factorize the above expansion
2x^2 - 9x + 7 = 2x(x - 1) - 7(x - 1)
Factor out x - 1
2x^2 - 9x + 7 = (2x -7)(x - 1)
Hence, the completely factored expression of 2x^2 - 9x + 7 is (2x -7)(x - 1)
Read more about polynomials at:
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(2x)(2x)=(x+10)(2x-3) what is x?
Answers
Answer:
x = 5/2 or x = 6
Step-by-step explanation:
(2x)(2x)=(x+10)(2x-3)
4x^2 = 2x^2 - 3x + 20x - 30
2x^2 - 17x + 30 = 0
(2x - 5)(x - 6) = 0
x = 5/2 or x = 6
Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service. a. What was her monthly income in the fi rst year after retirement?
Answers
Answer:
$1000
Explanation:
If the employee has worked there for 20 years and for every year its 50 dollars. That would mean its 50x20 which eqauls 1000.
The monthly income in the first year after retirement is $1000.
What is monthly income?Average monthly income is the amount you earn each month. Depending on your source of income, you can subtract insurance payments, rent allowances and other costs, such as federal and state taxes, from your total income every month. Net worth is your debt subtracted from your total assets.
Given that, Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service.
After working for 20 years, Janet has decided to retire from her job at a major department store.
The company has offered her a flat monthly retirement benefit of $50 for each year of service, which means that her monthly income in the first year after retirement would be $50 multiplied by 20, which is equal to $1000.
Hence, the monthly income in the first year after retirement is $1000.
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Solve the system using elimination.
Answers
Answer:
This equation has no solution
Step-by-step explanation:
if the same equation equals 2 different numbers then therefore there is no solution.
In which of the following functions would it be appropriate to use only positive integers for the domain? Select all that apply.
The function c(p) represents the cost for (P) people to attend the movies.
The function m(t) represents the miles driven over t hours.
The function t(m) represents the average high temperature for a given number of months.
The function p(w) represents the profit of a farmer who sells (w) whole watermelons.
The function (n) represents the number of person-hours it takes to assemble (n) engines in a factory.
Answers
Answer: The function c(p) represents the cost for (P) people to attend the movies.
The function t(m) represents the average high temperature for a given number of months.
Step-by-step explanation:
Which statements are true about exponential functions? Check all that apply.
Answers
Answer:
The answer is A
Step-by-step explanation:
its a multiple answer choice. so A , D
NEED HELP URGENTLY!!!!!
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 3x - 5 and g(z) = ²5 to
determine iff (z) andg(z) are Inverses of each other.
Answers
The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 3x - 5
Here, g(x) is not given clearly.
But we can identify the given function as an inverse of each other.
Let's suppose the ordered pairs are:
[x, f(x)] and [x, g(x)]
The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
f(0) = -5 so for (0, -5) on the f(x) list then (-5,0) must be on the g(x) list
f(1) = -2 so for (1, -2) on the f(x) list then (-2, 1) must be on the g(x) list
f(2) = 1 so for (2, 1) on the f(x) list then (1, 2) must be on the g(x) list
Let's suppose:
g(x) = (x+5)/3
g(-5) = 0
g(-2) = 1
g(1) = 2
So the ordered pair (-5, 0), (-2, 1), and (1, 2) are in the list of g(x).
Thus, the functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
Learn more about the function here:
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Based on the work provided, write the dividend as a product of two factors
Answers
Answer:
x4+2x3+x2+5x+b=x-2x3+x+3
Step-by-step explanation:
Given the two similar flags shown,find the perimeter of the larger flag
Answers
The sum of the external side of a figure is its perimeter. the perimeter of the larger flag is 48
Similar shapesShapes are known to be similar if the ratioof their similar sides is equal to a constant.
From the given diagram, find the scale factor of the large triangle
k = 12/4
k = 3
Determine the perimeter of the large flag
Perimeter = 3 * perimeter of small flag
Perimeter of large flag = 3 * 16 = 48
Hence the perimeter of the larger flag is 48
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Write down the next two terms in the sequence: 3, 15, 75 , ___, ___
answer pleass
I need it now
☹️
Answers
Answer:
375, 1875,
Step-by-step explanation:
hope this helps :)
cedric's fish tank is 2yd long by 21in wide by 3ft tall. What is the volume of Cedric's take in cubic in?
Answers
Answer:
129 cubic inches
Step-by-step explanation:
lxwxh L=Length W=Width H= Height
Length times width times height gives you the volume
1. convert all numbers to inches
2. Multiply them together(order does not matter)
Find the LCD of the rational expressions in the list
Answers
Answer:
30
Step-by-step explanation:
what number does 7 multiply by that also can be multiplied by 5? 30 is the least common denominator between 7 and 5.
please help me in this question please
Answers
Step-by-step explanation:
here is your answer, this is how you do it
Answer:
[tex]\boxed{\bf G. \: x = {25}^{o}} [/tex]
[tex]\boxed{\bf H. \: x = {20}^{o} }[/tex]
Step-by-step explanation:
In the given figure, the linear pairs are supplementary angles, meaning they should add up to 180°.
G)
[tex]\bf 2x + 34 + x + 71 = 18 {0}^{o} [/tex][tex]\bf 3x + 105 = 18 {0}^{o} [/tex][tex]\bf 3x = 180 - 105[/tex][tex]3x = 75[/tex][tex]\boxed{\bf x = {25}^{o} }[/tex]H)
[tex]\bf 2x + 4x + 3x = {180}^{o} [/tex][tex]\bf 9x = 180[/tex][tex]\boxed{\bf x = {20}^{o} }[/tex]«••••••••••••»«•••••••••••••»
x2 + y2 – 2y – 99 = 0
What is the center of this circle ?
],
What is the radius of this circle ?
units
Answers
Answer:
The center is at (h, k) : (0, -1) and the radius is 10. ... The radius is 10. That is, since r^2 = 100, r must be 10.
Step-by-step explanation:
hope this helps you!
9. Two fair dice are rolled. Find the odds of rolling the following sums.
(a) 2
(b) 6
(c) 9
(d) Between 5 and 8 (exclusive; that is, not including 5 or 8)
(e) Not more than 5
Answers
(b) 3/12=1/4
(c) 2/12 = 1/6
(d) 3/12 + 3/12 = 6/12 = 1/2
I think it’s right ???
2 7.1.2 Exam: Semester 1 Exam
Question 7 of 7
A part-time caregiver made $8944.58 last year. If he claimed himself as an
exemption for $3650 and had a $5700 standard deduction, what was his
taxable income last year?
O A. $5294.88
B. $3244.58
C. $0
O D. $405.42
Answers
Answer:$0
Step-by-step explanation:
What is the sum of 1/2plus 1/4use fractions strip to help
Answers
Answer:
Step-by-step e6/8 or in simple terms, 3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
1/2 is just 2/4
2/4+1/4 = 3/4
=)
Find the area of the composite figure. First, find the area of the triangle.
Please help acellus sucks
Answers
Step-by-step explanation:
Rectangle area= 40×30= 1200cm²
Triangle area= 20×20= 400cm²
Total are of composite figure= 1200+400=1600cm²
The height of a light pole in a magazine is 4 inches. The scale of the picture was given as 1 inch:24 inches. What would be the actual height of the light pole?
Answers
Answer:
96
Step-by-step explanation:
4 times 24 is 96