The absolute value function is defined as
[tex]|x| = \begin{cases}x & \text{for }x \ge 0 \\ -x & \text{for }x < 0\end{cases}[/tex]
If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.
If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.
But if x = 0, the derivative doesn't exist!
In order for the derivative of a function f(x) to exist at x = c, the limit
[tex]\displaystyle \lim_{x\to c}\frac{f(x) - f(c)}{x-c}[/tex]
must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.
If x approaches 0 from below (so x < 0), we have
[tex]\displaystyle \lim_{x\to 0^-}\frac{|x|}x = \lim_{x\to0^-}-\frac xx = -1[/tex]
whereas if x approaches 0 from above (so x > 0), we have
[tex]\displaystyle \lim_{x\to 0^+}\frac{|x|}x = \lim_{x\to0^+}\frac xx = 1[/tex]
But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.
Putting everything together, you can define the derivative of |x| as
[tex]\dfrac{d|x|}{dx} = \begin{cases}1 & \text{for } x > 0 \\ \text{unde fined} & \text{for }x = 0 \\ -1 & \text{for }x < 0 \end{cases}[/tex]
A 9-ounce can of peaches sells for $1.26. Find the unit price.
Answer:
0.14 per ounce
Step-by-step explanation:
1.26 ÷ 9= 0.14
Hope this helps! :)
The unit price of peach would be $0.14.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 9-ounce can of peaches sells for $1.26.
9-ounce can of peaches sells for $1.26.
Then -
1 ounce of peach will cost = (1.26/9) = $0.14
Therefore, the unit price of peach would be $0.14.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ2
6 weeks to 12 days answer?
7x+20=7x+20
help asap
step by step please
Answer:
The given equation is true for all x.
Step-by-step explanation:
3. Sally invested $5,000.00 in a savings account earning 3.49% simple interest. At the same time
Jon invested $3,000.00 in a money market account at a simple interest rate of 7.5%. How many
years will it take for the two to have the same amount of money in their accounts? How much
money do they have after that time period?
Answer:
ic hch7y8gygdr6dr6d7twwt7tfx7yuc yc i
pls help me out
4x - 10 = -6
Answer: x = 1
Step-by-step explanation:
Answer:
The value of x is 1
Step-by-step explanation:
4x - 10 = -6
Use APE or Additive Property of Equality
4x = 10 - 6
4x = 4
Use DPE or Division Property of Equality
4x/4 = 4/4
x = 1
Substitute it to the equation to check
4x - 10 = -6
4(1) - 10 = -6
4 - 10 = -6
-6 = -6
10 x 9= what is it help
Answer:
10
[tex]10 \times 9 \\ 90[/tex]
Answer:
90 :)
Step-by-step explanation:
10 x 9 = 90
= 90 is correct answer
(Hope this helps can I pls have brainlist (crown)☺️)
Please help me I need help with solving this equation worth 30 points
Answer:
1. -20
2. 27
3. 36
4. -200
how long is the Yangtze river
Answer:
3,915 mi
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Answer:
x2 + (y + 8)2 = 36
Step-by-step explanation:
:) took the test
The equations which represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
What is the Standard form of a Circle?Standard form of a circle is given by the equation,
(x - h)² + (y - k)² = r²
where, (h, k) is the center of the circle and r is the radius of the circle.
Given that,
A circle has a diameter of 12 units.
So radius = 12 / 2 = 6 units
Center of the circle lies on the Y axis.
So the x coordinate of the center of the circle will be 0.
So, in (h, k), h = 0
So the equation will be of the form,
(x - 0)² + (y - k)² = 6²
x² + (y - k)² = 36
Hence the options are x² + (y – 3)² = 36 and x² + (y + 8)² = 36.
Learn more about Equations of Circles here :
https://brainly.com/question/29288238
#SPJ7
Can someone please solve question 8
Answer:
22.84
Step-by-step explanation:
What is the equation of the circle in center - radius form: x² + y2 + 12x - 10y
- 7 = 0?
Answer:
Radius: √ 61
Step-by-step explanation:
Complete the square for x^ 2 + 12 x = ( x + 6 ) ^2 − 36
Substitute ( x + 6 ) 2 − 36 for x 2 + 12 x in the equation x 2 + y 2 + 12 x − 10 y = 0
= ( x + 6 ) 2 − 36 + y 2 − 10 y = 0
Move − 36 to the right side of the equation by adding 36 to both sides
= ( x + 6 ) 2 + y 2 − 10 y = 0 + 36
Then you know the rest: radius will be √ 61
The center coordinate of the circle is (6,5) with a radius = 7.34
What is the equation of the circle?The equation of the circle is: [tex](x-a)^{2} + (y-b)^{2} = r^{2} x^{2}[/tex]
Substituting the values in the equation:
[tex](x-a)^{2} + (y-b)^{2} = r^{2} x^{2} - 2ax + a^{2} + y^{2} - 2by +b^{2} - r^{2} = 0[/tex]
⇒ -2ax = -12x
⇒ a = 6.
-2by = -10y
b= 5.
⇒ a² + b² - r² = -7
⇒ 6² + 5² + r² = -7
⇒ 36 + 25 + r² = -7
⇒ r² = 54
⇒ r = 7.34
Center coordinate (6,5) with r = 7.34
Learn more about the equation of the circle here: brainly.com/question/1471134
#SPJ2
You are 5 feet tall and cast an 8-foot shadow. A lamppost nearby casts a shadow that is 20 feet. Which equation can you use to solve for the height (ℎ) of the lamppost?
6x-7y=7andx-7y=-8 find valve of x and y
Answer:
x = 3, y = 11/7.
Step-by-step explanation:
6x - 7y = 7
x - 7y = -8 Subtract:
5x = 15
x = 3
3 - 7y = -8
-7y = -11
y = 11/7.
Answer: x = 3 and y = 11/7
Step-by-step explanation: 6x-7y+(-6x) = 7+(-6x) -7y/-7 = -6x+7/-7 y = 6/7x-1 x-7 (6/7 (x) -1) = -8 -5x+7+(-7) = -8+(-7) -5x/-5 = -15/-5 x = 3 y = 6/7x-1 y = (6/7) (3) -1 y = 18/7-1 18/7-1/1 18/7-7/7 y= 11/7 x = 3 and y = 11/7
Help me with math!!!!
Answer:
-4
Step-by-step explanation:
so t is greater than -5, and for negatives, you need to get nearer zero.
wuts x uwu plssss 10 points
−2/9x+2.7=4
Answer:
x = -5.85
Step-by-step explanation:
Solve the equation
1) [tex]-\frac{2}{9} x + 2.7 = 4[/tex]
Subtract -2.7 on both sides by doing the inverse operation.
2) [tex]-\frac{2}{9}x = 1.3\\[/tex]
Multiply both sides by -9/2 to cancel out -2/9x, so that you can isolate "x" by itself.
3)[tex]x = -5.85[/tex]
Describe and correct the error in rewriting the expression.
6(y+8) = 6y+8
Describe the error:
Correct the error:
Answer:
error: forgot to distribute 6 to the 8
correction: 6(y+8) = 6y+48
Step-by-step explanation:
in distributive property: you must multiply the number on the outside to both of the numbers in the inside
help me with this problem thank youuup.
Step-by-step explanation:
it is a linear function, if the change in y is constant in relation to the changes of x.
in other words, if the slope y change/x change is the same for every point.
when we look at the table, we see x changes constantly by +2.
and y changes constantly by -6.
so, the change rate/slope is constantly -6/2 = -3.
and therefore it is a linear function.
the equation looks like (the slope is always the factor of x)
y = -3x + b
b we get by using one of the x,y pairs like 1,4
4 = -3×1 + b = -3 + b
b = 7
so, the full equation is
y = -3x + 7
Step-by-step explanation:
Given the table of values, {(-3, 16), (-1, 10), (1, 4), (3, -2), (5, -8)}:
We must determine whether the given relation or data can be modeled by a linear equation. It is necessary to analyze the pattern that exists between changes in y-values, along with the changes in x-values.
X-coordinates:Subtracting the x-coordinates provides a constant difference of 2:
Starting with the first two rows, given by the ordered pairs, (-3, 16) and (-1, 10): Subtract the two x-coordinates: -1 - (-3) = -1 + 3 = 2.For the second and third rows, given by the ordered pairs, (-1, 10) and (1, 4): Subtract the two x-coordinates: 1 - (-1) = 1 + 1 = 2.If you perform these same steps throught the remaining rows, then you'll get the same difference of 2.
Y-coordinates:We can perform the same steps for the y-coordinates. Subtracting the y-coordinates provides a constant difference of -6.
Starting with the first two rows, given by the ordered pairs, (-3, 16) and (-1, 10): Subtract the two y-coordinates: 10 - 16 = -6.For the second and third rows, given by the ordered pairs, (-1, 10) and (1, 4): Subtract the two y-coordinates: 4 - 10 = -6.If you perform these same steps throught the remaining rows, then you'll get the same difference of -6.
SlopeSince the constant change in y = -6, and the constant change in x = 2, then we can calculate for the slope as: Δy/Δx = -6/2 = - 3. Hence, the constant rate of change = -3.
As demonstrated throughout this post, we can infer that there is a linear pattern that exists between the x- and y-values.
Therefore, the data can be modeled by a linear equation because the rate of change is constant.
Linear Equation:In order to establish the linear equation that represents y as a function of x, we can use the slope, m = -3, and one of the given ordered pairs, (1, 4), to solve for the value of the y-intercept, b. Substitute these values into the slope-intercept form, y = mx + b:
y = mx + b
4 = (-3)1 + b
4 = -3 + b
Add 3 to both sides to isolate b:
4 + 3 = -3 + 3 + b
7 = b
Therefore, the linear equation that represents the given data is: y = -3x + 7.
(x + 1)(x + 2)(x + 1)(3x + 2)
Answer:
Is it the full question I mean what does it want next anyway?
But here's your answer :
3x^4 + 14x^3 + 23x^2 + 16x + 4
Urgent! At a baseball game, a vender sold a combined total of 241 sodas and hot dogs. The number of sodas sold was 55 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
Sodas = 148
Hot dogs = 93
Step-by-step explanation:
Let S and H stand for the number of Sodas and Hot dogs, respectively.
We are told that:
H + S = 241
We are also told that:
S = H + 55
Use the second expression for S (H+55) in the first equation:
H + S = 241
H + (H+55) = 241
2H + 55 = 241
2H = 186
H = 93
Since H = 93,
S = 93+55, or 148
148 + 93 = 241 [Checks]
Sodas = 148
Hot dogs = 93
(ASAP) helpp i need to get this done 3m
3(a-4) + 1= 9 - a
3(a-4) = 8 - a
3a-12 = 8 - a
4a = 20
a=5
I hope this helps! :)
Answer:
a=5
Step-by-step explanation:
3(a-4)+1=9-a
3a-12+1=9-a
3a-11=9-a
3a+a=9+11
4a=20
a=20÷4
=5
Use long division to divide x3 + x2 - 2x + 14 by x + 3. Choose the correct quotient.
Answer:
x2 - 2x + 4 (remainder 2).
or we could write it as
x2 - 2x + 4 + 2/(x+3)
Step-by-step explanation:
x2 - 2x + 4 <------ quotient.
x + 3 ) x3 + x2 - 2x + 14
x3 + 3x2
-2x^2 - 2x
-2x2 - 6x
4x + 14
4x + 12
2 <--------- remainder
Step-by-step explanation:
If a triangle has a base of 6 feet and a height of 5 feet, what is the area?
Answer:
15 square feet
Step-by-step explanation:
a = (1/2)bh
a = (1/2) * 6 * 5
a = 3 * 5
a = 15
15 square feet
Evaluate (25/36)^1/2
A 25/6
B 5/6
C 5/36
D 25/36
5/6 its doneeeeeeèeeeeee
The Cougars, a football team, must gain 10 yards in the next four plays to keep possession of
the ball. The Cougars gain 5 yards, lose 12 yards, gain 14 yards, and finally lose 8 yards. Do
the Cougars keep possession of the ball?
Answer:
No
Step-by-step explanation:
Gain 5= 5 to go
Lose 12= 7 to go
Gain 14= 7 to go
Lose 8=15 to go
taxi Cab Company B: $6.50 per ride and $0.50 per mile
Express in the table the cost of the cab ride given the number of miles. Hint: Fill in the table above using cost for company B.
Write an equation in slope-intercept form to represent the cost of a taxi ride using company B. Hint: use y= mx+b
Y = __________________
What does the slope mean in the context of this problem?
Hint: What changes the further you ride?
Using the slope - intercept relation, the equation which represents the cost of cab ride is y = 0.5x + 6.50
Cost per ride = $6.50Cost per mile = $0.50Using the slope - intercept relation :
y = bx + cb = change in cost per mile
c = constant price added for every taxi ride
Hence, the expression can be written thus :
y = 0.5x + 6.50Learn more : https://brainly.com/question/17225268
One number is 3 times another. If the difference between the numbers is 14, what is the larger number?
Answer:
21
Step-by-step explanation:
One number is 3 times another
x and 3x
difference between the numbers is 14,
3x - x = 14
simplify
2x = 14
Divide both sides by 2
x = 7
3x = 21
Answer:
The larger number is 21.
Step-by-step explanation:
let, the smaller number be x.
the larger number be 3*x =3x.
Now,
3x-x=14
or, 2x=14
or, x=14/2
x=7
here,
3x=3*x=3*7=21
Yes or No
Please answer
What’s 568 divided by 7
The 66-mm-diameter solid shaft is made of 2014-t6 aluminum and is subjected to the distributed and concentrated torsional loadings shown where t=1. 7 kn⋅m.
Answer:
bbc
Step-by-step explanation:
[ASAP] Which graph represents a direct variation?