Answer:
See explanation.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Functions
Function NotationExponential Property [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Property [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
We are given the following and are trying to find the second derivative at x = 2:
[tex]\displaystyle f(2) = 2[/tex]
[tex]\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}[/tex]
We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:
[tex]\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}[/tex]
When we differentiate this, we must follow the Chain Rule: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big][/tex]
Use the Basic Power Rule:
[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')[/tex]
We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:
[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big][/tex]
Simplifying it, we have:
[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big][/tex]
We can rewrite the 2nd derivative using exponential rules:
[tex]\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}[/tex]
To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:
[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}[/tex]
When we evaluate this using order of operations, we should obtain our answer:
[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Which of the following equations could be the result of using the comparison method to solve the system shown?
x + 2y = 6
x - 4y = 8
2y - 6 = 4y + 8
6 - 2y = -4y + 8
6 - 2y = 4y + 8
Answer:
6 -2y =4y + 8
Answer: 6 -2y =4y + 8
Step-by-step explanation:
Which of the following is the ratio of 5 cm to 10 km
Answer:
1/200000
Step-by-step explanation:
first 10 km equals to 1000000cm
so 5/1000000cm
equals to 1/200000
find the equation of the line that is parallel to y=x-3 and contains the points (3,-2)
Use the function z=7c to find the value of z when c=8.
Answer:
z = 56
Step-by-step explanation:
z = 7(8)
Can someone help me with this?
Answer:
Step-by-step explanation:
[tex]\frac{\sqrt{36x^3y^4}}{2x^{2/3}y^{-4}}=\frac{6x^{3/2}y^2}{2x^{2/3}y^{-4}}=3x^{5/6}y^6[/tex]
a=3, b=5/6, c=6
3*(5/6)*6= 15
who is piplup ???????? ~
Construct a 60° angle
Change 7 1/4 to an improper fraction
Answer:
29/4
Step-by-step explanation:
7 x 4 = 28
28 + 1
hope that helps!
Answer:
29/4
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
4 × 7 = 28
Step 2
Add the answer from Step 1 to the numerator
28 + 1 = 29
Step 3
Write answer from Step 2 over the denominator
29/4
Hope this helps!:)
Tickets for the Valentine Dance cost $3 per person or $5 per couple. The school ticket sales totaled $824 and there were 10 less couple tickets sold than 4 times the number of single tickets.
The quadrilaterals JKLM and PQRS are similar.
Find the length x of RS.
Will mark brainliest!
The measure of side x equivalent to RS is 42
Similar shapes are shapes that have both their sides and angles to be equal.
Since both quadrilaterals JKLM and PQRS are similar, we will take the ratio of the sides as shown;
4/24 = 7/x
1/6 = 7/x
Cross multiply
x = 42
Hence the measure of side x equivalent to RS is 42
Learn more on similar shapes here: https://brainly.com/question/12960403
Allen's daily regular wage is P1,420. This coming Christmas, his boss is asking him to work for 14 hours. How much is his DAILY RATE on that particular day?
Php 1,420
Php 2,840
Php 2,420
Php 1,840
Using proportions, it is found that his DAILY RATE on that particular day is of Php 2,420 .
This question is solved by proportions, using a rule of three.In a regular 8-hour day, Allen earns Php 1420. How much will he earn on a 14 hour day?The rule of three is:
8 hours - Php 1420
14 hours - x
Applying cross multiplication:
[tex]8x = 1420 \times 14[/tex]
[tex]x = \frac{1420 \times 14}{8}[/tex]
[tex]x = 2485[/tex]
The closest option is Php 2,420.
A similar problem is given at https://brainly.com/question/24372153
For this equation: I don't care what the answer is, I need to know how to solve for it. Thanks.
Which of the following sets shows all the numbers from the set {3, 4, 5, 6} that are part of the solution to the equation 5x + 4 < 29? (4 points)
{4, 5, 6}
{3, 4, 5}
{3, 4}
{3}
======================================================
Explanation:
Solve the inequality for x.
5x + 4 < 29
5x < 29-4
5x < 25
x < 25/5
x < 5
I subtracted 4 from both sides (step 2). Then I divided both sides by 5 to fully isolate x (step 4). The inequality sign stays the same the entire time.
Since x < 5, this means the original set {3,4,5,6} becomes {3,4} since these values make x < 5 a true statement. In other words, we erase 5 and 6 because something like 6 < 5 is false.
That's why {3, 4} is the final answer.
---------------
An alternative method is to go through the set {3,4,5,6} and plug those items one by one into the original inequality. If you get a true result, then it's part of the answer.
Let's try x = 3
5x + 4 < 29
5(3) + 4 < 29
15+4 < 29
19 < 29
We get a true statement at the end, so x = 3 is part of the solution set. A similar story happens for x = 4 as well.
If we tried x = 5, then,
5x + 4 < 29
5(5) + 4 < 29
25 + 4 < 29
29 < 29
which is false. No number is bigger than itself (or smaller than itself). Therefore, x = 5 is crossed out of the original set. You should get a false statement for x = 6, which means we'll kick this value out as well.
Bruno and Amelia have 112 newspapers to deliver. Bruno delivers three fourths of the news papers, Amelia delivers one seventh pf the papers. How many papers are left to be deliverd
Answer:
f
Step-by-step explanation:
As an estimation we are told £3 is €4.
Convert €32 to pounds.
use the midpoint formula to find the midpoint of the given segment on the coordinate plane
Answer:
Midpoint : (4,3)
Step-by-step explanation:
midpoint = [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
Where the x and y values are derived from the given points.
We are given points H and K which are at (2,2) and (6,4)
We have (x1,y1) = (2,2) so x1 = 2 and y2 = 2
As well as (x2,y2) = (6,4) so x2 = 6 and y2 = 4
To find the midpoint we simply plug in the values of x and y into the formula
Recall the formula [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
x1 = 2 , x2 = 6 , y1 = 2 and y2 = 4
plug in these values into the formula
[tex](\frac{2+6}{2} ,\frac{2+4}{2} )[/tex]
add top values: 2 + 6 = 8 and 2 + 4 = 6
[tex](\frac{8}{2} ,\frac{6}{2} )[/tex]
simplify fractions : 8/2 = 4 and 6/2 = 3
The midpoint is at [tex](4,3)[/tex]
A bowl contains 675 sweets which are coloured either red, blue or green.
The ratio of red sweets to blue sweets is 3:
The ratio of blue sweets to green sweets is 4 : 5
Calculate the number of blue sweets that are in the bowl.
Answer:
252 blue sweets
Step-by-step explanation:
red : blue
3 : 7 ( x4 )
12 : 28
blue : green
4 : 5 ( x7 )
28 : 35
red : blue : green
12 : 28 : 35
12 + 28 + 35 = 75
Blue Sweets:
675 x 28/75 = 252
What is the value of x
Answer:
x = 5
Step-by-step explanation:
Δ EAB and Δ EDC are similar by the AA postulate , so the ratio of corresponding sides are in proportion , that is
[tex]\frac{AB}{DC}[/tex] = [tex]\frac{EA}{ED}[/tex] , substitute values
[tex]\frac{10}{4}[/tex] = [tex]\frac{2x+10}{x+3}[/tex] ( cross- multiply )
10(x + 3) = 4(2x + 10 ) ← distribute parenthesis on both sides
10x + 30 = 8x + 40 ( subtract 8x from both sides )
2x + 30 = 40 ( subtract 30 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
What is the equation of the line that passes through (-6,-2) and had a slope of -1/6
Answer:
[tex]y = -\frac{1}{6}x - 3[/tex]
Step-by-step explanation:
Slope Intercept Form : [tex]y = mx + b[/tex]
Using our slope, -1/6, input it for m, then plug the point (-6, -2) for x and y
[tex]y = mx+b\\\\-2 = (-1/6)(-6) + b\\\\-2 = 1 + b\\\\b = -3[/tex]
Equation : [tex]y = -\frac{1}{6}x - 3[/tex]
-Chetan K
Bethany is working her way through school. She works two part-time jobs for a total of 23 hours a week. Job A pays $5.70 per hour, and Job B pays $7.10 per hour. How many hours did she work at each job the week that she made $143.70.
Step-by-step explanation:
x = number of hours A
y = number of hours B
x + y = 23
5.7x + 7.1y = 143.7
from the first equation we get
x = 23 - y
and that we use in the second equation
5.7×(23 - y) + 7.1y = 143.7
131.1 - 5.7y + 7.1y = 143.7
1.4y = 12.6
y = 12.6/1.4 = 9
x = 23 - y = 23 - 9 = 14
she was working 14 hours on job A and 9 hours on job B.
Answer:
she is rich
Step-by-step explanation:
please explain for brainlist
A town has approximately 1000 homes. The town council is considering plans for future development. Plan A calls for an increase of 200 homes per year. Plan B calls for a 10% increase each year. Write a function to model each plan and determine the number of homes each plan has after 3 years.
Answer:
Plan A: 1600 homes after 3 years Plan B: 1330 homes after 3 years
Step-by-step explanation:
Plan A.
200x3=600
1000+600=1600
1600 homes after 3 years
Plan B.
10% the first year =100 homes increased
10% the secound year = 110 homes increased
10% the third year = 121 homes increased
1330 homes after 3 years
It would be 1330 for plan B. And plan a 1600.
SOS, I really need help! I accidentally slept in.
Dynamite blue fire red grape purple
What is 12 times 135?
the answer for 135 times 12 is 1620
Answer:
1620
Step-by-step explanation:
u can time 12 by 135 or divide them
7 grade math hellp me
Answer:
P=25
Step-by-step explanation:
Can someone help me on this plzzz show work please
Answer:
That is the answer
The answer is
Please helppp me I need it now
Answer:
You can either choose B or D.
B. Does x = 5 satisfy the equation above. Explain?
C. is x =1/2 a solution of the equation above? Explain?
Answer:
B
Step-by-step explanation:
3(x +1) =3x +3
Plug it in
3(5+1)=3(5)+3
3(6)=15+3
18=18
Find a scale with a unit of 1 and choose the correct answer (for example, 1 cm=7 yards).
Car 18ft moele 5in
Scale: _____
1 in = 3.6 ft
1 ft=18 in
1 in = 10 ft
1 ft=11 in
Answer:
1 ft=18 in or 1ft=11in
Step-by-step explanation:
:D
what is the answer to the equation -7x-3x+2= -8x - 8
Answer:
x=5
Step-by-step explanation:
-7x-3x+2= -8x - 8
Add like terms
-7x-3x=-10x
-10x+2=-8x-8
+8x +8x
-2x+2=-8
-2 -2
-2x=-10
Divide by -2 to isolate the variable
x=5
Answer:
x = 5Step-by-step explanation:
what is the answer to the equation
-7x - 3x + 2= -8x - 8
-7x - 3x + 8x = -10
2x = -10
x = 5
----------------------
check
-7 * 5 - 3 * 5 + 2 = -8 * 5 - 8
-48 = -48
the answer is good
Cherie has 4 gift cards. Each gift card is worth $10. If she spends $23, how much will she have left?
Answer: She'll have $17 left.
Step-by-step explanation:
4 * 10 = 40
40 - 17 = 23
Hope this helps!
what is 1029384756 x55 pls help
Answer:
1029384756 x 55
= 56616161580
