Answer:
20
Step-by-step explanation:
15 divided by 3 is 5
15 over 4 days = 20
Calculus helpppppppppppppppp
Answer:
[tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
FunctionsFunction NotationExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Logarithms and Natural LogsLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Derivatives
Derivative Notation
Derivative 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) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Logarithmic Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x\sqrt[3]{1 + x^2}[/tex]
Step 2: Rewrite
[Equality Property] ln both sides: [tex]\displaystyle lny = ln(x\sqrt[3]{1 + x^2})[/tex]Logarithmic Property [Multiplying]: [tex]\displaystyle lny = ln(x) + ln(\sqrt[3]{1 + x^2})[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle lny = ln(x) + ln \bigg[ (1 + x^2)^\bigg{\frac{1}{3}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = ln(x) + \frac{1}{3}ln(1 + x^2)[/tex]Step 3: Differentiate
ln Derivative [Implicit Differentiation]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx} \bigg[ ln(x) + \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{d}{dx} \bigg[ \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{1}{3}\frac{d}{dx}[ln(1 + x^2)][/tex]ln Derivative [Chain Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \frac{d}{dx}[(1 + x^2)][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \bigg( \frac{d}{dx}[1] + \frac{d}{dx}[x^2] \bigg)[/tex]Basic Power Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot (2x^{2 - 1})[/tex]Simplify: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot 2x[/tex]Multiply: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{2x}{3(1 + x^2)}[/tex][Multiplication Property of Equality] Isolate y': [tex]\displaystyle y' = y \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex]Substitute in y: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex][Brackets] Add: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{5x^2 + 3}{3x(1 + x^2)} \bigg][/tex]Multiply: [tex]\displaystyle y' = \frac{(5x^2 + 3)\sqrt[3]{1 + x^2}}{3(1 + x^2)}[/tex]Simplify [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Implicit Differentiation
Book: College Calculus 10e
Need help if you have the time and i need explanation for this (NO LINKS PLS)
Answer:
ask ur question i will try to help
Step-by-step explanation:
what is 4 1/8 - 2 2/3 to the nearest whole number
Answer:
1 11/24
Step-by-step explanation:
:))
What is y/x = 8 proportional to?
Answer:
y is directly proportional to 8
while x is inversily proportional to 8
1. Which of the following is not a true statement?
Group of answer choices
Angle 1 and Angle 3 are supplementary angles.
Angle 2 and Angle 7 are congruent
Angle 5 and Angle 8 are congruent.
Angle 3 and Angle 7 are supplementary angles.
[tex]\bf{Hello!}[/tex]
Angle 3 and Angle 7 are supplementary is the wrong statement
Because, they are corresponding angles and they are equal.
Last month we had only five sunny days. There were 30 days in all last month.
What was the ratio of sunny days to the total number of days? What was the ratio
of sunny days to days that were not sunny?
Answer:
6
Step-by-step explanation:
30 ÷ 5 = 6
Answer:
6
Step-by-step explanation:
it is 6
Leanna opens a savings account with an initial balance of $100. She then deposits $50 each month. Use an equation, a table, and a graph to explain the relationship between the amount of money in the account, a, and the number of months since Leanna opened the account, m.
Part A Write an equation to represent the problem. Explain how the value of a changes as m increases.
Part B Make a table to show the relationship between m and a. Find 5 ordered pairs.
Part C Use your table from Part B to draw a graph to represent the situation.
Please answer all questions
See the attached picture:
A 33 gram sample of a substance that's
used for drug research has a k-value of
0.1124.
Find the substances half life and the round your answer to the nearest 10th
9514 1404 393
Answer:
6.2
Step-by-step explanation:
We presume your "k-value" is the k in the exponential decay term ...
e^(-kt) . . . where t is the number of time units
This is 1/2 when ...
ln(1/2) = -kt
t = ln(1/2)/(-k) = ln(2)/k
t = 0.69315/0.1124 ≈ 6.2
The half life is about 6.2 time units.
please help i have been stuck on this for 3 hours
Answer:
The one you selected is the correct one
Answer:
(5/7) x 56 = 40 is correct
Step-by-step explanation:
How have you been stuck on this for 3 hours
Please help will give brainliest
Answer:
A+B=180°(linear pair)
a+ 52°=180°
a=180°-52°
a=128° is your answer
Solve the following equation: *
Answer:
Step-by-step explanation:
x/3 + 6 = 17
Bringing like terms on one side
x/3 = 17 - 6
x/3 = 11
Dividing by 3 on both sides
x = 11/3
-2y + x +
3
How many terms are in the expression
Answer:3
Step-by-step explanation:
Answer choices
4 feet
5feet
6feet
8feet
Please help if you send a link I will report
Answer:
d
Step-by-step explanation:
only reasonable answer
which expression is equivalent to 6^4x6^3
Answer:
C - (6x6x6x6)(6x6x6)
Step-by-step explanation:
answer and show proof for branliest
Answer:
-2(4 - 1)
Step-by-step explanation:
Choice A: ❌
9-(-17)
9 + 17 = 26
Choice B: ❌
(4 - 16)/(-2)
(-12)/(-2)
6
Choice C: ✅
-2(4 - 1)
-2(3)
-6
Choice D: ❌
3 x (-2) x (-1)
-6 x (-1)
6
Answer:
- 2(4 - 1)
Step-by-step explanation:
9 - (- 17)
9 + 17 = 26
[tex]\frac{4 - 16}{-2}[/tex] = 12
- 2(4 - 1)
- 2(3) = - 6
3 × - 2 × - 1 = 6
WHAT IS 3/20 IN DECIMAL AND PERCENTAGE
) Cars are parked in line as they come off the assembly lines. There are three models: red cars which take up 2 spaces, blue cars which also take up 2 spaces, and green cars which take up only 1 space. Let an be the number of ways of filling the first n parking spaces with red, blue and green cars.
Answer:
Hello your question has some missing information below is the complete question
answer :
[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]
Step-by-step explanation:
Red car and Blue car take up 2 spaces each
Green cars take up 1 space
lets determine the number of ways of filling up the parking spaces
i) First lets assume the last space is filled by Green car then there will be [tex]n^{th}[/tex] space occupied hence there will be ( n - 1 ) spaces left to be filled in [tex]a_{n-1}[/tex] ways
ii) lets assume the last space is filled by either a Red car or a Blue car then there will be [tex]n^{th} + ( n -1 )^{st}[/tex] parking space occupied hence there will be
( n - 2 ) spaces left to be filled in [tex]a_{n-2}[/tex] ways
Hence A closed formula for [tex]a_{n}[/tex]
[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]
where : a1 = 1 way , a2 = 3 ways
You pick a card at random.
2 3 4 5
6 7 8 9
What is P(5)
Write your answer as a percentage.
Step-by-step explanation:
There are a total of 8 cards, you are picking only one card,
therefore P(5) =
[tex] \frac{1}{8} \times 100 \\ = \frac{100}{8} \\ = 12.5percent[/tex]
I can't figure this out
9514 1404 393
Answer:
143 in²
Step-by-step explanation:
The figure is dimensioned in such a way that it can be divided easily into three rectangular areas. The top rectangle is 10 in wide and 7 in high. The vertical rectangle below that is 4 in wide and 12 in high, and the square appendage on the right is 5 in square.
Then the total area is the sum of products of length and width:
A = (10 in)(7 in) + (4 in)(12 in) + (5 in)(5 in) = (70 +48 +25) in²
A = 143 in²
The area of the irregular figure is 143 in².
what is the value of x in each figure
PLEASE DON'T GIVE ME A LINK
Answer:
x=43
Step-by-step explanation:
3x+17+x-9=180
4x+8=180
4x=180-8
4x=172
x=43
What is the area of the school crossing sign represented below?
15 inches 15 inches
15 inches
15 inches
help me plsss
plz, help. I need it...
Answer: (6, 3)
Step-by-step explanation:
1 . What is the distance between the two points.
(0,5 1,3), (-0,4, -1,3) ?
2. What is the distance between the two points
(6, -3), (2, -4)
Amy needs to estimate how many students at her school like online testing. She needs to create a random sample of students. How should Amy collect her sample? Select two that apply.
O Amy should ask every 10th person leaving the school at the end of the day.
O Amy should ask 3 people at every table in the cafeteria
O Amy should ask her 10 closest friends.
O Amy should ask the 35 students in her honors math class
O Amy should ask the 50 students in the computer club.
Calculate the slope of a line that goes through points (3, 4) and (0, 0).
Question 5 options:
3/4
3
4
4/3
Answer:
4/3
Step-by-step explanation:
0-4/0-3
-4/0-3
-4/-3
4/3
Answer:
Step-by-step explanation:
3\4
P = 3. Q = -2. Solve 4PQ
Answer:
-24
Step-by-step explanation:
4(3)(-2) = -24
#The extremities of the diagonal of a square are (1,1 )and (-2, -1).Obtain the two other vertices and the equation of a next diagonal.
#
find the area of the triangle with vertices(1,2),(2,3),and(4,5).what inference can you draw about the points from your upshot?
Answer:
(i) (-3/2, 3/2) and (1/2, - 3/2)
6x + 4y = - 3
(ii) Points are col linear
Step-by-step explanation:
Let the coordinates of the point(lower) be (a, b) and that of upper be (x, y).
Using mid point formula,
Mid point of diagonal(using the given points) is:
= ( (-2+1)/2 , (-1+1)/2) = (-½ , 0)
Using (a, b) and (x, y) :
= ( (a+x)/2 , (b+y)/2 ) = (-1/2, 0)
Which means, a+x= -1 & b + y = 0
Therefore, x = - 1 - a & b = - y
Using distance formula, diagonal = √(-2-1)² + (-1-1)² = √13
Knowing the relation in diagonal and side, side = diagonal/√2 = √13/√2 = √(13/2)
Again using distance formula, diagonal = √13
=> √(x - a)² + (y - b)² = √13
=> (-1-a -a)² + (-b - b)² = 13
=> a² + b² + a = 3 ... (1) [solved directly]
Length of side = √(13/2)
=> √(a-(-2))² + (b-(-1))² = √(13/2)
=> a² + b² + 4a + 2b = 3/2 ...(2)
On solving (1) and (2):
a = 1/2 or -3/2, but a lies in 4th quadrant so a > 0, thus, a = 1/2
b = -3/2 or 3/2, but b lies in 4th quadrant so b < 0, b = -3/2
Therefore,
x = - 1 - a = -1 - 1/2 = -3/2
y = - b = - (-3/2) = 3/2
Vertices are (x, y) = (-3/2, 3/2) and (a, b) = (1/2, -3/2)
Equation is just a relation in y and x, for a relation:
Subtract (1) from (2):
3a + 2b = -3/2 => 6a + 4b = - 3
By merely replacing a, b by x, y
6x + 4y = -3 is the required equation
(ii):
Ar. of ∆ = ½ | 1(3 - 5) + 2(5 - 2) + 4(2 - 3) |
Ar. of ∆ = ½ | -2 + 6 - 4 | = 0
As the area of the ∆ is 0, the given points don't form ∆, they are col linear.
What is the unit rate for the following rate: 5 pounds of potatoes costs $10
Answer:
$2 per round of potatoes
Step-by-step explanation:
$10/5 pounds of potatoes= $2
In ABC, the measure of the largest angle is 16 less than 4 times the smallest angle. The measure of the middle angle is 7 more than half the measure of the largest angle. What is the measure of the middle angle?
Answer:
Step-by-step explanation:
Let A ≤ B ≤ C
largest angle is 16 less than 4 times the smallest angle
C = 4A-16
middle angle is 7 more than half the measure of the largest angle
B = C/2 + 7
A+B+C = 180°
A = 28 ⅐°
B = 55 2/7°
C = 96 4/7°
Please help thank you
Answer:
x = 140
Step-by-step explanation:
Using the exterior angle rule ( an exterior angle of a triangle is equal to the opposite interior angles of a triangle )
x is the interior angle and the given angles ( 50 and 90 ) are the opposite interior angles
So
x = 50 + 90
50 + 90 = 140
x = 140
Note: there is a right angle ( indicated by the little square. A right angle has a measure of 90 degrees so that's where the 90 came from)