Answers
The indicated derivatives in the question can be found to be :
a. = 3x^2 x e^(x^3)b. = (ln(x)/6) × x^((ln(x)/6) - 1)How to find the derivatives ?To find the derivative of e^(x^3) + log_3(pi) with respect to x, we apply the rules of differentiation to each term:
Using the chain rule, we have:
d/dx (e^(x^3)) = e^(x^3) x (3x^2)
The derivative of log_3(pi) is 0, because log_3(pi) is a constant and the derivative of a constant is 0.
So, the derivative of the entire expression is:
d/dx (e^(x^3) + log_3(pi)) = e^(x^3) x 3x^2 + 0 = 3x^2 x e^(x^3)
To find the derivative of (x^(1/6))^ln(x) with respect to x, we first simplify the expression by using the power rule of logarithms:
(x^(1/6))^ln(x) = x^(ln(x)/6)
Now, we find the derivative of x^(ln(x)/6) using the chain rule:
d/dx (x^(ln(x)/6)) = (ln(x)/6) × x^((ln(x)/6) - 1) × d/dx (x)
The derivative of x is 1, so:
d/dx ((x^(1/6))^ln(x)) = (ln(x)/6) × x^((ln(x)/6) - 1) × 1 = (ln(x)/6) × x^((ln(x)/6) - 1)
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Related Questions
Solve the equation for y in terms of x, and replace y with function notation f(x). Then find f(2).
y+3x^2=5
f(x)=?
f(2)=?
Answers
Answer:
[tex]f(x)=-3x^2+5[/tex]
[tex]f(2) = -7[/tex]
Step-by-step explanation:
Given equation:
[tex]y+3x^2=5[/tex]
To solve the equation for y in terms of x, simply subtract 3x² from both sides of the equation:
[tex]\implies y+3x^2-3x^2=5-3x^2[/tex]
[tex]\implies y=-3x^2+5[/tex]
Replace y with the function notation f(x):
[tex]f(x)=-3x^2+5[/tex]
Finally, to find the value of f(2), substitute x = 2 into the function:
[tex]\begin{aligned}\implies f(2)&=-3(2)^2+5\\&=-3(4)+5\\&=-12+5\\&=-7\end{aligned}[/tex]
Answer:
[tex]f(2) = - 7[/tex][tex] f(x) = 5 - 3x^2[/tex]Step-by-step explanation:
To find:-
The value of [tex]f(2)[/tex]Answer:-
We are here a given a equation, with some steps to follow, in order to find out the value of [tex]f(2)[/tex].
Step 1 :- Solve the equation in terms of y ,
The given equation to us is,
[tex]\longrightarrow y + 3x^2 = 5\\[/tex]
To solve for y , we need to transpose 3x² from LHS to RHS , by doing this , the sign changes from positive to neagative .
[tex]\longrightarrow y = 5 - 3x^2 \\[/tex]
Step 2 :- Replace y with function notation [tex]f(x)[/tex]
Just simply replace y here with f(x) as ,
[tex]\longrightarrow f(x) = 5 - 3x^2\\[/tex]
Step 3 :- Find f(2) .
To calculate the value of f(2) , we need to put x = 2 , in the above equation as ,
[tex]\longrightarrow f(2) = 5 - 3(2)^2\\[/tex]
Simplify,
[tex]\longrightarrow f(2) = 5 - 3(4)\\[/tex]
[tex]\longrightarrow f(2) = 5 - 12\\[/tex]
[tex]\longrightarrow \boxed{ \boldsymbol{f(2) = -7 }} \\[/tex]
Hence the required answer is -7 .
The federal government has developed the body mass index (bmi) to determine ideal weights. a person's bmi is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches. (a bmi of 19 to 25 corresponds to a healthy weight.) a 6-foot-tall person weighing 177 lb has bmi 24. find the bmi (to the nearest whole number) of a person whose weight is 176 lb and whose height is 77 in.
Answers
The BMI of a person whose weight is 176 lb and whose height is 77 inches is 21.
First, let's use the given information to find the constant of proportionality in the BMI formula:
BMI = k × (weight in pounds) / (height in inches)²
When the 6-foot-tall person weighing 177 lb has a BMI of 24, we can plug in the values and solve for k:
24 = k ₓ 177 / (72²)
k = 24 ₓ (72²) / 177
k ≈ 9.94
Now we can use this value of k to find the BMI of the person whose weight is 176 lb and whose height is 77 in:
BMI ≈ 21
BMI = 9.94 ₓ 176 / (77²)
Therefore, the BMI (to the nearest whole number) of the person is 21, which falls within the healthy weight range of 19 to 25.
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Screenshot, I WILL GIVE 20 POINTS AND BRAINLIST!!!!
Answers
Answer:
0.7 = 0.70, so 0.17 < 0.70
Solve the problem in the picture please!
The answer choices are
A) 5
B) 2
C) 200
D) 100
Answers
2
Step-by-step explanation:
as H-20 and W=10
So H-constant. (W)
H=2(10)
H=20
So constant is 2
Here is another riddle:
-The sum of two numbers is less than 2
-If we subtract the second number from the first, the difference is greater than 1
The riddle can be represented by a system of inequalities. Write a inequality for each statement.
Name a possible (ordered pair) solution to the riddle.
Answers
x + y < 2 (the sum of two numbers is less than 2)
x - y > 1 (if we subtract the second number from the first, the difference is greater than 1)
One possible ordered pair solution to this system of inequalities is:
x = 1.5
y = 0.5
When you add these two numbers, you get 2 which is less than 2. And when you subtract the second number (0.5) from the first number (1.5), you get 1 which is greater than 1. Therefore, this solution satisfies both inequalities in the system.
Triangle ABC aid dilated by a scale factor of 3. Which is an algebraic representation of the dilation?
Answers
Answer:
[tex](3x, 3y)[/tex]
Step-by-step explanation:
The scale factor is 3 so you multiply 3 by the (x,y) to get (3x,3y) as the scale factor
4 1/5 -5/3 subtract
how do i do this eqation
Answers
Answer:
38/15
Step-by-step explanation:
4 1/5 - 5/3
4 1/5 = 21/5
21/5 - 5/3 = 63/15 - 25/15 = 38/15
So, the answer is 38/15
can someone help me do this (will give brainliest if possible
Answers
Answer:
4) ∠1 and ∠2, ∠2 and ∠3
5) ∠1 and ∠3
6) x = 10
Step-by-step explanation:
Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.
Therefore, the pairs of adjacent angles in the given diagram are:
∠1 and ∠2∠2 and ∠3∠3 and ∠4∠4 and ∠5∠5 and ∠1Vertical angles are pairs of non-adjacent angles that are formed when two lines intersect. Vertical angles are congruent,
Therefore, the pair of vertical angles in the given diagram are:
∠1 and ∠3As ∠1 and ∠3 are the same measure:
⇒ m∠1 = m∠3
⇒ (9x)° = 90°
⇒ 9x = 90
⇒ 9x ÷ 9 = 90 ÷ 9
⇒ x = 10
Therefore, the value of x is 10.
Answer:
4) ∠1 and ∠2, ∠2 and ∠3.
5) ∠1 and ∠3.
6) x = 10.
Step-by-step explanation:
Explanations are given in attachment!
Nathan rolls a number cube and records the result of each roll in the table.
Number Cube
Number Rolled
Frequency
1
11
2
16
3
14
4
20
5
12
6
17
Which statements below represent the situation? Select three options.
Answers
The correct three options are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
Nathan rolled the number cube a total of 90 times.
The number 4 was rolled more frequently than any other number.
The number 2 was rolled the least frequently of all the numbers.
The total number of rolls for odd numbers is greater than the total number of rolls for even numbers.
The correct statements are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
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1
Type here to search
day
How many more points did Zara score than John?
i
C
Number of Points
Points Scored in Basketball Game
25
20
15
10
5
0
e g
Read and Interpret Scaled Bar Graphs - Quiz - Level C
Mateo
Zara
Player
John
Mila
DONE
7
4
1
2
0
5
points
8
9
6
3
76°F Mostly cloudy
X
Th
Answers
Answer:
yes
Step-by-step explanation:
john has 34 marbles
Solve the systems by elimination.
x -y = 11
5x + 6y = -44
Answers
Answer: (6,-5)
Step-by-step explanation:
What is the price per bag of cookies
Answers
Answer: 6.3 per bag
Step-by-step explanation:
31.50 divided by 5 is 6.3!!!!
Answer: 6.3
Step-by-step explanation:
Divide 31.50 with 5
[tex]5\sqrt{31.50}[/tex]
5 goes into 3 0 times so you do 31/5. You get 6 with 1 as the remainder since 6x5 is 30. Now you do 15/5 which is 3. You get 63 but you have to add the decimal between the 6 and 3 so you will get 6.3. Hope this helped.
Tom has $160,000 in his retirement account. It is earning an APR of 4.57%. What would be the monthly yield on the account for a 30-year period?
Answers
The monthly interest yield on Tom's retirement account for a 30-year period would be $637.71.
Assuming that the interest is compounded monthly, the monthly yield on Tom's retirement account with an APR of 4.57% for a 30-year period can be calculated using the formula:
Monthly Yield = (Principal × Monthly Interest Rate) ÷ (1 - (1 + Monthly Interest Rate[tex])^{(-Number of Months)}[/tex]
Here, Principal = $160,000
APR = 4.57%,
Number of Months = 30 years ÷ 12 months/year = 360 months.
First, we need to convert the APR to a monthly interest rate by dividing it by 12:
Monthly Interest Rate = 4.57% × 12
Monthly Interest Rate = 0.3808%
Monthly Yield = (160000 × 0.3808%) ÷ (1 - (1 + 0.3808%[tex])^{-360}[/tex]
Monthly Yield = $637.71
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PLS HELP ASP!!!
The state of Colorado is 4 centimeters long and 2 centimeters wide on a map. A cartographer wants to use a scale factor of 3.5 to enlarge the map. What is the area of the enlarged map?
98 cm2
42 cm2
28 cm2
8 cm2
Answers
Answer: 98 cm²
Step-by-step explanation:
When a cartographer enlarges a map with a scale factor, both the length and the width are multiplied by the scale factor. In this case, the scale factor is 3.5.
Original dimensions of Colorado on the map:
Length: 4 cm
Width: 2 cm
Enlarged dimensions using the scale factor of 3.5:
Length: 4 cm × 3.5 = 14 cm
Width: 2 cm × 3.5 = 7 cm
To find the area of the enlarged map, multiply the enlarged length and width:
Area = Length × Width
Area = 14 cm × 7 cm
Area = 98 cm²
The area of the enlarged map is 98 cm².
What is the solution to x^3+4x^2 >x+4?
Answers
Answer:
Step-by-step explanation:
it’s equals 0 I think
Please help meeee
describe an incident that shows how you were doing "selection" during the process of perception. Then, give your own example about a stereotype that you do.
Answers
The description of the incident is shown below
Describing the incidentOne incident that shows how selection works in the process of perception is when you are at a party and you hear your name being mentioned in a conversation across the room. In this situation, your attention is immediately drawn to the conversation, and you focus on it while filtering out other sounds and distractions around you.
This is an example of selective attention, where you choose to focus on a particular stimulus and ignore others.
As for an example of a stereotype that I have, it is that all people who live in a certain region or country behave in a particular way.
For instance, I may have the stereotype that people from a particular country are loud and aggressive.
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how will the product change if one number is increase by a factor of 12 and the other is decreased by a factor of 4
Answers
Using factors, we can conclude that the new product will be 48 time more than the old product.
Define factors?In mathematics, the factor of a number is a divisor of the inputted integer that entirely divides it, leaving no residue. We can use a variety of techniques, including the division method and the multiplication method, to identify a number's components.
Let the product be P.
Let the numbers be a and b.
Now,
P = a × b
According to the question.
Let a is increased by a factor of 12 and b by 4:
P = 12a × 4b
P = 48 × a × b
Hence, we can conclude that the product will increase by a factor of 48.
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x^3-6x^+2x-4 divided by x+2
Answers
Answer:
Step-by-step explanation:
Given RP = 22, RA = 6, and PQ is tangent to .R at Q, find PQ.
Answers
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{22}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{PQ} \end{cases} \\\\\\ PQ=\sqrt{ 22^2 - 6^2}\implies PQ=\sqrt{ 484 - 36 } \implies PQ=\sqrt{ 448 }\implies PQ\approx 21.17[/tex]
5)
Given:
Prove:
41 and 22 are complementary.
41 = 23
22= 24
23 and 24 are complementary.
2
3
4
Answers
[tex] \angle3 \: and \: \angle4 [/tex] are complementary.
What is Complementary angle?
If sum of two angles is 90° then we can say that those angles are complementary.
For example, if [tex] \angle \: a + \angle \: b = {90}^{o} [/tex] then angle a and angle b are complementary.
Here are some examples of complementary angles:
30 degrees and 60 degrees45 degrees and 45 degrees20 degrees and 70 degrees15 degrees and 75 degrees10 degrees and 80 degrees35 degrees and 55 degrees25 degrees and 65 degrees40 degrees and 50 degrees5 degrees and 85 degrees12 degrees and 78 degrees.Here given,
[tex] \angle1 \: and \angle2[/tex] are complimentary.
So,
[tex] \angle1 + \angle2 = {90}^{o} [/tex]
It is clear that [tex] \angle1, \angle2, \angle3, \angle4[/tex] are making a straight angle.
So, we can write,
[tex] \angle1 + \angle2 + \angle3 + \angle4 = {180}^{o} \\ {90}^{o} + \angle3 + \angle4 = {180}^{o} \\ \angle3 + \angle4 = {180}^{o} - {90}^{o} \\ \angle3 + \angle4 = {90}^{o} [/tex]
Here sum of angle 3 and angle 4 is 90°.
According to definition angle 3 and angle 4 are complimentary angles.
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find the answer to 9/16 in decimal form
Answers
Answer:
0.5625
Step-by-step explanation:
y = y₁ = m(x − x₁)
Show your work in the space provided below.
1. Find the equation of the line that has a slope of -4 and passes through the point (-3, 7).
Show your work below:
2. Find the equation of the line that passes through the points (4, -3) and (8,9).
Show your work below:
Answers
Answer:
see below
Step-by-step explanation:
The equation y - y₁ = m(x − x₁)
1. y - 7 = -4(x - -3)
y - 7 = -4(x + 3)
y = -4x - 12 + 7
y = -4x - 5
2. y - y₁ = m(x − x₁)
9 - -3 = m(8 - 4)
12 = 4m
m = 12/4 = 3
y = mx + b
-3 = 3(4) + b
b = - 3 - 12
b = -15
y = 3x - 15
8a = -12 + 2a me need helpppppppppppppp
Answers
Answer: a = -2
Step-by-step explanation:
8a = -12 + 2a
8a - 2a = -12
6a = -12
a = -12/6
a = -2
Quadrilateral ABCD is translated 5 units up. What are the coordinates of
quadrilateral A'B'C'D?
A
D
A(-5, 5)
D(-5, 1)
B' Y
G
C₁
8(-1,5)
C(1, 2)
OA. A'(-5, 0), B'(-1,0), C'(-1, -3),
D'(-5,-4)
OB. A'(-5, 10), B'(-1, 10), C'(-1,7),
D'(-5, 6)
C. A'(-10, 10), B'(-6, 10), C'(-6, 7),
D'(-10, 6)
D. A'(-10, 5), B'(-6, 5), C'(-6, 2),
D'(-10, 1)
Answers
Answer:
it should be B but I could be wrong
Step-by-step explanation:
B
PLS HELP :))
The property taxes on a house were $1265
. What was the tax rate if the house was valued at $115,000
? Follow the problem-solving process and round your answer to the nearest hundredth of a percent, if necessary.
Answers
The tax rate of a house valued at $115,000 with a property tax of $1265 is 110%. or $110 per $1,000 of property value.
What is property tax?The property tax is the levy imposed on the assessed value of the property of an individual or corporation.
Property tax is usually levied as a percentage of the assessed value.
Data and Calculations:Property tax = $1265
House value - $115,000
Tax rate = 110% [tex](\$1265\div\$115000 \times 100)[/tex]
Thus, the tax rate of a house valued at $115,000 with a property tax of $115,000 is 110%. or $110 per $1,000 of property value.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
Answers
The equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).
A rectangle has equal and parallel opposite sides.
A rectangle has two dimensions—length and width—because it is a two-dimensional form.
The rectangle's longer side is its length, while its shorter side is its breadth.
So, the area formula of the rectangle:
750 = l * w
750 = x * (x-5)
750 = x² - 5x
x² - 5x - 750 = 0
Equations in the options that are similar:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
Therefore, the equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
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Correct question:
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
a. y(y + 5) = 750
b. y2 – 5y = 750
c. 750 – y(y – 5) = 0
d. y(y – 5) + 750 = 0
e. (y + 25)(y – 30) = 0
Identify the shapes that make up the figure at the left. Then find the perimeter and area of the figure to the nearest hundredth.
Answers
Rectangle, semi circle, semi circle
Perimeter: 60.8
Area: 64.2
What is perimeter and area?In mathematics, the two key characteristics of two-dimensional forms are area and perimeter. The difference between area and perimeter is how much room each type of shape takes up.
Mathematical concepts like area and perimeter are crucial because they are applied to daily living. Any size and form, whether regular or irregular, can use this. Each design has a unique area and perimeter calculation. Forms like triangles, squares, rectangles, circles, spheres, etc. should be known to you. Here, the boundaries and surfaces of all forms are explained.
perimeter= 60.8
each of the three shapes' perimeters separately, then sum them all up to get 60.8.
area= 64.2
Calculate the area of each of the three shapes separately, then sum them all up to get 64.2.
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The complete question attached below,
The required size and perimeter of the Area are respectively 27.42 and 64.26 square units.
What is Perimeter of the shape?A shape's perimeter is its circumference. How are perimeters determined? By adding the lengths of each side of a shape, the border may be obtained.
A shape comprised of two circles and a rectangle has been provided.
the size of a circle = 12 - 6 = 6
then radius = 3 units
Perimeter = 3+3+3+3+3+3+π(3)
= 18 + 3.14(3)
= 18 + 9.42
= 27.42 units
and
Area = area of rectangle + area of two half circles
= 12(3) + π(3)²
= 36 + 28.26
= 64.26 sq units.
Therefore, the shape's needed area and perimeter are respectively 27.42 and 64.26 square units.
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Andy has -$45 in his checking account at the beginning of the week. At the end of the week he was paid $30 for moving the grass and $25 for vacuuming the house. How much money does Andy now have in his checking account?
Answers
Answer:
we need to add the money Andy earned to the negative balance he had. So, we have:
-$45 + $30 + $25 = $10
Therefore, Andy now has $10 in his checking account.
Answer:
Andy now has $10 in his checking account.
Step-by-step explanation:
Andy starts the week with -$45 in his checking account. When he gets paid $30 for mowing the grass and $25 for vacuuming the house, his total earnings for the week are:
$30 + $25 = $55
To find out how much money he now has in his checking account, we need to add his earnings to his starting balance of -$45. Adding a negative number is the same as subtracting a positive number, so we can write this as:
-$45 + $55 = $10
Therefore, Andy now has $10 in his checking account.
Write 4 as a logarithm with a base 4
Answers
Answer: Algebra Examples
Logarithm base 4 of 4 is 1.
Step-by-step explanation:
unity
The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.
Describe the transformations that would map the graph
of f(x) = x^2 + 1 to the graph of g(x) = (x − 3)^2 − 2.
Answers
The graph of [tex]g(x)[/tex] is the result of taking the graph of [tex]f(x)\\[/tex], shifting it right three units and down two units.