Answer:
[tex]\displaystyle y' = -100x^4(2x^5 - 1)[/tex]
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsFactoringFunctionsFunction NotationCalculus
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 [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (-4x^5 + 4)5x^5[/tex]
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(-4x^5 + 4)]5x^5 + (-4x^5 + 4)\frac{d}{dx}[5x^5][/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle y' = (5 \cdot -4x^{5 - 1} + 0)5x^5 + (-4x^5 + 4)(5 \cdot 5x^{5 - 1})[/tex]Simplify: [tex]\displaystyle y' = (-20x^4)5x^5 + (-4x^5 + 4)(25x^4)[/tex]Factor: [tex]\displaystyle y' = 5x^4 \bigg[ (-20x^4)x + (-4x^5 + 4)5 \bigg][/tex][Distributive Property] Distributive parenthesis: [tex]\displaystyle y' = 5x^4 \bigg[ -20x^5 - 20x^5 + 20 \bigg][/tex]Combine like terms: [tex]\displaystyle y' = 5x^4(-40x^5 + 20)[/tex]Factor: [tex]\displaystyle y' = -100x^4(2x^5 - 1)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
A sociologist wants to know the opinions of employed adult women about government funding for day care. She obtains a list of the 520 members of a local business and professional women's club and mails a questionnaire to 100 of these women selected at random. Only 48 questionnaires are returned
Answer:
stratified random sampling
Step-by-step explanation:
The sampling design that is involved in the above study is the stratified random sampling design. In the study the population of sample is divided into two kinds of members. The two kinds of members are the local business members and the professional club members in a local area. These are called the stratums. The sociologist wishes to collect data or information from these two types of people.
I'll give the brainliest!! The first three terms of the sequence is 23, 20, 17
What are the next two terms in this sequence
Answer:
26 29
Step-by-step explanation:
Darius took a road trip to their grandmother's house. They drove at a constant speed of 60 miles per hour for 2 hours. They took a break and then finished the rest of their trip driving at a constant speed of 50 miles per hour for 2 hours. What was the total distance, in miles, of Darius' trip?
Answer: 220 miles
Step-by-step explanation:
Distance travelled is calculated as:
= Speed × Time
Based on the scenario on the question, the total distance, in miles, of Darius' trip will be:
= (60 × 2) + (50 × 2)
= 120 + 100
= 220 miles
I need help on this pls
Answer:
y = 3x - 1
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define equation
y - 3x = -1
Step 2: Find Slope-Intercept Form
Add 3x to both sides: y = 3x - 1And we have our final answer!
Solve. Show each step. 5.4 2 6x 5 26 as a single answer
Answer:
x=10
Step-by-step explanation:
distribute -8 - 8(4b + 3)
I'll give you a pdf so you can see it yourself and the correct answer is -32b - 32b
Which equation can be used to find 55 percent of 900? StartFraction 55 times 1 Over 900 times 1 EndFraction = StartFraction 55 Over 900 EndFraction StartFraction 100 times 16.36 Over 55 times 16.36 EndFraction = StartFraction 1636 Over 899.8 EndFraction StartFraction 900 times 9 Over 100 times 9 EndFraction = StartFraction 8100 Over 900 EndFraction StartFraction 55 times 9 Over 100 times 9 EndFraction = StartFraction 495 Over 900 EndFraction
Answer:
Step-by-step explanation:
55/100*900=55*9
495.
Answer:
bro i cant find it make it do abc or d like come on
Step-by-step explanation:
PLEASE
A daredevil decides he wants to jump out of a plane and parachute to the U.S.S. Showboat. He knows he needs to leave the plane at an angle of 58˚ from vertical and he knows he wants to wait until the horizontal distance to the boat is 1000yd. How far away should the plane be from the boat to complete his aerial stunt successfully?
Answer:
1179 yards
Step-by-step explanation:
The question can be described by a right angled triangle.
The angle of depression of the boat from the plane = [tex]90^{o}[/tex] - 58˚
= [tex]32^{o}[/tex]
Let the distance from the plane to the boat be represented by x.
Thus, applying the appropriate trigonometric function, we have;
Cos θ = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos [tex]32^{o}[/tex] = [tex]\frac{1000}{x}[/tex]
x = [tex]\frac{1000}{Cos 32^{o} }[/tex]
= [tex]\frac{1000}{0.8481}[/tex]
= 1179.11
x = 1179 yds
The plane should be 1179 yards away from the boat.
20pts
Divide algebraic fraction pls
12a2/18b2÷4a/3b
Answer:
3a/6b
Step-by-step explanation:
12a^2/4a
= 12/4 * a^2/a
= 3a
18b^2/3b
= 18/3 * b^2/b
= 6b
Hence, the answer is 3a/6b.
Hope this helped!
PLEASE HELP ASAP 25 POINTS!!
Provide a picture if possible!
I NEED THIS ASAP
what is the answer to 1.97 x 10^3 =
If you want to leave an 18% tip for a waiter on a $54.35 meal, what would the total bill be?
$64.13
$9.78
$44.57
$8.15
Answer:
$64.13
Step-by-step explanation:
the tip would be added to the meal cost
Answer:
54.35+$9.78=64.13
Step-by-step explanation:
54.35*.18=9.78
Hope this helps :)
The width of a rectangular room is 80% of its length. It’s 15 feet long. What is the area of the room?
Answer:
180ft^2
Step-by-step explanation:
w = .8l = 15 x .8 = 12ft
A = l x w = 15 x 12 = 180ft^2
The total cost, c, in dollars to create calendars for a fundraiser can be found using the function c=5.5u+25 where u is the number of calendars made. If there are at least 10 calendars made, what is a possible domain for this function?
A: 10≤x≤100
B: {-12, -11, 12, 20, 50}
C: {10, 11, 12, 13, 14}
D: 0≤x<50
Answer:
The correct option is;
{10, 11, 12, 13. or 14}
Step-by-step explanation:
The given function for the total cost, c, to create calendars is c = 5.5u + 25
The domain of a function are the values of the input variables of the function with which the output (the values) of the function are found
Therefore, the domain of the given function are the values of the variable, u, in the function
Where;
u = The number of calendars made
∴ When u ≥ 10, we have;
The possible domain for the function are u = 10, 11, 12, 13. or 14...
Therefore, the correct option is {10, 11, 12, 13. or 14}
Find the volume of this cylinder.
Give your answer to 1 decimal place.
9 cm
20 cm
Answer:
Question is incomplete
Use volume v. =
Step-by-step explanation:
Pie×r^2 ×h
1)
x 0 1 2 3 4
f(x) _ _ _ _ _
Answer:
Calculated and given below:
1) f(x) = -14, 1, 6, 1, -142) f(x) = -4, 5, 8, 5, -43) f(x) = 27, 33, 35, 33, 274) f(x) = -5 , -8, -9, -8, -5 5) f(x) = -7 , -10, -11, -10, -7 6) f(x) = -7 , -34 , -43 , -34 , -7 7) f(x) = 47 , 17 , 7 , 17 , 47 8) f(x) = 29 , 8 , 1 , 8 , 29 9) f(x) = -19 , -1 , 5 , -1 , -19 10) f(x) = 21 , 9 , 5 , 9 , 21DEA if the diameter is 7 in
ayden has 5.5 gallons of gasoline in his suv’s fuel tank before it starts refilling. the capacity of the fuel tank in aydens suv is 21 gallons. what is an equation that relates the amount of gasoline ayden purchased, p, in gallons and the amount of gasoline in the fuel tank, A after the purchase? what values of P could be viable solutions?
Answer:
[tex]0<p\leq15.5[/tex]
Step-by-step explanation:
Amount of gasoline in the tank is 5.5 gallons
21 gallons is the capacity of the fuel tank in the car
A is the amount of gasoline in the fuel tank after purchase which will be less than or equal to 21 gallons.
So the equation will be
[tex]5.5+p\leq A\\\Rightarrow 5.5+p\leq 21\\\Rightarrow p\leq 21-5.5\\\Rightarrow p\leq 15.5[/tex]
So, the value of p is in the range of [tex](0,15.5][/tex] or [tex]0<p\leq15.5[/tex].
Is the graphed function linear?
O Yes, because each input value corresponds to
exactly one output value.
O Yes, because the outputs increase as the inputs
increase.
O No, because the graph is not continuous.
O No, because the curve indicates that the rate of
change is not constant.
Answer:
No, because the curve indicates that the rate of
change is not constant.
Im 99.9 sure
Step-by-step explanation:
No, because the curve indicates that the rate of change is not constant.
What is Linear function?The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
Given:
From the graph we can write the points as
(1, 0), (2, 25), (3, 50), (4, 100), (5, 150), (6, 200), (7, 290)
Since from the above points we can see that there is no constant rate of change followed by the points which the graph Curve.
Also, the linear function usually have the straight line graph.
Learn more about Linear function here:
https://brainly.com/question/20286983
#SPJ5
A large water reservoir can be well modeled with a hemisphere whose radius is 630 meters. Given the volume formula for a sphere, 4 3 3 V r , find the volume of water the reservoir can hold. Show your substitution. Express your answer in scientific notation with two decimal places of accuracy.
Answer:
[tex]V=5.23\times 10^8\ m^3[/tex]
Step-by-step explanation:
A large water reservoir can be well modeled with a hemisphere whose radius is 630 meters.
The volume of a hemisphere is given by :
[tex]V=\dfrac{2}{3}\pi r^3[/tex]
Substitute r = 630 m in the above formula
[tex]V=\dfrac{2}{3}\pi \times (630)^3\\\\=5.23\times 10^8\ m^3[/tex]
So, the water reservoir can hold [tex]5.23\times 10^8\ m^3[/tex] of water.
Please help
Person with the right answer I will mark Brainlyist
Answer:
The equation in the standard form is
[tex]y+2x=5[/tex]
Step-by-step explanation:
Given the points
(6, -7)(4, -3)Finding the slope between (6, -7) and (4, -3)
[tex]\left(x_1,\:y_1\right)=\left(6,\:-7\right),\:\left(x_2,\:y_2\right)=\left(4,\:-3\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-3-\left(-7\right)}{4-6}[/tex]
[tex]m=-2[/tex]
As the point-slope form is defined as
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = -2 and the point (6, -7)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-7\right)=-2\left(x-6\right)[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
converting the equation in standard form
[tex]y-\left(-7\right)=-2\left(x-6\right)[/tex]
[tex]y+7=-2\left(x-6\right)[/tex]
subtract 7 from both sides
[tex]y+7-7=-2\left(x-6\right)-7[/tex]
[tex]y=-2x+5[/tex]
[tex]y+2x=5[/tex]
Therefore, the equation in the standard form is
[tex]y+2x=5[/tex]
WILL GIVE BRAINLIEST determine if linear. if it is, find the rate of change
PLEASE HELP
what is the geometric mean of 4/5 and 2
Answer:
ok ummm 5
Step-by-step explanation:
Find the zero of the function.
g(x) = x2 + 22x + 121
The zero of the function is x=
Answer:
x = -11
Step-by-step explanation:
To find the zero of this function, factor the equation:
g(x) = [tex]x^{2} +22x+121[/tex]
g(x) = (x + 11) (x + 11)
g(x) = [tex](x+11)^{2}[/tex]
The zeros of a function are the values of x that will make g(x) equal 0. So, the zero of this function is -11, because -11 + 11 = 0. So, x = -11.
will mark BRAINLIESTT
Answer:
2.5
Step-by-step explanation:
16-13.50
Answer:
Muffins: $1.50
Bagels: $1.00
Step-by-step explanation:
Ight, so this is a system of equation. Let's find the variables first.
m = amount of muffins
b = amount of bagels
4b + 8m = 16
6b + 5m = 13.50
Any questions let me know! Hope this helps and have a great day!
i need help with this asappp
Which list has the numbers in order from least to greatest?
A -3, -8/3, 1/3, 4.7, 4
B-8/3, 1/3, -3, 4.7, 14
3,-8/3, 4 1/3, 4.7
-3, -8/3, 1/3, 74 4.7
Answer:b I think
Step-by-step explanation:
2π+x=180 solve for x!
Answer:
x=28.65
Step-by-step explanation:
2π+x=180
π+x=90
x=90/π
x is about 28.65
Answer:
Exact Form:
[tex]x=180-2\pi[/tex]
OR
Decimal Form:
[tex]x=173.71681469...[/tex]
Step-by-step explanation:
Step-By-Step on how to solve it is in the attached picture.
Hope this helps! :)
9 Modelling The inside of a saucepan has diameter 20 cm and height 13 cm.
The manufacturer claims that the pan has a capacity of 4 litres.
Is the claim correct?
Explain your answer.
Could i get help
Answer:
The inside of a saucepan has a cylindrical shape so the capacity of a saucepan is: [tex]V=\pi .(\frac{20}{2})^{2}.13=4084(cm^{3})=4.084(l)[/tex]
Step-by-step explanation:
When asked about favorite Thanksgiving leftovers, 40% of the people said ham, and 410 said turkey. Which food is more popular? How do you know?
ham by 60 percent :
i just dont