Answer:
1200$
Step-by-step explanation:
(840/(100-30))*100
(840/70)*100
12*100
1200
Differentiate the function.
y = (4x − 1)^2 (4 -x^5)^4
dy/dx=
Answer:
[tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
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]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (4x - 1)²(4 - x⁵)⁴
Step 2: Differentiate
Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[(4x - 1)^2](4 - x^5)^4 + (4x - 1)^2\frac{d}{dx}[(4 - x^5)^4][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(4x - 1)^{2 - 1} \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^{4 - 1} \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot \frac{d}{dx}[(4x - 1)]](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot \frac{d}{dx}[(4 - x^5)]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(4x - 1) \cdot 4x^{1 - 1}](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(4x - 1) \cdot 4](4 - x^5)^4 + (4x - 1)^2[4(4 - x^5)^3 \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 8(4x - 1)(4 - x^5)^4 - 20x^4(4x - 1)^2(4 - x^5)^3[/tex]Factor: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 2(4 - x^5) - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 5x^4(4x - 1) \bigg][/tex][Distributive Property] Distribute -5x⁴: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3 \bigg[ 8 - 2x^5 - 20x^5 + 5x^4 \bigg][/tex][Brackets] Combine like terms: [tex]\displaystyle y' = 4(4x - 1)(4 - x^5)^3(-22x^5 + 5x^4 + 8)[/tex]Factor: [tex]\displaystyle y' = -4(4x - 1)(4 - x^5)^3(22x^5 - 5x^4 - 8)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Simplify the following polynomial expression.
3x(-2x + 7) - 5(x -1) (4x -3)
The simplest polynomial expression is
-26x^2+56x-15
Answer: -26x^2 + 56x -15
Step-by-step explanation:
3x(-2x + 7) - 5(x -1) (4x -3)
-6x^2 + 21x - (5x + 5)(4x-3)
-6x^2 + 21x -20x^2 +15x + 20x -15
= -26x^2 + 56x -15
The sum of two consecutive numbers is 89. What are the two numbers? A. 43 and 46 B. 44 and 45 C. 38 and 51 D. 45 and 46
Answer:
C
Step-by-step explanation:
Its C
I don’t need you to explain just answer.
Answer:
domain= {-4,2,3,4}
range = {-4,0,2,3}
Give the domain and range.
Answer:
Domain is {-2,0,2}
Range is {4,6,8}
Step-by-step explanation:
The domain is the input or x values
Domain is {-2,0,2}
The range is the output or y values
Range is {4,6,8}
Help :(((((((((( please
Answer:
the ratio of the circumference of a circle to its diameter
Step-by-step explanation:
PLEASE HELP ME OUT PLEASE PLEASE IT WOULD BE HELPFUL THANK YOU
Answer:
D
Step-by-step explanation:
Starts with 2
2 x 2 = 4
4 x 2 = 8
8 x 2 = 16
and so on
Find the counterexample to one of the following statements
1). A triangle cannot have an angle that is greater than 90º .
2). The product of two positive numbers is always greater than their sum.
Answer:
1) You know that the addition of all interior angles of a triangle always should add up to 180°
Then, for example, we can construct a triangle with angles
100°, 40°, 40° such that
100° + 40° + 40° = 180°
So we have an example of a triangle that has one angle greater than 90°.
2) Suppose that we have the positive numbers 0.5 and 1.
The product is: P = 0.5*1 = 0.5
the sum is: S = 0.5 + 1 = 1.5
The sum is greater than the product.
The temperature falls from 0 degrees to -12.4 degrees in
13 1/2
hours. Which expression finds the change in temperature per
hour?
Answer:
Step-by-step explanation:
The temperature falls from 0 degrees to -12.4
0-(-12.4) = 12.4
12.4/13.4 degree per hours
0.9185 degrees/ hour
Sam has three identical tennis balls with a diameter of 2.7 inches. Determine the volume of all three tennis balls?
Your answer would be approximately 30.93
Volume of a sphere is V=4 /3πr^3
Two sides of a triangle have lengths of 5 and 9. Which inequalities
represent the possible lengths for the third side, x? *
Answer:
4 < x < 14
Step-by-step explanation:
The third side is between the difference and the sum of the other two sides
9-5 < x < 9+5
4 < x < 14
what is the difference for -22 - (-26)
Answer:
4
Step-by-step explanation:
Factor. x2−8x+16
(x+8)2
(x−4)2
(x+4)2
(x−8)2
Answer:
B
Step-by-step explanation:
[tex]x^2-8x+16= \\\\(x-4)(x-4)=\\\\(x-4)^2[/tex]
You can confirm this by working in reverse:
[tex](x-4)^2= \\\\(x-4)(x-4)=\\\\x^2-4x-4x+16=\\\\x^2-8x+16[/tex]
Hope this helps!
Answer:
(x−4)^2
Step-by-step explanation:
I did the test
13. Nine less than a number is no more than 8 and is no less than 3.
Step-by-step explanation:
I think we can choose the number 5 so
9 - 5 = 4 no more than 8 and less than 3
Answer:
[tex]&#x \in [12, 17][/tex]
Step-by-step explanation:
[tex]3 \leq x-9 \leq 8 \\ \\ \leq x-9 \\ 3+9 \leq x \\ \leq x[/tex]
[tex]&#x-9 \leq 8 \\&#x \leq 8+9 \\&#x \leq 17 \\ \leq x \leq 17[/tex]
[tex]&#x \in [12, 17][/tex]
3. a. Come up with a probability problem that deals with dependent events.
b. Solve the probability problem in part a. please need help I will be MARKING as BRIANILIST, thank you so much.
A girl has 20 marbles
10 are red, 7 are blue, and 3 are green
If she picks 5 marbles, without replacing them, what are the chances all 5 are red?
10/20 * 9/19 * 8/18 *7/17 * 6/16
1/2 * 9/19 * 4/9 * 7/17 * 3/8
1/2 * 1/19 * 3/2
1/76
Find the perimeter and area of the rectangle given below. A rectangle ABCD with vertices A(2,4), B(2,7), C(5,7), and D(5,4).
Answers:
Perimeter=6 units
Area=0 units ^2
please see the attached picture for full solution
hope it helps
Good luck on your assignment
whats a quadrilateral with two sides going in the same direction
Answer:
Trapezoid.
Step-by-step explanation:
That is a trapezoid ( in the UK a trapezium).
There is a pair of parallel sides.
Using the following image, solve for x.
Answer:
x=6
Step-by-step explanation:
(2+x)+1=2x-3
3+x=2x-3 . Combine like terms
6+x=2x Add 3 to both sides
x=6 Subtract X from both sides
AC =
Round your answer to the nearest hundredth.
B
6
70degrees
A
?
с
Answer:
AC ≈ 2.18 units
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan70° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{6}{AC}[/tex] ( multiply both sides by AC )
AC × tan70° = 6 ( divide both sides by tan70° )
AC = [tex]\frac{6}{tan70}[/tex] ≈ 2.18 ( to the nearest hundredth )
One angle is
angle is 65 degrees, the other is
90 degrees, what is my missing angle?
What is my first and last name?
Answer:
your missing angle is
90+65 = 155
180-155 = 25
so your missing angle is 25 degrees
For the graph, locate the x-intercept and y-intercept.
x-intercept = -4, 4, -8, or 8
y-intercept = -4, 4, -8, or 8
Answer:
The x-intercept is at
✔ (6, 0)
The y-intercept is at
✔ (0,-2)
Step-by-step explanation:
this is for the second question of this problem
Find the length of AB
Give your answer to 1 decimal place
Answer: 6.452cm.
As 1 decimal place it would be 6.5cm.
Answer:
6.9 cm
Step-by-step explanation:
a^2 + b^2 =C^2
a^2 + b^2 = 8^2
6.9^2 +4^2 =64
47.61 + 16 = 64
47.61 about 48
Solve for n
n+1 = 4(n-8)
0 n = 1
On = 8
0 n = 11
0 n = 16
Please help ASAP- will give brainliest! Picture Below
Answer:
c
Step-by-step explanation:
Answer:
A - ( 2, - 4 )
Step-by-step explanation:
M, N , O is reflected at the points (-2,2) - O (-5,3) - M (-2,4) - N, and the triangle MNO is rotated 180 degrees around the origin , Down once because the triangle is being rotated around the origin and then right which would be the answer A. Hope this Helps : )
Which best compares the volumes of cylinder X and cylinder Y?
A. The volume of cylinder X is less than the volume of cylinder Y.
B. The volume of cylinder X is equivalent to the volume of cylinder Y.
C. The volume of cylinder X is greater than the volume of cylinder Y.
D. There is not enough information to compare the volumes.
Considering the equation for the volume of a cylinder, it is found that the correct statement is:
A. The volume of cylinder X is less than the volume of cylinder Y.
What is the volume of a cylinder?
The volume of a cylinder of radius r and height h is given by:
[tex]V = \pi r^2h[/tex]
In this problem, cylinder Y suffered an inclination, hence it's radius increased, having a higher volume than cylinder A, as they have the same height, hence option A is correct.
More can be learned about the volume of a cylinder at https://brainly.com/question/9408912
Answer:
It is answer B
Step-by-step explanation:
this is because of law of Cavalieri which states that if a shape has the same radius(or length and base) and same height, it has the same volume.
Express the series using sigma notation. 6 + 9 + 12 + 15.
15
Σ 40
n=6
explanation; add all the numbers to get 40
6 is the first number and 15 is the last number
Answer: D on edg
Step-by-step explanation:
Marsha wanted to survey the students in the eighth grade about their favorite type of music. Which
group of students could she ask so that her sample is random?
Answer:
add more information
Step-by-step explanation:
Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle
Answer:
We find half the measure of the central angle of the circle. Where the given shape is a semi-circle, then the inscribed angle is half of 180, therefore, 90 degrees and a right angle is proven. We show this as Angle BAC is a RA 360 is the measure of circle 360/2 = 180 the semi circle Angle BAC is 180/2 = 90 degree.
Step-by-step explanation:
Hope it helps you!
Answer:
A circle measures 360 degrees, so a semicircle measures 180 degrees. By using the inscribed angle theorem, the measure of the inscribed angle would be half of 180 degrees, or 90 degrees, which is a right angle.
Step-by-step explanation:
Specifically from the edge answer just copy and paste
How do you convert a decimal into a mixed number 10.5
Answer:
10[tex]\frac{1}2}[/tex]
Step-by-step explanation:
10.5 represents a whole number of 10 and a leftover .5 value.
.5 represents one half
the fraction for one half is 1/2.
leaving you with 10[tex]\frac{1}{2\\}[/tex]
What is the measure of ZY, in degrees?