Answer:
5.714 (rounded to the nearest thousandth)
Step-by-step explanation:
i need help plssssssssssssss
Answer:
It doesn't show what the drop down is. However, both of those are linear expressions.
Sergio's expressionn siplifies to: 9+3x (because two minuses cancel each other).
Leon's expression cancels to 12+6x (because 9+3=12)
Step-by-step explanation:
You have to show the dropdown to be able to answer exactly what they are looking for as an answer.
A light bulb is designed by revolving the graph of:
[tex]y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}[/tex]
Over the interval 0 ≤ x ≤ 1/3 about the x-axis, where x and y are measured in feet. Find the surface area of the bulb and use the result to approximate the amount of glass needed to make the bulb. (Glass is 0.015 inch thick).
Answer:
[tex]\displaystyle 0.251327 \ in. \ of \ glass[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringCalculus
Differentiation
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
Integration Property: [tex]\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx[/tex]Fundamental Theorem of Calculus: [tex]\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)[/tex]Area between Two CurvesVolumes of RevolutionArc Length Formula: [tex]\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx[/tex]Surface Area Formula: [tex]\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}][/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}[/tex]Step 3: Integrate Pt. 1
Substitute [Surface Area]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx[/tex][Integral - √Radical] Expand/Add: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx[/tex][Integral - √Radical] Factor: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx[/tex][Integral - Simplify]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx[/tex][Integral] Integration Property: [tex]\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx[/tex]Step 4: Integrate Pt. 2
[Integral] Define: [tex]\displaystyle \int {|9x + 1|(3x - 1)} \, dx[/tex][Integral] Assumption of Positive/Correction Factors: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx[/tex][Integral] Expand - FOIL: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx[/tex][Integral] Integrate - Basic Power Rule: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)[/tex][Expression] Multiply: [tex]\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}[/tex]Step 5: Integrate Pt. 3
[Integral] Substitute/Integral - FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}[/tex][Integrate] Evaluate FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})[/tex][Expression] Multiply: [tex]\displaystyle SA = \frac{\pi}{27} \ ft^2[/tex]It is in ft² because it is given that our axis are in ft.
Step 6: Find Amount of Glass
Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.
Convert ft² to in²: [tex]\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2[/tex]Multiply: [tex]\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass[/tex]And we have our final answer! Hope this helped on your Calc BC journey!
What is the area of this figure?
Enter your answer in the box.
mm²
Composite figure composed of a a right triangle with a base of 3 mm and a height of 4 mm, and two rectangles, one with side lengths of 3mm and 4mm, the other with side lengths of 1 mm and 6 mm.
Answer:
18 mm²
Step-by-step explanation:
Firstly, I do not think the person above me has the correct answer.
Okay, so I am not very good at explaining things but I will try. When finding the area of a composite figure, you add Area A + Area B.
So for this equation, figure one has a length of 4mm and a width of 3mm. Remember when we are finding the area of a shape, we multiply Length times Width. So, figure one has an area of twelve. The Same applies to figure two. Figure two has a length of 1mm and a width of 6mm, we multiply one by six and get six. Now we add the area of the twelve and six and we get 18mm²
I understand that my explaining skills suck, so I will show it in an easier way
Area A = 4mm x 3mm
Area A = 12mm
Area B = 1mm x 6mm
Area B = 6mm
Area A + Area B = Total Area
12mm + 6mm = 18mm²
So, 18mm² will be your answer.
I hope this helps.
Sorry if it isn't helpful or correct.
The total area of the composed figure with right triangle and two rectangles is 24 square millimeters.
What is Area of Rectangle?The area of Rectangle is length times of width.
Composite figure has a right triangle and two rectangles.
right triangle with a base of 3 mm and a height of 4 mm
Area of triangle = 1/2×4×3
=6 square millimeter
Area of first rectangle with side lengths of 3mm and 4mm
Area of first rectangle = 3 × 4
= 12 square millimeter
Area of second rectangle with side lengths of 1mm and 6 mm
Area of second rectangle =1×6
=6 square millimeter
Total area is 6+12+6 which 24 square millimeters.
Hence, the total area of the composed figure with right triangle and two rectangles is 24 square millimeters.
To learn more on Rectangles click:
https://brainly.com/question/20693059
#SPJ3
A store sells a pound of bananas for $0.40 and a pound of cabbage for $0.56. Can you buy more pounds of bananas or cabbage with $7? How many more pounds?
Answer:
The bananas will cost $1.38.
Step-by-step explanation:
Explanation:
Multiply the number of pounds by the price per pound.
2.51lb×$0.55lb=$1.38
PLZ ANSWER QUICK IT WILL HELP A LOT!
Answer:
A
Step-by-step explanation:
The two triangles shown are similar. Find the value of b.
Answer:
Since the corresponding sides of similar triangles are proportional,
[tex]\frac{a}{b}= \frac{2.1}{1.4} =\frac{3}{2}[/tex]
A group of friends wants to go to the amusement park. They have no more than $275 to spend on parking and admission. Parking is $5, and tickets cost $27 per person, including tax. Write and solve an inequality which can be used to determine r, the number of people who can go to the amusement park.
Answer:
275=27x+5
Step-by-step explanation:
10 people can go to the park
27(10)+5=275
ANSWER FOR BRAINLIEST
Answer:
x = 10
Step-by-step explanation:
( 6x - 6 ) + ( 7x + 1 ) + 55 = 180
6x + 7x = 180 + 6 - 1 - 55
13x = 130
x = 10
Check:
6(10) - 6 = 56
7(10) - 1 = 69
55 + 56 + 69 = 180 ✔️
Pet Supplies make a profit of $5.50 per bag on the nine of natural dog food. If the store wants to make a profit of no less than $5200, how many bags of dog food does the store I need to sell?
Answer:
=> (5200 X 9)/5.5=8509
Step-by-step explanation:
what is the answer to 4x+10=26
Answer:
x=4
Step-by-step explanation:
4x+10=26
Subtract 10 from both sides
4x=16
Divide by 4
x=4
A mechanic charges $20.00 an hour, h for labor plus parts. If the parts cost $217.00, write a linear equation that will find the total cost, c.
Answer:
y=20x+217
Step-by-step explanation:
25. Explain the Error Jeremy factored 144x? – 100 as follows:
144x2 100 = (12x + 10)(12x – 10)
= 2(6x + 5)(6x – 5)
What was his error? Correct his work.
Given:
Consider the expression is
[tex]144x^2-100[/tex]
Jeremy factored the given expression and his steps are given.
To find:
The error in his solution.
Solution:
We have,
[tex]144x^2-100[/tex]
It can be written as
[tex]=12^2x^2-10^2[/tex]
[tex]=(12x)^2-10^2[/tex]
[tex]=(12x+10)(12x-10)[/tex] [tex][\because a^2-b^2=(a+b)(a-b)][/tex]
Taking out common factors from each parenthesis.
[tex]=2(6x+5)2(6x-5)[/tex]
[tex]=4(6x+5)(6x-5)[/tex]
So, Jeremy was incorrect because the common factor is [tex]2\times 2=4[/tex] instead of 2.
Therefore, Jeremy made his mistake in his last step.
Calculate or Simplify the value of each expression a {-8} . 2/3
Answer:
Step-by-step explanation:
[tex](-8)*\frac{2}{3}=\frrac{(-8)*2}{3}= \frac{-16}{3}[/tex]
Find the area of a rectangle whose length is 5 ½ feet long and 1 3/4 feet wide.
Answer:
11/2 x 7/4 = 77/8 = 9 5/8
Step-by-step explanation:
n the rectangle P Q R S , the side P Q is of length 2 and the side Q R is of length 4
Please i need the answer ASAP
here u go
In the rectangle PQRS , the side PQ is of length 2CM and the side QR is of length 4CM Points T and U lie inside the rectangle so that Triangle PQT and TRIANGLE RSU are equilateral triangles.PLS MARK ME AS BRAINLIST!!!!!
b2-5c
b=15 & c=9
if you can show the work it would be really helpful:)
What number is the same as distance from 0 on a number line as 1 1/2
Answer: What is the distance from 0 on a number line called?
The distance between a number's place on the number line and 0 is called the number's [absolute value]. To write the absolute value of a number, use short vertical lines (|) on either side of the number.
Step-by-step explanation:
Here's a hint. I hope this helps.
Division as Fractions - Word
Name
cach problem. Make sure to write your answer as a fraction.
Henry wanted to collect 65 pounds of cans in 7 days. How much should he
collect each day to reach his goal? Which two whole numbers does your
answer lie between?
Answer:
65/7
=9.28..lies btwn 9 and 10
Step-by-step explanation:
You want to add lace around the outside of your circular kitchen table cloth. If the diameter of the table cloth is 16 cm, then which of the following measurements would represent how much lace you need?
The length of lace would be the circumference of the circle.
Circumference = diameter x Pi
Circumference = 16pi cm
Circumference = 50.24 cm ( approximately)
Answer:
The circumference of the circle.
Step-by-step explanation:
Kate has 48 softballs. She wants to divide them evenly among b softball bags. Which expression represents how many softballs she should put into each bag?
Answer:
Softballs = (48/b)
Step-by-step explanation:
Given that,
Total number of softballs = 48
She wants to divide them evenly among b softball bags.
We need to find an expression that represents how many softballs she should put into each bag.
As it is dividing among b softball, it means we divide 48 and b. So,
[tex]s=\dfrac{48}{b}[/tex]
Hence, the required expression is (48/b).
Math equation with its graph
a) y=3x+2
b) y= -x+5
c) y= 2x-1
d) y= -4x
See picture attached
Please help
Answer:
y=3x+2 to B
y=-x+5 to D
y=2x-1 to C
y=-4x to A
Use synthetic division
1.
(2x3 - 5x2 + 3x + 7) = (x - 2)
Answer:
Step-by-step explanation: that should help
what does 40 centimeters equals in meters
Answer:
Its 0.4 meters!
Step-by-step explanation:
What is the unit rate per year?
Answer:
3.6
Step-by-step explanation:
divide 36 by 10 be sure it's the easiest part
Answer:
Unit rate per year is :---
[tex] \frac{(50.4 - 7.2)}{(14 - 2)} = \frac{43.2}{12} = \boxed{3.6 \: feet \: per \: year} \\[/tex]
3.6 feet per year is the right answer.Please I need help this is already late
the first would be A and hopes this helps
5/8^3+9-1/4^3= I really need help!!!
Answer: 3/8q^3 + 9
Step-by-step explanation:
1. combine like terms 5/8q^3 - 1/4q^3, need to make denominator the same to subtract so multiply 2/2 by 1/4q^3, 5/8q^3 - 2/8q^3 = 3/8q^3
2. final answer is : 3/8q^3 + 9
Hey Everyone I was asking anyone can help with this problem it would really appreciated.
Answer:
angle G = angle I
HGI=HIJ by RHS fact
HGI=HIJ corresponding angles are alwyas congurrent
A line passes through the point (-8, -9) and has a slope of 5/4
Write an equation in slope-intercept form for this line.
Answer:
y = 5/4x + 1
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer/how I got this answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
Answer:
y=(5/4)x(-8)+3
Step-by-step explanation:
EZ
Solve the system of equations by Linear Combination (Elimination)
6x - 2y = 16
x + 2y = 5
a) (3,1)
b) (1,3)
c) Infinite Many Solutions
d) No Solution
PLEASE PLEASE PLEASE HELPPP MEEE
PLEASE DUE IN 20 MINUTES!!!!!!
Write the quadratic function in standard form.
f(x) = (x + 14)2
Answer:
Step-by-step explanation:
It's essential that you use the symbol " ^ " to indicate exponentiation.
Expanding f(x) = (x + 14)^2 results in x^2 + 28x + 196 (which is in standard form)
