Answer:
y=6x
Step-by-step explanation:
In this function, the input is the variable x. The problem says that the output is six times the input, so we will need to multiply the input by 6. To write this as a function, set the output (y) equal to 6 times the input (x):
what is the slope of 2y + 8x = 20
Answer:
y=4x+10
Step-by-step explanation:
2y-8x-20=0
2y-8x=0+20
2y-8x=20
2y=8x+20
y=4x+10
Hope this will help!!:)
Which list shows the following set of numbers in descending order?
{-8, 0, -10, 2, -2}
Answer:
-10, -8, -2, 0, 2
Step-by-step explanation:
hope this helps!
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!
NEED HELP ASAP ILL GIVE BRAINLIST RN
For ΔABC, the measure in degrees of angles A, B, and C are 36, 3x, and 48 respectively. What is the value of x?
A
2
B
32
C
93
D
96
Answer:
B. 32
Step-by-step explanation:
[tex]\angle A + \angle B + \angle C = 180\\36 + 3x + 48 = 180 => 3x = 96 => x = 32[/tex]
Answer:
bgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbgbg
Step-by-step explanation:
How you Can find the area of a composite figure?
Answer:
Here are the steps to find the area of a composite figure.
1. Split the composite figure into simpler shapes.
2. Find the area of each of the simpler shapes.
3. Add the area of all the simpler shapes together.
4. You'll have the area of the composite figure.
Let me know if this helps!
1d - 2) = 6
4
What is the value of d + 3?
Step-by-step explanation:
6 c. 2 d. 6 e. a2 + 2a + 3 f. (x + h)2 + 2(x + h) + 3 9. a. 2 b. 0 c. 65/4 d. x2 + 1/x e. (s + h)2 + 1/(s +
Use the given x and y values to write a direct variation
equation.
x = 2, y = 30
Answer:
y = 15x
Step-by-step explanation:
Given x and y are in direct variation then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 2, y = 30, then
30 = 2k ( divide both sides by 2 )
15 = k
y = 15x ← equation of variation
Hi can you help me with this?
Answer:
-3.9/1
Step-by-step explanation:
Answer:
I think 5
Step-by-step explanation:
9 ×+1-4 hdjxnxnnxnx
Compute (4803) • 95. *
Answer:
456,285
zzzzzzzzzzzzzzzzzzzzz
A newborn baby weighs 8 pounds. At her three month check-up, her weight has increased by 60%. How much does she weigh at the check-up?
Answer: You have to multiply the weight by the precentage I think, which would be: 480 Pounds
Step-by-step explanation:
Answer:
12.8 pounds
Step-by-step explanation:
All you do is 8+60% = 12.8
Hope this helps! Please consider marking brainliest! I hope you have an amazing day. Always remember, your smart and you got this! -Alycia
Two parallel lines are cut by a transversal as shown below.
Suppose m<8=109. Find m<2 and m<3.
Answer:
measure 2 has to be 109 due to the alternate interior angles theorem. Measure 3 has to be 71 due to the supplementary angles theorem.
Angles 8 and 2 are alternate interior angles so they will be the same therefore,m∠2 and m∠3 will be 109° and 71° respectively.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—is known as the vertex.
Given two parallel lines a transversal.
Angles 8 and 2 are alternate interior angles.
m∠8 = m∠2
m∠2 = 108°
Now,m∠2 and m∠3 are supplementary angles.
Therefore,m∠3 = 180° - 108° = 71°
Hence "Angles 8 and 2 are alternate interior angles so they will be the same therefore,m∠2 and m∠3 will be 109° and 71° respectively".
For more about the angle,
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HELP PLEASE!!
Helen rolls a dice and flips a coin.
Calculate the probability that she gets a 4 and a tail.
Answer:
Step-by-step explanation:
The probability of getting a 4 is 1/6, the probability of getting a tails is 1/2. Add the two together 8/12. I don't know if its right but hopefully it helped.
Which equation represents the line that passes through
the points (2, 3) and (4, 7)?
Answer:
Step-by-step explanation:
(7 - 3)/(4 - 2) = 4/2 = 2
y - 3 = 2(x - 2)
y - 3 = 2x - 4
y = 2x - 1
help!! timed! find the domain and range pls!
Answer:
domain: (-infinity, infinity)
range [-41/4, infinity)
An architect designed a lobby wall to have an embedded circular clock. The equation (x – 4)^2 + (y – 7)^2 = 1, with units in meters, represents the location of the clock relative to the bottom left corner of the wall. How high above the ground is the center of the clock?
1 m
4 m
7 m
8 m
The height of the center of this circular clock (x - 4)² + (y - 7)² = 1, is 7 meters above the ground.
What are the types of equations of a circle?The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.
The standard equation of a circle is x² + y² = r².
The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².
We know the standard formula of a circle is x² + y² = r² centered at the origin.
Now, (x - h)² + (y - k)² = r² represents a circle centered at (h, k).
Given, The equation (x - 4)² + (y - 7)² = 1, with units in meters, represents the location of the clock relative to the bottom left corner of the wall.
Therefore, (4, 7) is the center of the clock in the x-y axis when the y-axis represents height so it is 7 meters above the ground.
learn more about circles here :
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hello My name es Liliana y arigato bye
Answer:
?????.... hii erica herrrr
Answer:
Hi Liliana i love your name! it's very pretty:) my name is Melody
Step-by-step explanation:
x-3y=7
2х-6у=12
Solve the following systems
Answer:
Step-by-step explanation:
this system doesnt have any solutions
if you multiply the first equation by 2 you will get
2x-6y=14
second equation is
2x-6y=12
the result will -12=14
no solutions
Distribute 3x ( -x + 4).
Find a value of x that is a solution to 5(x – 3) = x + 13.
Answer:
x = 7
Step-by-step explanation:
[tex]5(x-3)=x+13[/tex]
distribute
[tex]5x-15= x+13[/tex]
combine like terms
[tex]5x-x = 13 + 15[/tex]
[tex]4x=28[/tex]
x = 7
Answer:
x=7
Step-by-step explanation:
[tex]5(x-3)=x+13\\5x-15=x+13\\Subtract x from both sides \\4x-15=13\\Add 15 to both sides\\4x= 28\\Divide both sides by 4\\x=7[/tex]
Now check your answer
[tex]5(7-3)=7+13\\35-15=20\\20=20[/tex]
What is the next fraction in this sequence?
1
5
,
1
10
,
1
20
,
1
40
, ...
Answer:
1/80 (i think)
Step-by-step explanation:
The floor of a rectangular shed is 12 ft by 14 ft.
What is the area of the floor in square feet?
Answer:
Step-by-step explanation:
S=a*b=12*14=168feet²
Work out the percentage change to 2 decimal places when a price of £12 is increased to £15.99
BRAINLIEST N 15 POINTS
Table to Linear Equation
Answer:
Y=-5X+1
Step-by-step explanation:
Answer:
y = -5x + 1
Step-by-step explanation:
y = mx + b
m = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1}}[/tex] = [tex]\frac{-9-(-4)}{2-1} = -5[/tex]
y = -5x + b: then plug in a point to find b
-19 = -5(4) + b
-19 = -20 + b
b = 1
Plug in all the values to get: y = -5x + 1
Enter equations one at a time in order to send a line
through the coins to "capture" them.
Answer:
y = x + 3
y = 3x + 1
Step-by-step explanation:
This does it in two equations.
y = x + 3 and y = 3x + 1 equation will send 2 different lines through the coins to capture them
using the slope intercept equation,
y = mx + b
m = slope
b = y-intercept
let's pick 2 coordinate from the graph,
(-2, 1)(-1, 2)
m = 2 - 1 / -1 - (-2) = 1 / 1 = 1
1 = -2 + b
b = 3
Therefore,
y = x + 3
let check for another equation that will work for another line. Let's use the coordinates (-1, -2)(0, 1) to find slope.
Therefore,
m = 1 - (-2) / 0 - (-1) = 3 / 1 = 3
y = 3x + b
1 = 3(0) + b
b = 1
y = 3x + 1
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the store offers a 40% discount the regular price of a t-shirt is 22 what is the discount price?
Answer:
$8.80
Step-by-step explanation:
So because [tex]40\% = .4[/tex], then the equation is [tex].4 \times 22[/tex] which equals [tex]8.8[/tex], or $8.80.
−214=r−45
Help
Asp
Plz
Answer:
-169
Step-by-step explanation: add 45 on both sides
Answer:
r=-169
Step-by-step explanation:
I hope it helped bro
What is the slope of the graphed line?
Answer:
3/9
Step-by-step explanation:
3/9 because it goes up 3 right 9
Bobby had a box of berry flavored hard candies. Fifteen candies were strawberry flavored, twelve candies were blueberry flavored, and thirteen candies were raspberry flavored. Bobby picked one candy from the box without looking. What is the probability, written as a percent, that the candy he picked was not raspberry flavored?
15 strawberry
12 blueberry
13 raspberry
27/40
is this correct??
ONLY ANSWER IF YOU ARE FOR SURE RIGHT!
the question: “which trig. ratio woild you use to find the missing side?”
Answer:
Step-by-step explanation:
It's not the tangent. The tangent relates two sides neither of which is the hypotenuse, which you are given.
The trig ratio you would use is the one that relates the angle to the side opposite the angle and the hypotenuse.
That is the definition for the Sine.
Help plz
(1,-4)
(4,1))
(-1,-4)
(1,4)
Answer:
(1, -4)
Step-by-step explanation: