It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]
What is cube root 16y^4/x^6
in simplest form?
Cube root of the given expression [tex]\frac{16y^{4} }{x^{6} }[/tex] in simplest form is equals to [tex]\frac{2y }{x^{2} }\sqrt[3]{2y}[/tex].
What is cube root?" Cube root is defined as the number when multiply three times and produce result as one original number one time."
According to the question,
Given expression,
[tex]\frac{16y^{4} }{x^{6} }[/tex]
Cube root of the given expression is,
[tex]\sqrt[3]{\frac{16y^{4} }{x^{6} }} \\\\\implies \sqrt[3]{\frac{(2)^{3}(2) y^{3} (y)}{(x^{2}) ^{3} }}\\\\\implies \frac{2y}{x^{2} } \sqrt[3]{2y}[/tex]
Hence, cube root of the given expression [tex]\frac{16y^{4} }{x^{6} }[/tex] in simplest form is equals to [tex]\frac{2y }{x^{2} }\sqrt[3]{2y}[/tex].
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Answer:
B on edge
trust me bro
Given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?\
Answer:
The directrix is y=6 and focus is (0,4)
The equation of the parabola is,
20-4y=x²
In 1995 the U.S. federal government debt totaled 5 trillion dollars. In 2008 the total debt reached 10 trillion dollars. Which of the following statements about the doubling time of the U.S. federal debt is true based on this information?
Where are the statements?
GEOMETRY HELPPP PLEASEEE
Answer:
Step-by-step explanation:
Module 8: Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Describe how to eliminate the parameter to change from parametric to rectangular form. How does this ability help us with graphing parametric equations?
Answer:
rectangular equation, or an equation in rectangular form is an equation composed of variables like xx and yy which can be graphed on a regular Cartesian plane. For example y=4x+3y=4x+3 is a rectangular equation.
A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x,y)(x,y) , are represented as functions of a variable tt .
x=f(t)y=g(t)x=f(t)y=g(t)
These equations may or may not be graphed on Cartesian plane.
Step-by-step explanation:
I hope this helps
Given that f(x)=x^2 and g(x)=5x+2 , find (f-g)(2), if it exists.
Answer:
(f - g)(2) = -8
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x²
g(x) = 5x + 2
Step 2: Find
Substitute in functions: (f - g)(x) = x² - (5x + 2)[Distributive Property] Distribute negative: (f - g)(x) = x² - 5x - 2Substitute in x [Function (f - g)(x)]: (f - g)(2) = 2² - 5(2) - 2Evaluate: (f - g)(2) = -8Q2 (a). Workout the value of each expression:
i)
X-y when x =
10 and y = 15
n when m
10 and n= = 2
iii) f+2g when f= 5 and g = 10
30
m
Step-by-step explanation:
x=10, y=15
x-y = -5
n=10, m=2
n-m= 8
f=5, g=10
f+2g
5+2(10)
=25
please hello :(
The Venn diagram below shows the type of crops planted by 50 farmers in a particular area.
If a farmer is chosen at random, what is the probability that the farmer planted corn OR lettuce?
Answer:
D ( It may be because I think other two are non relative )
Answer:
b) 1\2
Step-by-step explanation:
A 3000-lb wrecking ball hangs from a 50-ft cable of density 5 lb/ft attached to a crane. Calculate the work done if the crane lifts the ball from ground level to 50 ft in the air by drawing in the cable.
Answer: 227,130 J (or 227 kJ).
How?:
When the force is in the same direction than the displacement, we can express the work of this force as: W = F x h
The force is equal to the total weight of the wrecking ball and the cable. The wrecking ball has a mass of 3000 lb. For the cable, we have to calculate the mass as:
Mc = l x p= 50ft x 7lb/ft= 350lb
The total mass is 3,350 lb.
The magnitude of the force is equal to the weight:
F= mg= 3,350lbf
The work done by this force is:
W=F x h= 3,350lbf x 50ft = 167,500lbf - ft
W= 167,500lbf - ft x 1.356J/1lbf - ft = 227,130 J (or 227 kJ).
Daphne has a rope that is 60 meters long. She wants to use it to mark the boundary of a circle whose radius is an integer. What's the largest possible radius for her circle, in meters?
9514 1404 393
Answer:
9 m
Step-by-step explanation:
The relationship between radius and circumference is ...
C = 2πr
Daphne wants r an integer such that ...
60 m ≥ 2πr
r ≤ (60 m)/(2π)
r ≤ (30/π) m ≈ 9.549 m
The largest integer radius Daphne can use is 9 meters.
The scores for a particular examination are normally distributed with a mean of 68.5% and a standard deviation of 8.2%. What is the probability that a student who wrote the examination had a mark between 80% and 100%? Give your answer to the nearest hundredth.
Answer:
[tex]P(80/100<x<100/100)=0.08[/tex]
Step-by-step explanation:
We are given that
Mean,[tex]\mu=68.5[/tex]%=68.5/100
Standard deviation, [tex]\sigma=8.2[/tex]%=8.2/100
We have to find the probability that a student who wrote the examination had a mark between 80% and 100%.
[tex]P(80/100<x<100/100)=P(\frac{80/100-68.5/100}{8.2/100}<\frac{x-\mu}{\sigma}<\frac{100/100-68.5/100}{8.2/100})[/tex]
[tex]P(80/100<x<100/100)=P(1.40<Z<3.84)[/tex]
We know that
[tex]P(a<Z<b)=P(Z<b)-P(Z<a)[/tex]
Using the formula
[tex]P(80/100<x<100/100)=P(Z<3.84)-P(Z<1.40)[/tex]
[tex]P(80/100<x<100/100)=0.99994-0.91924[/tex]
[tex]P(80/100<x<100/100)=0.0807\approx 0.08[/tex]
Point J is the midpoint of the line segment KI Find the length of JI.
Answer:
I belive i is 5
Step-by-step explanation:
On a piece of paper, graph y = 4x - 2. Then determine which answer matches the graph you drew.
Answer:
it's A
Step-by-step explanation:
start at 2 on the y axis and go up 4 and right 1
3x-2=2(x-5)
find the value of x
Now we have to,
find the required value of x.
Let's begin,
→ 3x-2 = 2(x-5)
→ 3x-2 = 2x-10
→ 3x-2x = -10+2
→ x = -8
Hence, value of x is -8.
Answer:
x = -8
Step-by-step explanation:
3x - 2 = 2 ( x + 5
Solve for x.
Let's solve,
3x - 2 = 2 ( x + 5 )
Step 1:- Distribute 2.
3x - 2 = 2 × x + 2 × 5
3x - 2 = 2x - 10
Step 2 :- Move constant to the right-hand and change their sign.
3x = 2x - 10 + 2
Step 3:- Add -10 and 2.
3x = 2x - 8
Step 4 :- Move variable to the left-hand side and change their sign.
3x - 2x = -8
Step 5 :- Subtract 2x from 2x.
x = -8
Hence, value of x = -8.
I need help with both questions.
Answer:
y = 17x
$595
Step-by-step explanation:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{85 - 51}{5 - 3}[/tex] = [tex]\frac{34}{2}[/tex] = 17 (find the slope, gradient or rate of change)
The y intercept is 0. Zero hours = 0 charge.
y = 17(35)
y = 595
What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2,4)
Answer:
[tex]y=-2.5x-9[/tex]
Step-by-step explanation:
One is given the following equation.
[tex]5x + 2y = 12[/tex]
The problem asks one to find a line that is parallel to this one, and passes through the point: [tex](-2, 4)[/tex]. The equation of the given line is in the standard format. The easiest approach to solve this problem is to change the equation of the given line into the slope-intercept format. The solve intercept format follows the following general equation:
[tex]y=mx+b[/tex]
Where (m) is the slope of the line and (b) is the y-intercept. Manipulate the given equation such that it follows this format:
[tex]5x+2y=12\\2y=12-5x\\y=6-2.5x\\\\y=-2.5x+6[/tex]
One property of parallel lines is that they have the same slope. Therefore, if one uses the slope-intercept format to represent the slope of the parallel line, then one can state the following:
[tex]y=-2.5x+b[/tex]
Substitute a given point on this line ([tex]-2,4[/tex]) , and solve for (b) to find (b):
[tex]y=-2.5x+b\\(4)=-2.5(-2)+b[/tex]
Simplify,
[tex]4=-2.5(-2)+b\\-4=5+b[/tex]
Inverse operations,
[tex]-4=5+b\\-9=b[/tex]
Substitute this back into the equation in slope-intercept form to find the equation of the parallel line:
[tex]y=-2.5x-9[/tex]
The annual membership fee at a local club is $100. After each year of membership, the fee is lowered by $8 a year. The
arithmetic sequence {100, 92, 84,...) models this situation.
Write an explicit function that describes the fee at the club after n years of membership. Then rewrite your function in the
slope-intercept form.
Answer:
y = 100 - 8(n - 1)
Step-by-step explanation:
I. if n = 1 or 1st year = 100 - 8(1-1) is 100
if n = 2 or 2nd year = 100 - 8(2-1) is 92
if n = 3 or 3rd year = 100 -8(3-1) is 84
Hope it'll help.
What are the solutions to the quadratic equation x^2-16=0
Answer:
x = ±4
Step-by-step explanation:
Hi there!
[tex]x^2-16=0[/tex]
Move 16 to the other side
[tex]x^2=16[/tex]
Take the square root of both sides
[tex]\sqrt{x^2}=\sqrt{16}\\x=\pm4[/tex]
I hope this helps!
yannie read 24 pages of a book. one fourth of the book is unread.how many pages are there?
Answer:
32
Step-by-step explanation:
24/3=8, 24+8=32
that's how I think of it
When taking a measurement with a pH meter, keep the instrument in the Choose... until it is needed. Rinse the pH meter with Choose... and gently pat dry. Place the meter in the sample solution, and record the measurement when the
Answer:
Storage solution; deionized water; stabilizes
Step-by-step explanation:
A pH scale measures the concentration of hydrogen ions in acidic and alkaline solutions.
In chemistry, pH literally means the power of hydrogen ions and it is a measure of the molar concentration of hydrogen ions in a particular solution; thus, specifying the acidity, neutrality or basicity of any chemical solution.
Mathematically, the pH of a solution is given by the formula;
[tex] pH = -log_{10}(H^{+}) [/tex]
On a pH scale, a solution with a pH of 7 is neutral, a solution with a pH below 7 is acidic and it's basic (alkaline) when it's pH is above 7.
A pH meter can be defined as a scientific instrument or device designed and developed for the measurement of the hydrogen-ion concentration in water-based solutions, in order to determine their level of acidity or alkanility.
As a general rule, when using a pH meter to take a measurement, you should keep it in a storage solution until it is needed. Also, a deionized water should be used to rinse the pH meter and gently pat dry.
Furthermore, the pH meter should be placed in a given sample solution and a reading of the measurement taken when the pH of the solution stabilizes
When taking a measurement with a pH meter, keep the instrument in the storage solution until it is needed. Rinse the pH meter with distilled water and gently pat dry.
The pH meter has been the instrument used for the measurement of the hydrogen ion concentration in a sample. The instrument has consisted of a probe that has been placed in the storage medium when it is not in use.
The working procedure of the pH meter has required the washing of pH meter with the distilled water and properly removing the excess water from the probe by pat dry.
The probe has been immersed in the sample and the pH has been recorded. After the experiment, the instrument has been again washed with the distilled water and get stored in the storage solution.
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An election ballot asks voters to select two city commissioners from a group of six candidates. In how many ways can this be done?
Answer:
15 ways
Step-by-step explanation:
There are 6 choices available for the first seat
There are 5 remaining choices for the second seat.
6(5) = 30 possible combinations
however, as the two seats are of equal power, the combination of AB is equal the the combination of BA etc, This eliminates half of the options.
What is the x- intercept y =2x^2-8x+6?
Answer:
see your answer in the image
with full detail
mark me brainlist
Step-by-step explanation:
Answer:
(3,0) , (1.0)
Step-by-step explanation:
Needs 20 characters even though the picture says it all.
whats the common difference of p+q, p , p-q
Answer:
- q
Step-by-step explanation:
p - ( p + q )
= p - p - q
= - q
p - q - p
= p - p - q
= - q
Common difference is - q.
Which of the following is true about congruent figures?
Eric wrote the number 57,378. How many
times greater is the value of the 7 in the thousands
place than in the tens place?
What is the reason for each step in the solution of the equation?
-5(x - 6) = 10x
Drag and drop the reasons into the boxes to correctly complete the table.
–5(x – 6) = 10x
Given
-5x + 30 = 10x
30 = 15x
2 = x
Division Property of Equality
Commutative Property
Addition Property of Equality
Given
Distributive Property
Answer:
Distributive property (-5 is being multiplied to x and - 6)
Addition property of equality (5x is being added in both side of the equation)
Division property of equality (15 is being devided in both side of the equation)
Brainliest please~
The reason for each step will be
Distributive property (-5 is being multiplied to x and - 6)
Addition property of equality (5x is being added in both sides of the equation)
Division property of equality (15 is being divided into both sides of the equation)
What are algebraic properties?
We can solve mathematical equations thanks to algebra's inherent characteristics. The algebraic properties are distributive property, addition property of equality, and division property of equality.
Given expressions are:-
-5x + 30 = 10x
30 = 15x
2 = x
-5x + 30 = 10x ⇒ Distributive property (-5 is being multiplied to x and - 6)
30 = 15x ⇒ Addition property of equality (5x is being added in both sides of the equation)
30 = 15x ⇒ Division property of equality (15 is being divided into both sides of the equation)
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I need Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
150.72 cm³314 cm³160 cm³48 cm³Step-by-step explanation:
Put the given numbers in the relevant formula and do the arithmetic.
right cylinder
V = πr²h = 3.14(4 cm)²(3 cm) = 3.14×48 cm³ = 150.72 cm³
cone
V = 1/3πr²h = 1/3(3.14)(5 cm)²(12 cm) = 3.14×100 cm³ = 314 cm³
pyramid of unknown shape
V = 1/3Bh = 1/3(16 cm²)(30 cm) = 160 cm³
square pyramid
V = 1/3s²h = 1/3(3 cm)²(16 cm) = 48 cm³
find the equation of a line perpendicular to 4x-y=4 that contains the points (0,3)
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Answer:
x + 4y = 12
Step-by-step explanation:
The perpendicular line can be found by swapping the x- and y-coefficients and negating one of them. Then those new coefficients can be used with the coordinates of the given point to find the required constant.
line: 4x -y = 4
perpendicular line: x +4y = constant
Through (0, 3):
0 +4(3) = constant = 12
The perpendicular line has standard form equation x +4y = 12.
Answer:
Step-by-step explanation:
y=-1/4x+3
WILL GIVE BRAINLIEST!!!!!!! A boy had 20 cents. He bought x pencils for 3 cents each. If y equals the number of pennies left, write an equation showing the dependence of y on x. What is the domain of the function?
Answer:
[tex]\displaystyle \text{Function: }{y=20-3x,\\\text{Domain: }(-\infty, \infty)\text{ or }\mathbb{R}[/tex]
Step-by-step explanation:
If the boy initially had 20 cents, then the total number of cents he will have left after purchasing [tex]x[/tex] pencils is equal to the total cost of the pencils subtracted from 20. The total cost of [tex]x[/tex] pencils, in cents, is equal to [tex]3x[/tex], since each pencil is 3 cents.
Therefore, the total amount, in cents, that the boy has left, [tex]y[/tex], is equal to [tex]20-3x[/tex]:
[tex]\displaystyle \text{Equation: }\boxed{y=20-3x}[/tex]
The domain of this function is [tex](-\infty, \infty)[/tex] or all real numbers [tex]\mathbb{R}[/tex].
