The given curve has equation
r(θ) = 9 + 8 cos(θ)
and its derivative is
dr/dθ = -8 sin(θ)
When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.
Differentiate these with respect to θ :
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
In polar coordinates, we have
y(θ) = r(θ) sin(θ)
x(θ) = r(θ) cos(θ)
and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.
The slope of the tangent line to the curve is dy/dx. By the chain rule,
dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)
dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))
When θ = π/3, the slope is
dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))
dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))
dy/dx = - 1/(17√3)
So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is
y - 13√3/2 = -1/(17√3) (x - 13/2)
y = -(x - 338)/(17√3)
Bank account A starts with $5,000 and grows by $1,000 each week. Bank account B starts with $1 and doubles each week.
1.which account has more money after one week?After two weeks?
Answer:
AStep-by-step explanation:
If bank A keeps adding on 1,000 and bank B is only doubling by 2 then A is much greater than B.
The account that has more money after one week is account A.
The account that has more money after two weeks is account A
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Account A:
Balance = $5000
Each week increase = $1000
Amount after one week.
= 5000 + 1000
= 6000
Amount after 2 weeks.
= 6000 + 1000
= 7000
Account B:
Balance = $1
Each week's increase = doubles the amount
Amount after 1 week.
= $2
Amount after 2 weeks.
= $4
Thus,
Account A has more money after one week.
Account A has more money after two weeks.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
b. One room is 8 ft wide and 12 ft long.
Another room is 9 ft wide and 15 ft
long. What is the difference in area?
Answer:
12-8
15-9
Step-by-step explanation:
Can somebody help me with social studies since nobody will?
Answer:
Yes! Sure I will, just follow me and I will follow you!
Then I get the notifications of your doubts.
Step-by-step explanation:
I love helping
Help me answer these questions
Answer:
Explanation below
Step-by-step explanation:
3. 46
4. 66
5. 30
6. 75
7. 18
8. 24
9. 33
10. 60
11. 16
12. 45
Ben gets $50 per day as wages and $6.00 as commission for every book he sells in a day. His daily earnings goal is $140.
Using the equation constructed in previous question, solve for the
number of books he must sell to meet his daily earnings goal.
Answer:
the basic wage is 50$
the extra to get 140$ is 90$(140-50)
.............
as for 1 book he get 6$
so for ? book he get 90$
then ? =(90$*1)/6$= 15 book
that's it hope i helped.
Enter the number
10.333333333333
rounded to the nearest hundredth (two decimal places):
Answer:
Step-by-step explanation:
This decimal rounded to the nearest 1/100 is 10.33 The next 3 in the 1/1000 place, is not large enough to influence the 3 in the hundredth place.
So the answer is 10.33
f(x)=3x 3 inverse function
Step-by-step explanation:
if I understand this correctly than you are looking for the inverse function of f(x) = y = 3x³.
the inverse function simply tries to calculate the original x it of the original y.
and then, to make it a formal function, we rename x to y and y to x.
y = 3x³
x³ = y/3
[tex]x = \sqrt[3]{ \frac{y}{3} } [/tex]
=> as "regular" function
[tex]y = {f}^{ - 1} (x)= \sqrt[3]{ \frac{x}{3} } [/tex]
Can someone please help me?
Answer: X=7/3
Step-by-step explanation:
3
+
2
=
2
+
1
3
3
3x+2=2x+\frac{13}{3}
3x+2=2x+313
Solve
1
Subtract
2
2
2
from both sides of the equation
3
+
2
=
2
+
1
3
3
3x+2=2x+\frac{13}{3}
3x+2=2x+313
3
+
2
−
2
=
2
+
1
3
3
−
2
3x+2{\color{#c92786}{-2}}=2x+\frac{13}{3}{\color{#c92786}{-2}}
3x+2−2=2x+313−2
2
Simplify
Subtract the numbers
Subtract the numbers
3
=
2
+
7
3
3x=2x+\frac{7}{3}
3x=2x+37
3
Subtract
2
2x
2x
from both sides of the equation
3
=
2
+
7
3
3x=2x+\frac{7}{3}
3x=2x+37
3
−
2
=
2
+
7
3
−
2
3x{\color{#c92786}{-2x}}=2x+\frac{7}{3}{\color{#c92786}{-2x}}
3x−2x=2x+37−2x
4
Simplify
Combine like terms
Multiply by 1
Combine like terms
=
7
3
x=\frac{7}{3}
x=37
Solution
=
7
3Order the numbers from least to greatest 0.607, 607, 6.07, 60.7
Answer:
0.607, 6.07, 60.7, 607
Step-by-step explanation:
-3/5-2/10= para ahorita plsss
Answer:
-0.8 GL HEHHEHHEHEHEHEHEHEHEHHEHEHEHHEHEH
45six +13six
Carry out the addition shown using base six notation
Step-by-step explanation:
45 6
13 6
_____ +
02 6
1
________
6 /..8
..... -6
_______
..... 2
0
_______
6/5
...5
_____
0
Review the federal income tax table.
Single
If Taxable Income Is between: Then the Tax Due Is:
$0 – $9700 10% of taxable income
$9701 – $39,475 $970+12% of the amount over $9700
$39,476 – $84,200 $4543+22% of the amount over $39,475
$84,201 – $160,725 $14,382.50+24% of the amount over $84,200
$160,726 – $204,100 $32,748.50+32% of the amount over $160,725
$204,101 – $510,300 $46,628.50+35% of the amount over $204,100
$510,301+ $153,798.50+37% of the amount over $510,300
Mustafa earned $95,000 in taxable income in a year from his job as a software developer. How much federal income tax does he owe? Enter your answer as a number rounded to the nearest cent, such as: $42,536.47.
9514 1404 393
Answer:
$16,974.50
Step-by-step explanation:
$14,382.50+24% of the amount over $84,200 is ...
$14,382.50 +0.24×(95,000 -84,200) = $14,382.50 +2592.00 = $16,974.50
Mustafa owes $16974.50 in federal income tax.
_____
Additional comment
Each row of the tax table can be simplified by multiplying out the expression it describes. For the row applicable to this problem, that becomes ...
14382.50 +0.24(amount -84200) = 14382.50 +0.24×amount -20208
= 024×amount -5825.50
Find what 2/4 is multipled by to to get 2/4 divided by 12. Then solve the problem. Do not reduce your answer.
Answer:
Step-by-step explanation:
Andrea saves 65 each day.if this is 25% of hair daily allowance, how much is her daily allowance
25/100 = x/65
100x = 1625
x = $16.25
$16.25 is her daily allowance
In a hand of cards, the ratio of black cards to red cards was 5 to 3. If the hand contained 15
black cards, which of the following proportions could be solved to find the number of red
cards?
Answer:
5:3 = 15:x
the answer would be 15 black cards to 9 red cards
Step-by-step explanation:
What is the value of the expression 4(80+ b) – 12, where b = 20?
-
328
3.352
c388
D. 412
please mark this answer as brainlist
-48 divided by what equals 6
Answer: the answer is -8
Step-by-step explanation:
Someone help me pls, this is a distance time graph
Answer:
it's b
Step-by-step explanation:
just took the test
what's the answer to
-12(d-5)-29=43
Answer:
d=-1
Step-by-step explanation:
The answer would be d = -1
Perform the indicated operation. Reduce to lowest terms if possible.
2 1/2 x 2 1/3
Answer:
Step-by-step explanation:
Convert mixed fraction to improper fraction.
[tex]2\dfrac{1}{2}*2\dfrac{1}{3}=\dfrac{5}{2}*\dfrac{7}{3}=\dfrac{5*7}{2*3}\\\\=\dfrac{35}{6}=5\dfrac{5}{6}[/tex]
what is % 12 of 104?
Answer:
12.48 is the answer
Step-by-step explanation:
have a great day
Answer:
12.48
Step-by-step explanation:
104×12=1248
1248 count to decimals
12.48
(-5.4, 4.7) and (0.6, 4.7) find the unit
Answer: 6 units
Step-by-step explanation:
|-5.4| + |0.6|
5.4 + 0.6 = 6 units
You hike 1.2 miles west from a trailhead and then receive a text from a friend. She
is.x miles west of the trailhead. You hike to meet her, and then you both hike back
to where you left off on the trail. You hiked 2.7 miles in total. Formulate an absolute
value equation to represent this situation,
Answer:
the answer is definitely 4
Mary cut a square piece of fabric with an area of 40 square feet. Which expression could be used to find the side length of the fabric?
Answer:
L = 6.3 or 6.4
Step-by-step explanation:
Just do the square root of 40, which is 6.3 or 6.4 (but I think 6.4 is a better answer)
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -3x +7
Step-by-step explanation:
how is this college level ?
what is 200 x 300 kakakkakakakakkaakkkak
Answer:
60000 ty ..............
Answer:
60000
..............
what a difficult question !!! Do not ask such difficult questions ..lol
Mixed numbers 204/5=
Answer:
Step 1 - Find Whole Number
Calculate out how many times the denominator goes into the numerator. To do that, divide 204 by 5 and keep only what is to the left of the decimal point:
204 / 5 = 40.8000 = 40
Step 2 - Find New Numerator
Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.
204 - (5 x 40) = 4
Step 3 - Get Solution
Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 204/5 as a mixed number is:
40
4
5
Improper Fraction To Mixed Number Converter
204/5 as a mixed number is not the only problem we solved. Go here to convert another improper fraction to a mixed number.
What is 204/6 as a Mixed Number?
Here is the next improper fraction on our list that we converted to a mixed number.
Terminology & Explanation
204 above the division line is called the numerator and 5 below the divison line is called the denominator.
We call the line that separates 204 and 5 the division line. It is also known as the fraction bar or vinculum.
204/5 is an improper fraction because the numerator is greater than the denominator.
A mixed number is an integer (whole number) and a proper fraction.
graph this linear equation
y-2=4(x-1)
x= 0,1
y= -2,2
Slope 4
Y-Intercept (0,-2)
Are the two lines parallel, perpendicular,
or neither?
y = 3x -4 and 3x +9y = 18
Prerequisites :-
1) The product of slope of two perpendicular lines is-1 .
2) The slope of two parallel lines is same .
Given two lines to us are ,
[tex] y = 3x - 4 [/tex]This line is in slope intercept form which is [tex] y = mx + c [/tex] . Comparing to which we get ,
[tex] m_1 = 3 [/tex]Again , the second line given to us is ,
[tex] 3x + 9y = 18 [/tex]Convert it into slope intercept form , we have ,
[tex]\implies 3( x + 3y ) = 18 [/tex]
Divide both sides by 3 ,
[tex]\implies x + 3y = 6 [/tex]
Solve for y ,
[tex]\implies y = \dfrac{-x}{3} + 2 [/tex]
On comparing to the slope intercept form ,
[tex] m_2 = \dfrac{-1}{3}[/tex]And the product both the slopes is ,
[tex]\implies m_1 \times m_2 = \dfrac{-1}{3}\times 3 =\boxed{\red{-1}}[/tex]
Hence the given two lines are perpendicular .
Last month, 3,477 people visited the zoo. This month, 2,941 people visited the zoo.
How many more people visited the zoo last month than visited this month?
Answer:
536 people
Step-by-step explanation:
3477-2941=536
Answer:
536 more visitors visited the zoo last month this month.
Step-by-step explanation:
just subtract