What are the outliers???
Rewrite the Cartesian equation y=-3 as a polar equation.
r
sin
θ
=
−
3
Explanation:
Imagine we have a point
P
with Rectangular (also called Cartesian) coordinates
(
x
,
y
)
and Polar coordinates
(
r
,
θ
)
.
The following diagram will help us visualise the situation better:
https://keisan.casio.com/exec/system/1223526375
https://keisan.casio.com/exec/system/1223526375
We can see that a right triangle is formed with sides
x
,
y
and
r
, as well as an angle
θ
.
We have to find the relation between the Cartesian and Polar coordinates, respectively.
By Pythagora's theorem, we get the result
r
2
=
x
2
+
y
2
The only properties we can say about
θ
are its trigonometric functions:
sin
θ
=
y
/
r
⇒
y
=
r
sin
θ
cos
θ
=
x
/
r
⇒
x
=
r
cos
θ
So we have the following relations:
⎧
⎪
⎨
⎪
⎩
r
2
=
x
2
+
y
2
y
=
r
sin
θ
x
=
r
cos
θ
Now, we can see that saying
y
=
−
3
in the Rectangular system is equivalent to say
r
sin
θ
=
−
3
Answer link
Jim G.
May 19, 2018
r
=
−
3
sin
θ
Explanation:
to convert from
cartesian to polar
∙
x
x
=
r
cos
θ
and
y
=
r
sin
θ
⇒
r
sin
θ
=
−
3
⇒
r
=
−
3
sin
θ
I need work shown as well
Answer:
Step-by-step explanation:
the area of the squared is 5 * 5 = 25
the area of the triangle is 1/2*base*height = 1/2*2*5= 5
the area of the circle is [tex]\pi[/tex][tex]r^{2}[/tex] = [tex]\pi[/tex][tex]2.5^{2}[/tex] = 19.625
now add the pieces up for the total
25+5+19.625 = 49.625 [tex]in^{2}[/tex]
:)
First, find the area of the semi-circle.
A= pi*radius squared
Find your radius. The diameter is 5, half of that is 2.5
Input into the formula
A= pi*2.5^2
=3.14*6.25
=19.625 in^2
You can round that to about 19.6 inches.
Find the area of the square
A=s^2
= 5^2
= 25 in^2
Find the area of the triangle.
A= b*h/2
= 2*5/2
= 10/2
= 5 in^2
Add it all up.
19.6+ 25 + 5= 49.6
∴ 49.6 in²
Best of luck!
The slope of a line is 0, and the y-intercept is 6. What is the equation written in slope intercept form.
Answer:
y=0x+6
Step-by-step explanation:
slope intercept form is: y=mx+b
ayme built a box in the shape of a rectangular prism with the dimensions shown. What is the volume of the box, in cubic inches? A rectangular prism has a length of 8 inches, a width of 2 inches, and a height of 4 inches. Use the formula V = l w h, where V represents the volume, l represents the length, w represents the width, and h represents the height. Inches cubed
Answer:
[tex]64(in)^{3} [/tex]
Step-by-step explanation:
The volume of a box is equal to the length l times the width w times the height h.
[tex](lenght) \times (width) \times (height)[/tex]
Substitute the values of the length l=8, the width w=2, and the height h=4 into the formula.
[tex]8 \times 2 \times 4[/tex]
Multiply 8 by 2.
[tex]16 \times 4[/tex]
Multiply 16 by 4.
[tex]64 {in}^{3} [/tex]
Hence, the volume of the rectangle prism is 64(in)³.
Answer:
64 in³Step-by-step explanation:
Given dimensions:
l = 8 inw = 2 inh = 4 inVolume of the prism is:
V = lwhV = 8*2*4 = 64 in³(5^{-8})(5^{-10})=(5
−8
)(5
−10
)=
Answer:
1
3814697265625
Decimal Form:
2.62144 ⋅ 10 / 13
Step-by-step explanation:
For the function f(x) = 1/4e^-x + e^x, prove that the arc length on any interval has the same value as the area under the curve.
Take an arbitrary interval [a, b], where a < b.
Compute the arc length L of y = f(x) over [a, b] :
[tex]L=\displaystyle\int_a^b\sqrt{1+\left(f'(x)\right)^2}\,\mathrm dx[/tex]
Now comptue the area A under the curve y = f(x) over [a, b] :
[tex]A=\displaystyle\int_a^bf(x)\,\mathrm dx[/tex]
We have
f (x) = 1/4 e ⁻ˣ + e ˣ → f ' (x) = -1/4 e ⁻ˣ + e ˣ
Then
√(1 + (f ' (x))²) = √(1 + (-1/4 e ⁻ˣ + e ˣ)²)
… = √(1 + 1/16 e ⁻²ˣ - 1/2 + e ²ˣ)
… = √(1/16 e ⁻²ˣ + 1/2 + e ²ˣ)
… = 1/4 √(e ⁻²ˣ + 8 + 16e ²ˣ)
… = 1/4 √((e ⁻ˣ + 4 e ˣ)²)
… = 1/4 (e ⁻ˣ + 4 e ˣ)
… = 1/4 e ⁻ˣ + e ˣ
… = f (x)
so both A = L for any choice of interval [a, b].
It is true that the arc length on any interval has the same value as the area under the curve.
How to prove the statementThe function is given as:
[tex]f(x) = \frac 14e^{-x} + e^x[/tex]
Differentiate the function
[tex]f'(x) = -\frac 14e^{-x} + e^x[/tex]
On any interval, the following must be true
[tex]f(x) =f'(x)[/tex]
and
[tex]f(x) = \sqrt{1 + (f'(x))^2}[/tex]
So, we have:
[tex]f(x) = \sqrt{1 + (-\frac 14e^{-x} + e^x)^2}[/tex]
Expand the exponents
[tex]f(x) = \sqrt{1 + (\frac{1}{16}e^{-2x} - \frac 12 + e^{2x})}[/tex]
Remove the bracket
[tex]f(x) = \sqrt{1 + \frac{1}{16}e^{-2x} - \frac 12 + e^{2x}}[/tex]
Evaluate the like terms
[tex]f(x) = \sqrt{\frac{1}{16}e^{-2x} + \frac 12 + e^{2x}}[/tex]
Multiply by 16/16
[tex]f(x) = \sqrt{\frac{16}{16}(\frac{1}{16}e^{-2x} + \frac 12 + e^{2x})}[/tex]
So, we have:
[tex]f(x) = \sqrt{\frac{1}{16}(e^{-2x} + 8 + 16e^{2x})}[/tex]
Take the square root of 1/16
[tex]f(x) = \frac{1}{4}\sqrt{e^{-2x} + 8 + 16e^{2x}}[/tex]
Express the radical as a perfect square
[tex]f(x) = \frac{1}{4}\sqrt{(e^{-x} + 4e^{x})^2}[/tex]
Evaluate the exponents
[tex]f(x) = \frac{1}{4} * (e^{-x} + 4e^{x})[/tex]
Evaluate the products
[tex]f(x) = \frac{1}{4}e^{-x} + e^{x}[/tex]
Hence, it has been proved that the arc length on any interval has the same value as the area under the curve.
Read more about areas at:
https://brainly.com/question/24487155
it took bryan one hour to ride 6 1/4 miles on his bike. how far will bryan be able to ride in 3 1/2 hours?
A 21 7/8
B 9 3/4
C 5 1/2
D 9 1/4
Why is 6P4 = 360 but 6C4 = 15?
Short answer (I write nPr = P(n, r) and nCr = C(n, r) ):
P (6, 4) = 6! / (6 - 4)! = 6! / 2! = 720 / 2 = 360
C (6, 4) = P (6, 4) / 4! = 6! / (4! (6 - 4)!) = 360 / 24 = 15
Long answer:
P(n, r) counts the number of permutations of n objects taken r at a time, given by
P(n, r) = n ! / (n - r )!
A permutation is a unique arrangement of objects such that the order in which they are arranged is taken into account. For example, if the objects in question are the numbers in the set {1, 2, 3}, then
• there are 3! = 6 total possible permutations if we take all 3 numbers at once:
123, 132, 213, 231, 312, 321
• there are 3!/(3-2)! = 3!/1! = 6 total permutations if we only take 2 numbers at once:
12, 13, 21, 23, 31, 32
• there are 3!/(3-1)! = 3!/2! = 3 total permutations if we take only 1 number at a time:
1, 2, 3
• and there is 3!/(3-0)! = 3!/3! = 1 way of permuting the 3 numbers without taking any of them:
(the permutation itself is just empty space)
By contrast, C(n, r) counts the combinations of n items taken r at a time, given by
C(n, r) = P(n, r) / r !
A combination is like a permutation, but the order of the objects doesn't matter. Continuing with the previous example of arrangements of the numbers from {1, 2, 3}, we have
• 3! / (3! (3-3)!) = 1 combination taking all 3 numbers at once:
123
(the other 5 permutations listed earlier are made up of the same numbers, so we consider them duplicates)
• 3! / (2! (3-2)!) = 3 combinations taking only 2 numbers at once:
12, 13, 23
• 3! / (1! (3-1)!) = 3 combinations taking only 1 number:
1, 2, 3
• 3! / (0! (3-0)!) = 1 combination taking none of them:
(again, empty space)
The main point is that the order of objects is considered across permutations, while it's ignored across combinations.
Christopher sold his dinette set for $245 through an online site, which charged him 9% of the selling price as commission. what is the commission?
Answer:
$22.05
Step-by-step explanation:
If a product has a sales commission, then one must divide the commission percent by (100) to convert the percent to a decimal. Then multiply the result by the price of the product to find the amount of money that will be given as a commission.
Applying this knowledge to the given problem, one must divide (9%) by (100) to convert to decimal form,
9% / 100 = 0.09
Now multiply the result by the price of the product (245) to find the amount given away in commission,
0.09 * 245 = 22.05
Pls help, I'll give brainlest
Answer:
b
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
When multiplying exponents, you would add the degrees.
A, B, and D's degrees add up to [tex]5^{-2}[/tex] , which is equal to 1/25.
C adds up to [tex]5^{2}[/tex], which is 25, therefore making it C
A doughnut shop wants to determine if there is a difference in donut sales at different times of the day and for different types of doughnuts. They are open in the morning, afternoon, and night, and offer the following flavors: vanilla, chocolate, red velvet, and marbled. There were a total of 48 sales recorded. The shop conducted a two-way ANOVA test and found an F test statistic for Flavor of 14.87. What would be the numerator degree of freedom for the F test statistic to determine if the factor flavor was significant
Solution :
Let
[tex]$k_1$[/tex] = number of levels for the factors 'flavors' = 4
(4 levels vanilla, chocolate, red velvet and marbled)
The degree of freedom for the factor 'flavors' = [tex]$k_1$[/tex] - 1
= 4 - 1
= 3
Now defining the F test statistics for testing the significance of the factors, 'flavors' :
F test statics = [tex]$=\frac{Ms\text{ (factor falvor)}}{Ms \text{ (errors)}}$[/tex] , Ms = mean square
where F = [tex]$F_{k_1-1}$[/tex], error df.
Thus the numerator degrees of the freedom for the F test statistics to determine if the factor flavor was significant is = [tex]$k_1$[/tex] - 1
= 4 - 1
= 3
There were 16 skittles in a bag there were 3 yellow, 4 red, 2 purple, 6 orange, and 1 green. What is the probability of pulling a red skittle (simplify your answer). The probability of a red is /
solve (x – 5)^2 = 17
Answer:
x = 5 ± √17
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsMultiple RootsStep-by-step explanation:
Step 1: Define
(x - 5)² = 17
Step 2: Solve for x
[Equality Property] Square root both sides: x - 5 = ±√17[Addition Property of Equality] Add 5 on both sides: x = 5 ± √17if 70kg is 20% of peter's weight, then what is peter's total weight!?
Find the difference: (6a + 6) - (3x - 2) - (2a + 4)
Answer:
4 a − 3 x + 4
Step-by-step explanation:
I just simplified everything together to get this answer.
Hope that this helped! :)
Have a great rest of your day/night!
Please thank me on my profile if this answer has helped you!
A bowl contains 10 red balls and 10 blue balls.A woman selects balls at random without looking at them. How many balls must she select to be sure of having at least three balls of the same color?
Answer:
5 balls
Step-by-step explanation:
Sorry if it's wrong.
Help me solve for x. 16^x = x^2
Auntie Sammy buys a hand bag. There was a discount
of 20%.
If Auntie Sammy paid $245, what was the original price?
Answer:
Step-by-step explanation:
I think the original proce would be $265
1. Subtract the percentage discount from 100
100 - 20= 80
2. Multiply the final price($245) by 100
245 × 100= 24,500
3. Divide the answer in step 2 by the answer in Step 1
24,500 ÷ 80= $306.25
answer is $306.25
How to check to ensure your answer is correct:
1. Multiply the "answer" by the discount price divided by 100. This will give the discount percentage in dollars.
$306.25 × 0.2( which is 20÷100)= $61.25(discount in dollars)
2. Subtract the discount in dollars from the "answer"
$306.25 - $61.25= $245(final price is the same as in the problem so it is correct)
OR
1. Multiply the original price by the number you get from step 1 in your problem divided by 100
$306.25 × 0.8(80 from the very first step divided by 100)= $245(the final price is the same given in the question)
It would take ___ hours to drive 240 miles from Boston to New York, if one drives at a constant speed of 40 mph.
Answer:
6 hours.
Step-by-step explanation:
To find how many hours it would take to drive a 240 mile distance at a constant speed of 40 miles per hour, you'd divide 240 by 40 and the result of that is 6.
Answer:
6 hours
Explanation:
240/40= 6
2 period class
No students
doing Different questions
due by Apr 14th, 11:59 PM -
One-step addition & subtraction equations
Solve the equation.
2 + y = 11
y =
Stuck? Watch a video or use a hint.
Report a pi
2+y=11
Answer:
2 + y = 11 y = 9
Step-by-step explanation:
Steps
2 + y = 11
subtract 2 from both sides
2 + y - 2 = 11 - 2
y = 9
Multiply 15 by 9 then divide by 2 fraction
Answer:
15x9 is 130 but, what u mean by divided by 2 fraction?
Step-by-step explanation:
135/ 2 this is correct unless you want a mixed fraction which is 67 and 1/2
how many five-miute segments are in 3\4 of an houre
i need help and fast is 23 points good
Answer: 9
Step-by-step explanation: because 3/4 of an hour is 45 minutes and 45/5 is 9 and it’s in 5 min segments that’s why you divide 45 by 5
sorry for the first one i read the question wrong
Answer each question below 26. A pair of shoes that normally costs $85 is now on sale for 45% off. What is the sale price of the shoes?
27. After Christmas, I was able to buy lights for 60% off. How much did I pay for lights that normally cost $12?
28. This past weekend, I went to Bed, Bath & Beyond to purchase a new frying pan. I was able to use a 20% off
coupon on one item. The frying pan was originally $40. What is the sale price of the frying pan?
29. When eating at a restaurant, it is recommended that you leave a 15% tip. If my bill was $24, how much
should I leave as a tip?
Answer:
26. $46.75
27. $4.80
28. $32.00
29. $3.60
Find the total surface area. Round to the nearest hundredth if necessary.
Answer:
166
Step-by-step explanation:
multiply the 6 by 2 and then multiply 13 by 10
to get 166
Resale Value Garland Mills purchased a certain piece of machinery 2 years ago for $500,000. Its present resale value is $420,000. Assuming that the machine's resale value decreases exponentially, what will it be (in dollars) 4 years from now? (Round your answer to the nearest dollar.)
Answer:
260,000
Step-by-step explanation:
The value decreases by 40,000 per year (500000-42000/2 years) the value will decrease by 240000 in six (4 years plus 2 years already passed) years. 6 x 40,000 =240000
So, the value should be 260,000 (500000-240000)
Or
year 1 500000-40000=460000
year 2 460000-40000=420000
year 3 420000-40000=380000
year 4 380000-40000=340000
year 5 340000-40000=300000
year 6 300000-40000=260000
The machine's resale value Garland Mills purchased in 4 years from now will be; $353,049
What is the future value amount?
We are told that the machines present resale value is $420000. Now formula for future value is;
Future value = present value * exp(cx)
Thus;
$420,000 = $500,000 * exp(2c)
420000/500000 = exp(4c)
2c = In(420000/500000)
c = -0.087
Future value = present value * exp(cx)
Future value = $500,000 * exp(-0.087 * 4)
Future value = $353,049
Therefore, the machine's resale value in 4 years from now will be $353,049
Read more about future value amount at; https://brainly.com/question/13961729
find the area of the shade sector of the circle
Step-by-step explanation:
We need to find the area of the shaded region. We see that the region next to that has a central angle of 120°. Also we know that angle in a straight line is 180° . So the measure of central angle of that shaded region will be 180° - 120° = 60° . Now we can use the formula of area of sector to find out the area of the shaded region.
[tex]\tt\to Area = \dfrac{\Theta}{360^o}\times \pi r^2 \\\\\tt\to Area = \dfrac{60^o}{360^o}\times \pi (8cm)^2 \\\\\tt\to Area =\dfrac{\pi \times 64}{6}cm^2\\\\\to\boxed{\orange{\tt Area_{(Shaded)}= 10.66\pi cm^2}}[/tex]
A square has an area of 100 square meters.
What is the perimeter of the square?
Answer:
40 square meters
Step-by-step explanation:
Perimeter means to add up all sides.
area means one side times one side
10 times 10 makes 100 so i am guessing each side is 10
10 + 10 + 10 + 10 = 40
Please help ! Please help! I will heart you !
Answer:
x = 65
Step-by-step explanation:
x + 115 = 180
x = 65
Answer:
65 degrees
Step-by-step explanation:
180-115=65 degrees
The line that 115 degrees is on is equal to 180.
you decide to go to a star gazing event there are 12 people in the group
Answer:
whts the question??
Step-by-step explanation: