The polar form of the equation represents all the points with a distance of 8 from the origin, which is a circumference with a radius of 8, centered on the origin.
What is the polar form of the equation?The polar form is represented with the aid of polar coordinates of real and imaginary numbers in the coordinate system.
The horizontal and the vertical axis of the polar form denote the real axis and the imaginary axis, respectively.
The given equation to polar form is;
[tex]\rm x^2+y^2=64[/tex]
Using the formulae that link Cartesian to Polar coordinates.
x = rcosθ and y = rsinθ
Substitute these values into the equation.
[tex]\rm x^2+y^2=64\\\\(rcos\theta)^2+(rsin\theta)^2=64\\\\r^2cos^2\theta +r^2sin^2\theta =64\\\\r^2(cos\theta^2+sin\theta^2)=64\\\\Where ; \ sin^2\theta + cos^2\theta=1\\\\r^2(1)=64\\\\ r^2=8^2\\\\r=8[/tex]
Hence, the polar form of the equation represents all the points with a distance of 8 from the origin, which is a circumference with a radius of 8, centered on the origin.
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Reuben has bought 30 pounds of dog food. He feeds his dog 3/5 pounds for each meal. For how many meals will the food last?
Answer:
50
Step-by-step explanation:
3*50=150. 150/5=30 pounds
Are the ratios 8:3 and 4:1 equivalent?
Answer:
No.
Step-by-step explanation:
8:3 = 8/3
4:1 = 4/1 = 8/2
8/2 is not = 8/3
pls help me classify this
First image -Pentagon(Five sides).
Second image-Equilateral triangle(All sides are equal).
100pts Find mPQ in the circle to the right
We need indirectly m<POQ
See NR is a straight line so the three angles situated underneath are linear pair and supplementary
m<POQ
180-(82+63)180-14535°Answer:
C) 35°
Step-by-step explanation:
From inspection of the given diagram, it appears that the line segment NOR is the diameter of the circle (where point O is the center).
Angles on a straight line sum to 180°
⇒ ∠NOP + ∠POQ + ∠QOR = 180°
⇒ 82° + ∠POQ + 63° = 180°
⇒ ∠POQ = 180° - 82° - 63°
⇒ ∠POQ = 35°
As an arc measure equals its corresponding central angle measure:
[tex]\sf \implies \overset{\frown}{PQ}= \angle POQ[/tex]
[tex]\sf \implies \overset{\frown}{PQ}=35^{\circ}[/tex]
Use the quadratic formula to solve for X.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
What are the center and radius of the circle with equation x^2 + y^2 - 4x - 6y + 8 = 0?
Answer:
centre : (2;3)
radius :
[tex] \sqrt{5} [/tex]
What is the 43rd term of a Arithmetic sequence 3, 5, 7
Answer:
87
Step-by-step explanation:
common difference = d = 2
an = a1 + (n-1)*d
a43 = 3 + 42*2 = 87
1. Suppose a married man and woman both carry the gene for cystic fibrosis but don't
have the disease themselves. According to the laws of genetics, the probability that
any child they have will develop cystic fibrosis is .25.
a) Explain what this probability means.
b) If the couple has 4 children, is one of them guaranteed to have cystic fibrosis.
Answer:
a) Probability is the chance or possibility that an event will occur.
b) No,
just as the question states there is a 25% chance of this event happening in a child, so no matter the number of children they have the chances of them getting cystic fibrosis is 25% for each child and it's never guaranteed.
The volume of a sphere is V=4/3 pie r 3
where r is the radius of the
sphere. Determine the volume of the sphere where the radius is
measured at 6 inches.
a 288pie 3
b 216 pie 3
C 144 pie 3
d 48 pie 3
Answer:
A. 288pi in^3
Step-by-step explanation:
s
ee image
Find the y-intercept of the line 11x - 8y = -1.
write your answer as an integer or as a simplified proper or improper fraction, not as an
ordered pair.
submit
Answer:
1/8
Step-by-step explanation:
I'd start by rearranging the terms for y:
11x-8y=-1
-8y=-1-11x
y=[tex]\frac{-1-11x}{-8}[/tex]
The x-intercept is found when x equals 0, so substitute 0 for x in this new equation to find the y-intercept:
[tex]y=\frac{-1-11x}{-8} \\y=\frac{-1-11(0)}{-8}\\ y=\frac{-1-0}{-8} \\y=\frac{-1}{-8}\\ y=\frac{1}{8}[/tex]
The y-intercept is 1/8
what is the value of the expression 1 cubed, 2 cubed, and 3 cubed
1³ + 2³ + 3³
1 + 8 + 27
36
hope it helps..!!!
In a class of 35 students, 20 offer Physics, 18 offer Chemistry and 2 offer neither Physics nor Chemistry. i) Illustrate the information on a Venn diagram. ii) How many students offer all the two subjects? ii) How many students offer Physics? iv) How many students offer only one subject?
Answer:
Given:
35 = Total number of students20 = Physics students18 = Chemistry students2 = Neither Physics or Chemistry studentsTo construct the Venn diagram:
Draw 2 circles overlapping.As 2 students study neither subject, place the number 2 in the box outside the circles.
Calculate the number of students who study both subjects (central overlapping section):
Physics students + Chemistry students + neither students - Total students
= 20 + 18 + 2 - 35 = 5
Place the number 5 in the central overlapping section.
⇒ Left section = Physics students - both subjects
= 20 - 5
= 15
⇒ Right section = Chemistry students - both students
= 18 - 5
= 13
i) See attachment
ii) Physics and Chemistry = 5 students
iii) Physics only = 15 students
iv) One subject only = 15 + 13 = 28 students
What is the equation for the function shown in FACTORED FORM?
Answer:
f(x) = (x + 1)(x - 4)
Step-by-step explanation:
let f be the function
FACTORED FORM of f :
f(x) = a(x - p)(x - q)
Where p and q are the roots/zeros of f
and ‘a’ is a real number.
=================================
Find p and q :
The roots of f are the x-coordinates where the graph crosses the x-axis, which can be read from the graph: x = -1 and x = 4 ⇒ p = -1 and q = 4.
then f(x) = a(x + 1)(x - 4)
Find ‘a’ :
f(3) = -4 ⇒ a((3) + 1)((3) - 4) = -4 ⇒ a(4)(-1) = -4 ⇒ -4a = -4 ⇒ a = 1
Therefore, f(x) = (x + 1)(x - 4)
Norman gave 1/3 of his money to his wife. He divided the remainder equally between his 3 children. What fraction of his money did each of his children receive?
How is perimeter helpful in daily life?
Answer:
so you can know how long an objects size on the outside
1. what is the product of 3.62 and 9.8?
2. Express 5/6 as a percentage
3. find 500,000 less than 1031001 ?
4. Express 75% as a fraction in the lowest term .
5. Express 2.50 as a percentage
6. simplify 18 + 0.8 - 1.293
7. find the cost of a shirt with a price tag of £29•00
8. Anna was given £50.00.she bought a mathematical set for £15.50 and an exercise book £2.30.how much change will she receive .
Answer:
1. 35.476
2. 83.33%
3. 531001
4. 3/4
5. 250%
6. 17.507
7. £29•00
8. 32
Step-by-step explanation:
math is done on calculator :)
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
La respuesta es A
Step-by-step explanation:
simplemente tienes que multiplicar 7 x 3 que te da 21 y luego tienes que sumar el 2 del numerador (siempre multiplica el o los enteros por el denominador y sumale el numerador)
Answer:
A
Step-by-step explanation:
The larger number in a mixed number represents how many "wholes" of the fraction there are. The fraction in a mixed number is sort of like the "leftovers", the amount that doesn't fit into a whole number. In this case, the whole number is 7, meaning there are 7 amounts of 3/3. You would multiply the whole number by the number in the denominator of the fraction, which would equal 21. The improper fraction of the whole number would be 21/3 (21 divided by 3 equals 7). Now you would add that to the fraction 2/3. The answer would be 23/3.
I hope this makes some type of sense, I didn't explain it very well.
Find areas of the triangles.
Answer:
2.75
Explain
1 3/5 = 8/5
3 7/16 = 55/16
8/5 x 55/ 16 = 440/80
440/80 : 2 = 5.5
5.5 / 2 = 2.75
Simple as that
You can check the calculator
Answer:
2.72
Step-by-step explanation:
1 3/5 is 1.6 and 3 7/16 is 3.4 so 1.6 x 3.4=5.44 and 5.44/2 is 2.72 sq u
need help with all of these questions you see on the top. there the red squares. please someone smart. this is one of the problems I need to finish this tonight. ( Both Parts )
Answer:
433.5 cm^3
Step-by-step explanation:
The volume of a cylinder is its base area times height. Therefore it can be said that:
V = 23π x 6
This is 433.539786195, which when rounded to the nearest tenth is 433.5.
(20 points) Enter the y coordinate of the solution to this system of equations.
6x + y = 8
x − 2y = 10
Answer:
y=-4
Step-by-step explanation:
graph each equation or solve by elimination/subtitution. Easiest way is using Desmos graphing calculator
I need help, I have a test tomorrow and I didn't understand this exercise
Answer:
Step-by-step explanation:
Circumference = 2(pi)r
Radius = Circumference/2(pi)
Circumference = 37.68
Radius = 37.68/2(pi)
Radius = about 59.18760559
Reggie has $240 in a savings account at the beginning of the summer. He wants to have at least $450 in the account by the end of the summer. He deposits $35 each week. What is the shortest amount of time Reggie needs to deposit money into his account?
Answer:
6 weeks
Step-by-step explanation:
Since Reggie has $240 in the account already we first subtract this $240 from the $450. 450 - 240 = 210. Now since he deposits $35 a week and needs to hit at least 210 to reach is goal of $450 for the summer then we need to divide 210/35 to see the amount of weeks. 210/35 = 6. So 6 weeks is the shortest time.
Please help me geometry proof for trapezoid
A trapezoid is a quadrilateral that has two parallel sides with a height.
The proof for trapezoidFrom the diagram, AK = 1/2(AD-BC)
The combination of the bases of the equilateral triangle and the parallelogram is = the base of the trapezoid.
Therefore, BC = AD - 2AK
Make AK the subject of formula,
AK= 1/2 (AD -BC)
From the second equation given,KD = 1/2(AD - BC). This is wrong because of the following,
BC is parallel to KD.
Therefore length of KD = BC - AK and not KD = 1/2(AD - BC).
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I was absent the entire time my teacher taught this lesson, please help me
Answer:
1 - 4/9
2 - 1/9
3 - 5/9
Step-by-step explanation:
1 - Look on the left side for all two-letter combinations with only one R. We can see four. (YR, GR, RG, RY). Divide by the total number of outcomes (9).
2 - There is only one with two yellows, so divide 1 by 9.
3 - Same as before, we find 4 with 1 green and 1 with 2 green. We have to include the new one since it says atleast one. Add 1 and 4 and then divide by 9.
A colony of 10,710 bacteria doubles in size every 129 minutes. What will the population b
516 minutes from now?
The population after 516 minutes is 171360 bacteria
How to determine the population after 516 minutesFrom the question, we have the following parameters that can be used in our computation:
Initial, a = 10,710 bacteria
Rate = doubles i.e. 2
Using the above as a guide, we have the following:
f(x) = a(2)^x
Where x is the time
516 minutes is 4 times 129 minutes
This means that
x = 516/129 = 4
So the population after 516 minutes can be calculated as follows:
f(4) = 10710 * (2)^4
Evaluate
f(4) = 171360
Hence, the population is 171360
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I need this asap
13 points (SHOW WORK)
Answer: 23
6*6=36 total area
3*3=9
2*2=4
9+4=13
36-13=23 shaded area
Answer answer questions please
Answer: 2 1/4
Step-by-step explanation: theirs 2 whole so with that theirs another circle cut in 4th's and 1 is shaded so 1/4.
Answer: choice c , 2 and 1 over 4
Step-by-step explanation: as the first 2 circles are fully shared but only one 1 over 4 from the third circle is shaded so 2 and 1 over 4 as a mixed numbers . Which means 2 full circles and 1 over 4 of the third circle . HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST .THANKS .
Find the area of the triangle. MY GRADE PLEASE HELP!
Answer:
B:21
Step-by-step explanation:
Area of parallelogram=315=base ×hight .
base =x
hight= 15
15 × x = 315
x= 315/15
=21
The length of a rectangular floor is two ft more than its width. If the area of the floor is 63 ft, find the length and the width of the floor.
Answer:
width = 7 and length = 9
Step-by-step explanation:
Let's assume width = w, and length = 2 + w
So area of a rectangle = width * length
63 ft² = w (2 + w)
63 = 2w + w²
w² + 2w - 63 = 0
Use the quadratic formula to solve this
here, a = 1, b = 2 and c = -63
w = 7 or -9
The dimensions of a rectangle cannot be negative. So we take the dimension, w = 7.
Width = 7 and Length = 7+2 = 9
Solve x^2 =-25, where x is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Answer: x = ±5i
Step-by-step explanation:
√x2 = √−25
x = √−1 ∗ 25
x = i√25
x = ±i5
