1:Under what condition will the line px+py+r=0 mat be a normal to the circke x²+y²+2gx+2fy+c=0
2:prove that the two circles x²+y²+2ax+c²=0 and x²+y²+2by+c²=0 touch if
[tex]\frac{1}{a²}+\frac{1}{b²}=\frac{1}{c²}[/tex]
Answers
Answer:
#1The normal overlaps with the diameter, so it passes through the center.
Let's find the center of the circle:
x² + y² + 2gx + 2fy + c = 0(x + g)² + (y + f)² = c + g² + f²The center is:
(-g, -f)Since the line passes through (-g, -f) the equation of the line becomes:
p(-g) + p(-f) + r = 0r = p(g + f)This is the required condition
#2
Rewrite equations and find centers and radius of both circles.
Circle 1
x² + y² + 2ax + c² = 0 (x + a)² + y² = a² - c²The center is (-a, 0) and radius is √(a² - c²)Circle 2
x² + y² + 2by + c² = 0 x² + (y + b)² = b² - c²The center is (0, -b) and radius is √(b² - c²)The distance between two centers is same as sum of the radius of them:
d = √(a² + b²)Sum of radiuses:
√(a² - c²) + √(b² - c²)Since they are same we have:
√(a² + b²) = √(a² - c²) + √(b² - c²)Square both sides:
a² + b² = a² - c² + b² - c² + 2√(a² - c²)(b² - c²)2c² = 2√(a² - c²)(b² - c²)Square both sides:
c⁴ = (a² - c²)(b² - c²)c⁴ = a²b² - a²c² - b²c² + c⁴a²c² + b²c² = a²b²Divide both sides by a²b²c²:
1/a² + 1/b² = 1/c²Proved
Answer:
Answer is in the picture
Related Questions
What is 2 to the power of four thirds equal to?
cube root of 8
square root of 8
cube root of 16
square root of 16
NO LINKS
Answers
Answer:
This is the cube root of 16
Step-by-step explanation:
2 ^ (4/3)
2^4 = 16
16 ^(1/3)
This is the cube root of 16
Answer:
This is the cube root of 16
Step-by-step explanation:
Question 8 of 10
The linearized regression equation for an exponential data set is
log y = 0.23x + 0.8, where x is the number of years and y is the population
What is the predicted population when x - 10? Round your answer to the
nearest whole number.
A. 81,963
B. 200
C. 3
D. 1259
.
Answers
Answer:
log y = 3
Step-by-step explanation:
Substitute 10 for x, obtaining the following:
log y = 0.23(10) + 0.8, or
log y = 2.3 + 0.8, or 3.10, or (to the nearest whole number):
log y = 3
PLSSSSS HELP!!!!!!!!!!
Answers
Answer:
3x-26=2x(because they are vertical angle)
or,3x-2x=26
therefore x=26
Answer:
Step-by-step explanation:
2x + (3x-26) = 90
5x = 90+26
5x = 116
x = 116/5
x = 23.2
Beezlebum's Toy Store can't keep their stackable block set in stock! The blocks completely fill a box shaped like a rectangular prism that is 14 inches long, 14 inches wide, and 21 inches tall. The cube-shaped blocks in the set are 3.5 inches along each edge.
How many blocks are in the set?
Write your answer as a whole number or decimal. Do not round.
Answers
9514 1404 393
Answer:
96
Step-by-step explanation:
In terms of blocks, the box dimensions are ...
(14 in)/(3.5 in/block) = 4 blocks
(21 in)/(3.5 in/block) = 6 blocks
Then the volume in terms of blocks is ...
V = LWH
V = (4)(4)(6) = 96 . . . . blocks
There are 96 blocks in the set.
Need help with this equation if anyone can respond
Answers
Answer:
120 yards is the answer to the equation
What is a polygon?
a. A closed plane figure made up of line segments
b. An open plane figure made up of line segments
c. A closed plane figure made up of rays
d. An open plane figure made up of rays
Answers
Answer:
A. A closed plane figure made up of line segments
Step-by-step explanation:
Answer:
A closed plane figure made up of line segments
HELP?!?
Write the prime factorization for these numbers
1. 235
2. 460
3. 582
4. 297
5. 777
6. 624
Answers
Step-by-step explanation:
hear is answer in attachment
Answer:
1. 5 x 47 show tree of 5 x 47 and then stop both are pf
2. 2^2 × 5 × 23 show tree of 10 x 46 and then 2 x 5 (under10) and 2x23 (under 46) and then stop 2,2,5,23 are all pf
3. 2 x 3 x 97 show tree 3 x 194 and 2 x 97 and circle pf 2,3,97
4. 3^3 x 11 show tree of 3 x 99 then 3 x 33 then 3 x 11 to show 3,3,3,11 as pf
5. 3 x 7 x 37 show tree as 777/7 = 111/37 = 3 to show 3,7,37 as pf
6. 2^4 x 3 x 13 show tree as 2 x 312 2 x 156 2 x 78 2 x 39 3 x 13 to show 2,2,2,2,3,13 all as pf
Step-by-step explanation:
What should be capitalize in a passage
Answers
Proper nouns
Every first word in a sentence
Hope this absolutely helps!
SpaceMarsh
D
76
21. In the last three basketball games,
Paula has scored 21, 25, and
15 points p. Which inequality does
not describe the numbers of points
she has scored?
Ap> 21
Bps 25
cp< 30
Dp 2 10
Answers
Answer:
A
Step-by-step explanation:
Note that
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
for example : 2 < 3 means 2 is less than 3
3 >2 means 3 is greater than 2
Paula's 3 scores are greater than 15 and less than 26
p> 21 implies her score is greater than 21. this is wrong because there is a score of 15
y= 2x + 1
y = -3x +6
Solve the solution to this system of linear equations
(Please help)
Answers
Answer:
yeahh, i'm proud of you
Step-by-step explanation:
will give brainly please help now <3
Answers
Answer:
16 ounces/minute
Step-by-step explanation:
1 pound = 16 ounce
60 pound = 960 ounce
1 hour = 60 minute
960/60 = 16
A cylindrical container has a diameter of 14 cm and a height of 10 cm, as
shown in the diagram. What is the volume of this container to the nearest
tenth of a cubic centimeter?*
14cm
10cm
1539.4
6157.5
490.0
219.9
Answers
Answer:
1539.4
Step-by-step explanation:
Steps:
Volume of a cylinder= πr²h
radius= diameter/2
= 14/2
= 7 cm
Volume= π x 7² x 10
= 1539.38
= 1539.4 cm³
Answer:
1539.4
Step-by-step explanation:
to find the area of a cylinder, you solve pi x radius²
3.14 x 7² = 153.94
then you multiply times the height
153.94 x 10 = 1549.4
According to Money magazine, Maryland had the highest median annual household income of any state in at (Time website). Assume that annual household income in Maryland follows a normal distribution with a median of and standard deviation of . a. What is the probability that a household in Maryland has an annual income of or more (to 4 decimals)
Answers
Answer:
The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean income and [tex]\sigma[/tex] is the standard deviation of incomes.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
What is the probability that a household in Maryland has an annual income of X or more?
The probability that a household in Maryland has an annual income of X or more is 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean income and [tex]\sigma[/tex] is the standard deviation of incomes.
Tony is building a new silo to store corn as animal feed. It will be a cylinder topped with a half-sphere, and must store 21 000 t of corn. The entire silo can be filled with corn. Tony wants to minimize the surface area of the silo to reduce materials and paint costs. He has the following information:
• 1 cubic m of corn has a mass of 700 kg.
• Building costs are $8/m2, taxes included.
• Paint comes in 3.8 L cans.
Each can covers 40 sq m and costs $35,
taxes included.
• Corn costs $140 per tonne ($140/t), taxes
included.
What is the total cost to build, paint, and fill a silo with the least surface area?
Answers
Answer:
The total bill is $6900 because 69 is a man which hair is multi colour
Question 11
Find the volume.
Answers
Answer:
volume of the cube=15×15×15
=3375 in³
volume of the cylinder=πr²h
=π×7²×14
=686π
volume of the figure=3375+686π
the answer is first option
PLEASE PLEASE HELP!!!!
Find the volume of the triangular pyramid to the nearest whole number
A) 170in³
B) 340in³
C) 680in³
D) 1,020³
Answers
I need help anyone?
Answers
Answer:
0
Step-by-step explanation:
When you substitute x=1 for f(1),
you get f(1)=0
and the absolute value of 0 is 0.
hope I answered it correct.
please give brainliest, thanks!
A teacher wishes to choose a group of students to help with a presentation. If he needs 2 boys and 3
girls to help with the project and has 14 boys and 12 girls in his classroom, in how many ways can he
make the selection?
Answers
Choosing 2 boys can be done in 14 x 13 = 182 ways.
But this puts them in order ( first and second) which is not required so the unordered number ways is 182 / 2 = 91
Choosing 3 girls can be done in 12 x 11 x 10 = 1320 ways but 3 girls can appear in 3! ways = 6.
The number of unordered selections of 3 girls = 1320 / 6 = 220
The total number of selections is 91 x 220 = 20020.
If you thought the answer was 240240 it is because you used permutations rather than combinations.
If you are still confused, remember choosing Alan and Bruce is the same as choosing Bruce and Alan.
For the girls you could choose CDE, CED, DCE, DEC, ECD OR EDC and still get exactly the same 3 girls.
Write the equation of a line with a slope of −2 and a y-intercept of 5.
Answers
9514 1404 393
Answer:
y = -2x +5
Step-by-step explanation:
The slope-intercept form of the equation for a line is ...
y = mx + b . . . . . . . . . line with slope m and y-intercept b
You want a line with slope -2 and y-intercept 5, so your equation is ...
y = -2x + 5
A sample of 2,000 was sought to estimate the average achievement in science of fifth graders in a city’s public schools. The average fifth grade enrollment in the city’s elementary schools is 100 students. Thus, 20 schools were randomly selected and within each of those schools all fifth graders were tested. What sampling technique was used?
Answers
Answer:
"Clustering sampling" is the correct answer.
Step-by-step explanation:
If our entire demographic has been separated into segments or groupings, people employ clustering sampling. Those same groupings constitute diverse structurally and therefore are necessarily the same thing uniform.Researchers choose certain of the globular groupings, which are taken throughout the sampling one for each of the specified cluster centers.Triangle F E D is cut by line segment H G. Line segment H G goes from side F D to side E D. The length of E G is 6 and the length of F H is 8. Lines E F and G H are parallel.
What is the length of Line segment G D?
GD =
Answers
Answer:
10.5
Step-by-step explanation:
built different
Triangle F E D is cut by line segment H G. Line segment H G goes from side F D to side E D. The length of E G is 6 and the length of F H is 8. Lines E F and G H are parallel. 5.5 is the the length of Line segment G D.
What is triangle?A triangle is a polygon that has three vertices on each of its three sides. The point shaped inside the triangle is equivalent to 180 degrees. It implies that the amount of the inside points of a triangle is equivalent to 180°. This is a polygon with the fewest sides.
To put it another way, a triangle is a two-dimensional figure with three sides and interior angles of 180 degrees. Six main types of triangles are distinguished by their angles and side lengths. Allow us to examine exhaustively about the six kinds of triangles. In light of the length of the sides, the triangle is arranged
EG / GD = FH / HD
6 / GD = 8 / 2
GD = 22 / 4
GD = 5.5
Therefore, 5.5 is the the length of Line segment G D.
To know more about triangle, here:
https://brainly.com/question/2773823
#SPJ7
solve for x 64 = 2^3x
Answers
Answer: X=0 , 1.03355778
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Can someone’s please help
Answers
Answer:
4.87 ft
Step-by-step explanation:
The height of the skylight =
The height of the blue △ - the height of the red △
Let b ft be the height of the blue △.
sin 60° = [tex]\frac{b}{25} [/tex]
b = 25 sin 60°
Let r ft be the height of the red △.
tan 40° = [tex] \frac{r}{20} [/tex]
r = 20 tan 40°
The height of the skylight
= 25 sin 60° - 20 tan 40°
= 4.87 ft (rounded to the nearest hundredth)
What’s the distance ?
Answers
Answer:
[tex]3[/tex]
Step-by-step explanation:
This problem asks one to find the length of the given line. Another way to think about this problem is to believe that the problem asks one to find the distance from one point to another. The endpoints on this line are the following,
[tex](4,2), (5, 5)[/tex]
The formula to find the distance between two points on a 2-dimensional coordinate plane is as follows,
[tex]D=\sqrt{(x_1-x_2)^2*(y_1-y_2)^2}[/tex]
Substitute the endpoints of the line into the formula and solve for the distance between the points,
[tex]D=\sqrt{(4-5)^2*(2-5)^2}[/tex]
Simplify, solve for the distance between the two points,
[tex]D=\sqrt{(4-5)^2*(2-5)^2}[/tex]
[tex]D=\sqrt{(-1)^2*(-3)^2}\\\\D=\sqrt{1*9}\\\\D=\sqrt{9}\\\\D=3[/tex]
Use the correct function to find the missing angle y measurement to the
nearest whole degree. Then using the checkboxes, select the function you
used, and the answer you found rounded to the nearest degree. (SELECT
2 ANSWERS - READ CAREFULLY) Work points are build into the results. *
18 in
yo
20 in.
Cos
Tan
64 degrees
Sin
42 degrees
26 degrees
Answers
Answer:
Cos;
26 degrees
Step-by-step explanation:
Recall: SOH CAH TOA
Reference angle = y°
Adjacent side = 18 in.
Hypotenuse = 20 in.
We would apply the trigonometric function CAH since we are dealing with the Adjacent side (A) and the Hypotenuse (H). Thus:
Cos y° = Adj/Hyp
Cos y° = 18/20
Cos y° = 0.9
y° = cos^{-1}(0.9)
y = 25.8419328° ≈ 26 degrees (nearest whole degree)
The answers are:
Cos and 26 degrees
The maximum load that a cylindrical column with a circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. A 9 meter column 2 meters in a diameter will support 64 metric tons. How many metric tons can be supported by a column 13 meters high and 5 meters in diameter? Round to the nearest whole metric ton
Answers
Answer:
2396
Step-by-step explanation:
Let the diameter = d
Let the height = h
Formula
Metric Tons = k * d^4 / h^2
Solution
Metric Tons = 64
d = 2
h = 9
k = ?
(You can't do the second part by not using a ratio unless you put k in and solve for it)
64 = 2^4 k / 9^2
64 = 8 *k / 81
64 * 81 / 8 = k
5184 / 8 = k
k = 648
Solve for the second example
Metric Tons = d^4 * k / h^2
Metric Tons = ?
d = 5
h = 13
k = 648
Metric Tons = 5^4 * 648 / 13^2
Metric Tons = 625 * 648 / 169
Metric Tons = 2396 rounded.
Explain how to do this and provide with an answer.
Answers
Answer:
V=480m^2
Step-by-step explanation:
Help plz I’m so confused
Answers
u never multiply the bottoms only the top so it will give u 6 since theyre both negatives
-
answer = 6/7
Answer and Step-by-step explanation:
Simply multiply the numerator by the numerator, and the denominator by the denominator.
[tex]-\frac{2}{7}[/tex] × [tex]-\frac{3}{7}[/tex] = [tex]\frac{6}{49}[/tex]
#teamtrees #PAW (Plant And Water)
2b(to the power of 2)= 2.83
Answers
Step-by-step explanation:
2b²=2.83
b²=1.415
b=1.18953
A married couple filing jointly with a taxable income of $240,000 and a $7000 tax credit. The tax owed is?
Answers
Answer:
247000 ?
Step-by-step explanation:
If I understand this right then that should be the answer. I added 240000 and 7000
