The equation of the sphere is [tex]x^{2} + y^{2} + z^{2} = c^{2}[/tex].
A sphere with the simple equation r=c in spherical dimensions has the Cartesian equation [tex]x^{2} + y^{2} + z^{2} = c^{2}[/tex]
[tex]r^{2} = (x-h)^{2} + (y-k)^{2} + (z-l)^{2} \\r^{2} = (3-1)^{2} +(4-2)^{2} + (-5+4)^{2} \\r^{2} = 2^{2} + 2^{2} + -1^{2}\\ r^{2} = 4+4+1\\ r^{2} = 9[/tex]
[tex]= > r = \sqrt{9} \\[/tex]
r=3
What is the sphere's cartesian equation?Laplace's equation and the Helmholtz equation, two significant partial differential equations that appear in numerous physical issues, provide the separation of variables in spherical coordinates. The x-axis, which is horizontal, and the y-axis, which is vertical, make up the Cartesian coordinate system. In this system, equations for lines will include both the x and y variables. One example of a line in this system is the equation 2x + y = 2.
The coordinate system primarily utilized in three-dimensional systems is spherical coordinates of the system, represented as (r, ). The spherical coordinate system is used to determine the surface area in three dimensions. Three numbers are specified by these coordinates: the radial distance, the polar angles, and the azimuthal angle.
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Given the equation of y-1=-9/2(x+7) what is the slope of any line parallel? M= blank
Answer:
Step-by-step explanation:
y - 1 = -9/2 (x + 7)
Distribute -9/2:
y - 1 = -9/2x - 63/2
Add 1 on both sides to isolate y:
(y - 1) + 1 = (-9/2x - 63/2) + 1
y = -9/2x -61/2
A line parallel to another has the same slope as that line so both slopes are -9/2.
M = -9/2
Type the correct answer in each box. Use numerals instead of words.
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
The equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation of the parabola is y = 2 · x · (x - 4).
What is the equation of the parabola seen in a graph?
Herein we find a representation of a quadratic function on a Cartesian plane, whose formula in vertex form is presented below:
y - k = C · (x - h)²
Where:
(h, k) - Vertex of the parabola.C - Vertex constantBy direct inspection we find that the equation of the parabola has a vertex at (h, k) = (2, - 8) and the point (x, y) = (4, 0). Then, the vertex constant is:
C = (y - k) / (x - h)²
C = (0 + 8) / (4 - 2)²
C = 8 / 4
C = 2
Then, the equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation is determined by algebra:
y + 8 = 2 · (x - 2)²
y = 2 · (x - 2)² - 8
y = 2 · (x² - 4 · x + 4) - 8
y = 2 · x² - 8 · x + 8 - 8
y = 2 · x² - 8 · x
y = 2 · x · (x - 4)
The factored form of the equation of the parabola is y = 2 · x · (x - 4).
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Hskskleksjejejekekosksososowowowkwkwkkw
Answer:
x = -168
Step-by-step explanation:
Multiply both sides of the equation by 4.
= -x = 168
Multiply both sides by −1.
x = -168
Hope it helps!!!
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At 9:00 AM the temperature was -15°C in Anchorage. The
proceeded to rise 4°C each hour. What was the
at 2:00PM.
CAN SOMEONE HELP ME WITH THIS QUESTION
Answer:
5°C
Step-by-step explanation:
(add 4 each hour)
9AM:-15°C
10AM:-11°C
11AM:-7°C
12AM:-3°C
1AM:1°C
2AM:5°C
8. Mason read 12 books in 4 months. If he reads at a
constant rate, how many books did he read each month?
Give your answer as a whole number or a FRACTION in
simplest form.
What is the remainder for 3,167 / 28
45 POINTS!!!
Answer:
113 with a remainder of 3
Step-by-step explanation:
the shortest distance between two points on a sphere is group of answer choices a straight line an arc of a great circle an arc of a small circle
The shortest path between two points on the sphere is the arc of a great circle. Thus, option C is correct.
According to the statement
We have to find about the distance.
So, For this purpose, we know that the
The distance between two points is that the length of the path connecting them.
From the given information:
We have to search out that the the shortest distance between two points on a sphere.
Then we all know that the
Sphere is that the set of all points in three-dimensional space lying the identical distance from a given point, or the results of rotating a circle about one in every of its diameters.
Then
The shortest path between two points on the sphere is that the arc of a good circle.
According to this the option C is correct.
So, The shortest path between two points on the sphere is the arc of a great circle. Thus, option C is correct.
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find the absolute value |-2|
Answer:
2.
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −2 and 0 is 2.
Hope this helps.
Answer:
2
Step-by-step explanation:
Let's solve the equation step by step
|-2|
= 2
Which series of transformations shows that pentagon A is congruent to pentagon B?
A.
Reflect pentagon A over the y-axis, rotate it 180° clockwise about the origin, and translate it 3 units up.
B.
Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.
C.
Rotate pentagon A 90° clockwise about the origin, reflect it over the x-axis, and translate it 6 units to the left.
D.
Reflect pentagon A over the y-axis and translate it 2 units to the left and 8 units up.
Using translation concepts, the series of transformations that shows that pentagon A is congruent to pentagon B is:
B. Rotate pentagon A 90° clockwise about the point (1, 1), reflect it over the x-axis, and translate it 3 units to the left.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, we have that the Pentagons have different orientations, meaning that it was rotated, eliminating options A and D.
For the vertices to reach the position they reached in Pentagon B, there had to be a shift left, and before the shift left, the Pentagon must have been entirely at the fourth quadrant, meaning that it was reflected about the point (1,1), and option B is correct.
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HELP AGAIN PLEASE ITS DUE SOON
Help please(work provided)
Answer is angle 2
Reason
two angles are adjacent angles when they share the common vertex and a side.
See attached picture
BE is the perpendicular bisector of AD. Find the value of each variable.
14. AC = 5x - 7 and DC = 8x - 28
15. m/ACB = (7y - 8)°
Answer:
ac =13x-35
m/abc = 7y-8
Step-by-step explanation:
in first to minus of same base
second it remain same because it can't be subracted with different base
alan is driving west at a rate of 50 mph towards a intersection. beatrice is driving north at 60 mph away from the same intersection. at what rate is the distance them changing when alan is 0.6 mile and beatrice is 0.8 mile from the intersection?
Distance between Alan and Beatrice is changing at the rate of 102.667 mph.
What is time?Time is the continuous flow of existence and the events that take place in what appears to be an unbreakable sequence from the past, present, and forward into the future. Time is often referred to be a fourth spatial dimension in addition to the three others.
Philosophers, theologians, and scientists have long considered time to be an important subject of study, but they have never been able to agree on a definition of time that can be used across all of these fields without becoming circular. However, a wide range of fields, including business, industry, sports, the sciences, and the performing arts, all include some form of the concept of time into their own measurement schemes.
[tex]D_{x}=60t\\D_{y}=x-50t\\D=\sqrt{(D_{x})^2+(D_{y})^{2}} \\D=\sqrt{(60t)^2+(x-50t)^2}[/tex]
where t is time and D is the distance
We know, S=D*D
So,
[tex]S=3600t^2+x^2+2500t^2-100xt\\\frac{dS}{dt} = 7200t+5000t-100x\\=12200*\frac{8}{600}-100*0.6\\ =\frac{308}{3}[/tex]
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pls help shading inequalities
The three inequalities that satisfies all the points in the unshaded region of the graph of inequalities are;
The three inequalities that satisfies all the points in the unshaded region are;
x ≤ 5y ≤ 102•x + y ≥ 10What are the inequality notation that can be used to represent the unshaded region.1) The inequality that represents the unshaded region to the left of the vertical dashed line at x = 5 is found as follows;
A region to the left of a vertical dashed line in inequality is represented by the less than or equal to symbol, ≤. The region to the right is represented by ≥
The region to the left of the dashed line, x = 5 is therefore;
x ≤ 5.2) The region located below the dashed line y = 10 is represented by the inequality;
y ≤ 103) The slope, m, of the dashed line that extends from point (0, 10) to point (5, 0) is given by the equation;
m = (0 - 10)/(5 - 0) = -2
The equation of the line is therefore;
y - 0 = -2 × (x - 5) = -2•x + 10
y = -2•x + 10
Which gives;
y + 2•x = 10
2•x + y = 10
The inequality that represents the region to the right of the line 2•x + y = 10 is therefore;
2•x + y ≥ 10
The compound inequality, that represents the unshaded region is therefore;
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please help math look in image 50 points
Answer:
1740
Step-by-step explanation:
Since the 10 has an exponent of 3, we can move the decimal of 1.74 to the left 3 times, which gives us 1740.
Answer:1740
Step-by-step explanation:
10x10=100
100x10=1000
1.74x1000=1740
HOPE THIS HELLPPPSSS : )
The quotient of 24 and d
Answer:
The quotient of 24 and d would be [tex]\frac{24}{d}[/tex]
Step-by-step explanation:
Quotient is the answer of a division problem. So, you would divide 24 by d.
Watch help video
Adriel drove 216 miles in 8 hours. If he continued at the same rate, how far would he
travel in 3 hours?
Answer:
miles Submit Answer
SAMSUNG
attempt 1 out of 2
Answer:
bkjjb.l kkllkk kk. lkm j. km j. kk. k mgdv. nutdc
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -2 ≤ x ≤ 3? -10 Go -8 -6 -4 -2 100 80 60 20 -20 -40 -60 -80 -100 2 8 10
Answer:
1 + 1 = 2 a i esta la respjesta
Step-by-step explanation:jijiji
Can someone pls help me with this one T—T
Answer:
13. x = 2 - 5y
14. x= 6y + 2
PLEASE PLEASE PLEASE ANSWER CONFIDENTLY
Evaluate the expression when p = 5
-|-3p|
Answer:
-15
Step-by-step explanation:
p = 5
- | -3(5 | = - | -15 | = - | 15 | = -15
John weighs 145 pounds and is gaining 2 pounds per month. Jim weighs 210 pounds and is losing 3 pounds per month. In how many months will they weigh the same?
Answer:
I believe the answer is 13 months.
Step-by-step explanation:
First you make an equation.
* 145 + 2x = 210 - 3x
* After you solve it!
> 145 = 210 - 5x
> -65 = - 5x
> -65/-5 = x
> 13 = x
It's going take 13 months for both to be on the same weight.
I hope you get this right.
what is the answer for b?
Answer:
4
Step-by-step explanation:
2+2=4 dummy
four points, a, b, c, and d, lie on a circle having a circumference of 17 units. b is 5 units counterclockwise from a. c is 3 units clockwise from a. d is 11 units clockwise from a and 6 units counterclockwise from a. what is the order of the points, starting with a and going clockwise around the circle?
The order of the points starting with a and going clockwise around the circle is;
a ⇒ c ⇒d ⇒b
Here,
Four points, a, b, c, and d, lie on a circle having a circumference of 17 units.
b is 5 units counterclockwise from a.
c is 3 units clockwise from a.
d is 11 units clockwise from a and 6 units counterclockwise from a.
We have to find, The order of the points starting with a and going clockwise around the circle.
What is Circumference of circle?
The circumference is the distance around a circle or any curved geometrical shape.
Now,
b is 5 units counterclockwise from a.
b ⇒ a
c is 3 units clockwise from a.
b ⇒ a ⇒ c
d is 11 units clockwise from a and 6 units counterclockwise from a.
d ⇒ b ⇒a ⇒ c ⇒d
So, when we draw all points on circle we get;
The order of the points starting with a and going clockwise around the circle is;
a ⇒ c ⇒d ⇒b
This is shown in figure.
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If a={a,b,c,d,e,h}, b={b,c,d,f,g} and c {a,c,e,f,h,i}, then verify that
A) a-(b union c)=(a-b) intersection (a-c)
B) a intersection (b-c) =(a intersection b)-(a intersection c)
From given A={a,b,c,d,e,h}, B={b,c,d,f,g} and C= {a,c,e,f,h,i}
result related to union and intersection of sets are verified
A). A- (B∪C)=(A - B)∩ (A- C)
B). A∩(B-C) =(A∩B) - (A∩C)
As given,
A={a,b,c,d,e,h}
B={b,c,d,f,g}
C={a,c,e,f,h,i}
A). A- (B∪C)={a,b,c,d,e,h} - { a,b,c,d,e,f,g,h,i}
= { }
(A - B)∩ (A- C)={a,e,h} ∩ {b,d}
={ }
⇒A- (B∪C)=(A - B)∩ (A- C)
B) A∩(B-C)={a,b,c,d,e,h} ∩{b,d,g}
={b,d}
(A∩B) - (A∩C)={b,c,d} -{a,c,e}
={b,d}
⇒A∩(B-C)=(A∩B) -(A∩C)
Therefore, from given A={a,b,c,d,e,h}, B={b,c,d,f,g} and C= {a,c,e,f,h,i}
result related to union and intersection of sets are verified
A). A- (B∪C) =(A - B)∩ (A- C)
B). A∩(B-C)=(A∩B) - (A∩C)
The complete question is:
If A={a,b,c,d,e,h}, B={b,c,d,f,g} and C= {a,c,e,f,h,i}, then verify that
A). A- (B∪C) = (A - B)∩ (A- C)
B). A∩(B-C) = (A∩B) - (A∩C)
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Fill in the missing amounts (do not use commas or decimal points.)
Here are the missing amounts :
A = $2100
B = $300
C = $50
D = $270
E = $945
F = $1,345
What are the missing amounts?
Receipts represents income to the company. It is a source of cash inflow. Expenses represents cash outflow. Net cash flow is the difference between receipts and expenses. Cumulate balance is the sum of the net cash flow of the previous periods and the net cash flow of the present period.
A = Net cash flow + expenses
1975 + 125 = 2100
B = Receipts - expense
$2225 - $1925 = $300
C = Receipts - expense
$2050 - $2000 = $50
D = Net cash flow = $270
E = cumulative balance in April + net cash flow in May
$570 + $375 = $945
F = = cumulative balance in July + net cash flow in August
$1120 + $225 = $1,345
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33/25 as a decimal rounded to the nearest tenth
Answer:1.3
Step-by-step explanation:
33/22=1.32
Round to nearest 10th
1.32=1.3
The width of a rectangle measures (10p - 9q) centimeters, and its length measures
(7p+8q) centimeters. Which expression represents the perimeter, in centimeters,
of the rectangle?
The expression represents the perimeter, in centimeters, of the rectangle is P = 30q + 2p
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as:
P = 2(l+w)
l = (7p+8q) cm
w = (10p - 9q) cm
Substitute
P = 2(7p+8q+10p-9q)
P = 2(15q+p)
P = 30q + 2p
Hence the expression represents the perimeter, in centimeters, of the rectangle is P = 30q + 2p
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Important Please Help!!!!
Answer:
angle bisector
Step-by-step explanation:
the construction shows an angle bisector.
the line EG bisects ∠ FED
list the digits that repeat:
2/11 = 0. [?] [ ]
enter the number that belongs in the green box (or just boxes)
Answer:
0.18
Step-by-step explanation:
you just need to divide 2÷11 until 2 decimal places
on june 28, 2012 the u.s. supreme court upheld the much debated 2010 healthcare law, declaring it constitutional. a gallup poll released the day after this decision indicates that 46% of 1,012 americans agree with this decision. at a 95% confidence level, this sample has a 3% margin of error. based on this information, determine if the following statements are true or false, and explain your reasoning.
a. False. The sample is 46%. We are 95% that the proportion of the population is between 43% and 49%.
b. True, this is the correct interpretation of a confidence interval of proportions.
c. False. The confidence interval does not say anything about the proportion of samples, just about the population.
d. False. As the confidence level decreases, so does z, which means that the margin of error decreases.
In a sample with a number n of people surveyed with a probability of success of, and a confidence level of, we have the following confidence interval of proportions.
In which
z is the score that has a p-value of.
The margin of error is:
So the confidence interval can be written as:
Interpreting a confidence interval:
x% confidence interval between (a,b) means that we are 95% sure that the true proportion of the population is between a and b.
In this problem, we have that:
95% confidence interval between (43%, 49%).
a. We are 95% confident that between 43% and 49% of Americans in this sample support the decision of the U.S. Supreme Court on the 2010 healthcare law.
False. The sample is 46%. We are 95% that the proportion of the population is between 43% and 49%.
b. We are 95% confident that between 43% and 49% of Americans support the decision of the U.S. Supreme Court on the 2010 healthcare law.
True, this is the correct interpretation of a confidence interval of proportions.
c. If we considered many random samples of 1,012 Americans, and we calculated the sample proportions of those who support the decision of the U.S. Supreme Court, 95% of those sample proportions will be between 43% and 49%.
False. The confidence interval does not say anything about the proportion of samples, just about the population.
d. The margin of error at a 90% confidence level would be higher than 3%.
False
As the confidence level decreases, so does z, which means that the margin of error decreases.
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