Answer:
The standard equation of the sphere is [tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]
Step-by-step explanation:
From the question, the end point are (3,-2,4) and (7,12,4)
Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.
The midpoint can be calculated thus
Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]
Let the first endpoint be represented as [tex](x_{1}, y_{1}, z_{1})[/tex] and the second endpoint be [tex](x_{2}, y_{2}, z_{2})[/tex].
Hence,
Midpoint = [tex](\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})[/tex]
Midpoint = [tex](\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})[/tex]
Midpoint = [tex](\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\[/tex]
Midpoint = [tex](5, 5, 4)[/tex]
This is the center of the sphere.
Now, we will determine the distance (diameter) of the sphere
The distance is given by
[tex]d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }[/tex]
[tex]d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}[/tex]
[tex]d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}[/tex]
[tex]d = \sqrt{16 +196 + 0[/tex]
[tex]d =\sqrt{212}[/tex]
[tex]d = 2\sqrt{53}[/tex]
This is the diameter
To find the radius, r
From [tex]Radius = \frac{Diameter}{2}[/tex]
[tex]Radius = \frac{2\sqrt{53} }{2}[/tex]
∴ [tex]Radius = \sqrt{53}[/tex]
r = [tex]\sqrt{53}[/tex]
Now, we can write the standard equation of the sphere since we know the center and the radius
Center of the sphere is [tex](5, 5, 4)[/tex]
Radius of the sphere is [tex]\sqrt{53}[/tex]
The equation of a sphere of radius r and center [tex](h,k,l)[/tex] is given by
[tex](x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}[/tex]
Hence, the equation of the sphere of radius [tex]\sqrt{53}[/tex] and center [tex](5, 5, 4)[/tex] is
[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}[/tex]
[tex](x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53[/tex]
This is the standard equation of the sphere
Is pi rational?? helppppp
Answer:
Yes
Step-by-step explanation:
Pi is a rational number, because it goes on forever.
In 9 days a group of workers can plant 54 acres what’s there rate in acres per day
Answer:
Step-by-step explanation:
9 3/4 acres in 3 3/8 days = 9 6/8 acres in 3 3/8 days
(72 + 6)/8 = 78/8
(24 + 3)/8 = 27/8
78/8 divided by 27/8 = 78/27 = 26/9 or 2 8/9 acres/day
The enrollment in fall 1993 was 14.3 million. If you were to use the model of 1993 what would the enrollment be?
Answer:
Why is college important? It’s a question you may have heard among friends, or perhaps you’ve even wondered yourself about the benefits of earning a degree. And it’s a good question to be asking as you consider your future—and everything that will include, from earnings potential to starting or switching your career. Here are five facts you should know as you consider the value of a college education.
1. People with college degrees earn more on average.
According to averages calculated by the US Bureau of Labor Statistics (BLS), people with a bachelor’s degree earn around 64% more per week than individuals with a high school diploma, and around 40% more than those with an associate’s degree. Those with an associate’s degree earn around 17% more than those with a high school diploma.
Over the course of a year (52 weeks), those percentage differences add up. For example, if you compare the average median annual earnings for those with a bachelor’s degree to those with a high school diploma, you’ll discover a difference of almost $24,000 per year in income.
2. College can help you expand your network.
Salary is far from the only answer for why is college important. You may have heard this before, but who you know and who your friends know is important. No matter how talented you are, a strong network can help you start and advance in your career.
At an Art Institutes school, you’ll not only have the chance to connect with instructors* who have worked in their fields, but you can also meet students in a variety of creative fields. These diverse connections may well benefit you in the future. Plus, you can also participate in professional groups, community activities, and industry conferences where you can grow your circle even more. Your Career Services department may also connect you with alumni in your field and can continue to provide networking support after graduation!
3. Gaining new skills can help enhance your current career.
Building your skill set and industry knowledge can help you move forward in your current career, and the skills you learn go beyond the obvious. At The Art Institutes, not only can you build your technical and artistic skills, but you can also develop your critical thinking, communication, and teamwork.
Earning your degree can demonstrate to a current employer that you’re serious about your career, and that you’re prepared to take on bigger projects and more responsibility. In the long term, when you apply to new jobs in your field, having a degree can provide you with a competitive edge. Even if the job doesn’t require a degree, your education—along with the quality of your work—may help you stand out among applica
Step-by-step explanation:
the value of the function f(x)=6x + 3 at 4 is
solution
Answer:
here we go 6×4+3
now 24+3
hence the answer is
27 ans
Answer:
x = -2
Step-by-step explanation:
f(x) = 6 x + 3×4
f(x) = 6 x + 12
6 (x + 2) = f(x)
x = -2
Hope I helped! Please label me as Brainliest!
Jeremy Sullivan delivers newspapers for the Dispatch. He receives 14.20 per
paper, 6 days a week (for the daily paper), and 500 for the Sunday paper. He
delivers 124 daily papers each day and 151 Sunday papers each week. What is
his total pay for the week?
Answer:
Total earnings per week
=18114.8¢
Step-by-step explanation:
He receives 14.20¢ per paper, 6 days a week.
He receives 50¢ for the Sunday paper.
He delivers
124 daily papers each day
He earns= 124*14.20*6
He earns=10564.8¢
151 Sunday papers each week.
He earns= 151*50
He earns= 7550¢
Total earnings per week
=10564.8+7550
=18114.8¢
describe the correct error a student made when solving the equation 4=-2(x-3) what is the correc scolution?
Answer:
x =1
Step-by-step explanation: Correct solution
[tex]4=-2(x-3) \\\\\mathrm{Switch\:sides}\\-2\left(x-3\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x-3\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x-3=-2\\x-3+3=-2+3\\\\Simplify\\x = 1[/tex]
Which equation has no solution?
Answer:
B) -6 (w - 4) + 8w = 2 (w + 9) has no solution
Step-by-step explanation:
{7, 8, 9, 10} {9, 10, 11, 12} Which of the following shows the intersection of the sets? A. {9, 10} B. {7, 8, 9, 10} C. {9, 10, 11, 12} D. {7, 8, 9, 10, 11, 12}
Answer:
{ 9 , 10 }Option A is the correct option.
Step-by-step explanation:
Let the sets be A and B
A = { 7 , 8 , 9 , 10 }
B = { 9 , 10 , 11 , 12 }
The intersection of sets A and B is the set of all ements which belongs to both A and B.
The intersection of sets A and N is denoted by ( A ∩ B ) and read as A intersection B.
A ∩ B = { 7 , 8 , 9 , 10 } { 9 , 10 , 11 , 11 , 12 }
Now, list the elements which are present in both sets. A ∩ B = { 9 , 10 }
Hope I helped!
Best regards!
Answer:
its a
Step-by-step explanation:
what’s -14 = -2(2x+2)
How do you do letter b?
Answer: 175
Step-by-step explanation:
[tex]g(35)= \int\limits^{35}_0 {f(x)} \, dx =\int\limits^{30}_0 {f(x)} \, dx +\int\limits^{35}_{30} {f(x)} \, dx[/tex]
= 137.5 + 37.5
= 175
Answer:
g(35) = 137.5
Step-by-step explanation:
g(35) = g(30) + [g(35) - g(30)]
g(35) = 100 + 5(15)/2
g(35) = 137.5
What is the answer please help you can change my life.
Answer:
The side length is irrational
Step-by-step explanation:
Because the square root of 23 or 20+3 is a non-perfect square root and it's a never ending decimal.
Identify a pattern in each lists of numbers. Then use this pattern to find the next number. 17,13,9,5,1
Answer:
-5 -9 -13....
Step-by-step explanation:
17-4=13 so you basically minus 3 each time.
Which of the following is an example of stratified sampling when obtaining a sample of 100 high school students? A. Choosing 100 students at random from a specific grade level at a high school.B. Choosing 100 students sitting in one random section of the cafeteria at a high school.C. Choosing 25 students at random from each of four different grade levels at a high school.D. Choosing 100 students at random from a high school. E. Choosing 100 students at random from an AP Statistics class at a high school.
Answer:
Option C - Choosing 25 students at random from each of four different grade levels at a high school
Step-by-step explanation:
For us to achieve the conditions for a stratified random sample, the target population must be split into different groups which in this case, it's grade levels.
Looking at the 5 options given in the question, Options A, B, D and E are random but they are not truly stratified in their sampling approach. This is because the sample population must be selected at random from each of these groups and it's only option C which is choosing 25 students from each of four different grade levels or groups that reflects that.
The relative growth rate for a certain type of bacteria population is 85% per hour. A small culture has formed and in just 2 hours the count shows to be 12,500 bacteria in the culture. What is the initial number of bacteria in the culture?
Answer:
3663 bacteria
Step-by-step explanation:
On Sunday, the temperature dropped 24° in 6 hours. What was the average change in temperature per hour?
Answer:
The temperature drops 4° every hour
Step-by-step explanation:
Step 1:
24° ÷ 6
Step 2:
24 : 6 = 4 : 1
Answer:
4
Hope This Helps :)
Answer:
[tex]\boxed {\tt -4 \textdegree \ per \ hour }[/tex]
Step-by-step explanation:
This question asks us to find the average rate of change in temperature per hour.
Therefore, we must divide the temperature change by the hours.
[tex]rate \ of \ change =\frac{temperature \ change}{hours}[/tex]
The temperature dropped 24 degrees in 6 hours. Since it dropped, the change was negative.
[tex]temperature \ change = -24 \textdegree \\hours = 6 \ hours[/tex]
Substitute the values into the formula.
[tex]rate \ of \ change =\frac{-24 \textdegree}{6 \ hours}[/tex]
Divide.
[tex]rate \ of \ change = - 4 \textdegree / hour[/tex]
The average change in temperature was -4° per hour. The temperature dropped 4 degrees each hour.
HELLLLLPPPPPPP PLZZZZZZ HELP A$AP PLZZZZZZZZZ I WILL MARK BRAINLEST
Answer:
$430
Step-by-step explanation:
Step 1:
300 - 50
Step 2:
350 + 20
Step 2:
370 + 60
Answer:
$430
Hope This Helps :)
Let u = (−2, 3, 1), v = (−1, −1, 2), and 3u − 2v − 4w = (3, 2, −3). Find: a. The vector w.b. -2u + 3v - 5w
Answer:
(a) w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
(b) -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])
Step-by-step explanation:
Given:
u = (−2, 3, 1)
=> u = -2i + 3j + k --------------------------(i)
v = (−1, −1, 2)
=> v = -i - j + 2k --------------------(ii)
3u − 2v − 4w = (3, 2, −3)
=> 3u − 2v − 4w = 3i + 2j - 3k ------------------(iii)
(A) TO FIND THE VECTOR w
Let:
w = (a, b, c) = ai + bj + ck
(a) Substitute u, v and w into equation (iii)
3u − 2v − 4w = 3i + 2j - 3k
3(-2i + 3j + k) - 2(-i - j + 2k) - 4(ai + bj + ck) = 3i + 2j - 3k
(b) Solve the equation in step (a) by opening the brackets and collecting like terms
(-6i + 9j + 3k) - (-2i - 2j + 4k) - (4ai + 4bj + 4ck) = 3i + 2j - 3k
open brackets
-6i + 9j + 3k + 2i + 2j - 4k - 4ai - 4bj - 4ck = 3i + 2j - 3k
collect like terms
-6i + 2i - 4ai + 9j + 2j - 4bj + 3k - 4k - 4ck = 3i + 2j - 3k
i(-4 - 4a) + j(11 - 4b) + k(-1 - 4c) = 3i + 2j - 3k
(c) Solve for a, b and c in step (b)
Comparing both sides of the equation, we have;
-4 - 4a = 3 ----------(*)
11 - 4b = 2 -----------(**)
-1 - 4c = -3 ------------(***)
From (*)
4a = -4 - 3
4a = -7
a = [tex]\frac{-7}{4}[/tex]
From (**)
4b = 11 - 2
4b = 9
b = [tex]\frac{9}{4}[/tex]
From (***)
-1 - 4c = -3
4c = -1 + 3
4c = 2
c = [tex]\frac{2}{4}[/tex]
c = [tex]\frac{1}{2}[/tex]
Remember that
w = (a, b, c)
w = ai + bj + ck
Therefore,
w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
(B) TO FIND -2u + 3v - 5w
Remember that;
u = (−2, 3, 1)
v = (−1, −1, 2),
w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
Substitute u, v, w into the expression as follows;
-2(−2, 3, 1) + 3(−1, −1, 2) - 5[tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]
Expand
(4, -6, -2) + (−3, −3, 6) - [tex](\frac{-35}{4} , \frac{45}{4}, \frac{5}{2})[/tex]
Collect like terms
(4-3+[tex]\frac{35}{4}[/tex], -6-3-[tex]\frac{45}{4}[/tex], -2+6-[tex]\frac{5}{2}[/tex])
Solve
([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])
Therefore, -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])
Circle B is shown. Line segments C B, D B, and E B are radii and they form 3 congruent angles. What does Arc C D E describe? a minor arc a major arc a semicircle a chord
Answer:
a major arc
Step-by-step explanation:
A circle is the locus of point in which has a given distance from a fixed point (center of the circle).
B is the center of the circle C B, D B, and E B are radii forming 3 congruent angle. Since the sum of angles in a circle is 360°, the 3 line segments form 3 congruent angles of 120° each (360/3).
Therefore the angle measure of Arc C D E = Arc CD + Arc DE = 120° + 120° = 240°
A major arc is an arc greater than a semicircle (> 180°). This means that Arc C D E is a major arc
Answer:
a major arc
Step-by-step explanation:
a major arc
a major arc
a major arc
a major arc
a major arc
a major arc
a major arc
Find an equation of the line having the given slope and containing the given point. m=-5 (5,7)
Answer:
y = -5x + 32
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write in known variables
slope m = -5
y = -5x + b
Step 2: Find b
7 = -5(5) + b
7 = -25 + b
b = 32
Step 3: Write linear equation
y = -5x + 32
Answer:
y - 7 = -5(x - 5)
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope of -5 and contains the point (5,7).
We want to write the equation of this line.
The equation of this line can be written in three ways:
Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.Either one of these ways works, but let's use point-slope form, as that form is the easiest.
SolvingWe can immediately substitute the values into the formula to get the equation.
We can start with the slope; replace m with -5 in the formula.
[tex]y-y_1=m(x-x_1)[/tex] => [tex]y-y_1=-5(x-x_1)[/tex]
Now, we can replace [tex]x_1[/tex] and [tex]y_1[/tex] with 5 and 7 respectively to get:
y - 7 = -5(x - 5)
which of the following gives all of the sets that contain -1/2?
A. the sets of all rational numbers and the set of all real numbers
B. the set of all natural numbers and the set of all irrational numbers
C. the set of all intergers and the set of rational numbers
D. the set of all natural numbers, the set of rational numbers, and the set of all real numbers
Answer:
B the set of all natural numbers and the ser of all
Answer:
B D B C
Step-by-step explanation:
rational numbers, real numbers
3
irrational
rational
a. Z, Q, R b. Q, R c. N, Z, Q, R d. R
3
8
= 0.375, nonrepeating, terminating; 5
6
=
0.83, repeating, nonterminating; 12
15 = 0.8,
nonrepeating, terminating; 7
11 = 0.63,
repeating, nonterminating
real, irrational; real, rational, whole
Answers may vary. Sample: − 50
A total of 6.2 percent of the prime time viewing audience watched shows on ABC, 8.1 percent watched shows on CBS, 7.4 percent on Fox, 6.4 percent on NBC, 3.1 percent on Warner Brothers, and 2.8 percent on UPN. A total of 66 percent of the audience watched shows on other cable networks, such as CNN and ESPN.
What will be the prime time viewing percentage of the pie chart for the following data? (Only consider the viewers watching non-cable news.) (Round your answers to 2 decimal places.)
Answer:
For each one it is shown below
Step-by-step explanation:
The computation of the prime time viewing percentage for the following data is shown below:l;
but before that we need do the total which is
= 6.2% + 8.1% + 7.4% + 6.4% + 3.1% + 2.8%
= 34%
Now for each one the viewing percentage is
For ABC
[tex]= \frac{6.2}{34}[/tex]
= 18.24%
For CBS
[tex]= \frac{8.1}{34}[/tex]
= 23.82%
For NBC
[tex]= \frac{6.4}{34}[/tex]
= 18.82%
For Warner brothers
[tex]= \frac{3.1}{34}[/tex]
= 9.12%
For fox
[tex]= \frac{7.4}{34}[/tex]
= 21.76%
For UPN
[tex]= \frac{2.8}{34}[/tex]
= 8.24%
state the solutions for the quadratic equation depicted in the graph.
Answer:
(-4,0), (-3,0)
Step-by-step explanation:
The solution of a quadratic equation is simply when the graph crosses the x-axis. This is because at that point, the function will equal 0.
From the graph, we can see that the graph touches the x-axis at x=-4 and x=-3.
Therefore, our solutions for the graphed quadratic is x=-4 and x=-3.
And we're done!
A ball is thrown into the air. Its height (in feet) t seconds later is given by h(t)=64t−16t^2 a) What is the height of the ball 1 second after it has been thrown? b) After how many seconds does the ball hit the ground? c) At what time(s) is the ball 30 feet above the ground?
Answer:
A) 48 feet
B) 4 seconds
C) 0.54 seconds and 3.46 seconds
Step-by-step explanation:
So we have the function:
[tex]h(t)=64t-16t^2[/tex]
Which represents the height h(t) of the ball after t seconds.
A)
To find the height of the ball 1 second after it has been thrown, substitute 1 for t. Thus:
[tex]h(1)=64(1)-16(1)^2[/tex]
Simplify:
[tex]h(1)=64-16[/tex]
Subtract:
[tex]h(1)=48[/tex]
So, after 1 second, the height of the ball is 48 feet above the ground.
B)
To find out how many seconds after being thrown does the ball hit the ground, we'll set h(t) to 0. 0 means that it will be 0 feet above ground level: in other words, on the ground. So:
[tex]0=64t-16t^2[/tex]
Solve for t. Factor out a 16t:
[tex]0=16t(4-t)[/tex]
Zero Product Property:
[tex]16t=0\text{ or } 4-t=0[/tex]
Solve for t:
[tex]t=0\text{ or } t=4[/tex]
We'll ignore the first zero. So, the ball lands after 4 seconds of being thrown into the air.
C)
To find out at what time(s) the ball is 30 feet above the ground, set h(t) to 30 and solve for t:
[tex]30=64t-16t^2[/tex]
First, divide everything by 2 to simplify things:
[tex]15=32t-8t^2[/tex]
Subtract 15 from both sides:
[tex]-8t^2+32t-15=0[/tex]
Now, to find the zeros, we can use the quadratic formula. a is -8, b is 32, and c is -15. Thus:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute:
[tex]x=\frac{-32\pm\sqrt{32^2-4(-8)(-15)}}{2(-8)}[/tex]
Simplify:
[tex]x=\frac{32\pm\sqrt{544}}{16}[/tex]
Use a calculator. Approximate:
[tex]x\approx0.5422\text{ or } x\approx 3.4577[/tex]
So, the ball is 30 feet above the ground after 0.54 seconds and 3.46 seconds.
And we're done :)
The total cost C (in dollars) of playing an online game is given by the literal equation C = 30x + 50, where x is the number of months you play the game. Solve the equation for x. How many months do you play the game when you spend $170? $260?
Answer:
4 months and 7 months
Step-by-step explanation:
C = 30x + 50
C is cost so when we spend $170 we can solve for x.
$170 = 30x + 50
170 - 50 = 30x + 50 - 50
170 - 50 = 30x
120 = 30x
120/30 = 30x/30
120/30 = x
4 = x
So he has played 4 months when he spends $170
C is cost so when we spend $260 we can solve for x.
$260 = 30x + 50
260 - 50 = 30x + 50 - 50
260 - 50 = 30x
210 = 30x
210/30 = 30x/30
210/30 = x
7 = x
So he has played 7 months when he spends $260
solve for x: -2x - 4 > 8
Steps to solve:
-2x - 4 > 8
~Add 4 to both sides
-2x > 12
~Divide -2 to both sides
x < -6
Best of Luck!
After a 65% reduction you purchase a new washing machine on sale for $196. What was the original price of the washing machine
Answer:
$323.40
Step-by-step explanation:
(4.5 x 104) + (300) =
Answer:
768
Step-by-step explanation:
30 pts + brainliest to best answer
Answer:
D) 7 1/5
Step-by-step explanation:
2 2/5 is equivalent to 12/5 then if you divide it by 1/3 you will get 7 1/5 or 7.2
Look at the graph. On a coordinate plane, a graph increases through (negative 1, 4), levels off at (0, negative 3), and then increases up through (2, 5). Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (–1, –4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (–1, –4) and (0, -3) to be StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction = StartFraction 1 Over 1 EndFraction = 1. and the rate of change between the points (0, -3) and (2, 5) to be StartFraction 5 minus (negative 3) Over 2 minus 0 EndFraction = StartFraction 8 Over 2 EndFraction = 4. Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong? The points (–1, –4), (0, –3), and (2, 5) are not all on the graph. The expressions StartFraction negative 3 minus (negative 4) Over 0 minus (negative 1) EndFraction and StartFraction negative 3 minus (negative 5) Over 2 minus 0 EndFraction both equal 1. She miscalculated the rates of change. Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.
Answer:
Answer is A
explanation:
there is no point (0.-3) on the graph.
Answer:
it's D edg 2020
Step-by-step explanation:
tyler says that Figure B is a scaled copy of Figure A because all of the peaks are half as tall.
Answer:
No
Step-by-step explanation:
For the smaller figure to be a scaled copy, the figure would have to be half as wide as well,