Find the equation of a sphere if one of its diameters has endpoints: (-14. -3, -6) and (-4, 7, 4) Note that you must move everything to the left hand side of the equation and that we desire the coefficients of the quadratic terms to be 1.

Answers

Answer 1

Answer:

[tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]

Step-by-step explanation:

From the question we are told that:

Diameters has endpoints: [tex](-14. -3, -6) & (-4, 7, 4)[/tex]

Generally the equation for Center of The sphere is mathematically given by

 [tex]C=(\frac{-14+(-4)}{2},\frac{-3+(7)}{2},\frac{-6+(4)}{2})[/tex]

 [tex]C=(9,2,-1)[/tex]

Generally the equation for Radius of the sphere is mathematically given by

 [tex]R=\sqrt{(9-2)^2+(2-9)^2+(-1-2)^2}[/tex]

 [tex]R=\sqrt{107}[/tex]

Therefore the Equation of the Sphere is

 [tex](x-9)^2+(y-2)^2+(z+1)^2=107[/tex]

 [tex](x^2-18x+81)+(y^2-4y+4+(z^2+2z+1))=107[/tex]

 [tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]


Related Questions

it took thandile 30minutes to fly the distance of 192,4kilometers between pilanesburg nationalpark an johannesburg.calculate the average speed of the aircraft in kilometres per hour

Answers

Answer:

Average speed = 3848 km / h

Step-by-step explanation:

Given:

It took Thandile 30 minutes to fly the distance of 1924 km between Pilanesburg National Park and Johannesburg.

To find:

Calculate the average speed.

Solution:

Average speed = distance / time

30 min = 0.5 h => 1924 / 0.5

= 3848 km / hours

Answer:

Average speed = 3848 km / h

hope this helps.....

On a number line what nomber is 3 units to the left of 3​

Answers

Answer:

Hello There!!

Step-by-step explanation:

The answer is 0. The number is 3 and you move 3 units to the left which is toward the negative numbers sides below zero which equals the answer as 0. [3-3=0.]

hope this helps,have a great day!!

~Pinky~

Step-by-step explanation:

7On a number line what nomber is 3 units to the left of 3

if the sum of five consecutive even integers is 740 what is the largest value of this

Answers

9514 1404 393

Answer:

  152

Step-by-step explanation:

The third one is their average, so is 740/5 = 148. The largest is 4 more than that, so ...

  the largest value of the group is 152

_____

The numbers are 144, 146, 148, 150, 152.

The largest number when sum of five consecutive even integers is 740 is 152.

What is consecutive numbers?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Example: 1,2,3,4,5,6

                1,3,5,7,9,11

                 2,4,6,8,10,12

Difference between nearer numbers always equal

Given,

There are 5 consecutive even integers.

Then difference between each nearer number is 2

Let the first number be x

Then another 4 numbers be

(x + 2), (x + 4), (x + 6), (x + 8)

Now

According to question

(x + x + 2 + x + 4 + x + 6 + x + 8) = 740

5x = 740 - 20

x = 144

And the highest number is x + 8 = 152

Learn more about Numbers:

https://brainly.com/question/17429689

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help..............................................................

Answers

Answer:

This will now be ⁴√(7^9)

Step-by-step explanation:

c=4

a=7

b=9

The diameter of a circle is 15 in. Find its circumference in terms of \piπ

Answers

Answer:

15π in

Step-by-step explanation:

In order to solve this, we need to know that the circumference of a circle can be found by using the following formula...

Circumference = dπ   (where d is the diameter of the circle)

Therefore the circumference equals...

Circumference = dπ = 15π in

[tex]\boxed{Given:}[/tex]

Diameter of the circle "[tex]d[/tex]" = 15 in.

[tex]\boxed{To\:find:}[/tex]

The circumference of the circle (in terms of π).

[tex]\boxed{Solution:}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:15\:π\:in.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]

[tex] = \pi \times 15 \: in \\ \\ = 15 \: \pi \: in[/tex]

Therefore, the circumference of the circle is 15 π in.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

Help please If f(x) = -3x - 5 and g(x) = 4x-2, find (1-9)(x).

Answers

9514 1404 393

Answer:

  -7x -3

Step-by-step explanation:

(f -g)(x) = f(x) -g(x) = (-3x -5) -(4x -2)

(f -g)(x) = -3x -5 -4x +2 = (-3-4)x +(-5+2)

(f -g)(x) = -7x -3

I’m looking at one of my past tests and I don’t remember how I solved this. Can someone explain please :)

Answers

Answer:

Step-by-step explanation:

588000-540000=48000

48000/540000=8.8%

8.8%/2 years =4.4%

9 cm
7 cm
7 cm
7 cm
The area of one of the bases of the above figure is about 21.2 cm2. The
surface area of the figure is?
A. 273.4 cm2
B. 210.4 cm2
C. 231.4 cm2
D. none of the above

Answers

Answer:

d

Step-by-step explanation:

none of the above mhhmm

Answer:

the answer to the question is 231.4 cm^2

Step-by-step explanation:

just got it wrong  

Solve for angle C please

Answers

Answer:

13.3 cm

Step-by-step explanation:

We can use the Pythagoream Theorem to identify any missing angles!

[tex]a^{2} +b^2=c^2[/tex]

In this case, will leave c for a^2!

[tex]a^2+20^2=24^2[/tex]

[tex]a^2+400=576[/tex]

[tex]576-400=a^2[/tex]

[tex]a^2=176[/tex]

[tex]\sqrt{176} = 13.3[/tex]

Explain why the set of polynomials is closed under subtraction

Answers

Answer:

Polynomials are closed under addition. When subtracting polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the difference has variables and exponents which are already classified as belonging to polynomials.

Step-by-step explanation:

mace
II. Directions: Solve for the answers of the problems below.
3. Bruno is running in a plaza having a radius of 75 meters. After having a complete round, he
wants to check if how many meters he ran. Please help Bruno.

Answers

Answer:

150

Step-by-step explanation:

radius is the half of one whole circle so

75 is the half to complete it add another 75

so 75+75 = 150

carry on learning

correct me if im wrong

if im right follow me

Find the value of x

A. 20
B. 28
C. 10
D. 50/7

Answers

Answer:

x=28

Step-by-step explanation:

Step 1, comparing triangles:

Let us look at [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].

They both share [tex]\angle A[/tex] ([tex]\angle A=\angle A[/tex])[tex]\angle ABC = \angle BDE[/tex] (Corresponding Angle Theorem)[tex]\angle ACB = \angle CED[/tex] (Corresponding Angle Theorem)

Therefore, because of AAA (Angle Angle Angle), [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] are similar.

Step 2:

Because the two triangles are similar, their sides should be proportional. Notice that [tex]\overline{AB}[/tex] and [tex]\overline {AD}[/tex] should be proportional.

Therefore, [tex]\overline{AB}[/tex]: [tex]\overline {AD}[/tex] =

[tex]12:30+12=\\12:42=\\2:7[/tex]

(Note, [tex]\overline {AD}[/tex] =  [tex]\overline{AB}[/tex]+ [tex]\overline{BD}[/tex]=12+30)

Step 3:

We figured out that  [tex]\triangle ABC[/tex]  and  [tex]\triangle ADE[/tex] have proportional sides of 2:7. Therefore,  [tex]\overline{BC}[/tex] and [tex]\overline{DE}[/tex] should also have a ratio of 2:7.

[tex]8: \overline{DE}=2:7\\8:\overline{DE}=8:28\\\overline{DE}=\fbox{28}[/tex]

x=28

I hope this helps! Let me know if you have any questions :)

Answer:

x = 20

Step-by-step explanation:

If we look at the given diagram, we will see that ΔABC and ΔADE are similar. Because they a similar we know that corresponding sides are in proportion. In order to solve this question, we need to know what the coefficient of similarity is.

AB and AD are corresponding sides, in order to get from 12 to 30 we need to multiple 12 by 2.5. That means that the coefficient of similarity between the two triangles is 2.5. To get x (length of DE) we need to multiply the length of BC by the coefficient of similarity. And so we get...

x = 2.5(BC)

x = 2.5(8)

x = 20

find measure of indicated arc please!

Answers

Answer:

94 degrees

Step-by-step explanation:

the mean of three numbers is 8 two of the numbers are 6 and 11 work out the third number

show workibf out

Answers

Answer:

7

Step-by-step explanation:

To find the number, first multiply 8 by 3, since that is how you find the mean.

8 x 3 = 24 (total)

x + 6 + 11 = 24

x = 24 - 6 - 11

x = 7

Inverse:

7 + 6 + 11 = 24

Mean = 24/3 = 8

Hope this helps!

Use this table of values for the rate of rainfall over time.
Rate of Rainfall (mm per hour) Time 6:00 am 20 6.15 am 28 630 am 3.0 645 am 35 7:00 am 3.8 7:15 am 42 7:30 am 4.8 7:45 am 5.6 8:00 am 4.0 8.15 am 3.3 8:30 am 1.8 8:45 am 0.4 9:00 am 1.2.
An approximation of the total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is
a. 9.3 mm.
b. 9.6 mm.

Answers

Solution :

Here the subintervals of equal length will be :

[tex][6:00, 6:30], [6:30, 7:00], [7:00, 7:30], [7:30, 8:00], [8:00, 8:30], [8:30, 9:00][/tex]

So thee mid points are

[tex]x_1 = 6:15, \ x_2=6:45, \ x_3=7:15, \ x_4=7:45, \ x_5, 8:15, \ x_6 = 8:45[/tex]

The length of each sub-interval is = [tex]\frac{9-6}{6} = \frac{3}{6} = 0.5[/tex]

So, total amount of rainfall will be :

[tex]$=0.5 \sum^6_{i=1} f(x_i)$[/tex]

[tex]$=0.5\left( f(x_1)+f(x_2)+....+ f(x_6)\right)$[/tex]

= 0.5 (2.8 + 3.5 + 4.2 + 5.6 + 3.3 + 0.4)

= 0.5 (19.8)

= 9.9

The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.

Given that,

The rate of rainfall (mm per hour) over time.

Rate of rainfall;

6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00

Time  

2.0  2.8   3.0   3.5    3.8    4.2   4.8   5.6   4.0   3.3   1.8  0.4   1.2  

We have to determine,

0.4 9:00 am 1.2.

The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is?

According to the question,

Rate of rainfall;

6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00

Time  

2.0  2.8   3.0   3.5    3.8    4.2   4.8   5.6   4.0   3.3   1.8  0.4   1.2  

Here, the midpoints sum with 6 equal subintervals are,

[tex]\rm x_1 = 6;15, \ x _2 = 6;45, \ x_3 = 7;15, \ x_4 = 7;45, x_5 = 8;15 , \ x_6 = 8;45[/tex]

Then, the length of each subinterval is,

[tex]= \dfrac{9-6}{6}\\\\= \dfrac{3}{6}\\\\= \dfrac{1}{2}[/tex]

The total amount of rainfall that falls between 6;00 to 9;00 am using the midpoint subinterval is,

[tex]\rm = \dfrac{1}{2} \sum^{6}_{i=0} f(x_i)\\\\= \dfrac{1}{2} \sum^{6}_{i=0} f(x_1)+ f(x_2) + f(x_3) + f(x_4) +f(x_5)+f(x_6)\\\\= \dfrac{1}{2} (2.8+ 3.5+4.2+ 5.6+3.3+0.4}\\\\= \dfrac{1}{2} \times 19.8\\\\= 9.9[/tex]

Hence, The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.

For more details refer to the link given below.

https://brainly.com/question/795909

(2-i)(2+i) please lmk the answer to this question.

Answers

The answer would be 5

Answer:

[tex]5[/tex]

Step-by-step explanation:

[tex](2−i)(2+i)[/tex]

[tex]2(2+i)−i(2+i)\\ 2⋅2+2i−i(2+i) \\2⋅2+2i−i⋅2−ii[/tex]

[tex]4+2i−2i \\ 5+2i−2i \\ 5+0 \\ 5[/tex]

Hope it is helpful...

kathy runs a 26.2-mi;e marathon at an average pace of 6.2 minutes per mile how long will it take her to finish the marathon round your answer to the nearest minute

Answers

Answer:

162 minutes

Step-by-step explanation:

Since she takes 6.2 minutes a mile, you multiply it by 26.2 for every mile. 6.2x26.2= 162.44, then round it to 162

PLS HELP ASAP !!!! PLS !! will mark whoever gets it right as brainliest !

Answers

Answer:

128° because its vertical with ∠1

I think, but I'm not sure.

A research team conducts a survey to determine the area of land used for farming in Iowa. The team randomly selects house addresses and sends the survey by mail. Which type of sampling method is the research team using?
A. Systematic random sampling.
B. Simple random sampling.
C. Multi-stage sampling.
D. Cluster sampling.

Answers

Answer:

B. Simple random sampling.

Step-by-step explanation:

From the question we are informed about a research team conducts a survey to determine the area of land used for farming in Iowa. The team randomly selects house addresses and sends the survey by mail. In this case, the type of sampling method used is the Simple random sampling. A simple random sample can be regarded as a subset of a statistical population, whereby each member of this subset posses an equal probability of them being chosen. A simple random sample can be portrayed as an unbiased representation of a group.

Simple random sampling is utilized in to culling smaller sample size out of larger population so that it can be used to research and make generalizations as regards larger group.

Find c. Round to the nearest tenth:

Answers

Step-by-step explanation:

what is the question please

Levers are not a problem in the mechanical system. But, if you put two different simple machines that do not cooperate, they will be able to make the question that you need to. T or F

Answers

What was that? F maybe

Answer:

True

Step-by-step explanation:

I am assuming that you are asking if two different simple machines that do not cooperate will work or not.

The answer to that is True.

Two things that do not work together will not work together. The two simple machines can not work with each other.

So, the answer is True. Best of Luck!

which of the following best describes the slope of the line below? pls help asap

Answers

Answer:

Step-by-step explanation:

Undefined.

The answer to that is Undefined

LA=
Round your answer to the nearest hundredth.
С
7
A
?
8
B

Answers

Answer:48.81

Step-by-step explanation:

Hope it helps

How much interest will be earned on a $1600 investment at 7.72% compounded
quarterly for 9 years?

Answers

56% interest will be earned

What is the approximate value of the y intercept and what does it mean in this example?

Answers

Answer:

Step-by-step explanation:

By using the utility for the line of best fit,

Equation of the line of best fit will be,

y = 1.5x + 1.32

Here, y - intercept of the line = 1.32

Here, y-intercept represents the amount of bean production when the level of water applied was zero.

The measure of the angle of depression from the top of a 270 m building tweet park bench on the ground is 63° 43’.How far Where is the park bench from the building? round to the nearest whole number

Answers

Answer:

547 m

Step-by-step explanation:

Given :

Angle of depression, θ = 63°43' ; 43/60 = 0.7167 = 63 + 0.7167 = 63.7167°

The height, h = 270

The distance of park bench from the building, d is given by :

Tan θ = opposite / Adjacent

Tan 63.7167 = d / 270

d = 270 * Tan 63.7167

d = 546.70459

d, distance of Park bench from building is 547 m

Which equation would have the steepest graph? Explain how you know?

Answers

Answer:

y = 3/8 x

Step-by-step explanation:

the smaller the number the steeper the graph

Translate and solve: 82% of what number is 369?

Answers

Answer:

82% of what number is 369

82% of 450 is 369

Answer:

number is 450

Step-by-step explanation:

let the number be x

82% of x=369

[tex]\frac{82}{100}[/tex]x = 369

82x=369*100

x=36900/82

x=450

question- pls help me find the ans​

Answers

Answer:

(c) 3,5 is the correct answer

the following is a summary of the violent crime rate violent crimes per 100,000 population we're all states of a country in a certain year complete parts a through D

Answers

Answer:

yes indeed it is

Step-by-step explanation:

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