Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.

Answers

Answer 1

Answer:

Answer:

The equation of the sphere with center (-3, 2 , 5) and radius 4 is $(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

The intersection of the sphere with the yz- plane gave the equation $(y-2)^(2) + (z-5)^(2) = 7$ which is a 2D- circle with center (0,2,5) and radius $√(7)$ .

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

$(x-a)^(2) +(y-b)^(2) + (z-c)^(2) = r^(2)$

where, $x,$ $y,$ and $z$ are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center, (-3, 2 , 5) and radius 4 becomes

$(x-a)^(2) +(y-b)^(2) + (z-c)^(2) = r^(2)$

$(x-(-3))^(2) +(y-(2))^(2) + (z-(5))^(2) = 4^(2)$

Then,

$(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The $yz -$ plane is where $x = 0$ , then we set $x = 0$

Them the equation $(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$ becomes

$(0+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

$(3)^(2) +(y-2)^(2) + (z-5)^(2) = 16\n9 +(y-2)^(2) + (z-5)^(2) = 16\n(y-2)^(2) + (z-5)^(2) = 16 - 9\n(y-2)^(2) + (z-5)^(2) = 7$

This equation is the equation of a 2D- circle with center (0,2,5) and radius $√(7)$

This is the part of the sphere that intersects with the yz-plane.

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What is the y-intercept of the graph below.

What is the slope of this line? Enter your answer as a fraction in simplest term in
the box.

Answers

The slope of the line is 1/4.

What is slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given points:

(0, 6) and (8, 8)

Now, slope = $(y_2 - y_1)/ ( x_2- x_1)$

slope= ( 8- 6)/ (8-0)

slope = 2/8

slope= 1/4

Hence, the slope of the line is 1/4.

Learn more about slope of line here:

brainly.com/question/3605446

#SPJ2

Answer:

$slope=(1)/(4)$

Step-by-step explanation:

The slope of a line can be seen as:

$(rise)/(run)$

Rise over run is the change in the y values over the change in x values. For example, in this graph, you would start on one of the points given. From there, you would move up first. After moving up a certain number of spaces, you would move to the side until you reach the other point.

In the graph, you would move up until you are in line with one of the other points. Starting at (-4,5), move up one space, then to the left 4 spaces to reach the point (0,6). Using the spaces moved in the rise over run:

$(1)/(4) =(rise)/(run)=slope$

Therefore, the slope is $(1)/(4)$ .

This is true for any two points on the line.

:Done

*When you move up, the number will be positive $((+y)/(x) )$ . If you move down, the number will be negative $((-y)/(x) )$ . If you move left, the number will be positive $((y)/(+x))$ . If you move right, the number will be negative $((y)/(-x) )$ . Keep this in mind. It is very important.

**Always move along the y-axis first, then move along the x-axis. If you do it the other way, the slope will be wrong.

A shoe store recorded the price (in dollars) of 175 pairs of women's shoes and 175 pairs of men's shoes. The data collected was used to create the following table.

Answers

Answer:

Most of the mens shoes in the data sets cost more than the womens shoes

Step-by-step explanation:

i did this and got it correct

A restaurant has 33,500 gallon aquarium and a 500 gallon aquarium. How many times greater is the capacity of the larger aquarium than the smaller aquarium?

Answers

Answer:

Step-by-step explanation:

33,500/500 = 67

To check our work:

67 x 500 = 33,500

Answer:

67 percentStep-by-step explanation:

Express the number as a ratio of integers. 3.469 = 3.469469469

Answers

If you're looking for a fractional representation of the non-terminating decimal,
3.469469469....
then:

Let x=3.469469469.....
then
1000x-x=(3469.469469469...) - (3.469469469....)
999x = 3466
x=3466 / 999
= 3+469/999
$=3(469)/(999)$

Danielle has a crate of books in four different genres: fantasy, nonfiction, thrillers, and romance. She randomly picks a book from the crate and replaces it. She repeats this experiment 60 times and gets the results shown in the table.Book Genre Times Picked

fiction 12

nonfiction 18

thriller 24

romance 6

Which genre of book does Danielle likely have the most of?

Answers

Answer:

Thriller, 24

Step-by-step explanation:

It has the most books shown.

Answer:

iM nOT toO suRE BUT I THINK ITS THRILLER BECAUSE IT HAS 24 AND 60/24=2.5

Step-by-step explanation:

Which conclusion can be drawn from the data?Question 9 options:

For ten weeks, City A received less rainfall, on average, than City B.

The range between the maximum and minimum values for City B is greater than the range between maximum and minimum values for City A.

During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

The median for City A is less than the median for City B.

Answers

Answer:

During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

Step-by-step explanation:

Given the data :

City A :

Reordered data:

0, 0.2, 0.2, 0.3, 0.4, 1, 1.3, 1.5, 2.5, 3

City B :

Reordered data:

0, 0, 0.1, 0.1, 0.2, 0.3, 0.4, 1, 1, 1

Using a calculator :

Mean Rainfall for City A = 1.04

Mean rainfall for city B = 0.41

Range : maximum - minimum

City A = 3 - 0 = 3

City B = 1 - 0 = 1

Mode (most occurring) :

City A = 0.2

City B = 1

Median :

City A = 0.7

City B = 0.25

The only true conclusion in the options given that can be drawn from the data is that ;During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

Answer:

the Answer is C.

Step-by-step explanation:

I just took the test

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