Which point is located at (-7, -10)? point N point O point A point E

Find an equation of the sphere through the point (4,3,-1) and has center (3,8,1).

sleet_krkn [62]

Answer:

$(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30$

Step-by-step explanation:

The general equation of a sphere is as follows:

$(x - x_{c})^{2} + (y - y_{c})^{2} + (z - z_{c})^{2} = r^{2}$

In which the center is $(x_{c}, y_{c}, z_{c}$ , and r is the radius.

In this problem, we have that:

$x_{c} = 3, y_{c} = 8, z_{c} = 1$

So

$(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = r^{2}$

through the point (4,3,-1)

This leads us to find the radius.

$(4 - 3)^{2} + (3 - 8)^{2} + (-1 - 1)^{2} = r^{2}$

$r^{2} = 1 + 25 + 4$

$r^{2} = 30$

So the equation of the sphere is:

$(x - 3)^{2} + (y - 8)^{2} + (z - 1)^{2} = 30$

6 0

3 years ago

I have a total of 29 coins-they are quarters and dimes. Together they amount to $5.60. How many quarters do I have? How many dim

Anna007 [38]

450/25= 18

where 450 is $4.50 and 25 is one quarter. there will be 18 quarters.

560-450=110

110/10=11

where 110 is $1.10 and 10 is one dime. there will be 11 dimes.

11+18= 29

where 11 is total number of dimes and 18 is total number of quarters. and 29 is total number of coins

6 0

3 years ago

Read 2 more answers

Y=x+5 x-5y=-9 Can someone please help ASAP

Dmitriy789 [7]

X = -4
Y = 1

1 = -4 + 5
-4 - 5(1) = -9

7 0

2 years ago

What is 3 1/3 divided by 1/3

saveliy_v [14]

Convert 3 1/3 into a improper fraction:
= 10/3

Then flip the other fraction around and multiply them together:
1/3 -> 3/1
(10*3)/(3*1) = 30/3 = (30/3)/(3/3) = 10/1 = 10

The answer is 10

4 0

3 years ago

Read 2 more answers

The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”

balandron [24]

Example of use of terms:
Statement: If it is far, we take a bus.
Inverse: If it is not far, we do not take a bus.
Converse: If we take a bus, it is far.
Contrapositive: If we do not take a bus, it is not far.

We also know that
1. The inverse of the inverse is the statement itself, and similarly for converse and contrapositive.
2. Only the contrapositive is logically equivalent to the original statement.
This means that the converse and inverse are logically different from the original statement.

Now back to the given statement.
To find the original statement, we find the contrapositive of the contrapositive.
We then find the converse from the original statement, as in the example above.

Original statement
(note that in English, if it is not worth X dollars, means if it is not worth AT LEAST X dollars")
contrapositive of

"If an item is not worth five dimes, then it is not worth two quarters.”
is the negation of the converse, which become
"If an item is worth two quarters, then it is worth (at least) five dimes."

The converse of the previous statement is therefore
"If an item is worth (at least) five dimes then it is worth two quarters"

In this particular case, we can also take advantage of the fact that the contrapositive is the negation of the converse. So all we have to do is the provide the negation of each component of the contrapositive to get the converse:
"If an item is worth (at least) five dimes, then it is worth two quarters".
as before.

Note that the converse does NOT logically mean the same as the original statement.

6 0

3 years ago