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3 years ago

Write the general equation for the circle that passes through the points:

Mathematics

1 answer:

Rus_ich [418]3 years ago

4 0

Answer:

x² + y² − 8x − 6y = 0

Step-by-step explanation:

The conic form of a circle is:

x² + y² + Dx + Ey + F = 0

Plugging in the three points:

(1)² + (7)² + D(1) + E(7) + F = 0

(8)² + (6)² + D(8) + E(6) + F = 0

(7)² + (-1)² + D(7) + E(-1) + F = 0

Simplifying:

50 + D + 7E + F = 0

100 + 8D + 6E + F = 0

50 + 7D − E + F = 0

Subtracting the first equation from the third:

(50 + 7D − E + F) − (50 + D + 7E + F) = 0

6D − 8E = 0

3D = 4E

Now if we subtract the third equation from the second:

(100 + 8D + 6E + F) − (50 + 7D − E + F) = 0

50 + D + 7E = 0

150 + 3D + 21E = 0

Substituting:

150 + 4E + 21E = 0

150 + 25E = 0

E = -6

Therefore, D = -8.

Plugging into any equation to find F:

50 + (-8) + 7(-6) + F = 0

F = 0

The equation of the circle is:

x² + y² − 8x − 6y = 0

Graph:

desmos.com/calculator/davg3d3lic

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A train leaves the station at time = 0. Traveling at a constant speed, the train travels 330 kilometers in 3 hours. Answers part

amid [387]

Answer:

The function that relates the distance traveled d to the time t is

f(t) = 110t, where d = f(t)

Step-by-step explanation:

From the question, we were told that the train is At a constant speed, the train travels 330 kilometers in 3 hours

We were told to write function that relates the distance traveled d to the time t, we can do this by writing a linear equation with those functions

Since we are told that the train travels 330 kilometers in 3 hours, then we can say the train travel (330/3) kilometers in 1 hour which means it travel 110 kilometers in 1 hour

Then d= 110t---------------eqn(1)

If if t = 0, then d = 0, as well since at t=0 the train is at the station

At t = 1 then d = 110.

From equation (1) d can be replaced by f(t) then we have

f(t) = 110t----------------eqn(2)

Now we replace d by f (t), because d = f t):

f(t) = 120t

Therefore, The function that relates the distance traveled d to the time is f(t) = 120t

5 0

3 years ago

Victor buys some six-packs of soda for a party. He buys 42 cans in all. How many six-packs of soda did Victor buy?

Whitepunk [10]

Answer: 7

Step-by-step explanation: 7*6=42

5 0

3 years ago

Read 2 more answers

The product of a number and its ___________ is

Alex

Reciprocal

Explanation:
I know what I know and this is one of those things

3 0

3 years ago

Read 2 more answers

Rob ran 27.2 miles less than Jasmine last week. Rob ran 10 miles. How many miles did Jasmine run?

jeka94

Answer:

Jasmine ran last week 37.2 miles

Step-by-step explanation:

Let

x ----> number of miles Rob ran last week

y ----> number of miles Jasmine ran last week

we know that

x=y-27.2 ----> equation A

x=10 ----> equation B

Substitute equation B in equation A and solve for y

10=y-27.2

y=10+27.2

y=37.2 miles

4 0

3 years ago

Surveys indicate that two-thirds of all voters in Ward 5 plan on choosing Spike Jones for commissioner. If there are 500 voters

olya-2409 [2.1K]

<u>Answer:</u>

333 people of ward 5 are going to be voting for Spike Jones.

<u>Solution:</u>

We have been given that two-thirds of all voters in Ward 5 plan on choosing Spike Jones for commissioner.

There are 500 voters in Ward 5.

Since 2/3 of all voters in Ward 5 are voting for Spike Jones the remaining 1/3 will not be voting for him.

To find out how many people in ward 5 are exactly voting for Spike Jones. We need to calculate how much is two thirds of 500 is.

This is done as follows:

$\begin{array}{l}{\frac{2}{3} \times 500} \\\\ {=\frac{1000}{3}} \\\\ {=333.334}\end{array}$

Since people cannot be denoted in decimal points we have to round it off to a whole number. That’s is 333.

Therefore 333 people of ward 5 are going to be voting for Spike Jones.

4 0

3 years ago