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3 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(0,1), B(2, 1) , and C(2, 5) ?

1 answer:

4 0

The circumcenter is where the perpendicular bisectors meet.
if you sketch the triangle, you will see that it is a right triangle, with the right angle vertex at (2,1)
one perpendicular bisector is x=1, another perpendicular bisector is y=3
they meet at (1,3)
so (1,3) is the answer.

You might be interested in

A runner starts at the beginning of a runners' path and runs at a constant rate of 6 mi/hr. Fifteen minutes later a second runne

MatroZZZ [7]

Answer:

45 minutes

Step-by-step explanation:

let after t hours they meet after the second runner starts.

15 minutes=1/4 hour.

6(t+1/4)=8t

6t+6/4=8t

8t-6t=6/4

2t=3/2

t=3/2* 1/2=3/4 hours=45 minutes

6 0

3 years ago

Read 2 more answers

What is two and two fourths plus one third

kkurt [141]

Answer:

2 5/6

Step-by-step explanation:

2 2/4 + 1/3

First, you have to make the bottoms of the fraction the same, by figuring out the lowest common denominator. In this case it would be 12. 4x3 = 12. 3x4 = 12.

Multiply the top number by the same number you multiplied the bottom by.

We multiplied the 4 by 3, so we would also multiply the 2 by 3 (which would be 6).

Do the same for the second fraction. 1x4 = 4.

Now we have 2 6/12 + 4/12. We add the top numbers together and we get 10/12.

Now we have to reduce the fractions. We can do this in this situation by just dividing the top and bottom numbers by 2.

2 5/6

8 0

3 years ago

Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a fun

WITCHER [35]

Answer:

Required solution (a) $f(x,y,z)=xyz+3z^2+C$ (b) 40.

Step-by-step explanation:

Given,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k$

(a) Let,

$F(x,y,z)=yz \uvec i +xz\uvec j+(xy+6z)\uvex k=f_x \uvec{i} +f_y \uvex{j}+f_z\uvec{k}$

Then,

$f_x=yz,f_y=xz,f_z=xy+6z$

Integrating $f_x$ we get,

$f(x,y,z)=xyz+g(y,z)$

Differentiate this with respect to y we get,

$f_y=xz+g'(y,z)$

compairinfg with $f_y=xz$ of the given function we get,

$g'(y,z)=0\implies g(y,z)=0+h(z)\implies g(y,z)=h(z)$

Then,

$f(x,y,z)=xyz+h(z)$

Again differentiate with respect to z we get,

$f_z=xy+h'(z)=xy+6z$

on compairing we get,

$h'(z)=6z\implies h(z)=3z^2+C$ (By integrating h'(z)) where C is integration constant. Hence,

$f(x,y,z)=xyz+3z^2+C$

(b) Next, to find the itegration,

$\int_C \vec{F}.dr=\int_C \nabla f. d\vec{r}=f(5,4,2)-f(2,0,-2)=(52+C)-(12+C)=40$

3 0

3 years ago

Here are some prices customers paid for different items at a farmer’s market. Find the cost for 1 pound of each item.

posledela

Answer:

1 pounds of apples $=$ $\$ 1·25

1 pounds of cheese $=$ $\$ 7

1 pounds of coffee beans $=$ $\$ 5·5

1 pounds of fudge $=$ $\$ 9

1 pounds of pumpkin $=$ $\$ 0·88

Step-by-step explanation:

Unit Rate is the ratio between two different quantities with different units

The ratio of cost per items is

$=$ $\frac{dollars}{pounds}$

4 pounds of apples $= \$ 5

4 pounds $= \$ 5

Divided 4 both the side

1 pounds of apples $=$ $\$ 1·25

$\frac{1}{2}$ pounds of cheese $= \$ 3·50

$\frac{1}{2}$ pounds $= \$ 3·50

Divided $\frac{1}{2}$ both the side

1 pounds of cheese $=$ $\$ 7

$\frac{3}{2}$ pounds of coffe beans $= \$ 8·25

$\frac{3}{2}$ pounds $= \$ 8·25

Divided $\frac{3}{2}$ both the side

1 pounds of coffee beans $=$ $\$ 5·5

$\frac{3}{4}$ pounds of fudge $= \$ 6·75

$\frac{3}{4}$ pounds $= \$ 6·75

Divided $\frac{3}{4}$ both the side

1 pounds of fudge $=$ $\$ 9

$\frac{25}{4}$ pounds of pumpkin is $= \$ 5·50

$\frac{25}{4}$ pounds $= \$ 5·50

Divided $\frac{25}{4}$ both the side

1 pounds of pumpkin $=$ $\$ 0·88

8 0

3 years ago

Teri went shopping with $300. Her Christmas shopping list is: 5 barbies for $10.50 each,, earbuds for $45, 3 sweaters for $22 ea

Romashka [77]

5 times 10.50 = $52.5

An additional $45

3 times 22 = $66

An other additional $65

The total price her shopping list costs is 229.5

Now, $300 - $229.5 = $70.5

Teri will have $70.50 left after buying these items.

3 0

3 years ago