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4 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(4,10), B(10, 10) , and C(10, 2) ?

Mathematics

1 answer:

const2013 [10]4 years ago

4 0

Answer:

(7,6)

Step-by-step explanation:

Triangle ABC with vertices at points A(4,10), B(10, 10) , and C(10, 2) is a right triangle with the hypotenuse AC.

The circumcenter of the right triangle is the midpoint of the hypotenuse.

Find the coordinates of the midpoint O of the hypotenuse AC:

$x_O=\dfrac{4+10}{2}=7\\ \\y_O=\dfrac{10+2}{2}=6$

So, O(7,6)

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The trip took 57 hour

7 0

3 years ago

I don't know how to solve it.

Nataly [62]

Step-by-step explanation:

Take the first derivative

$\frac{d}{dx} ( {x}^{3} - 3x)$

$3 {x}^{2} - 3$

Set the derivative equal to 0.

$3 {x}^{2} - 3 = 0$

$3 {x}^{2} = 3$

${x}^{2} = 1$

$x = 1$

$x = - 1$

For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).

For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.

Since we are going to Positve to negative slope, we have a local max at x=-1

Plug in -1 for x into the original function

$( - 1) {}^{3} - 3( - 1) = 2$

So the local max is 2 and occurs at x=-1,

For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.

Since we are going to decreasing to increasing, we have minimum at x=1,

Plug in 1 for x into original function

${1}^{3} - 3(1)$

$1 - 3 = - 2$

So the local min occurs at -2, at x=1

8 0

2 years ago

Please help!!!!!! Solve for x:

nordsb [41]

A
Explanation: You want to get x by itself. So add +7 to -7 to cancel it out, do the same thing to 4.
x-7=4
+7+7
x=11
x

8 0

2 years ago

Which of the following is the balance for a single $3,200 deposit in an account with an APR of 2.6% that compounds interest quar

Flauer [41]

Answer:

$FV= 3200(1+\frac{0.026}{3})^{3(6)}=3200 (1.008667)^{54}= 50994.590$

Step-by-step explanation:

For this case we can use the formula for the future value with compound interest given by:

$FV= P (1+\frac{r}{n})^{nt}$ (1)

For this case since the interest is compounded quarterly we have 3 periods each year, since we have 3 quarters in a year.

r represent the rate =0.026

t = 6 represent the number of years

P = 3200 represent the amount invested at the begin

If we apply the formula (1) we got:

$FV= 3200(1+\frac{0.026}{3})^{3(6)}=3200 (1.008667)^{54}= 50994.590$

So then the balance after 6 years would be approximately 50995 with the conditions provided.

7 0

3 years ago

0,5.<img src="https://tex.z-dn.net/?f=%5Csqrt%7B0%2C09%7D" id="TexFormula1" title="\sqrt{0,09}" alt="\sqrt{0,09}" align="absmidd

Komok [63]

Answer:

0.21

Step-by-step explanation:

The given expression is :

$0.5\times \sqrt{0.09}-2\sqrt{0.05}+\sqrt \frac{1}{4}$

We need to solve it.

We know that,

$\sqrt{0.09}=0.3\ and\ \sqrt{0.05}=0.223$

So,

$0.5\times \sqrt{0.09}-2\sqrt{0.05}+\sqrt \frac{1}{4}=0.5\times 0.3-2\times 0.22+0.5\\\\=0.21$

$=\dfrac{21}{100}$

So, the value of the given expression is equal to 0.21.

8 0

3 years ago