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3 years ago

A circle has a center of (5, 2) and a radius of 10. Which the fallowing points will the circle pass through ?

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

5 0

Answer:

centre of the circle(h,k)=(5,2)

radius(r)=10

Step-by-step explanation:

Now,

equation of the circle is giveb by (x-h)^2+(y-k)^2=r^2

or,(x-5)^2+(y-2)^2=(10)^2

or,x^2-10x+25+y^2-4y+4=100

or,x^2+y^2-10x-4y+29-100=0

or,x^2+y^2-10x-4y-71=0

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When rolling two 6-sided dice, what is the probability of rolling a sum of 7 and 11?

RSB [31]

Answer:

We have two 6-sided dice.

Each one of them has 6 possible outcomes.

The total number of outcomes for the pair, will be equal to the product between the numbers of outcomes for each one of them

Then the total number of outcomes is:

C = 6*6 = 36.

The number of outcomes where the sum of the dice are 7 are:

1 and 6

6 and 1

2 and 5

5 and 2

3 and 4

4 and 3

So we have 6 outcomes where the sum of both numbers is equal to 7.

The probability of rolling a pair such that the sum is equal to 7, is equal to the quotient between the number of outcomes that meet this condition (6) and the total number of outcomes (36)

The probability is:

P = 6/36 = 1/6

Now let's do the same for 11.

The outcomes where the sum is 11 are:

5 and 6

6 and 5

So we have two outcomes.

In this case, the probability will be:

P = 2/36 = 1/18

5 0

3 years ago

What does the arc AC equal?

Nimfa-mama [501]

The measure of an arc is the measure of its central angle, which is indicated as

Answer: 90°

right there in the figure.

7 0

3 years ago

An open rectangular box with a square bottom must have a surface area of A square inches. Write a formula for the volume of the

skelet666 [1.2K]

The surface area of the box is being referred to as A
The surface area will be the sum of the four rectangular sides' areas and the base area.
Base area = x²
Rectangular side area = xh
A = x² + 4xh
Volume is, as you said,
V = x²h
Lets substitute h from the formula of A to obtain A in our final answer. Substituting x is possible, but more difficult
(A - x²)/4x = h
V = (x²) * (A - x²)/4x
V = (Ax - x³)/4

5 0

3 years ago

Read 2 more answers

Hi i need help with this "The cost of a theme park ticket is $25. The cost for 2 ticket is $50 what is the cost of 4 theme park

Bumek [7]

Answer:

$100

Step-by-step explanation:

If 1=$25, 2=$50, then 4*25=100 and 50*2=100

3 0

3 years ago

A particle moves along line segments from the origin to the points (2, 0, 0), (2, 4, 1), (0, 4, 1), and back to the origin under

Shkiper50 [21]

The work is equal to the line integral of $\vec F$ over each line segment.

Parameterize the paths

from (0, 0, 0) to (2, 0, 0) by $\vec r_1(t)=t\,\vec\imath$ with $0\le t\le2$ ,
from (2, 0, 0) to (2, 4, 1) by $\vec r_2(t)=2\,\vec\imath+4t\,\vec\jmath+t\,\vec k$ with $0\le t\le1$ ,
from (2, 4, 1) to (0, 4, 1) by $\vec r_3(t)=(2-t)\,\vec\imath+4\,\vec\jmath+\vec k$ with $0\le t\le2$ , and
from (0, 4, 1) to (0, 0, 0) by $\vec r_4(t)=(4-4t)\,\vec\jmath+(1-t)\,\vec k$ with $0\le t\le1$

The work done by $\vec F$ over each segment (call them $C_1,\ldots,C_4$ ) is

$\displaystyle\int_{C_1}\vec F\cdot\mathrm d\vec r_1=\int_0^2\vec0\cdot\vec\imath\,\mathrm dt=0$

$\displaystyle\int_{C_2}\vec F\cdot\mathrm d\vec r_2=\int_0^1(t^2\,\vec\imath+24t\,\vec\jmath+32t^2\,\vec k)\cdot(4\,\vec\jmath+\vec k)\,\mathrm dt=\int_0^1(96t+32t^2)\,\mathrm dt=\frac{176}3$

$\displaystyle\int_{C_3}\vec F\cdot\mathrm d\vec r_3=\int_0^2(\vec\imath+(24-12t)\,\vec\jmath+32\,\vec k)\cdot(-\vec\imath)\,\mathrm dr=-\int_0^2\mathrm dt=-2$

$\displaystyle\int_{C_4}\vec F\cdot\mathrm d\vec r_4=\int_0^1((1-t)^2\,\vec\imath+2(4-4t)^2\,\vec k)\cdot(-4\,\vec\jmath-\vec k)\,\mathrm dt=-2\int_0^1(4-4t)^2\,\mathrm dt=-\frac{32}3$

Then the total work done by $\vec F$ over the particle's path is 46.

8 0

4 years ago