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2 years ago

What is the distance between the points (4,3) and (1,-1) on the coordinate plane

Mathematics

2 answers:

spayn [35]2 years ago

8 0

Answer:

5 units

Step-by-step explanation:

All that you have to do is use the pythagorean theorem. You can tell that the distance on the x-axis is 3 and on the y-axis is 4, just by subtracting (1,-1) from (4, 3). Then, square the sides, add them, and find the square root of the answer.

4x4 = 16

3x3 = 9

16 + 9 = 25

The square root of 25 is 5. Your answer is 5.

Mariulka [41]2 years ago

7 0

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have the points (4, 3) and (1, -1). Substitute:

$d=\sqrt{(1-4)^2+(-1-3)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$

<h3>Answer: The distance between the points (4, 3) and (1, -1) is equal 5 units.</h3>

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2 Points

myrzilka [38]

Answer:

Step-by-step explanation:

First find the circumference of the circle with radius of 9 inches:

$C=2\pi r=2\pi \cdot 9=18\pi \ inches$

The full angle has 360°, so, to find the length of the arc DE, you can write:

$360^{\circ}\ - \ 18\pi \\ \\145^{\circ}\ - \ x$

which yields a proportion:

$\dfrac{360}{145}=\dfrac{18\pi}{x}\\ \\360x=145\cdot 18\pi\\ \\x=\dfrac{145\cdot 18\pi }{360}=\dfrac{145\pi}{20}=7.25\pi\approx 22.8\ inches$

6 0

2 years ago

After sitting on a shelf for a while, a can of soda at room temperature (73 F) is placed inside a refrigerator and slowly cools.

Alona [7]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling here:

$T(t)=T_s+(T_0-T_s)^{-kt$

where T(t) is the temp of something after a certain amount of time, t, has gone by; Ts is the surrounding temp, and T0 is the initial temp. k is the constant of cooling. We need to first solve for this using the information given. Filling in what we know:

$53=35+(73-35)^{-35k$ which can simplify a bit to

$53=35+(38)^{-35k$ and $18=38^{-35k$

Take the natural log of both sides:

$ln(18)=ln(38)^{-35k$

Taking the natural log allows us to pull that exponent down out front:

$ln(18)=-35k*ln(38)$

and now we can divide both sides by ln(38) to get

-35k = .794585 so

k = -.023

Now that have the value for k, we can go on to solve the rest of the problem which is asking us the temp of the soda after 70 minutes. Filling in using the k value and the new time of 70 minutes:

$T(t)=35+(38)^{70(-.023)$ and

$T(t)=35+(38)^{-1.61$ and

$T(t)=35+.0028612013$ and

T(t) = 35 F, basically the temp of the fridge, which is not surprising!

5 0

2 years ago

Describe the rule for the sequence 2, 1, 2/3, 1/2, 2/5, 1/3, 1/7,...

Triss [41]

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the <em>n</em>th term in the sequence is multiplied by <em>n</em>/(<em>n</em> + 1) to get the (<em>n</em> + 1)th term.

Recursively, the sequence is given by

$\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}$

We can solve this exactly by iterating:

$a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots$

and so on down to

$a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1$

$a_n=\dfrac{(n-1)!}{n!}a_1$

and with lots of cancellation, we end up with

$a_n=\dfrac{a_1}n=\boxed{\dfrac2n}$

6 0

2 years ago

Help center of circle

Lelu [443]

Answer:

Center = (7, - 5)

Radius = 3

Step-by-step explanation:

${x}^{2} + {y}^{2} + 14x - 10y + 65 = 0 \\ {x}^{2} + 14x + {y}^{2} - 10 + 65 = 0 \\ ( {x}^{2} + 14x + {7}^{2}) - {7}^{2} + ({y}^{2} - 10y + {5}^{2}) \\- {5}^{2} + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 - 25 + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 + 40= 0 \\ (x + 7)^{2} + (y - 5)^{2} - 9= 0 \\ (x + 7)^{2} + (y - 5)^{2} = 9 \\ (x + 7)^{2} + (y - 5)^{2} = {3}^{2} \\ equating \: it \: with \: \\ (x - h)^{2} + (y - k)^{2} = {r}^{2} \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3$