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2 years ago

The radius of a circle is 8 inches. What is the angle of an arc 2π inches long?

Mathematics

1 answer:

Y_Kistochka [10]2 years ago

3 0

Answer:

π/4 radians

Step-by-step explanation:

The arc length formula is s = rФ, where Ф is the central angle (in radians).

Here, r = 8 inches and s = arc length = 2π inches. We need to find the central angle, Ф. The formula given above is s = rФ, or, equivalently,

Ф = s/r.

Here, the central angle is Ф = s/r = 2π/8, or π/4 radians.

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What two rational expressions sum to 3x+4/x^2-6x+5?

Lubov Fominskaja [6]

Answer:

$\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}$

Step-by-step explanation:

The given rational expression is:

$\frac{3x+4}{x^{2}-6x+5} = \frac{3x+4}{(x-1)(x-5)}$

We can use concept of Partial Fractions to solve this problem. Let,

$\frac{3x+4}{(x-1)(x-5)}=\frac{A}{x-1} +\frac{B}{x-5}$

Multiplying both sides by (x - 1)(x - 5), we get:

$3x+4=A(x-5)+B(x-1)$

Substituting x = 5, we get:

$3(5)+4=A(5-5)+B(5-1)\\\\ 15+4=0+4B\\\\ 19=4B\\\\ B=\frac{19}{4}$

Substituting x = 1, we get:

$3(1)+4=A(1-5)+B(1-1)\\\\ 7=-4A\\\\ A=-\frac{7}{4}$

Substituting the value of A and B, back in the original equation, we get:

$\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}$

4 0

2 years ago

What is the domain of the relation {(2, 8), (0, 8), (–1, 5), (–1, 3), (–2, 3)}?

lesya [120]

(2,0,-1,-1,-2) that is the domain from what I remember. Hope that help

6 0

3 years ago

Read 2 more answers

Help what is the slope of the line?

Vera_Pavlovna [14]

9514 1404 393

Answer:

8/5 = 1.6

Step-by-step explanation:

It looks like the line crosses grid points (-4, -4) and (1, 4). This means the slope is ...

m = (y2 -y1)/(x2 -x1)

m = (4 -(-4))/(1 -(-4)) = 8/5 = 1.6

The slope of the line seems to be about 8/5, or 1.6.

6 0

3 years ago

On any day, the probability of rain is 0.3. The occurrence of rain on any day is independent of the occurrence of rain on any ot

Sunny_sXe [5.5K]

Answer:

0.47178 = 47.178%

Step-by-step explanation:

Put simply, this question is asking the probability of having rain atleast twice in the next 5 days. The easiest way that comes to mind is reverse count - find the probability of it not happening. There are two cases for this:

Raining only once:

This has a .7^4 * 0.3 * 5 chance

Raining no times:

This has a .7^5 chance

Adding these together you get 0.52822

This is the inverse probability, so to find the actual probability, subtract it from 1.

P = 0.47178

8 0

2 years ago

What is the factorization of the trinomial below -x^2+x+42

aksik [14]

For the given trinomial

$a=-1, b=1 ,c=42$

We need to multiply a by c
$-1 \times 42 = - 42$

We split the middle term with these two factors
$7,-6$
To obtain,

$- {x}^{2} + 7x -6x + 42$
We now factor

$- {x}^{2} + x + 42 \: = x( - x + 7) + 6( - x + 7)$
This implies

$- {x}^{2} + x + 42: = (x + 6)(7 - x)$

4 0

3 years ago

Read 2 more answers