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4 years ago

Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.

Mathematics

1 answer:

Paul [167]4 years ago

6 0

Answer:

5 rad

Step-by-step explanation:

Recall that the length of an arc of circumference is given by the formula:

$Arc\,Length=\theta\,*\,radius$ , where $\theta$ is the subtended angle [in radians] from the circumference's center.

Therefore in this case, you know the arc length (81.5 cm), and the radius (16.3 cm), and can solve for the angle $\theta$ using the above equation as shown below:

$Arc\,Length=\theta\,*\,radius\\81.5\,cm = \theta\,*\,16.3\,cm\\\frac{81.5}{16.3} = \theta\\\theta=5\,rad$

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...... trying to find domain, range rel max rel min end behavior inc intervals dec intervals. zeros..... I'm a mom trying to hel

Fiesta28 [93]

Answer:

The values are evaluated below.

Step-by-step explanation:

Given function is

$-x^4-7x^3-12x^2$

We have to find the domain, range, rel max, rel min, end behaviour, increasing or decreasing intervals and zeros of polynomial.

Domain:

The domain of a function is the set of all possible values of x for the given function.

Here domain is set of all real numbers R.

Range:

The range is the resulting y-values we get after substituting all the possible x-values.From the graph we see that

The range is $-\infty$

Relative maxima and minima of a function, are the largest and smallest value of the function on an entire domain of function.

Relative max of $-x^4-7x^3-12x^2$ is 0 at x=0

and $\frac{3}{512}(133\sqrt57-471)$ at $x=\frac{-21}{8}-\frac{\sqrt57}{8}$

Relative min is

$\frac{-3}{512}(471+133\sqrt57)$ at $x=\frac{-21}{8}+\frac{\sqrt57}{8}$

From the graph we see that

End behaviour is As $\\x->\infty, f(x)->-\infty\\x->-\infty, f(x)->-\infty\\$

Increasing intervals and decreasing intervals are

Increasing: $\frac{1}{8}(\sqrt57-21)$

Decreasing: $\frac{1}{8}(-21-\sqrt57)$

Zeroes are :

$-x^4-7x^3-12x^2=0$

⇒ $(-x^2)(x^2+7x+12)=0$

⇒ $(-x^2)(x+3)(x+4)=0$

Hence, zeroes are 0, 0, -3, -4

3 0

3 years ago

Read 2 more answers

Keith’s gas tank is 1/3 full. After he buys 2 gallons of gas, it is 1/2 full. How many gallons can Keith’s tank hold?

madam [21]

It will be 3 cuz why not lol

6 0

3 years ago

Read 2 more answers

Write problem out please

Gekata [30.6K]

Answer:

21.25 m

Step-by-step explanation:

y = Ax² + Bx + C

Set the origin at the middle of the span so that the point (0, 0) is on the curve

0 = A(0)² + B(0) + C means C = 0

The points (200, 85) and (-200, 85) are on the curve

85 = A(200)² + B(200)

85 = A(-200)² + B(-200)

85 - 40000A - B(200) = 85 - 40000A + B(200)

- B(200) = B(200)

-400B = 0

B = 0

85 = A(200)²

A = 85/40000

y = 85x²/40000

y = 85(100)²/40000 = 21.25 m

5 0

3 years ago

Simplify the expression. Write the answer with positive exponents only. Assume the variable represents a nonzero real number.

luda_lava [24]

Answer:

$\frac{1}{w^{29}}$

Step-by-step explanation:

The given expression is $\frac{w^{-7}(w^{-9})^2}{w^4}$ .

Since, $w^{-7}=\frac{1}{w^7}$

And $w^{9}=\frac{1}{w^9}$

Expression will become,

$\frac{w^{-7}(w^{-9})^2}{w^4}=\frac{\frac{1}{w^7}(\frac{1}{w^9})^2}{w^4}$

$=\frac{\frac{1}{w^7\times w^{18}}}{w^4}$

$=\frac{\frac{1}{w^{(7+18)}}}{w^4}$

$=\frac{1}{w^{25}}\times \frac{1}{w^4}$

$=\frac{1}{w^{25}\times w^4}$

$=\frac{1}{w^{29}}$

Therefore, Simplified form of the given expression will be $\frac{1}{w^{29}}$ .

3 0

3 years ago

if the value of the home is increasing by 1800 per year. if it is worth 170,000 today what will it be worth in four years

tatuchka [14]

Answer:

177,200

Step-by-step explanation:

3 0

3 years ago