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4 years ago

What is the length of an arc defined by a 60 degree central angle in a circle with a radius of 5 in.?

Mathematics

1 answer:

Natali [406]4 years ago

3 0

Answer:

5.24 in

Step-by-step explanation:

The arc length is calculated as

arc = circumference × fraction of circle

= 2πr × $\frac{60}{360}$

= 2π × 5 × $\frac{1}{6}$

= $\frac{10\pi }{6}$ ≈ 5.24 in (2 dec. places )

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2x - 5y + 3z 5x + 9y - 2z

SIZIF [17.4K]

Answer:

3xz5+2x+4y−2z

Step-by-step explanation:

2x−5y+3z5x+9y−2z

=2x+−5y+3xz5+9y+−2z

Combine Like Terms:

=2x+−5y+3xz5+9y+−2z

=(3xz5)+(2x)+(−5y+9y)+(−2z)

=3xz5+2x+4y+−2z

7 0

3 years ago

Let f(x)=9-x^2, g(x)=3-x. Find (f-g)(x) and its domain

Lynna [10]

Answer:

$(f-g)(x)=-x^2+x+6$

Domain:

$(-\infty,\infty)$

Step-by-step explanation:

we are given

$f(x)=9-x^2$

$g(x)=3-x$

Calculation of (f-g)(x):

$(f-g)(x)=f(x)-g(x)$

we can plug it

$(f-g)(x)=9-x^2-(3-x)$

now, we can simplify it

$(f-g)(x)=9-x^2-3+x$

$(f-g)(x)=6-x^2+x$

$(f-g)(x)=-x^2+x+6$

Domain:

we know that

domain is all possible values of x for which any function is defined

and f(x),g(x) and (f-g)(x) are polynomials

so, domain will be all real numbers

so, we get

$(-\infty,\infty)$

4 0

4 years ago

Suppose f and g are continuous functions such that g(2) = 6 and lim x → 2 [3f(x) + f(x)g(x)] = 36. find f(2).

True [87]

Answer: f(2) = 4

Step-by-step explanation:

F(x) and g(x) are said to be continuous functions

Lim x=2 [3f(x) + f(x)g(x)] = 36

g(x) = 2

Limit x=2

[3f(2) + f(2)g(2)] = 36

[3f(2) + f(2) . 6] = 36

[3f(2) + 6f(2)] = 36

9f(2) = 36

Divide both sides by 9

f(2) = 36/9

f(2) = 4

7 0

3 years ago

2. The Soccer Club is selling T-shirts and washing cars to raise money for a summer trip. Last week, the club raised $292.50 by

igor_vitrenko [27]

X = t-shirts y = cars
A.
292.55 = 15x + 12y
747.5 = 45x + 10y.
B.
292.55 = 15x + 12(0)
292.55 = 15x
$19.5 = x
C.
292.55 = 15(0) + 12y
292.55 = 12y
$24.37 = y

3 0

3 years ago

5. Patricia is on the edge of the top of a mountain and notices that a kayak on the lake is 30 meters

zhuklara [117]

The distance from the kayak to the mountain to the nearest whole number is 43 meters.

The situation will form a right angle triangle as shown below in the diagram.

<h3>Properties of a right angle triangle:</h3>

One of its angle is 90 degrees.
The sides and angle can be found by using trigonometric ratios.

The height(opposite side) of the triangle is the kayak distance from the mountain to the lake below. The distance from the kayak to the mountain is the adjacent side of the triangle.

Therefore, using trigonometric ratios,

tan 35 = opposite / adjacent

tan 35° = 30 / a

a = 30 / tan 35°

a = 30 / 0.70020753821

a = 42.8444402023

a = 42.84 meters

a ≈ 43 meters

learn more on the angle of depression: brainly.com/question/13969247?referrer=searchResults

8 0

3 years ago