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3 years ago

What is the length of the arc by a central angle of 85 degrees and a radius of 8cm to the nearest tenth of a cm?

Mathematics

1 answer:

Anvisha [2.4K]3 years ago

8 0

9514 1404 393

Answer:

11.9 cm

Step-by-step explanation:

Arc length is given by ...

s = rθ . . . . . . θ is the central angle in radians

Your central angle is 85°, so is (85/180)π radians = 17/36π radians.

Then the arc length is ...

s = (8 cm)(17/36π) ≈ 11.9 cm

The length of the 85° arc is about 11.9 cm.

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3 years ago

The sum of 3 integers is 194. the sum of the first and second integers exceeds the third by 80. The third integer is 45 less tha

kirill115 [55]

Let
x = first integer
y = second integer
z = third integer
First equation: x + y + z = 194
Second equation: x + y = z + 80
Third equation: z = x - 45

Let's find the values of x, y and z.
Substitute 3rd eq to 1st eq:
x + y + x - 45 = 194
2x + y = 45 + 194
y = -2x + 239

Plug in both we have solved for y and the 3rd eq to the 2nd eq to find x
x + (-2x + 239) = (x - 45) + 80
x - 2x - x = -45 + 80 - 239
-2x = -204
x = -204/-2
x = 102

Solving for y,
y = -2(102) + 239
y = 35

Solving for z,
z = 102 - 45
z = 57

5 0

3 years ago

the axis of symmetry of a quadratic equation is x = –3. if one of the zeroes of the equation is 4, what is the other zero?

FinnZ [79.3K]

ANSWER

The other zero is

$x = - 10$

EXPLANATION

The axis of symmetry serves as the midpoint of the two zeroes.

We were given that the axis of symmetry of the quadratic equation is
$x = - 3$

We were also given that, one of the zeroes of the quadratic equation is
$x = 4$

Let the other zero of the quadratic equation be
$x = p$

,then, we apply the midpoint formula to find the value of
$p$

Since it is the x-values of the intercepts that gives the solution, we use only the x-value part of the midpoint formula which is given by,

$\frac{x_1 + x_2}{2} = axis \: of \: symmetry$

We substitute to obtain,

$\frac{p + 4}{2} = - 3$

We multiply through by 2 to get,

$p + 4 = - 6$

This implies that,

$p = - 6 - 4$

$p = - 10$

3 0

3 years ago

Read 2 more answers

Barry is thinking of a number.

Virty [35]

Answer:

10 and 30

Step-by-step explanation:

Let's focus on the first 2 parts of the hints :

The number must be even and a factor of 30 :

Let's write out the factors of 30 :

1 , 2 , 3 , 5 , 6 , 10 , 15 , 30

Now let's pick out the even ones :

2 , 6 , 10 , 30

Now let's take out the multiples of 5 :

10 and 30

These are the answers

Hope this helped and have a good day

7 0

1 year ago