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2 years ago

Find the arc length of AB. Round your answer to the nearest hundredth.

Mathematics

1 answer:

Fantom [35]2 years ago

5 0

The arc length of AB is 8 m (app.)

Explanation:

Given that the radius of the circle is 8 m.

The central angle is 60°

We need to determine the arc length of AB

The arc length of AB can be determined using the formula,

$arc \ length=\frac{central \ angle}{360^{\circ}} \times circumference$

Substituting central angle = 60° and circumference = 2πr in the above formula, we get,

$arc \ length=\frac{60^{\circ}}{360^{\circ}} \times 2 \pi(8)$

Simplifying the terms, we get,

$arc \ length=\frac{8 \pi }{3}$

Dividing, we get,

$arc \ length=8.37758041$

$arc \ length=8(app.)$

Hence, the arc length is approximately equal to 8.

Therefore, the arc length of AB is 8 m

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A rectangular block measures 3 cm x 4 cm x 3 cm how much water would it displace?

nika2105 [10]

Answer:

36c^3m^3x^2

Step-by-step explanation:

you first multiply 3 cm by 4 cm by 3 cm to get 36 cm.
its mass in air and its effective mass when submerged in water (density = 1 gram per cubic centimeter).
1.0 g/cm3
then you get the answer 36c^3m^3x^2

4 0

2 years ago

Mya is a performance athlete. She wants to use a function to represent the number of calories that she burns while training, whe

Lerok [7]

Answer:

The actual number of calories that Mya burned when she

trained for 30 minutes is 240.

Step-by-step explanation:

We have an exponential function that is the best fit for the number of calories Mya burns, in function of time (minutes).

The function is:

$y=45.3e^{0.0548x}$

Where y: calories burned, and x: training time.

Whenever we use regression models, we have a real value and a predicted value. The difference between them, the measure we want to minimize when we adjust with this typo of models, is called residual.

In the table is shown as one of the columns.

For example, for x=10 minutes, we have a real value of 30 and a predicted value of 78.36, so the residual becomes e=30-78.36=-48.36.

$e=y-\hat y=30-78.36=-48.36$

For x=30 minutes, we have only the residual, that has a value of 5.53. That means that the predicted value, which we can calculate, is 5.53 below the real value.

The predicted value for x=30 is:

$y(30)=45.3e^{0.0548*30}=45.3*5.18=234.47$

Using the equation for the residual e, we can calcualte the actual number of calories that Mya burned in 30 minutes:

$e=y-\hat y=y-234.47=5.53\\\\y=234.47+5.53\\\\y=240$

4 0

2 years ago

Luz drives at an average speed of 45 miles per hour. She has driven for 3 hours and has travelled a distance of 135 miles. This

julia-pushkina [17]

Answer:

$(y-135)=45(x-3)$

Step-by-step explanation:

Let x represents the number of hours and y represents the number of miles.

We are told that Luz drives at an average speed of 45 miles per hour. She has driven for 3 hours and has traveled a distance of 135 miles.

We can see from our given information that slope of line is 45 as with each increase in number of hours (x), change in distance (y) is 45.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{135-0}{3-0}$

$m=\frac{135}{3}$

$m=45$

Since the equation of line in point-slope form is : $(y-y_1)=m(x-x_1)$ , where m represents slope of line and $(y_1,x_1)$ represents a point the line passes through.

Upon substituting our given values in point-slope form of equation we will get,

$(y-135)=45(x-3)$

Therefore, the equation represented in point-slope form will be: $(y-135)=45(x-3)$ .

4 0

2 years ago

Read 2 more answers

You want to surround the perimeter of a garden with 35 stones. You need to place a certain number of large and small stones, and

coldgirl [10]

Answer:

You will need 7 large and 28 small stones.

Step-by-step explanation:

x = the number of large stones

y = the number of small stones

x + y = 35

for every large stone, you want to use 4 small stones:

y = 4x

by solving the system of equations:

x + y = 35

y = 4x

we find:

x = 7 large stones

y = 28 small stones

5 0

2 years ago

Match the real-world descriptions with the features they represent within the context of Melissa’s garden. Not all tiles will be

ycow [4]

The features in a function can be used to describe real-world events. The features and their match are:

domain: all possible lengths of the tomato patch
y - intercept: area of the bell pepper patch when the length of the tomato patch is 0
x - intercept: length of the tomato patch when the area of the bell pepper patch is 0
range: all possible areas of the bell pepper patch

For Melissa's garden, the input and output variables are:

Input: tomato patch
Output: bell pepper patch

The range is the list of possible output values, while the domain is the list of possible input values.

This means that: the range is all possible areas of the bell pepper patch while the domain is all possible lengths of the tomato patch

Also, the x and y intercepts are when the values of the output and input variables are 0, respectively.

Using the above comparison;

The y - intercept is the area of the bell pepper patch when the length of the tomato patch is 0, while the x - intercept is the length of the tomato patch when the area of the bell pepper patch is 0.