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NeTakaya
3 years ago
15

Determine the arc length of a circle that has a 7-centimeter radius and a central angle that is 40 degrees. Use 3.14 for π and r

ound your answer to the nearest hundredth.
Mathematics
1 answer:
agasfer [191]3 years ago
6 0
Given:
Radius = 7cm
Central angle (theta) = 40 degrees

Asked:
Arc length (s)

SOLUTION:
s = 2*pi*radius*(central angle/360)
s = 2(3.14)(7cm)(40 degrees/360 degrees)
s = 4.88 cm

Therefore, the arc length of the circle is 4.88 centimeters.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.


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Alexxandr [17]

Answer:

  • (a)  area = 3y^2 +14y +16
  • (b)  perimeter = 8y +20

Step-by-step explanation:

Part of the point of Algebra is that you can work with things that stand for numbers (almost) as easily as working with numbers themselves. Here, you are given values that stand for the length and width of the rectangle.

(a) You know the area of a rectangle is found by multiplying its length by its width. The same is true when length and width are algebraic expressions that stand for those numbers.

  <u>Given:</u> length = 3y+8, width = y+2

  <u>Find:</u> area = length × width

  <u>Solution:</u>

     area = (3y+8) × (y+2)

Using the distributive property, we can perform this multiplication in essentially the same way we would for the numbers 38 and 12.

     area = 3y(y +2) +8(y +2)           equivalent to 30(12) +8(12)

     = 3y^2 +6y +8y +16                  equivalent to 30·10 +30·2 +8·10 +8·2

     area = 3y^2 +14y +16              equivalent to 3·10^2 +14·10 +16

(Of course, with numbers, there are relationships between units and tens and hundreds that let us further combine terms. When variables are involved, we can combine terms with the same power of the variable, but we cannot combine "y" terms with "y^2" terms the way we can with numbers.)

___

(b) The perimeter is the sum of the lengths of the four sides of the rectangle. Since two of those sides are "length" and two are "width", we can write ...

  perimeter = 2(length + width)

Making the substitution for length and width as defined above, we have

  perimeter = 2((3y+8) + (y+2))

  = 2(3y+y + 8+2) = 2(4y +10)

  perimeter = 8y +20

5 0
3 years ago
A line passes through (5,-2) with a slope of 1/4. Write the equation in slope-intercept<br> form.
trapecia [35]

Answer: y = \frac{1}{4}x - 3 \frac{1}{4}

Step-by-step explanation:

    Slope-intercept form is in the form of y=<em>m</em>x + <em>b</em> where m is the slope and b is the y-intercept.

    We are given the slope, so we will plug this in.

y = <em>m</em>x + <em>b</em>

y = (\frac{1}{4})x + <em>b</em>

<em />

    Now, we will solve for the y-intercept by plugging in the point they give us.

y = (\frac{1}{4})x + <em>b</em>

(-2) = (\frac{1}{4})(5) + <em>b</em>

-2 = 1.25 + <em>b</em>

-3 \frac{1}{4} = <em>b</em>

<em />

    Lastly, we will plug this variable into the equation we wrote above for our final answer.

y = \frac{1}{4}x - 3 \frac{1}{4}

    <em>Read more about writing a </em><em>slope-intercept form</em><em> equation for this problem here:</em>

<em>brainly.com/question/13874293</em>

4 0
1 year ago
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Determine if the graph shows two quantities that vary directly. If possible, determine the constant of proportionality using the
tia_tia [17]

Answer:

Option C is correct option.

Step-by-step explanation:

We need to find k constant of proportionality

In the graph below let us take the values of x and y

x=150 , y=50

x=300, y=100

x=450, y=150

Now finding k using the formula: k=\frac{y}{x}

Putting values of x and y to find k

For x=150 , y=50 k = 50/150, k =1/3

For x=300, y=100 , k=100/300 , k=1/3

For x=450, y=150, k= 150/450 , k=1/3

Since for values of x and y, k = 1/3 is constant so, the graph shows two quantities that vary directly.

So, Option C is correct option.

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Answer:

Step-by-step explanation:

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