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2 years ago

Determine the angle at the centre of a circle with radius 12.0 cm for an arc length of of 21.0 cm.

Mathematics

1 answer:

nata0808 [166]2 years ago

7 0

Answer:

$\theta=\dfrac{7}{4}\ \text{radian}$

Step-by-step explanation:

We have,

Radius of the circle is 12 cm

Arc length, l = 21 cm

It is required to find the central angle of the circle. The formula for the length of an arc of a circle is :

$l=r\times \theta$

$\theta$ is central angle

$\theta=\dfrac{l}{r}\\\\\theta=\dfrac{21}{12}\\\\\theta=\dfrac{7}{4}\ \text{radian}$

So, the angle at the centre of the circle is $\dfrac{7}{4}\ \text{radian}$ .

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phoebe needs to use 3/4 cup to make one batch of cookies how many batches can she make with 12 cups of sugar?

sattari [20]

$\bf \begin{array}{ccll}\stackrel{sugar}{cups}&\stackrel{cookies}{batches}\\\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\\frac{3}{4}&1\\\\12&b\end{array}\implies \cfrac{\quad \frac{3}{4}\quad }{12}=\cfrac{1}{b}\implies \cfrac{\quad \frac{3}{4}\quad }{\frac{12}{1}}=\cfrac{1}{b}\\\\\\\cfrac{3}{4}\cdot \cfrac{1}{12}=\cfrac{1}{b}\implies \cfrac{3}{48}=\cfrac{1}{b}\implies 3b=48\implies b=\cfrac{48}{3}\implies b=16$

4 0

2 years ago

Read 2 more answers

Please show all work!! this is algebra.

Mnenie [13.5K]

Franco:
3x+2y=19
Caryl:
2x+4y=24

now use elimination

-2(3x+2y=19)
1(2x+4y=24)
=
-6x-4y=-38
2x+4y=24
add them together
which equals -4x=-14
divide both sides by -4
-4x/-4=-14/-4
x=7/2

we found x, so we subsitute it into the the original equation

3x+2y=19
3(7/2)2y=19
2y+21/2=19
-21/2 -21/2
2y=17/2
divide by 2 on both sides
2y/2= 17/2/2
y=17/4

so x= 7/2 and y= 17/4

8 0

1 year ago

I added a screenshot of my question

Anastasy [175]

<h2>Answer:</h2>

$y=\frac{1}{3}x+4$

<h2>Explanation:</h2>

Slope-intercept form:

What the variables mean:

Y=the y axis

m=the slope

x=the x-axis

b=the y intercept (the point on the line that crosses the y-axis)

To Calculate the Slope:

1. Find any 2 points on the line

2. The number of units the second point is above the first is the numerator

3. The number of units the second point is to the right of the first is a denominator

(Please see the picture attached)

$y=\frac{1}{3}x+b$

To Find the Y-Intercept:

1. Find the point on the line that crosses the y-axis

(Please see the picture attached)

$y=\frac{1}{3}x+4$

5 0

2 years ago

The cup was filled at a constant rate. It started empty. After 2 seconds, it held 70 cm cubed of water.Find the percent of the c

Helen [10]

Answer:

In 3 seconds the cup is filled with $105\ cm^3$ <u>.</u>

Step-by-step explanation:

Given:

2 seconds = $70\ cm^3$ water

We need to find the percent of the cup that is filled with water after 3 seconds.

Solution:

Now Given:

The cup was filled at a constant rate.

First we will find the volume of water filled in the cup after 1 seconds.

2 seconds = $70\ cm^3$ water

1 seconds = Volume of water filled in 1 second.

By Using Unitary method we get;

Volume of water filled in 1 second = $\frac{70}{2}= 35\ cm^3$

Now we will find the volume of water filled in the cup after 3 seconds.

1 second = $35\ cm^3$ of water is filled

3 seconds = volume of water filled in the cup after 3 seconds

Again by using Unitary method we get;

volume of water filled in the cup after 3 seconds = $35 \times 3 = 105\ cm^3$

Hence In 3 seconds the cup is filled with $105\ cm^3$ .

To find the percent of the cup filled with water after 3 seconds we would required the dimensions of the cup which is not available in the question.

6 0

2 years ago

15PTS PLEASE HELP ASAP!<br> (dont write random answers pls)

Goryan [66]

Answer:

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Step-by-step explanation:

4 0

2 years ago