1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Irina-Kira [14]
3 years ago
11

A central angle theta in a circle of radius 7 m is subtended by an arc of length 8 m. Find the measure of theta in degrees. (Rou

nd your answer to one decimal theta = ___. Find the measure of theta in radians. theta = ___ rad.
Mathematics
1 answer:
gogolik [260]3 years ago
8 0

Answer: In degrees , The measure of \theta=65.5^{\circ}

In radians , the measure of  \theta =\dfrac{8}{7}\text{ radians}.

Step-by-step explanation:

We know that the formula for length of arc is given by :-

l=\theta r

, where \theta = Central angle subtended by arc.

r= radius of the circle.

As per given , we have

Radius of circle : r=7 m

Length of arc : l=  8 m

Substitute these values in the above formula , we get

8=\theta (7)\\\\\Rightarrow\ \theta =\dfrac{8}{7}\text{ radians}

Hence, the measure of \theta =\dfrac{8}{7}\text{ radians}.

To convert it into degrees we multiply it with \dfrac{180^{\circ}}{\pi}

The measure of \theta =\dfrac{8}{7}\times\dfrac{180^{\circ}}{\pi}

=(\dfrac{8\times180}{7\times3.14})^{\circ}=65.5141037307^{\circ}

\approx65.5^{\circ}

Hence, the measure of \theta=65.5^{\circ}

You might be interested in
A savings account earns 5% simple interest per year. The principal is $1200. What is the balance after 4 years?
stiv31 [10]
The formula of the Simple Interest is:
I=PRT
P for Principle Amount     ($1200)
R for Rate                        (5%=\frac{5}{100} = 0.05)
T for Time in years          (4 years)
I = 1200 × 0.05 × 4
  = $240

Add the interest to the principle amount to check the balance
$1200 + $240 = $1440

7 0
3 years ago
Read 2 more answers
If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid
Artist 52 [7]
Check the picture below.  Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm².  Also, recall, the base is a square, thus, length = width = x.

\bf \textit{volume of a rectangular prism}\\\\&#10;V=lwh\quad &#10;\begin{cases}&#10;l = length\\&#10;w=width\\&#10;h=height\\&#10;-----\\&#10;w=l=x&#10;\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\&#10;-------------------------------\\\\&#10;\textit{surface area}\\\\&#10;S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h&#10;\\\\\\&#10;\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\&#10;-------------------------------\\\\&#10;V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3

so.. that'd be the V(x) for such box, now, where is the maximum point at?

\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2&#10;\\\\\\&#10;\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100&#10;\\\\\\&#10;x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it.  Check the second picture below.

so, the volume will then be at   \bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3

6 0
3 years ago
<img src="https://tex.z-dn.net/?f=54x2y%20-%2012x2y2" id="TexFormula1" title="54x2y - 12x2y2" alt="54x2y - 12x2y2" align="absmid
Free_Kalibri [48]

Answer:

6x²y(9 - 2y)

Step-by-step explanation:

Step 1: Factor out GCF

6(9x²y - 2x²y²)

Step 2: Factor out <em>x²</em>

6x²(9y - 2y²)

Step 3: Factor out <em>y</em>

6x²y(9 - 2y)

And we have our factored answer.

7 0
3 years ago
Read 2 more answers
Christopher works at the power plant for the southwest part of his home state. For peak operational performance, his department
Licemer1 [7]

Answer:

B) To maintain peak performance for every 50 generators, there are 10 inspectors.

Step-by-step explanation:

For peak operational:

3 electricians for each generator.  ⇒  1 Generator : 3 Electricians

4 inspectors for every 60 electricians. ⇒  60 Electricians : 4 Inspectors

Now, the number of generators the state has now = 50

Let us assume the number of  inspectors  required by the power plant  = m

Now, from the given ratios:

For, 3 electrician there  is 1 generator

⇒ For, 3 x 20 Electrician  there is 1  x 20 Generators.

or, for 60 Electrician there are 20 Generators.   (1)

Also, for 60 Electrician there are 4 inspectors.    (2)

⇒From (1) and (2), we get:

For every 20 generators, there are 4 inspectors.

And, from what we have assumed  For every 50 generators, there are m inspectors.

So, by the RATIO OF PROPORTION:

\frac{20}{4}  = \frac{50}{m}\\ \implies  m = 50 \times\frac{4}{20}  = 10

or, m = 10

Hence, to maintain peak performance for every 50 generators, there are 10 inspectors.

3 0
3 years ago
What is true about the sides KNM?
Archy [21]
Kn=nm is the answer
3 0
3 years ago
Other questions:
  • Brainliest + Points! I choose A, Am I correct?
    13·2 answers
  • 2 ways to tell if there is a proportional relationship
    13·1 answer
  • I need help to solve this​
    5·1 answer
  • a student reads at a rate of 16 pages per day. Which order pair would be on a graph of this relationship
    5·1 answer
  • Derive these identities using the addition or subtraction formulas for sine or cosine: sinacosb=(sin(a+b)+sin(a-b))/2
    9·1 answer
  • at 7:00 am the temperature in wilton was -6 degrees. by 8:00 am the temperature was 2 degrees. what is the difference in the tem
    8·2 answers
  • Which is greater 900 cm or 9000mm
    7·2 answers
  • Pliss solve and give evidence
    13·2 answers
  • PLS HELP I HAVE TO SUBMIT THIS SOON
    11·1 answer
  • If 3y + 3 = y + 7 is the same as y + y +y + 1 + 1 + 1 = y + 1 + 1 + 1 + 1+ 1 + 1 + 1, then how can we isolate 'y' without disrup
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!