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Alex787 [66]
3 years ago
5

Which number sentence is true?

Mathematics
1 answer:
PIT_PIT [208]3 years ago
7 0

I'm pretty sure it's 8.5 > 2.97

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Find The art length of a sector with an area of 8 square units.
frez [133]
\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
A=8\\
r=4
\end{cases}\implies 8=\cfrac{\theta \pi 4^2}{360}\implies \cfrac{8\cdot 360}{4^2\pi }=\theta 
\\\\\\
\cfrac{2880}{16\pi }=\theta \implies \boxed{\cfrac{180}{\pi }=\theta }\\\\
-------------------------------\\\\

\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
\theta =\frac{180}{\pi }\\
r=4
\end{cases}\implies s=\cfrac{\frac{180}{\underline{\pi} }\underline{\pi} \cdot 4}{180}\implies s=\cfrac{\underline{180}\cdot 4}{\underline{180}}
\\\\\\
\boxed{s=4}

if you do a quick calculation on what that angle is, you'll notice that it is exactly 1 radian, and an angle of 1 radian, has an arc that is the same length as its radius.

that's pretty much what one-radian stands for, an angle, whose arc is the same length as its radius.
6 0
3 years ago
Julie and Eric row their boat (at a constant speed) 55 miles downstream for 5 hours, helped by the
Archy [21]

Answer: C = 3 mph is the rate of the current.

Step-by-step explanation:

Hey there!

<u />

<u>You can use the distance formula (d = rt) to solve this problem.  </u>

Downstream trip: d = 55 miles, t = 5 hours, and r = R + C  

R + C is their rowing speed (R) plus the rate of the current (C).  

Upstream trip: d = 55 miles, t = 11 hours, and r = R - C

R - C is their rowing speed (R) minus the rate of the current (C).  

Downstream: 55 mi. = (R + C)5 hrs. Divide both sides by 5: R + C = 11

Upstream: 55 mi. = (R - C)11 hrs. Divide both sides by 11: R - C = 5

<u>Calculations</u>

R + C = 11 Subtract C from both sides.

R = 11 - C Substitute this into: R - C = 5

(11 - C) - C = 5 Simplify and solve for C

11 - 2C = 5 Add 2C to both sides.

11 = 2C + 5 Subtract 5 from both sides.

6 = 2C Divide both sides by 2

C = 3 mph is the rate of the current.

~I hope I helped you! :)~

5 0
3 years ago
Katie bought 2 one gallon bottles for a party. Her guest drank 5/4 gallons of juice. What is the fraction of juice leftover? Sho
frosja888 [35]

Answer:

3/4 gallons of juice

Step-by-step explanation:

Katie bought 2 one-gallon bottles for a party.

2 one-gallon bottles = 2-gallon bottles of juice

We are told that:

Her guest drank 5/4 gallons of juice.

The fraction of juice leftover is calculated as:

2 gallons of juice - 5/4 gallons of juice

2 - 5/4

Lowest Common Denominator = 4

2/1 - 5/4

= 8 - 5/4

= 3/4 gallons of juice

Therefore, the fraction of juice leftover is 3/4 gallons of juice

7 0
2 years ago
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month,
san4es73 [151]
Victoria's method is linear because the number of minutes increase by an equal number (15) every month.

Workings in the attachments below. The green line is the function that has been set up for Victoria. The lines that form a curved looking graph belong to the function that was set up for Zach.

8 0
3 years ago
Add my s. n. a. p. c. h. a. t. its kribbytheking i add back .
romanna [79]
Ahhh bet your a female right?
4 0
2 years ago
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