A circle is a curve sketched out by a point moving in a plane. The area of the sector PQR is 41.346 units².
<h3>What is a circle?</h3>
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given the radius of the circle is 8 units, while the angle of the sector is 74°. Therefore, the area of the sector is,
Area of the sector = π×R²×(74/360)
= π × 8² × 0.20556
= 41.346 units²
Hence, the area of the sector PQR is 41.346 units².
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For this case we have the following equation:
sine (40) = b / 20
From here, we must clear the value of b.
Clearing we have:
b = 20 * sine (40)
b = 12.85575219
Rounding to the nearest tenth we have:
b = 12.86 cm
Answer:
b = 12.86 cm
Dennis = 12 km'h
Kathy = 20 km/h
Step-by-step explanation:
- Lets first establish that time is the same for both Kathy and Dennis and we can therefore assign is the value of <em>t</em>
- Kathy is cycling 8km/h faster than Dennis. Therefore if Dennis is doing <em>x </em>km/h Kathy is doing (<em>x</em>+8)km/h
- If it takes Kathy<em> t </em>time to cycle for 60 km at (<em>x</em>+8)km/h, we can derive the time <em>t </em>as;
(<em>x</em>+8)* <em>t </em>= 60
<em>t</em> = 60/(<em>x</em>+8)
- We can now use this time to establsish how fast Dennis is cycling. Dennis, using a speed of <em>x</em> km/h takes the same time (60/(<em>x</em>+8)) to cycle for 36 km. Therefore;
<em>x</em> * 60/(x+8) = 36
= 60x/(x+8) = 36
36 (x + 8) = 60x
36x + 288 = 60x
288 = 60x – 36x
288 = 24x
12 =<em> x </em>
Dennis is cycling at 12 km/h
Kathy is doing x + 8
= 12 + 8 = 20 km/h
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Answer:
x = 14 and 2/3
Step-by-step explanation:
Make an equation where x is the number.
2x - 15 = 7 + 1/2x
Then, solve the equation.
multiply both sides by 2 to get rid of the fraction
4x - 30 = 14 + x
subtract x from both sides
3x - 30 = 14
add 30 to both sides
3x = 44
divide both sides by 3
x = 14 and 2/3
