Image below, rotation for point (5,-2) gives you (2,5).
9514 1404 393
Answer:
-15/16
Step-by-step explanation:
The sum of a geometric series with first term a1 is ...
S = a1/(1 -r)
Then the common ratio (r) is ...
r = 1 -a1/S
For the given values, the ratio is ...
r = 1 - 124/64 = -15/16
The common ratio is -15/16.
Money earned by restaurant on Friday=$1073
Money earned by restaurant on Saturday=$1108
Let Money earned by restaurant on Sunday=$x
Average=$1000
Number of observation=3
⇒ 3× 1000=1073+1108+x
⇒3000= 2 181+x
⇒3000-2181=x
⇒x=819
The restaurant needs to earn on Sunday to average $1000 per day over the three-day period=$819
Answer:
x=−32/5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
1/2(1/4x−3/5)=1/4(2/5+3/4x)
(1/2)(1/4x)+(1/2)(−3/5)=(1/4)(2/5)+(1/4)(3/4x)(Distribute)(1/2)(1/4x)+(1/2)(−3/5)=(1/4)(2/5)+(1/4)(3/4x)(Distribute)
1/8x+−3/10=1/10+3/16x
1/8x+−3/10=3/16x+1/10
Step 2: Subtract 3/16x from both sides.
1/8x+−3/10−3/16x=3/16x+1/10−3/16x
−1/16x+−3/10=1/10
Step 3: Add 3/10 to both sides.
−1/16x+−3/10+3/10=1/10+3/10
−1/16x=2/5
Step 4: Multiply both sides by 16/(-1).
(16/−1)*(−1/16x)=(16/−1)*(2/5)
x=−3/25
Answer:
33/16
Step-by-step explanation:
x = y⁴/8 + 1/(4y²), 1 ≤ y ≤ 2
dx/dy = y³/2 − 1/(2y³)
Arc length is:
s = ∫ ds
s = ∫ √(1 + (dx/dy)²) dy
s = ∫₁² √(1 + (y³/2 − 1/(2y³))²) dy
s = ∫₁² √(1 + y⁶/4 − ½ + 1/(4y⁶)) dy
s = ∫₁² √(½ + y⁶/4 + 1/(4y⁶)) dy
s = ∫₁² ½ √(2 + y⁶ + 1/y⁶) dy
s = ∫₁² ½ √(y³ + 1/y³)² dy
s = ∫₁² ½ (y³ + 1/y³) dy
s = ½ (y⁴/4 − 1/(2y²)) |₁²
s = ½ (16/4 − 1/8) − ½ (1/4 − 1/2)
s = 33/16
