Answer:
< - 5, 3.5 >
Step-by-step explanation:
A single translation is required to map A onto B
Consider the point (5, 3 ) on A and the corresponding point (0, 6.5) on B
the translation is < 0 - 5, 6.5 - 3 > = < - 5, 3.5 >
Answer:
Step-by-step explanation:
7x - 15 = 4x - 12
3x - 15 = -12
3x = 3
x = 1
y = 7(1) - 15
y = 7 - 15
y = -8
(1, -8)
Answer:
(x - 4)(x + 4)(x - 1)(x + 1)
Step-by-step explanation:
Given
- 17x² + 16
Use the substitution u = x², then
u² - 17u + 16
Consider the factors of the constant term (+ 16) which sum to give the coefficient of the u- term (- 17)
The factors are - 16 and - 1, then
u² - 17u + 16
= (u - 16)(u - 1) ← replace u by x²
= (x² - 16)(x² - 1) ← both factors are difference of squares
= (x - 4)(x + 4)(x - 1)(x + 1)
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
