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. A driver notices an upcoming speed limit change from 45 mi/h (20 m/s) to 25 mi/h (11 m/s). If she estimates the speed limit will change in 50 m, what acceleration is needed to reach the new speed limit before it begins?
From ear level down the wishing well, a coin is dropped by Liza. The coin falls a distance of 7.00 m before it strikes the water. If the speed of sound is 343 m/s, how long after Liza releases the coin will she hear a splash?
Show, by the use of the truth table (truth matrix), that the (p v q) v [(¬p) ʌ (¬q)] is a contradiction.
Show that ¬p →(q → r) and q → (p V r) are logically equivalent.
Determine the spontaneity of the dissociation of ammonium nitrate the compound used in cold packs interpret the values obtained from the calculations
A bird can fly 25 km/h. How long does it take to fly 3.5 km?
Use row reduction algorithm to solve the following system of equations.
x1 − 7x2 + 6x4 = 5
x3 − 2x4 = −3
−x1 + 7x2 − 4x3 + 2x4 = 7
(a) Use Euclidean algorithm to find the gcd of 105 and 231.
(b) Use mathematical induction to show that
1 · 1! + 2 · 2! + · · · + n · n! = (n + 1)! − 1
(c) Show that the relation ∼ defined on R as a ∼ b if b−a ∈ Q, is an equivalence relation.
Also, find the equivalence class of 1.
Spheres A, B, and C have charges +8.0 𝐶, +12.0 𝐶, and −5.0 𝐶, respectively. The three spheres are allowed to touch each other simultaneously and then separated. (a) What is the total charge on the three spheres before and after touching each other? (b) What is the final charge on each sphere assuming they are identical? (c) What is the final charge on each sphere assuming that 𝑟_𝐴=𝑟_𝐵=2𝑟_𝐶?
The probabilities that a surgeon operates on 3,4,5,6 or 7 patients in any one day are 0.15, 0.20, 1.25, 0.20, and 0.20, respectively.
#340153 on Dec 2023