Let B = 5.40 m at 60.0°. C and A have equal magnitudes. The
direction angle...
Let B = 5.40 m at 60.0°. C and A have equal magnitudes. The
direction angle of C is larger than that of A by 25.0°. Let A · B =
27.9 m2 and B · C = 36.9 m2. Find the magnitude (in m) and
direction (in degrees) of A.
The three displacement vectors in the drawing have magnitudes of
A = 4.95 m, B = 5.93 m, and C = 3.59 m.
Find the resultant
((a) magnitude and (b)
directional angle) of the three vectors by means of the component
method. Express the directional angle as an angle above the
positive or negative x axis. A=2nd quadrant 20 degrees B= 1st
quadrant 60 degrees C=on Y axis at 270 degrees
Let vector B = 5.50 m at 60°. Let vector C have the same
magnitude as vector A and a direction angle greater than that of
vector A by 25°. Let vector A · vector B = 27.0 m2 and vector B ·
vector C = 34.5 m2. Find the magnitude and direction of vector
A.
An object is launched at a velocity of 20 m/s in a direction
making an angle of 25 degrees upward with the horizontal.
a) What is the maximum height reached by the object?
b) What is the total flight time (between launch and touching
the ground) of the object?
c) What is the horizontal range (maximum x above ground) of the
object?
d) What is the magnitude of the horizontal component of the
velocity of the object just before it...
Four displacement vectors, A,
B, C, and D, are
shown in the diagram below. Their magnitudes
are: A = 16.2 m, B = 11.0 m,
C = 12.0 m, and D = 24.0 m
What is the magnitude, in meters, and direction, in degrees, of
the resultant vector sum of A, B, C, and D?
Give the direction as an angle measured counterclockwise from
the +x direction.
The displacement vectors A and B shown in the figure below both
have magnitudes of 2.50 m. The direction of vector A is θ = 35.5°.
(a) Find A + B graphically. magnitude m direction °
counterclockwise from the +x axis (b) Find A − B graphically.
magnitude m direction ° counterclockwise from the +x axis (c) Find
B − A graphically. magnitude m direction ° counterclockwise from
the +x axis (d) Find A − 2B graphically. magnitude m direction...
Each part of (Figure 1) shows one or more point charges. The charges have equal magnitudes.
A) For case (a), if a positive charge is moved from position i to position f, does the electric potential energy increase, decrease, or stay the same?
For case (a), if a positive charge is moved from position to position, does the electric potential energy increase, decrease, or stay the same?
Electric potential energy increases.
Electric potential energy decreases.
Electric potential...
Three point charges have equal magnitudes, two being positive
and one negative. These charges are fixed to the corners of an
equilateral triangle, as the drawing shows. The magnitude of each
of the charges is 3.5 μC, and the lengths of the sides of the
triangle are 2.0 cm. Calculate the magnitude of the net force that
each charge experiences.
Let a,b be an element in the integers with a greater or equal to
1. Then there exist unique q, r in the integers such that b=aq+r
where z less than or equal r less than or equal a+(z-1). Prove the
Theorem.
(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then
a∣c.
(B) Let p ≥ 2. Prove that if 2p−1 is prime, then p
must also be prime.
(Abstract Algebra)
Let a < c < b, and let f be defined on [a,b]. Show that f
∈ R[a,b] if and only if f ∈ R[a, c] and f ∈ R[c, b]. Moreover,
Integral a,b f = integral a,c f + integral c,b f .