Aframe hanging on a wall is held by two cables. the tension in each cable is 30 n, and the cables make an angle of 45° with the horizontal, as shown in the picture. what is the weight of the frame? a) 10.2 n b) 21.2 n c) 32.4 n d) 42.4 n

(D) 42.4N

Explanation:

Since the frame is at rest, the net force acting on it must be 0. There are three forces acting on it: the gravity and the opposing forces of the two cables.

Since the gravity is a vertical force, we are only interested in the vertical components of the remaining forces. The net force equation is

F_net = 0 = F_g -2 * F_y

The vertical force of one cable (using the information in the drawing) is:

F_y = 30N * sin 45 deg = 21.21N

Now the weight can be determined:

0 = F_g - 2 * F_y

F_g= 2 * F_y = 2 * 21.21N = 42.4N

The weight of the frame is about 42.4N.

Vector:T₁+T₂+F=0 , you put the vectors where you need, on the site I'm not going to put them

We design the relationship on the vertical axis Oy:

T₁sinα+T₂sinα=0

T₁=T₂=>2Tsinα=0

We design the relationship on the horizontal axis Ox :

2Tcosα-F=0=>F=2Tcosα=2*30*√2/2=30√2=42.4 N

The right answer is D

you cant move and you feel like someones pushing you down onto your bed it can feel like you want to get up but you just can't it can be extremely scary

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.