All categories

4 years ago

1 Verify the identity. Show your work. cot θ ∙ sec θ = csc θ

1 answer:

6 0

To verify the identity, we can make use of the basic trigonometric identities:
cot θ = cos θ / sin θ
sec θ = 1 / cos θ
csc θ = 1 / sin θ

Using these identities:
cot θ ∙ sec θ = (cos θ / sin θ ) ( 1 / cos θ)

We can cancel out cos θ, leaving us with
cot θ ∙ sec θ = 1 / sin θ
cot θ ∙ sec θ = = csc θ

You might be interested in

Help me with this please

Marianna [84]

Answer:

Family

1. Definition of a family

A family is a group of people living together in a home related by blood, marriage or adoption.

2. Two function of the family are;

socialization for the children in the family.
love and happiness should be in a family for it to be function.

3. Two types of family are;

Single parent family- this family includes one parent and his or her child, we can say it's an incomplete family.
nuclear family- this family includes the two parents and their children or child, this family is known as the complete family.

4. Two roles and responsibilities of the parents and children in the home are;

both parents must and should protect their child or children from harm.
the children must have respect for the family.

Accident in the Home

1. Definition of accident in the home

accidents in the home are common to persons of all ages, therefore home accidents occurs in one's home that may cause an result an injury of a person

2. Two types of accident in the home

falls
minor cuts and wounds

3. The two uses of cereals in cooking

Cereals in cooking are used as thickened agents.

4. complete table

1. minor cuts and wounds

Causes: these are caused by broken glasses, contact with sharp instruments such as knife, pins and needles.
Prevention: this can be prevented by keeping the Sharp tools in safe places after used

2. Poisoning

Causes: poisoning can caused by in a result from children taking tablets for sweets, which can lead to death.
preventions: you can prevent this by avoiding poisoning from the from the home or you could put it at a safe place that you know the child cannot get it.

Care labels

1. definition of care label

care labels can be defined as a permanent label or we can say a tag, which contains regular instructions that is attached at the back of a cloth.

3. two classification of carbohydrates

Mono
poly

6 0

3 years ago

A 3.00 kg block moving 2.09 m/s

Talja [164]

Answer:11.64kgm/s

Explanation:

4 0

3 years ago

How are mountain ecosystems different from other ecosystems?

Andreyy89

Answer:

They host three or more distinct ecosystems at different elevations.

Explanation:

I checked it, and its right.

3 0

3 years ago

A magnetic compass is placed near an insulated copper wire. When the wire is connected to a battery and a current is created, th

Luba_88 [7]

4

Every current through a wire produced a magnetic field. And since the magnetic field of Earth is weak, it will get attracted towards the wire.

4 0

3 years ago

Read 2 more answers

Imagine two billiard balls on a pool table. Ball A has a mass of 7 kilograms and ball B has a mass of 2 kilograms. The initial v

wlad13 [49]

1) In a perfectly inelastic collision, the two balls stick together after the collision. In this type of collision, the total kinetic energy of the system is not conserved, while the total momentum is conserved.
If we call $v_f$ the final velocity of the two balls that stick together, the conservation of the total momentum before and after the collision can be written as
$m_a v_{Ai} + m_b v_{Bi} = (m_A+m_B)v_f$ (1)
where
$m_A=7 kg$ is the mass of ball A
$m_B=2 kg$ is the mass of ball B
$v_{Ai}=6 m/s$ is the initial velocity of ball A
$v_{Bi}=-12 m/s$ is the initial velocity of ball B (taken with a negative sign, since it goes in the opposite direction of ball A)

If we solve (1) to find $v_f$ , we find that the final velocity of the balls is
$v_f= \frac{m_Av_{Ai}+m_Bv_{Bi}}{m_A+m_B}= \frac{(7\cdot 6)+(2 \cdot (- 12))}{7+2}= \frac{18}{9}=2 m/s$
and the positive sign means the two balls are going to the right.

2) I assume here we are talking about an elastic collision. In this case, both total momentum and total kinetic energy are conserved:
$m_A v_{Ai}+m_B v_{Bi} = m_A v_{fA} + m_B v_{fB}$
$\frac{1}{2}m_A v_{Ai}^2+ \frac{1}{2}m_B v_{Bi}^2= \frac{1}{2}m_Av_{fA}^2+ \frac{1}{2}m_B v_{fB}^2$
where
$v_{fA}$ is the final velocity of ball A
$v_{fB}$ is the final velocity of ball B

If we solve simultaneously the two equations, we find:
$v_{fA}= \frac{v_{Ai}(m_A-m_B)+2m_Bv_{Bi}}{m_A+m_B} = \frac{(6)(7-2)+2(2)(-12)}{7+2}=-2 m/s$
$v_{fB}= \frac{v_{Bi}(m_B-m_A)+2m_Av_{Ai}}{m_A+m_B} = \frac{(-12)(2-7)+2(7)(6)}{7+2}= \frac{144}{9}=16 m/s$
So, after the collision, ball A moves to the left with velocity v=-2 m/s and ball B moves to the right with velocity v=16 m/s.

3) The total momentum before and after the collision is conserved.
In fact, the total momentum before the collision is:
$p_i = m_A v_{A} + m_B v_{fB} = (7\cdot 6)+(2 \cdot (-12))=42-24=18 m/s$
and the total momentum after the collision is:
$p_f = m_A v_{A} + m_B v_{fB} = (7\cdot (-2))+(2 \cdot 16)=-14+32=18 m/s$

3 0

3 years ago