HELP ANSWER QUESTION 1

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

Fittoniya [83]

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

6 0

4 years ago

If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 64 ft/sec, its height after t seconds

stepan [7]

Answer:

a) $s_{max} = 96\,ft$ , b) $v(4.449\,s) = -78.368\,\frac{ft}{s}$

Explanation:

a) The maximum height is obtained with the help of the First and Second Derivative Tests:

First Derivative

$v(t) = 64 - 32\cdot t$

$64 - 32\cdot t = 0$

$t = 2\,s$

Second Derivative

$a(t) = -32$ (absolute maximum)

The maximum height reached by the ball is:

$s (2\,s) = 32 + 64\cdot (2\,s) - 16\cdot (2\,s)^{2}$

$s_{max} = 96\,ft$

b) The time required by the ball to hit the ground is:

$32+64\cdot t - 16\cdot t^{2} = 0$

$-16\cdot (t^{2}-4\cdot t - 2) = 0$

$t^{2}-4\cdot t - 2 = 0$

$(t -4.449)\cdot (t+0.449)\approx 0$

Just one root offers a solution that is physically reasonable:

$t = 4.449\,s$

The velocity of the ball when it hits the ground is:

$v(4.449\,s) = 64 - 32\cdot (4.449\,s)$

$v(4.449\,s) = -78.368\,\frac{ft}{s}$

6 0

3 years ago

Read 2 more answers

If the pendulum is taken into the orbiting space station what will happen to the bob? if the pendulum is taken into the orbiting

mezya [45]

Check the attached file for the answer.

3 0

4 years ago

Explain

fenix001 [56]

Answer and Explanation:

--> MRI (Magnetic Resonance Imaging) is an imaging technique that involves the use of radio waves and magnetic field to generate high detailed images of the human body. It's clinical applications includes:

• Bone and joint MRI: these are done to check for bone and joint problems such as bone marrow disorders, arthritis, or bone tumours.

• A Spine MRI: This is used to investigate the spinal disc and innervations for disorders such as spinal tumours.

• Chest MRI: This is used to detect abnormalities of the heart, heart valves and coronary arteries.

--> X-RAY: These are electromagnetic waves of short wavelength with high penetrating power. They are produced when fast moving electrons strike a mass of heavy atoms such as those of metals. It's applications includes:

• They are used to detect hidden cracks in materials.

• They are used to show broken bones in human body.

• They are used in the study of internal structures of crystals.

• In agriculture, x-rays are used in killing germs.

--> ULTRASOUND: This makes use of high frequency sounds to detect abnormalities in the human body. An ultrasound machine transmits sound waves into the body which are reflected at the surfaces between the tissues of different density. It can also be used in different disciplines such as imaging, cleaning, mixing, navigation and communication It's applications includes:

•. Detection of Cracks: when applied on metallic surface under investigation, high frequency sound wave reflects back which and be predicted and recorded.

--> INFRARED RADIATION: This is a type of electromagnetic radiation with wavelength longer than visible light. It is visible to the human eye and most heated surfaces transmits infrared radiation. It's applications includes:

• it is used for the purpose of sensing and detection. For example the night vision goggles and infrared cameras. Remote control makes use of infrared light waves to change channels in the television.

7 0

3 years ago

A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of m

anzhelika [568]

Answer:

Momentum after collision will be 6000 kgm/sec

Explanation:

We have given mass of the whale = 1000

Initial velocity v = 6 m/sec

It collides with other mass of 200 kg which is at stationary

Initial momentum of the whale = 1000×6 = 6000 kgm/sec

We have to find the momentum after collision

From conservation of momentum

Initial momentum = final momentum

So final momentum = 6000 kgm/sec

5 0

3 years ago