Which is a step in proof by mathematical induction?

If the fence is open at a fifty-degree angle how much more angles until it flat on the wall

Alinara [238K]

Well flat means open so 180°
180° - 50° = 130° is the answer

4 0

3 years ago

Two resistors, with resistances R1 and R2, are connected in series. R1 is normally distributed with mean 100 ohms and standard d

puteri [66]

Answer:

The probability that R2 is bigger than R1 is P=0.9633.

Step-by-step explanation:

We need to compute the probability that R2 is bigger than R1:

$P(R_2>R_1)$

To do this, we define a new variable Das the difference between the two resistances:

$D=R_2-R_1$

Then,

$P(R_2>R_1)=P(R_2-R_1>0)=P(D>0)$

As R1 and R2 are normal random variables, the properties of D are:

$\mu_D=\mu_{R2}-\mu_{R1}=120-100=20\\\\\sigma_D=\sqrt{\sigma_{R2}^2+\sigma_{R1}^2}=\sqrt{10^2+5^2}=\sqrt{100+25}=\sqrt{125}=11.18$

Then, we can calculate the z-value for D=0

$z=\frac{x-\mu}{\sigma} =\frac{0-20}{11.18}=\frac{-20}{11.18}= -1.79$

$P(D>0)=P(z>-1.79)=0.9633$

8 0

3 years ago

Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 16cm and a height of 8cm, at the ra

andriy [413]

Let h=height of water
Let r=radius of water surface
r/h=16/8 =2, so r=2h.
The volume of water is:
v=(1/3)×π×r²×h
=(1/3)×π×(2h)²×h
=4/3πh³
dv/dh=4πh^2
By chain rule:
dv/dt=dv/dh×dh/dt
but
dv/dt=4
thus:
4=(4πh)×dh/dt
dh/dt=4/(4πh²)
when h=6cm we have:
dh/dt=4/(4π6²)
=0.00884 cm³/min

8 0

4 years ago

Read 2 more answers

The selling price of a house is Rs. 8 million. If the agent receives a commission of 3% up to Rs. 3 million and above 2%, the ag

belka [17]

Answer:

jshshshsjsjshsjsgdhgdhgdhgd

7 0

3 years ago

If the graph of y=cos⁡θ has a change in amplitude and a vertical translation, the equation becomes y=acos⁡θ+d, where a,d∈N and 0

worty [1.4K]

Answer:

The amplitude is 3 and the downward vertical translation is 4 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some facts about the cosine function

- The Amplitude of cos(x) is the height from the center line to the

peak (or to the trough). Or we can measure the height from

highest to lowest points and divide that by 2.

- The Vertical Shift is how far the function is shifted vertically from

the usual position.

* Now lets solve the question

∵ y = cos(Ф)

- There is a change in amplitude, it becomes a

- There is a vertical translation by b units

∴ y = a cos(Ф) + d

* Now lets look to the graph to find a and d

- From the graph:

∵ The highest value is -1

∵ The lowest value is -7

∴ The amplitude a = (-1 - -7)/2 = (-1 + 7)/2 = 6/2 = 3

∵ The highest value of y = cos(Ф) is 1

∵ The amplitude is 3

∴ The highest value of y = acos(Ф) = 3

∵ The highest value of y = acos(Ф) + d is -1

∴ d = 3 - (-1) = 4 ⇒ means downward vertical translation by 4

∴ y = 3 cos(Ф) - 4

* The amplitude is 3 and the downward vertical translation is 4

3 0

3 years ago