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3 years ago

Verify each identity: (tanx+tany)/(1-tanxtany)=(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny),

1 answer:

8 0

Solution:
(tanx + tany)/(1-tanxtany) is equal to the formula of tan(x+y)
sinxcosy + cosxsiny = is equal to the formula of sin(x+y)formula
cosxcosy - sinxsiny) = is equal to the formula of cos(x+y)

So this means that
tan(x+y) = sin(x+y)/cos(x+y)

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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

KengaRu [80]

Answer:

Using the ratio and proportion method, we find that on an average 1.875 rooms can be painted per gallon.

Step-by-step explanation:

Concept: Use the method of ratio and proportion. Given that for 2/5 gallons of paint, we can paint 3/4 of rooms. So, for one gallon of paint, divide 2/5 by 3/4.

2/5 gallons of paint = 3/4 rooms

1 gallon of paint = $\frac{\frac{3}{4} }{\frac{2}{5} } = \frac{15}{8} =1.875$ rooms

So, on an average they can paint 1.875 rooms per gallon.

For more explanation, refer the following link

brainly.com/question/11243787

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8 0

2 years ago

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company prod

tekilochka [14]

Answer:

C) 515 hours.

D) 500 hours

c) sample 3

Step-by-step explanation:

1. Sample 2 mean = x2`= ∑x2/n2= 2060/4= 515 hours

Sample Service Life (hours)

1 2 3

495 525 470

500 515 480

505 505 460

x1`= ∑x1/n1= 2000/4= 500 hours

x2`= ∑x2/n2= 2060/4= 515 hours

x3`= ∑x3/n3= 1880/4= 470 hours

2. The mean of the sampling distribution of sample means for whenever service life is in control is 500 hours . It is the given mean in the question and the limits are determined by using μ ± σ , μ±2 σ or μ ± 3 σ.

In this question the limits are determined by using μ ± σ .

3. Upper control limit = UCL = 520 hours

Lower Control Limit= LCL = 480 Hours

Sample 1 mean = x1`= ∑x1/n1= 2000/4= 500 hours

Sample 2 mean = x2`= ∑x2/n2= 2060/4= 515 hours

Sample 3 mean = x3`= ∑x3/n3= 1880/4= 470 hours

This means that the sample mean must lie within the range 480-520 hours but sample 3 has a mean of 470 which is out of the given limit.

We see that the sample 3 mean is lower than the LCL. The other two means are within the given UCL and LCL.

This can be shown by the diagram.

8 0

3 years ago

And how many map squares did we survive more than 29 plant species

denis-greek [22]

Answer:

Hello your question is incomplete attached Below is the missing histogram

answer: 10 map squares

Step-by-step explanation:

There are 10 map squares that did survive more than 29 pant species because from the given diagram we can see that the plant species above 29 are spotted in 4 map squares ( i.e. from spot 30 to 39 ) and 6 map squares ( i.e. from 30 to 49 )

hence the total number of map squares = 4 + 6 = 10 map squares

4 0

3 years ago

Prince Ivan rides gray wolf and a constant speed from kings castle to the magic apple garden in five hours. on the return trip t

borishaifa [10]

Answer:

The original speed of the grey wolf can be 9 and/or 48 km/hour

Step-by-step explanation:

There are two trips. One to King Castle (KC) to Magic Apple Garden (MAG), and then back (MAG - KC).

First trip: KC - MAG

It takes the same distance as MAG - KC so distance can be D for both.

Then it is stated that it takes 5 hours or 300mins for him to go from KC - MAG, and the speed is constant.

Let x be speed.

So the equation for this is:

D=5x

Second trip: MAG - KC

Here he goes 36 mi at constant speed (x), then picks up his speed by 3 km/hour (x+3).

For Time:

He reaches to KC, 15 mins earlier than KC - MAG, so he reaches there in 4.75 hours or in 275 min.

The problem splits into two as there are two different times, for the two parts of the journey or distance for MAG - KC.

Let T#1 = a, and T#2 = b.

Let D#2 = D-36

The equation for a:

a = 36/x --> This is he is at a constant speed and went for 36mi.

The equation for b:

b = (x+3)/D#2

These two equation have to be added as (a+b) = 4.75 --> 4.75 is the total time for MAG - KC.

So the equation is:

36/x + (5x-36)/x+3 = 4.75 --> Knowing (a+b) = 4.75, just put 4.75 as the equal, and add the fractions that equal (a) and (b).

Now Solve:

36/x + (5x-36)/x+3 = 4.75

0.25s^2 + 108 + 5s^2 - 36s = 4.75s*(s+3)

0.25s^2 - 14.25s + 108 = 0

(14.25 +- Square root (203.06 - 108))/0.5

(14.25 +- Square root (95.0625))/0.5

(14.25 +- 9.75)/0.5

Answer:

s = 9, s=48.

Therefore the original speed of the grey wolf can be 9 and/or 48 km/hour.

8 0

3 years ago

T = AB-5 for A what would be the answer for A

Ainat [17]

The given equation solved for A is A = (T + 5)/ B

<h3>Solving linear equation</h3>

From the question, we are to solve the given equation for A

To solve the equation for A, we will simply make A the subject of the equation

The given equation is

T = AB - 5

Solving for A

T = AB - 5

Add 5 to both sides of the equation

T + 5 = AB - 5 + 5

T + 5 = AB

Divide both sides of the equation by B

That is,

(T + 5)/B = AB/B

(T + 5)/B = A

∴ A = (T + 5)/ B

Hence, the given equation solved for A is A = (T + 5)/ B

Learn more on Solving linear equation here: brainly.com/question/1531728

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3 0

2 years ago