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2 years ago

What is the derivative of y=3tan(x)y=3 tan (x) ?

Mathematics

2 answers:

maw [93]2 years ago

6 0

$y=3tanx\\\\tanx=\frac{sinx}{cosx}\Rightarrow y=\frac{3sinx}{cosx}\\\\\\y'=\frac{(3sinx)'cosx-3sinx(cosx)'}{(cosx)^2}=\frac{3cosxcosx-3sinx(-sinx)}{cos^2x}=\frac{3cos^2x+3sin^2x}{cos^2x}\\\\=\frac{3(cos^2x+sin^2x)}{cos^2x}=\frac{3(1)}{cos^2x}=\frac{3}{cos^2x}\\\\-------------------\\\\sin^2x+cos^2x=1$

viva [34]2 years ago

6 0

Answer is in the attachment below. Use the "product rule".

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Help With Proving Theorems

ira [324]

Remember that when two angles are vertical angles, their angle measurements are the same, as the angles are congruent.

Note the Vertical Angle Theorem. Angles vertically opposite (directly opposite) when two lines intersect are congruent with each other.

Now note that supplementary means 180°

Set the equation. Let the angles = x

2x = 180

Isolate the x. Note the equal sign. What you do to one side, you do to the other. Divide 2 from both sides

(2x)/2 = (180)/2

x = 180/2

x = 90

90° is the measurement of each angle.

~Rise Above the Ordinary

8 0

3 years ago

Nationwide survey of college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking, acc

UkoKoshka [18]

Answer:

The probability of number who disapprove of smoking pot daily is from 7 to 9 is 0.6293.

The probability of number who disapprove of smoking pot daily is at most 5 is 0.038601

The probability of number who disapprove of smoking pot daily is is not less than 8 is 0.723655.

Step-by-step explanation:

The number of seniors that disapprove smoking pot daily X follows binomial distribution with n=12 and p=0.7 because

1. The opinion of seniors are independent.

2. There are two possible outcome approve or disapprove.

3. The probability of seniors disapproves smoking pot daily is constant for each trail i.e. p=0.7.

4. The opinion is asked from 12 senior i.e. fixed number of trails.

The probability of the number of seniors that disapprove smoking pot daily can be computed as

$P(X=x)=nCxp^{x} q^{n-x}$

Here, n=12, p=0.7 and q=0.3.

P(number who disapprove of smoking pot daily is from 7 to 9)=P(7≤X≤9)=?

P(7≤X≤9)=P(X=7)+P(X=8)+P(X=9)

$P(X=7)=12C7(0.7)^{7} 0.3^{5}$ = 0.158496

$P(X=8)=12C8(0.7)^{8} 0.3^{4}$ = 0.231140

$P(X=9)=12C9(0.7)^{9} 0.3^{3}$ = 0.239700

P(7≤X≤9)=0.158496+0.231140+0.239700

P(7≤X≤9)=0.6293

The probability of number who disapprove of smoking pot daily is from 7 to 9 is 0.6293.

P(number who disapprove of smoking pot daily is at most 5)=P(X≤5)=?

P(X≤5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)

$P(X=0)=12C0(0.7)^{0} 0.3^{12}$ = 0.000001

$P(X=1)=12C1(0.7)^{1} 0.3^{11}$ = 0.000015

$P(X=2)=12C2(0.7)^{2} 0.3^{10}$ = 0.000191

$P(X=3)=12C3(0.7)^{3} 0.3^{9}$ = 0.001485

$P(X=4)=12C4(0.7)^{4} 0.3^{8}$ = 0.007798

$P(X=5)=12C5(0.7)^{5} 0.3^{7}$ = 0.029111

P(X≤5)=0.000001+ 0.000015+ 0.000191+ 0.001485+ 0.007798+ 0.029111

P(X≤5)=0.038601

The probability of number who disapprove of smoking pot daily is at most 5 is 0.038601.

P(number who disapprove of smoking pot daily is not less than 8)=P(X≥8)=?

P(X≥8)=1- P(X<8)

P(X≥8)= 1-P(X≤7)

P(X≤7)=P(X≤5)+P(X=6)+P(X=7)

$P(X=6)=12C6(0.7)^{6} 0.3^{6}$ = 0.079248

$P(X=7)=12C7(0.7)^{7} 0.3^{5}$ = 0.158496

P(X≤7)=0.038601+ 0.079248+ 0.158496

P(X≤7)=0.276345

P(X≥8)=1-0.276345

P(X≥8)=0.723655

The probability of number who disapprove of smoking pot daily is is not less than 8 is 0.723655.

4 0

2 years ago

Helpp how do u do 33 and 34??

oksano4ka [1.4K]

I only know the answer to #34. Its 50 degrees becuase the letter C in the middle of the diameter which then goes down to radius then you do 100 divided by 2 and get 50

4 0

3 years ago

Read 2 more answers

Solve the following equation for x 4x - 6y=20

choli [55]

Answer:

x = $\frac{3}{2}$ y + 20

[Given]

4x - 6y = 20

[Add 6y to both sides of the equation]

4x = 6y + 20

[Divide both sides of the equation by 4]

x = $\frac{6}{4}$ y + 20

[Simplify $\frac{6}{4}$ , both 6 and 4 are divisible by 2]

x = $\frac{3}{2}$ y + 20

5 0

1 year ago

Read 2 more answers

Write an equation of the line that passes through (1,2) and is parallel to the line y=−5x+4.

Mkey [24]

Answer:

y=-5x+7

Step-by-step explanation:

if the line is parallel then the slope must be the same so you have the slope now you must use the point slope form which is y-y1=m(x-x1) m standing for the slope which is -5, y1 standing for 2, x1 standing for 1. Now plug it into the equation. y-2=-5(x-1) now solve.

6 0

3 years ago