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-1     1/25

-1*1/25

-1/25

38

1) dy / dx (1 / x)   =   -1/x^2

2) the slope of the tangent at "a"  = -1/a^2

3)  Equation of the tangent =

y - 1/a = ( -1 /a^2) ( x - a)  

y = -x / a^2    +  2/a

y = [ 2a - x ] / a^2

B.   I think you want to know where the tangent line intersects the y and x axis.

Wnen x = 0, y = 2/a   this is the y intercept   = (0, 2/a)

When  y = 0, x = 2a    this is the x intercept  = (2a, 0 )

C. I think you want to find the area of a triangle bounded by the tangent line and both axis....if so, we have......

A = (1/2)(b)(h)    =  (1/2)(2a)(2/a)  = 4 / 2   = 2 sq units........this is a constant area that does NOT depend upon "a"

D.  We have

sqrt ( [2/a]^2 + [2a]^2 )  = 5       square both sides

4/a^2   + 4a^2   = 25       multiply through by a^2

4 + 4a^4  = 25a^2     rearrange

4a^4 - 25a^2 + 4 = 0

In the first quadrant, we have two solutions  ...   a ≈ .40536   and a ≈ 2.4669

So   we have ( .40536, 1/.40536) and (2.4669, and 1/ 2.4669 )

Here's a graph of both tangent line solutions......note that the total length of both tangent lines between their intersections with the x and y axis ≈  5

https://www.desmos.com/calculator/km8gajbnnl

5 is the answer to your question.

30-(-19)*6+5

30-(-114)+5

30+114+5

144+5

149

Hallo arie 466

What is 132/1 divided by 27/8 =

132 / 27/8=132 X 8/27=1,056/27=39 1/9

whats the greatests common factor of 30 and 75

30=2 X 3 X 5

75=3 X 5 X 5

As you can see 5 is the GCF

34 octillion 286 septillion 227 sextillion 579 quintillion 387 quadrillion 45 trillion 481 billion 691 million 386 thousand 875

the answer is 15

In March, Isaiah and Freddie had the same amount of money in their savings accounts. In April, Isaiah deposited $210 into his account. Freddie increased the money in his account by 15%. When they compared their balances, they found that they were still equal.

How much money did they both have in their accounts in March?

We have

x + 210  = 1.15x        where x is the amount in their accounts in March....subtract x from both sides

210 = .15x   divide both sides by .15

x = $ 1400

The ages of three brothers is 83 years . The oldest brother is twice the age of the middle and the middle brother is 5 years older than the youngest . Define a variable . Write and solve an equation to determine the ages of the three brothers.

Let a be the age of youngest brother, we have:

a +5=age of middle brother, and,

2(a + 5)=age of oldest brother, then we have:

a + a + 5 + 2(a + 5)=83

2a + 5 + 2a + 10=83

4a=68

a=17 The age of youngest brother

17 + 5=22 The age of middle brother

22 X 2=44 The age of oldest brother, so that:

17 + 22 +44=83

Thank U so much

Since they got equal total scores....let the value of each correct multiple choice question = V....and we have

18V + 19 =  15V + 31     subtract 15V, 19 from each side

3V = 12    divide both sides by 3

V = 4    →  the multiple choice questions were worth 4 points each

666 dun dun duuuuunn

Equation A is the correct answer.

The frig. original price was $1,000, so that we have:

$1,000 - 15%=$1,000 - $150

$850=$850

This is exact. Your marks :

You deserved a chocolate mufin for such a good report card !

P.S.: If you don't like chocolate or prefer another flavor, tell me, I'll find it.

How many air molecules are in a 11.5×12.0×10.0 ft room? Assume atmospheric pressure of 1.00 atm, a room temperature of 20.0 ∘C, and ideal behavior.

Volume conversion:There are 28.2 liters in one cubic foot.

11.5 X 12 X 10 X 28.2=38,916 Liters of air in the room.

Since 1 Liter=2.652×10^22 molecules, therefore:

2.652×10^22 molecules X 38,916 Liters=1.032 X 10^29 molecules of air in the room.

sqrt(sqrt(3)+sqrt(2))+sqrt(sqrt(3)-sqrt(2)) =

sqrt(1.7320+1.4142) + sqrt(1.7320-1.4142)=

sqrt(3.1462) + sqrt(0.3178)=

1.77375 + 0.56374=2.33749.....etc.

=2.33754178896073......etc

1. There are 18 letters and 6 are vowels 

6 / 18   = 1/3   chance that a vowel is picked

2. first letter of the alphabet = a   and there are two of them....so...

2 / 18  = 1/9  

3. there are 3 'T's"    ....so.....

3 / 18  =   1/6

6N = 10      divide both sides by 6

N = 10/6

sqrt(sqrt(3)+sqrt(2))+sqrt(sqrt(3)-sqrt(2))  =

sqrt ( 3.1462643699419723)  - sqrt ( 0.3178372451957822)  ≈  1.21

20

√400=20

Here's my best guesses for the last one :

1) 4n   .....   not  geometric ......    the first few terms are :  4, 8, 12, 16.......

This is  an arithmetic series, instead   

2)  n⁴  .....not geometric  ......the first few terms are :   1, 16, 81, 256

Note that the geometric difference between the first and second terms = 16, but between the 2nd and 3rd terms is only 81 / 16 .....geometric series always have a constant difference between terms

3)   3ⁿ / 5 ^{n + 1}   let's examine the first few terms before making any speculation....we have.....

3/25, 9/125/, 27/ 625........

The ratio of the second term to the first = [9/ 125] /[ [3 / 25] =  3/5

The ratio of the 3rd to the second = 3/5

So....it appears to be geometric   ....proof....

[ 3 ^{n + 1} / 5 ^{n + 2} ] / [3ⁿ / 5 ^{n + 1} ]  =    [ 3 ^{n + 1} / 5 ^{n + 2} ] * [ 5 ^{n + 1} / 3ⁿ ]  =  3 / 5

4)  3 + 3n    .....here's the first few terms......

6, 9, 12,  15.........   this is obviously not geometric........the ratio between the 2nd term to the first = 3/2   ...but the ratio between the 3rd and 2nd = 12/9 = 4/3