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x^2+7x+4=0

2 Soloutions

setting up for success

circumference of the circle divided by radius of the circle

My questiom is a 70 foot diameter clarifier drops 5 inches in 15 minutes during a calibration test on a was pump. Calculate the was pumping rate in gallons per minute. It says to convert the inches into feet and divide by the time it took for it to drop

The diameter isn't related to the height.....the height might be any positve value....

Thus......the volume depends on both the diameter  and height ....

The hrizontal asymptote occurs at  3 / -5    =  -3 / 5   =  -0.6

Here's a graph : https://www.desmos.com/calculator/8mj0jllvgy

So how could i find the height whem all i have is the diameter? I know my diameter is 70 which would make my radius 35 but not sure how to figure height out 

You can't.....you must also know the height....

This is a little tricky !!!......we want to first get x by itself

y = (2x-1)/(x+2)   multiply   both sides by x +  2

y(x +2)  = 2x - 1

xy + 2y =  2x - 1

xy - 2x =  -2y - 1

x ( y - 2)  = -(2y + 1 )   divide  both sides by y - 2

x  =  -(2y + 1) / (y - 2)     .......now ...."swap"  x and y

y  = - (2x + 1) / ( x - 2)     and for y, write  f^-1 (x)

f^-1 (x )  =  - (2x + 1) / (x - 2)

Use the change-of-base theorem

log_a b   =      log b  /  log a

So

log₂  15471   =      log (15471) / log (2)  ≈  13.9173

Correction, the answer is 1

1+(.10)10=2

the answer is 2

x^3+7x^2-3x-21;  -7   is a zero

Factor  by grouping

x^2 ( x + 7) - 3(x + 7)  =  0

(x + 7)  ( x ^2  - 3 )  = 0

We   know  the  zero  of the first factor.....to find the zeroes of the second, we have

x^2  - 3   = 0     add 3 to both sides

x^2  =  3         take  both positive and negative roots

x =  ± √3

n^(2/3)  = 216

Take each side to the 3/2 power

[n^(2/3)]^(3/2)   =  216 ^(3/2)  

n   =  [ √ 216 ] ^3

n = [ √ (36 * 6) ] ^3

n = [ 6  √6 ] ^3

n = 6^3 * (√6)^3 

n  =  216 * [√6 ]^2 * √6

n  =  216 * 6  * √6

n = 1296√6

I'll take those 5 pepperonies  !!!!

A   = Pe^(r*t)     ....note...... r = 2.88%   =   .0288   

So

A   = 455e^(.0288 * 15)   ≈ $700.85

Problem 1:

If 

f(2)=f(4)=0, f(3)=−2

x = 2  and x = 4 are roots    and the vertex  lies at  (3, -2)......so we know that

0  = a(2 - 3)^2  - 2   simplify

0 = a (-1)^2  - 2

0 =  a - 2   →   a = 2

So...our function is f(x)  = 2(x - 3)^2 - 2

Check   that x = 4 produces a zero

2(4 - 3)^2 - 2    =   2(1)^2  - 2   =   2 - 2  = 0

Problem 2:

If

Zeroes at 1± sqrt(2),  y-intercept at –4

The  x value of the vertex will be the average of the sum of the roots =

  [  1 + sqrt (2) +  1 - sqrt(2) ] / 2    = 2 / 2   = 1

And the x coordinate of the vertex  =  -B/ [ 2A]   implies that

-B/ [2A]  = 1   which implies that

-B  =  2A   which implies that

B = -2A

So  we have the following :

y  =  Ax^2  + Bx + C     and substituting for B

y = Ax^2  - (2A)x + C

And since the y intercept is at - 4 , then

-4  = A(0)^  -2A(0)  + C

-4  =  0 + 0 + C

-4 = C

So we have that

y = Ax^2 -2Ax - 4

And we know that

0  =  A(1 + sqrt(2))^2  - 2A(1 + sqrt(2))   - 4

4 = A ( 1 + 2sqrt(2) + 2)  - 2A  - 2Asqrt(2)

4 =  A + 2Asqrt(2) + 2A - 2A - 2Asqrt(2)

4 = A       ....    and  B  = -2A =  -8

So  we have

y = 4x^2 - 8x - 4

Here's a graph that confirms this : https://www.desmos.com/calculator/ba8scvgskt

Approx.  with a repeating decimal 108.3333.

a)  Buying one more lb. of apples means that you have .20 less to spend on grapes, since apples are .20 lb.

 Since grapes are .60 / lb.  then .20 less to spend on grapes means that you  will buy  20/ 60 = 1/3 lbs less  or  (-1/3)

b)  The slope of g as it relates to  a   is   (-1/3)/ 1   =   -1/3

c)   You can buy   18/.60   =  30 lbs. of grapes if you buy no apples

d) The function  would  be    →  g  = (-1/3)a  + 30

Check this.....if we bought 30 lbs. of apples we would spend $6 .....then...we could buy

[18 - 6] /.60  = 12/.60  =  20lbs  of grapes

Plugging these into the function

20  = (-1/3)30  + 30

20  =  -10 + 30

20  = 20    !!!!

Your question isn't clear....but......

If 3/8 tons are left after using 4/9 of the seed.....he strated with

(3/8)/(4/9)  =   (3/8) * (9/4)  =  27 / 34 tons

If he started with 3/8 tons .... then he used  3/8 * 4/9  =  12 / 72  =   1/6 tons

cos theta  =  ±√  ( 1 - sin^2 theta)  = 

±√  ( 1 - (15/17)^2 ) 

±√ (289 - 225) / 17  =

±√64 / 17   =

± 8/17          the sign depends upon the quadrant where "theta" lies

Yep......it will add, subtract, multiply and divide fractions...just make sure to enclose each fraction with a set of parentheses.....like this →  (2/3) + (5/8)   ......etc.

MJ....when you're answering a question.....if you select the little "horseshoe" symbol to the left of the "smiley face" symbol......you will see a keypad with many different characters on it.....

I also use this to make some other special symbols :

http://math.typeit.org/

It actually depends on what kind of fraction problem your working with. If you want, I can solve the problem for you. What is it?

A farmer has 3/8 ton of seed.He uses 4/9 of the seed in one field.How many tons of seed did the farmer use in the field?

3/8 - 4/9 = ?

3- 4 = 1

4- 9 = 1

1/1 = 1

The farmer used exactly one ton of seed in the field. 

Money galore, dont spend it all on one 'bar'