All Answers

#2

+129839

+1

Excellent, tertre......!!!!

CPhillDec 23, 2018

#1

+4619

+2

The shortest length should be greater than their difference. Thus, the answer is $13-9+1=4+1=\boxed{5}$ cm.

tertreDec 23, 2018

#1

+129839

+1

41% = .41

So.....

41% of 28244.66 =

.41 * 28244.66 =

$11580.31

CPhillDec 23, 2018

#2

+118653

+2

Good logic PM

MelodyDec 23, 2018

#3

0

Thanks for the reply!

Height of windmill = 3cm = height of object

Height of virtual image = 90 cm = h

Lens strength = 10 dpt = focal length 10 cm

Formula: 1/f = 1/v +1/u

1/10 = 1/3 + 1/u

1/u = 1/f - 1/u

1/u = 1/10 - 1/3

1/u = -0,2333 or - 7/30

-v /u = - 7/30 / 1/3 = -0,1

so it'd be C then?

GuestDec 23, 2018

#1

+129839

+1

Notice that we have 3 + 4 + 5 = 12 equal parts of 120m = 10 m each

3 of these = 30m

4 of these = 40m

5 of these i= 50m

A 3-4-5 triangle is a Pythagorean right triangle....so.....each side of this triangle is 10 times as much

So..We have a right triangle with legs of 30m and 40m and a hypotenuse of 50m

The area is product of legs / 2 = 30 * 40 / 2 = 600 m^2

CPhillDec 23, 2018

#8

+118653

+2

Oh and you can appologize for wasting CPhills time too!

MelodyDec 23, 2018

#7

+118653

+2

What do you mean 'nevermind!'

You asked a question and CPhill went to a lot of effort to answer it for you.

The next thing for you to do is to say thank you!

MelodyDec 23, 2018

#2

+129839

+1

Good job, PM......!!!!!

CPhillDec 23, 2018

#1

+775

+1

a = 9, b = 8, c = 7, and d = 1

9.87 - 0.1 = 9.77. The largest possible value is $\boxed{9.77}$.

- PM

PartialMathematicianDec 23, 2018

#6

+775

+3

So the answer is $\left(\frac{1}{\left(\frac{13}{2}+\frac{3}{2}\sqrt{17}\right)}\right)+\left(\frac{1}{\left(\frac{13}{2}-\frac{3}{2}\sqrt{17}\right)}\right) = \boxed{\dfrac{13}{4}}$.

- PM

PartialMathematicianDec 23, 2018

#5

+129839

+4

The roots are

13 + 3√17 13 - 3√17

_________ and _________

2 2

So

The reciprocal sum is

2 2

_________ + _________

13 + 3√17 13 - 3√17

2 [ 13 - 3√17] + 2 [ 13 + 2√13 ]

__________________________

169 - 9(17)

52 13

____ = ___

16 4

CPhillDec 23, 2018

#4

+775

+2

Note that in this equation, $x_1 + x_2 = 13$ and $x_1x_2 = 4$.

PartialMathematicianDec 23, 2018

#3

+775

+2

But yes, a good solution would include the use of Vieta's formula.

In the quadratic polynomial $P(x) = ax^2 + bx + c$, the roots $x_1$ and $x_2$ satisfy $x_1 + x_2 = -\dfrac{b}{a}$ and $x_1 x_2 = \dfrac{c}{a}$.

PartialMathematicianDec 23, 2018

#2

+775

+2

Using the quadratic formula, we have the two solutions $\dfrac{13}{2} + \dfrac{3}{2}\sqrt{17}$ and $\dfrac{13}{2} - \dfrac{3}{2}\sqrt{17}$. The reciprocals would be $\dfrac{1}{\dfrac{13}{2} + \dfrac{3}{2}\sqrt{17}}$ and $\dfrac{1}{\dfrac{13}{2} - \dfrac{3}{2}\sqrt{17}}$. Adding them together, we have $\left(\frac{1}{\left(\frac{13}{2}+\frac{3}{2}\sqrt{17}\right)}\right)+\left(\frac{1}{\left(\frac{13}{2}-\frac{3}{2}\sqrt{17}\right)}\right) = \boxed{\dfrac{13}{4}}$.

- PM