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Strike441 [17]
3 years ago
12

2+2= what smart ppl ....

Mathematics
1 answer:
tangare [24]3 years ago
6 0

Answer:

It equals 420.

Step-by-step explanation:

You might be interested in
Urgent, It is a Calculus question and I’ll appreciate your help. Thanks
BaLLatris [955]

Answer:

  4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

  (12p)(12r) = -1

  r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

  slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

  tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

__

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

  slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

  6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

  d^2 = (6r^2 -6p^2)^2 +(r -p)^2

  d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

  Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

<em>Comment on the solution</em>

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.

6 0
3 years ago
Solve: (x ÷ 4) + 8 = 38
Rainbow [258]
First you have to rewrite the equation:
(x ÷ 4) + 8 = 38

Second you have to write the division as fraction:
(¼x) + 8 = 38

Third you have to take off the unecessary bracket:

¼x + 8 = 38

Fourth multiply 8 and 38 by 4
x + 32 = 152

Fifth step move the constant to the right hand and change the sign.
x = 152 - 32

Then subtract:

x = 120

Hope this helps :))
5 0
2 years ago
Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.
Alexus [3.1K]
(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k

nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix

I will only convert the 1st one fully, you should be able to do the rest

1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
 (-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)

k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5

basically completee the square with x and find P by force factoring a 4 out

2.  directix: y=-1.75

3. directix: y=1.5

4. directix: y=17.25

5. d: -37.5

6. d: 9.25

7. d=2.625

order them yourself

7 0
3 years ago
Solve the equation for a? z=mab. a)a=z+mb b)a=z-mb c)a= mb/z d)a=z/mb
Bingel [31]

Answer:

a = z/mb

Step-by-step explanation:

Given:

\displaystyle \large{z=mab}

To solve for a, divide both sides by the variables mb to isolate a-term.

\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}

Simplify the expression and we finally have solved for a-term.

\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}

Therefore, the answer to this question is a = z/mb.

Please let me know if you have any questions regarding my answer or explanation!

4 0
2 years ago
Can someone please help me I posted this multiple times but no one answers pls help me quick​
mario62 [17]
You would have to make 465=1550-7 1/2 x and find x
Subtract 1550 from both sides
-1085=-7 1/2x
Divide -7 1/2 on both sides
And the answer is 144 2/3
Sorry about ur bad luck
6 0
2 years ago
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