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You should try using induction.

Express your answer in scientific notation.
2.8⋅10^−3−0.00065 =2.8⋅10−3−0.00065    (forgot ^ ?)

Hello Guest!

\(2.8⋅10^{−3}−0.00065=2.8\cdot 10^{-3}-6.5\cdot 10^{-4} \color{blue}=2.15 \times 10^{-3}\)

  !

ASAP PLEASE!

Solve:       ( x² + x + 1 ) ( x² + x + 2 )  =  12

Multiply out:  x⁴ + 2x³ + 4x² + 3x + 2  =  12

Rewrite:       x⁴ + 2x³ + 4x² + 3x - 10  =  0

There are two rational solutions; you can find them by trying all the factors of -10:

     1, -1, 2, -2, 5, -5, 10, -10          (two of these will work)

After you have these two solutions, you can divide their factors out of the original problem.

This will give you a quadratic that can be solved by using the quadratic equation.

sin(20^o)[ tan(10^o) + cot(10^o) ] 

1)            =  sin(20^o) · tan(10^o)  +  sin(20^o) · cot(10^o)

2)           =  sin(20^o) · sin(10^o) / cos(10^o)  +  sin(20^o) · cos(10^o) / sin(10^o )

3)            =  sin(20^o) · sin²(10^o) / [ sin(10^o) · cos(10^o ) ]  +  sin(20^o) · cos²(10^o) / [ sin(10^o) · cos(10^o ) ] 

4)            =  [ sin(20^o) · sin²(10^o) + sin(20^o) · cos²(10^o) ] / [ sin(10^o) · cos(10^o ) ] 

5)            =  [ sin(20^o) · ( sin²(10^o) + cos²(10^o) ) ] / [ sin(10^o) · cos(10^o ) ] 

6)            =  [ sin(20^o) · 1 ] / [ sin(10^o) · cos(10^o ) ] 

7)            =  [ 2 · sin(10^o) · cos(10^o) ] / [ sin(10^o) · cos(10^o ) ] 

8)            =  2

1)  Distribute

2)  Rewrite tan as sin/cos; rewrite cot as cos/sin

3)  Write with the common denominator of sin(10^o) · cos(10^o )

4)  Write with a single denominator

5)  Factor out sin(20^o)

6)  Use the fact that sin² + cos²  =  1

7)  Use the fact that sin(2x)  =  2sin(x)cos(x)

8)  Cancel

The slope of  y  =  x + k  is 1.

We need to find where the slope of  y  =  x²  is 1.

Find the first derivative of y:  y'  =  2x     This formula will give us the slope of  y  =  x²  at every point.

When does  2x  =  1?     --->     x  =  1/2.

So, when  x  =  1/2,  the slope of   y  =  x²  is 1.

When  x  =  1/2,  y  =  x²   --->   y  =  (1/2)²  =  1/4.

So the point of intersection of the line and the parabola is the point  (1/2, 1/4).

The equation of the line will be:  y - 1/4  =  1(x - 1/2)   --->   y  =  x - 1/4

1)  Find the midpoint of the two points.

2)  Find the slope of the line that connects those two points.

3)  Find the negative reciprocal of the slope of step 2). This will be the slope of the perpendicular bisector.

4)  Use the point-slope form for the equation of the line (the perpendicular bisector).

     Use the answer to step 1) for the point.

     Use the answer to step 2) for the slope.

5)  Rewrite the equation of step 4) into y = mx + b form.

6)  From step 5), pick out the value of m and the value of b.

7)  Add the two values of step 6) together to get the answer.

Let  L  represent the length of the rectangle and  W  represent the width.

L · W  =  32          2L + 2W  =  24   --->   L + W  =  12   --->   W  =  12 - L

L · W  =  32     --->     L · (12 - L)  =  32     --->     12L - L²  =  32

                       --->     0  =  L² - 12L + 32     --->     0  =  (L - 8)(L - 4)     

Length  =  8     and     Width  =  4.

The distance from the center of the circle to the top side = 2.

The distance from the center of the circle to the right side = 4.

The distance from the center of the circle to the top-right corner  =  r

Using the Pythagorean Theorem:  r²  =  2² + 4²  =  4 + 16  =  20    --->     r  =  sqrt(20)

The area of the circle is:  pi · sqrt(20)²  =  20pi

The area of the rectangle is  8 · 4  =  32

The area of the shaded region  =  20pi - 32

what on earth

O I didn't know that. Thanks for letting me know!

That is called the "Collatz's Conjecture" and it is not for you or me, but for top-notch mathematicians to prove or disprove! Good luck !

sumfor(n, 0, 49, (-1)^n * (99  nCr  (2*n))=-562,949,953,421,312 - A very strange result !!.

So no head?

Sucky sucky (-;

Let  A  =  center of the top-left circle.

Let  B  =  center of the top-right circle.

Let  C  =  center of the bottom circle.

Draw AB; label the point of tangency of the two circle  X.

Draw AC; its length is 24 + 16  =  40.

AX  =  24.

Use the Pythagorean Theorem to find XC:  XC² + XA²  =  AB²     --->     XC² + 24²  =  40²

Solving:  XC  =  32.

The width of the rectangle is  24 + 24 + 24 + 24  =  96

The height of the rectangle is:  24 + 32 + 16  =  72

From these two dimensions, you can find the area.

e) Post your homework online and hope that someone does it all for you.

Area = 6912.