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svetlana [45]
3 years ago
7

Pls answer this.....really need help pleaseee <3

Mathematics
2 answers:
faust18 [17]3 years ago
8 0

Answer:

Step-by-step explanation:

1. 1.2×10³ as an ordinary number?

1.2\times\:10^3\\\\10^3=1000\\\\=1000\times\:1.2\\\\=1200

2.

200  000= 2\times 10^5\\\\200  000 =200\times 10^3

54000 =54\times 10^3\\\\

327000 = 327\times 10^3\\\\327000 = 32.7\times 10^4

3.

149 000 000\:km \\\\=149\times 10^6\\ or\\14.9\times 10^7

4.

5.

0.05 = 50\times 10^-^3\\ \\0.807=807\times 10^-^3\\\\0.00261=2.61\times 10^-^3

6.

0.000139\:m = 1.39\times 10^-4

7. I think all the numbers are written in standard form

Art [367]3 years ago
3 0

Answer:

1.) 1200

2.) 200,000= 2.0 × 10⁵ .  54000 = 5.4 × 10⁴ .  127000 = 1.27 × 10⁵

3.) 149000000 = 1.49  × 10⁸

4.) 2.5 × 10⁻² = 0.025

5.)  5 × 10⁻² .  8 × 10⁻¹    0.00261 = 2 × 10⁻³

6.)  0.000139m  = 1.39 × 10⁻⁴

7.) <em>0.6 × 10⁶</em> changes to 6.0 × 10⁵

<em>0.54 × 10⁻¹²</em><em>  </em>changes to 5.4 × 10⁻¹³

8 × 10⁻⁵ changes to 8.0 × 10⁻⁵

10 × 10³ changes to 10 × 10⁴

44 × 10⁷  changes to 4.4 × 10⁸

1 × 10² changes to 1.0× 10²

Step-by-step explanation:

1. <u>Positive</u> exponents: Whatever the Power of 10 in standard form, move the decimal that many places to the right.

2,3 & 7.  Standard Form <u>always</u> uses <em><u>One digit to the left of the decima</u></em><em>l</em>, then some power of 10. That digit must be equal or greater than 1, but less than 10. <em>T</em><em><u>here must be at least one digit to the right of the decimal,</u></em> even if it is 0.

4. <u>Negative</u> exponents: Whatever the Power of 10 in Standard Form, move the decimal that many places to the l<u>eft</u> to write as a regular decimal (old fashioned)

5 & 6. Reverse of 4.  How many places you moved the  decimal to the right, thats the number you put as the negative exponent of 10 in Standard Form.

7. AAUGH! Same as 2 & 3 but more confusing! There are <em><u>rules!</u></em>

I hope this helps.

Check out Scientific Notation, another name for Standard Form.

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Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x = 3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ​?

Answer:

The  generally expression for the slope of y  = 2x^2 + 4x is  y' =  4x +4

The graph is shown on the first uploaded image

The  generally expression for the slope of y=2x^2+4 is   y' =  4x

Step-by-step explanation:

From the question we are told that

  The  equation of the curve is y  = 2x^2 + 4x

First we differentiate the equation

So  

     y' =  4x +4

Therefore the generally expression for the slope tangent to the curve y=2x^2+4x is   y' =  4x +4

The  next step is to substitute for x =  3 and  x =  0.5

So  for x_1 =  3

    y' =  4(3) +4

     y' =m_1=  16

And  for  x_2 =  0.5

      y' =  4(0.5) +4

       y' =m_2=  6

Here m_1  and  m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So  at x_1 =  3

   y_1  = 2(3)^2 + 4(3)

  y_1  =  21

So the coordinate for the first tangent line is  

    (x_1 , y_1 ) =  (3 ,  21)

At  x_2 = 0.5      

    y_2  = 2(0.5)^2 + 4(0.5)

=>  y_2  = 2.5

So the coordinate for the second  tangent line is  

    (x_2 , y_2 ) =  (0.5 ,  2.5)

Next we obtain the equation for the tangent lines

 So generally the slope is mathematically represented as

        m  =  \frac{y - y_1 }{x-x_1}

For   (x_1 , y_1 ) =  (-3 ,  21) and  y' =m_1=  16

       16 =  \frac{y -21 }{x-3)}

=>    y   = 16x - 27

For  (x_2 , y_2 ) =  (0.5 ,  2.5) and  y' =m_2=  6

       6  =  \frac{y -2.5 }{x-0.5}

       y  = 6x -0.5

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating  y=2x^2+4 as follows

     y' =  4x

     

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