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Sidana [21]
3 years ago
6

Video Example EXAMPLE 1 Find the linearization of the function f(x) = x + 1 at a = 3 and use it to approximate the numbers 3.98

and 4.05 . Are these approximations overestimates or underestimates? SOLUTION The derivative of f(x) = (x + 1)1/2 is f '(x) = Correct: Your answer is correct. . and so we have f(3) = 2 Correct: Your answer is correct. and f '(3) = 1/4 Correct: Your answer is correct. . Putting these values into this equation, we see that the linearization is

Mathematics
1 answer:
Blizzard [7]3 years ago
4 0

Answer:

  the linearization is y = 1/4x +5/4

  the linearization will produce <em>overestimates</em>

  the values computed from this linearization are ...

     f(3.98) ≈ 2.245

     f(4.05) ≈ 2.2625

Step-by-step explanation:

Apparently, you have ...

  f(x)=\sqrt{x+1}

from which you have correctly determined that ...

  f'(x)=\dfrac{1}{2\sqrt{x+1}}

so that f(3) = 2 and f'(3) = 1/4. Putting these values into the point-slope form of the equation of a line, we get the linearization ...

  g(x) = (1/4)(x -3) +2

  g(x) = (1/4)x +5/4

__

The values from this linearization will be overestimates, as the curve f(x) is concave downward everywhere. The tangent (linearization) is necessarily above the curve everywhere.

__

At the given values, we find ...

  g(3.98) = 2.245

  g(4.05) = 2.2625

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Can someone please help me I really need help please help me
scZoUnD [109]

Answer:

18.87 square cm.

Step-by-step explanation:

The area of the rectangle will be (4 + 4) * 4, since the length of the rectangle would be the diameter of the circle, and the width of the rectangle would be the radius. (4 + 4) * 4 = 8 * 4 = 32 square cm.

Then, we can calculate the area of the semicircle. The area of a circle is pi * r^2, so the area of a semicircle will be half of that. pi * (4^2) / 2 = pi * 16 / 2 = 8pi. 8 * 3.14159265 = 25.1327412 square cm.

The shaded area of the middle of the shape will then be 32 - 25.1327412 = 6.8672588 square cm.

The two triangles will have the same area. Their bases will be 14 minus the diameter of the circle, then divide that by 2 to get each separate base. 14 - 8 = 6 / 2 = 3. The heights of the triangles will be the radius of the circle, or 4 cm.

1/2 * 3 * 4 = 1/2 * 12 = 12/2 = 6. That is the area of one triangle, so the area of both triangles would be 6 * 2 = 12 square cm.

6.8672588 + 12 = 18.8672588, or 18.87 square cm.

Hope this helps!

3 0
2 years ago
Read 2 more answers
C. 3x-7=2x-5 solve for x, simplify
igomit [66]

3x - 7 = 2x - 5<em>     add 7 to both sides</em>

3x = 2x + 2         <em>subtract 2x from borh sides</em>

<h3>x = 2</h3>

Check:

L = 3(2) - 7 = 6 - 7 = -1

R = 2(2) - 5 = 4 - 5 = -1

L = R  CORRECT! :)

4 0
2 years ago
Read 2 more answers
, Hayley sold 20 tickets to the school play for a total of $225 early bird tickets were $10 and regular price tickets were $15 w
Lady_Fox [76]

Answer:

15 early tickets were sold and 5 regular tickets were sold.

Step-by-step explanation:

Let x be the number of early bird tickets sold and y be the number of regular tickets sold.

Total number of tickets sold = 20

Thus, we can write the equation,

x + y = 20

Cost of early bird ticket = $10

Cost of regular tickets = $15

Total cost = $225

Thus, we can write the equation,

225 = 10x + 15y

We solve the equation by elimination method by multiplying first equation by 10 and subtracting.

10x + 15y-(10x+10y) = 225 - 200\\5y = 25\\\Rightarrow y=5\\x + 5 = 20\\\Rightarrow x = 15

Thus, 15 early tickets were sold and 5 regular tickets were sold.

5 0
3 years ago
Which statement is true about this data set? 3, 1, 6, 4, 4, 4, 3, 2, 5, 3 Options: The data set has six modes. The data set has
sineoko [7]
I took that at grade 3 but I forgot it I am sorry
5 0
3 years ago
Duane And his family are playing a game Dwayne scores 11 points each tile matches 1/3 point model the solution with an equation
Luba_88 [7]

Answer:

33 tiles

Step-by-step explanation:

Given

1\ tile = \frac{1}{3}\ points

Required

Determine the number of tiles in 11 points

Represent this with x. So, we have:

1\ tile = \frac{1}{3}\ points

x = 11\ points

Cross Multiply

x * \frac{1}{3} = 11 * 1

Multiply through by 3

3*x * \frac{1}{3} = 11 * 1*3

x = 33

6 0
3 years ago
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