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Alborosie
2 years ago
6

Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.

Mathematics
1 answer:
Sliva [168]2 years ago
4 0

Answer:

  • g(2.95) ≈ -1.8; g(3.05) ≈ -0.2
  • A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.

Step-by-step explanation:

(a) The linear approximation of g(x) at x=b will be ...

  g(x) ≈ g'(b)(x -b) +g(b)

Using the given relations, this is ...

  g'(3) = 3² +7 = 16

  g(x) ≈ 16(x -3) -1

Then the points of interest are ...

  g(2.95) ≈ 16(2.95 -3) -1 = -1.8

  g(3.05) ≈ 16(3.05 -3) -1 = -0.2

__

(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)

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Suppose you drive a car 392 mi on a tank of gas. The tank holds 14 gallons. The number of miles traveled vaties directly with th
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Preliminary Problem

Givens

Miles = m = 392 miles

Gallons =  G = 14 gallons

Miles per gallon = mpg

Formula

miles = miles per gallon * number of gallons.

Solve

392 = mpg * 14                         Divide by 14

392 / 14 = mpg

28 = mpg  which is really quite good.  Our vehicle gets 44 mpg but it's a 4 cylinder. It's meant to get that kind of milage.

Part A

Let x = the number of gallons used

Let y = the number of miles driven

y = k*x

Part B

y = k* x

k =28 mpg

11700 = 28*x

11700 /28 = x

x = 417.86

If this is incorrect please put some more facts in. The question does not seem complete.


7 0
3 years ago
What is x- and y- intercept of -7x + 2y= 14
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The y-intercept is (0,7) and the x-intercept is (-2,0).
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3 years ago
A triangle has side lengths of (7.8v+2.6)(7.8v+2.6) centimeters, (5.3v+4.5)(5.3v+4.5) centimeters, and (2.4w-6.7)(2.4w−6.7) cent
Citrus2011 [14]

Given:

A triangle has side lengths of (7.8v+2.6) centimeters, (5.3v+4.5) centimeters, and (2.4w-6.7) centimeters.

To find:

The expression which represents the perimeter, in centimeters, of the triangle.

Solution:

We know that

Perimeter of a triangle = Sum of length of all sides of the triangle

Perimeter=(7.8v+2.6)+(5.3v+4.5)+(2.4w-6.7)

Now, combine like terms.

Perimeter=(7.8v+5.3v)+(2.4w)+(2.6+4.5-6.7)

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3 years ago
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3 0
2 years ago
An airplane has 29 seats. The price for a coach seat is $600 in the price for a first class seat is $1050. The airline collected
In-s [12.5K]

Answer:

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Step-by-step explanation:

let the number of coach seats be C and number of first class seats be F

given that the total number of seats is 29,

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also given that each coach seat = $600, each 1st class seat is $1050 and a total of $21900 was collected,

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we have 2 equations and 2 unknowns, we can solve the system of equations by elimination

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by elimination, subtract eq 2 from eq 3

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1,050C - 600C = 8,550  

450C = 8550

C = 855 /450

C = 19

7 0
3 years ago
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