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AysviL [449]
3 years ago
8

Find quadratic polynomial which best fits the function f(x)=e^x and x=0, in the sense that g(0)= f(0), and g'(0) = f'(0), and g"

(0) = f"(0).
g(x)=?
Mathematics
1 answer:
Dmitriy789 [7]3 years ago
3 0
Let g(x)=ax^2+bx+c. Then

\begin{cases}g(0)=c\\g'(0)=b\\g''(0)=2a\end{cases}

Meanwhile, since f(x)=e^x, you have f(0)=f'(0)=f''(0)=e^0=1.

It follows that a=\dfrac12, b=1, and c=1, so that the quadratic fit for f(x)=e^x that satisfies the given points is

g(x)=\dfrac12x^2+x+1

Note that this is just the second-order Taylor polynomial for e^x about x=0.
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the ratio of sallys height is 7:8. if the sum of their heights is 90 inches. how tall are sally and jack?
pickupchik [31]

Answer:

Sally is 42 in. tall, and Jack is 48 in. tall.

Step-by-step explanation:

There are some words missing in the problem.

Perhaps the problem was meant to read:

"The ratio of Sally's height to Jack's height is 7:8. If the sum of their heights is 90 inches, how tall are Sally and Jack?"

Solution:

The ratio of the heights is 7:8.

Sally could measure 7 inches and Jack 8 inches, but then when you add the heights, 7 in. + 8 in. = 15 in. which is not 90 inches.

If you multiply both numbers in a ratio by the same number, the new numbers are still in the same ratio.

Multiply 7 and 8 by 2. You get 14 and 16. Maybe Sally is 14 in. tall and Jack is 16 in. tall. Add the heights, 14 in. + 16 in. = 30 in. This is also not 90 in.

We can keep on guessing what number to multiply by 7 and 8 by so their sum is 90, but we can use algebra to write an equation and not have to go through many guesses.

There is a number, x, that when you multiply 7 and 8 by x, the sum of the products is 90. We don't know what x is, but we can write an equation and solve for x.

The numbers in the ratio are 7x and 8x.

7x and 8x are still in the ratio 7:8.

Now we add the numbers 7x and 8x and set the sum equal to 90. Then we solve for x.

7x + 8x = 90

15x = 90

x = 6

We get x = 6. Now we know we need to multiply both 7 and 8 by 6 to get the heights we need.

7 in. * 6 = 42 in.

8 in. * 6 = 48 in.

Check: 42 in. + 48 in. = 90 in.

Answer: Sally is 42 in. tall, and Jack is 48 in. tall.

7 0
2 years ago
Solve the equation for x.
valentina_108 [34]

Answer:

Solve for  

x

by simplifying both sides of the equation, then isolating the variable.

Exact Form:

x

=

5 /4

Decimal Form:

x

=

1.25

Mixed Number Form:

x

=

1  1/4

Step-by-step explanation:

THE ANSWER IS C

4 0
2 years ago
PLZZZZZZZ HELPPPPPP MEEEEEE THISSSS ISSSS DUEEEEEE IN 15 MINTUES
dimaraw [331]

Answer:

C, Linear

General Formulas and Concepts:

<u>Algebra I </u>

  • Linear - Proportional relationship y = mx + b
  • Nonlinear - Any graph that has a degree x higher than 1

Step-by-step explanation:

<u>Step 1: Define</u>

y = 7x + 14

<u>Step 2: Identify</u>

We see a linear equation (proportional relationship). Therefore, we have a linear equation.

3 0
2 years ago
Read 2 more answers
UNIT 8
DochEvi [55]

For the first figure the Circumference of the circle is: 5.3\ip\pi cm.

For the second figure the Circumference of the circle is: 80\ip\pi inch.

<h3>What is Circumference of the Circle?</h3>

The circumference of a circle is defined as the linear distance around it.

i.e.,  C= 2 *\pi*r

  • For First Figure,

Circumference of the circle:

= 2 *\pi*r

= 2 *\pi* \frac{5.3}{2}

= 2 *\pi*2.65

Circumference= 5.3*\pi cm

  • For the second Figure,

Circumference = 2 *\pi*r

= 2 *\pi*40

 = 80 *\pi

Circumference =80\pi \;inch

For the first figure the Circumference of the circle is: 5.3\ip\pi cm.

For the second figure the Circumference of the circle is: 80\ip\pi inch.

Learn more about circumference of circle here:

brainly.com/question/23239017

#SPJ1

4 0
2 years ago
Which expression is equivalent to the given polynomial expression?
PilotLPTM [1.2K]

Answer:

-4 a^2 - 3 b

Step-by-step explanation:

8 0
3 years ago
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