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Delicious77 [7]

3 years ago

8

dan spent half of his allowance going to the movies he washed the family car and earn $10 what is his weekly allowance if you en

ded up with $24

1 answer:

Angelina_Jolie [31]3 years ago

7 0

12 to 14 is his weekly allowance

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Hannah is making cakes for the bake sale at her school. Each cake requires 1 1/2 cups of sugar. How many complete cakes can Hann

denis23 [38]

Answer:

4

Step-by-step explanation:

Divide 6 3/4 by 1 1/2

Convert into improper fractions, 27/4 and 3/2

$\frac{27}{4} / \frac{3}{2}$

$\frac{27}{4} * \frac{2}{3}$

$\frac{9}{2} = 4.5$

The question asks for the number of whole cakes, so the answer would be 4.

6 0

2 years ago

Read 2 more answers

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function.

Lunna [17]

Answer:

The first three nonzero terms in the Maclaurin series is

$\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }$

Step-by-step explanation:

GIven that:

$f(x) = 5e^{-x^2} cos (4x)$

The Maclaurin series of cos x can be expressed as :

$\mathtt{cos \ x = \sum \limits ^{\infty}_{n =0} (-1)^n \dfrac{x^{2n}}{2!} = 1 - \dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+... \ \ \ (1)}$

$\mathtt{e^{-2^x} = \sum \limits^{\infty}_{n=0} \ \dfrac{(-x^2)^n}{n!} = \sum \limits ^{\infty}_{n=0} (-1)^n \ \dfrac{x^{2n} }{x!} = 1 -x^2+ \dfrac{x^4}{2!} -\dfrac{x^6}{3!}+... \ \ \ (2)}$

From equation(1), substituting x with (4x), Then:

$\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}- \dfrac{(4x)^6}{6!}+...}$

The first three terms of cos (4x) is:

$\mathtt{cos (4x) = 1 - \dfrac{(4x)^2}{2!}+ \dfrac{(4x)^4}{4!}-...}$

$\mathtt{cos (4x) = 1 - \dfrac{16x^2}{2}+ \dfrac{256x^4}{24}-...}$

$\mathtt{cos (4x) = 1 - 8x^2+ \dfrac{32x^4}{3}-... \ \ \ (3)}$

Multiplying equation (2) with (3); we have :

$\mathtt{ e^{-x^2} cos (4x) = ( 1- x^2 + \dfrac{x^4}{2!} ) \times ( 1 - 8x^2 + \dfrac{32 \ x^4}{3} ) }$

$\mathtt{ e^{-x^2} cos (4x) = ( 1+ (-8-1)x^2 + (\dfrac{32}{3} + \dfrac{1}{2}+8)x^4 + ...) }$

$\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + (\dfrac{64+3+48}{6})x^4+ ...) }$

$\mathtt{ e^{-x^2} cos (4x) = ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }$

Finally , multiplying 5 with $\mathtt{ e^{-x^2} cos (4x) }$ ; we have:

The first three nonzero terms in the Maclaurin series is

$\mathbf{ 5e^{-x^2} cos (4x) }= \mathbf{ 5 ( 1 -9x^2 + \dfrac{115}{6}x^4+ ...) }$

7 0

3 years ago

Which of the following values can be found by using the formula √1+cos^2 0?

Sati [7]

Let's check

Remove root over and simplify 1+cot²Ø

1+cos²theta/sin²theta
sin²Ø+cos²Ø/sin²Ø
1/sin²Ø
cosec²Ø

Putting root over

cscØ

Sin can be found also along with csc

5 0

2 years ago

Devya sold shirts to raise money for a school trip. The amount of money she received from her sales is proportional to the numbe

azamat

It might be C. I used the process of elimination, so I'm not so certain

8 0

4 years ago

In ΔDEF, e = 8.7 inches, ∠F=8° and ∠D=34°. Find the length of f, to the nearest 10th of an inch.

fomenos

Answer:

1.8 in

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers