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3 years ago

Problem #2: Ethan bought plates and cups for his upcoming birthday party. He

Mathematics

1 answer:

podryga [215]3 years ago

3 0

Create an equation.

2c + c = 102

3c = 102

c = 34

Ethan buys 34 cups and 68 plates.

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Use the appropriate substitutions to write down the first four nonzero terms of the Maclaurin series for the binomial (1+3x)^(-1

PolarNik [594]

Answer:

First term=1

Second term=-x

Third term= $2x^2$

Fourth term = $-\frac{28}{3!}x^3$

Step-by-step explanation:

We are given that function

$f(x)=(1+3x)^{-1/3}$

We have to find the first four non zero terms of the Maclaurin series for the binomial.

Maclaurin series of function f(x) is given by

$f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....$

$f(0)=(1+3x)^{\frac{-1}{3}}=1$

$f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}$

$f'(0)=-1$

$f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}$

$f''(0)=4$

$f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}$

$f'''(0)=-28$

Substitute the values we get

$(1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...$

$(1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...$

First term=1

Second term=-x

Third term= $2x^2$

Fourth term = $-\frac{28}{3!}x^3$

5 0

3 years ago

Approximately how many times greater is 2.3 than 1.15 ?

Elan Coil [88]

If you divide 2.3 by 1.15 to find out how much greater it is, the answer is 2.

3 0

4 years ago

Select the proper order from least to greatest for 1/2, 5/6, 2/7, 4/2. A. 2/7, 1/2, 5/6, 4/2. B. 2/7, 5/6, 1/2, 4/2 C. 4/2, 2/7,

Elanso [62]

2/7 < 0.5
1/2 = 0.5 
5/6 > 0.5 
4/2 = 2

I hoped I helped. :)

4 0

3 years ago

Can someone please help?

marta [7]

Answer:

3. definiton of angle bisector

4. substitution property (of equality)

5. 2x+14=34

5. subtraction property of equality

6. 2x = 20

6. subtraction property of equality

4 0

3 years ago

PLEASE HELP THANK YOU SO MUCH IN ADVANCE. IF POSSIBLE PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER

natka813 [3]

Answer:

Step-by-step explanation:

To be right triangle has to verify the Pythagorean Theorem

hypothenuse² = (side 1 )² + (side 2)²

Since the hypothenuse is the largest of the sides we consider the largest number the hypothenuse and check the relation.

16, 30, 34

34² = 16²+30²; 1156 = 1156 ✅

16, 30, 34 are measurements of a right triangle

8, 14, 16

16² = 8² +14²; 256 = 260 ❌

8, 14, 16 is not a right triangle

10, 12, 16

16² = 10² +12²; 256 = 244 ❌

10, 12, 16 is not a right triangle

5, 12, 13

13² = 12²+5²; 169 = 169 ✅

5, 12, 13 are measurements of a right triangle

8 0

2 years ago