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stepladder [879]
3 years ago
13

Marta is making two different charms for necklace one charm has a 1 cm diameter and a 3.14 cm circumference of a similar charm h

as a diameter of 4 cm what is the circumference
Mathematics
1 answer:
EastWind [94]3 years ago
3 0
From what I can pick up from your problem statement, you want to know "<span>a similar charm has a diameter of 4 cm what is the circumference."  Please, would you use proper punctuation in your writing, for greater clarity:

"A</span><span> similar charm has a diameter of 4 cm.  What is the circumference?"

The formula for the circumference of a circle, when the diameter is known, is 

C=</span>\pid               or  C=pi*d

In this case, with diamter 4 cm, the circumference, C, is 4pi cm.
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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa
Nataly_w [17]

Answer:

The first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

coefficient of x^{2} in the expansion of (2+x - x^{2})^{6} = (240 - 192) = 48

Step-by-step explanation:

(2+x)^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})

= 6_{C_{0}} \times x^{0} \times 2^{6}  + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4} + terms involving higher powers of x

= 64 + 192 \times x^{1} + 240 \times x^{2} + terms involving higher powers of x

so, the first 3 terms in the expansion of (2 + x)^{6} , in ascending power of x are,

64 , 192 \times x^{1} {\textrm{  and  }}240 \times x^{2}

Again,

(2+x - x^{2})^{6}

= \sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})

Now, by inspection,

the term x^{2} comes from k =5 and k = 6

for k = 5, the coefficient of  x^{2}  is , (-32) \times 6 = -192

for k = 6 , the coefficient of x^{2} is, 6_{C_{2}} \times 2^{4} = 240

so,   coefficient of x^{2} in the final expression = (240 - 192) = 48

3 0
3 years ago
As you move up a linear demand​ curve, the price elasticity of demand in absolute value A. decreases. B. increases. C. stays the
Andreyy89

Answer:

The answers to the questions are;

B. increases.  

C. ​inelastic; increase.

Step-by-step explanation:

The price elasticity of demand for a linear demand in absolute value curve becomes smaller and smaller as we move downwards of the curve.

When the price elasticity of demand is calculated along a linear demand curve. This is so as for each pair of points at which the price elasticity of demand is calculated, the quantity demanded and the price change are somewhat  similar, but as we move towards the top of the demand curve, the high prices and the low quantities shows the increase in demand elasticity.

Also in the inelastic region, as it can be shown by the areas of the rectangles formed by to adjacent price points, increase in price, increases the total revenue.

6 0
3 years ago
The temperatures (in degrees Fahrenheit) in Long Island recorded by the weather bureau over a week were 42, 49, 53, 55, 50, 47,
Ghella [55]
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3 years ago
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How do you solve #21?
Inessa05 [86]
5x^3+8x^2/3x^4-16x^2=x^2(5x+8)/x^2(3x^2-16)=5x+8/3x^2-16
lim x--->0 5x+8/3x^2-16=8/-16=-1/2
6 0
3 years ago
What is the perimeter of a rectangle with a length of (x^2+x) and a width of (2x^2+3x)
Mazyrski [523]

Answer:

Perimeter = 6x² + 8x

Step-by-step explanation:

Perimeter = 2(length + width)

perimeter = 2((x²+x)+(2x²+3x))

perimeter = 2(x²+2x² + x+3x)

perimeter = 2(3x² + 4x)

perimeter = 2*3x² + 2*4x

perimeter = 6x² + 8x

5 0
3 years ago
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