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4 years ago

Suppose a varies directly as b, and a=7 when b=2 find b when a =21

1 answer:

6 0

Because α varies directley to β
$\alpha = k \beta$
(k = constant)

α=7 when β=2
7= 2k
k= $\frac{7}{2}$

so when α=21
21= $\frac{7}{2}$ b
b= 6

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U.S. craft-beer breweries (breweries that make fewer than 6 million barrels annually and are less than 25% owned by big brewerie

yarga [219]

Answer:

(a) a = 43.25 , b = 41 and c = 1547

(b) The number of craft-beer breweries in 2016 = 4643

Step-by-step explanation:

Given that the number of small craft-beer breweries from 2008 to 2012 is modeled by using a quadratic function of the form f(t) = at² + bt + c where a, b, and c are constants and t is measured in years, with t = 0 corresponding to 2008.

(a) Now we have to find these constants given f(0) = 1547, f(2) = 1802, and f(4) = 2403.

So, f(0) = $a*(0)^{2} + b*(0) + c$ which implies that c = 1547.

f(2) = $a*(2)^{2} + b*(2) + c$ = 4a + 2b + c

4a + 2b + c = 1802 ----------- [Equation 1]

f(4) = $a*(4)^{2} + b*(4) + c$ = 16a + 4b + c

16a + 4b + c = 2403 ----------- [Equation 2]

Further solving Equation 1 we get; 4a + 2b + 1547 = 1802

4a + 2b = 1802 - 1547 ; 4a + 2b = 255 ----------- [Equation 3]

Further solving Equation 2 we get; 16a + 4b + 1547 = 2403

16a + 4b = 2403 - 1547 ; 16a + 4b = 856 ----------- [Equation 4]

Now, Solving Equation 3 and 4 we get ;

a = 43.25 and b = 41 .

Therefore, values of constants a, b and c are 43.25, 41 and 1547 respectively.

(b) So, model we obtained in part (a) is represented as :

f(t) = $43.25t^{2} + 41t + 1547$

Now to estimate the number of craft-beer breweries in 2016, assuming that the trend continued we know that t would be 8 as 2016 - 2008 = 8 years.

So, f(8) = $43.25*(8)^{2} + 41*8 + 1547$ = 4643.

6 0

4 years ago

Find the value of a given <img src="https://tex.z-dn.net/?f=5%5Ea%5C%5C" id="TexFormula1" title="5^a\\" alt="5^a\\" align="absmi

ddd [48]

Answer:

a = 2/3

Step-by-step explanation:

A cube root is the same as a 1/3 power. The square of that gives a 2/3 power.

a = 2/3

_____

Additional comment

You can see the relationship between a root index and an exponent if you consider what the root means.

Consider a cube root, for example. When you cube the root, you get the original number:

(∛x)·(∛x)·(∛x) = x

Now, let's write the root as a power of x: x^a.

(x^a)·(x^a)·(x^a) = x . . . . . where x^a = ∛x

We know this product is ...

x^(a+a+a) = x^(3a) = x^1

This tells us that ...

3a = 1 ⇒ a = 1/3

That is, ∛x = x^(1/3).

Of course an n-th root is multiplied by itself n times to get the original number, so the corresponding exponent is x^(1/n).

5 0

2 years ago

What’s 12 and what’s 14 ?

ankoles [38]

Answer:12√(3)

Step-by-step explanation:

2√(108)

2 x √(108)

2 x √(36 x 3)

2 x √(36) x √(3)

2 x 6 x √(3)

12 x √(3)

12√(3)

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4 years ago

John borrowed $1200 from his credit union at 18% simple interest. He agrees to repay the loan by making

kakasveta [241]

1200 (1+.8 * 30/12) = 1740.00
1740.00 - 1200 = $540

4 0

3 years ago

$0.2963 rounded to the nearest cent

kotykmax [81]

Answer:

0.2963 = about 0.3 cents

8 0

4 years ago

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