Decimals that contain a zero in the tenth position can be thought of as a fraction over 100 as the tenth isn't occupied and the hundredth correlates to the 100 as a denominator. The same goes for a number with the tenth position occupied. These decimals would be put over 10 as they are occupying that position in the decimal.

7 0

2 years ago

2. Express each of the following as a rational number in the form of p/q<br> Where q≠0

ANTONII [103]

Step-by-step explanation:

We need to find each of the following as a rational number in the form of p/q

(a) (3/7)² (b) (7/9)³ (c) (-2/3)⁴

Solution,

(a) (3/7)²

$(\dfrac{3}{7})^2=\dfrac{9}{49}$

(b) (7/9)³

$(\dfrac{7}{9})^3=\dfrac{7\times 7\times 7}{9\times 9\times 9}\\\\=\dfrac{343}{729}$

$(\dfrac{-2}{3})^4=\dfrac{-2\times -2\times -2\times -2}{3\times 3\times 3\times 3}\\\\=\dfrac{16}{81}$

Hence, this is the required solution.

4 0

2 years ago

Which technique is best to use for x² + 4x = 15

viktelen [127]

U want to go x2 plus x so its x3 then 4x3times -15 so x=3.33333

6 0

2 years ago

A local chicken farmer is constructing a set of eight pens to cage his chickens as shown in the diagram below. He has decided to

Vilka [71]

Primary equation: A(x)= (5y)(3X)
Secondary equation: 5y+3X=1000
y=200-(3X)/5
A(x)=3X(1000-3X)
A(x)=3000X-9X²

Now, find the derivative of A(x) to find the max... here's the work for that, or you could guess and check.

A'(x)=3000-18X

Set derivative equal to 0

0=3000-18X
166.6666666=X

Now test the intervals

(0,166.6666) (166.66666, 1000)
1st derivative is + 1st derivative is -

Plug the X value back into the secondary equation
5y+3(166.666666)=1000
5Y=500
Y=5

Answer:
X= 166.6666666666
Y=5

Please note, this is entry level calculus, and your teacher may expect you to use a different, longer route such as guess and check.

6 0

2 years ago