Question

Solve 32x−1​−23−x​=4x​ A rectangle is three times as long as it is wide. If its Perimeter is 56 cm. find the width if the rectangle. Find the value of 2πgl​​ when π=371​,1=98 and g=32 If I=R2+W2L2​E​ Make R the subject of the formula

Answer 1

1, x=(24/27)

2. The width (x) is = 7 cm

3. 1163456 (Assuming the value given for π is correct)

4. R= (I-W2L2​E)/2, assuming "R2" is "2R."

Explanation:

1. 32x−1​−23−x​=4x​

31x-24=4x

27x = 24

x = (24/27)

2. Let x be the width of the rectangle. It's length would be 3x ("three times as long as it is wide').

We can write:

w = x , and

l = 3x

The perimeter of a rectangle is 2w + 2l, where w and l are width and length, respectively.

Perimeter: 2w + 2l = 56 cm

Now use the values of w and l derived above:

2w + 2l = 56 cm

2(x) + 2(3x) = 56 cm

8x = 56 cm

x = 7 cm

The width (x) is = 7 cm

CHECK:

Width = 7 cm

Length = 21 cm

Perimeter = 2*7 cm + 2*21 cm

Perimeter = (14 + 42) cm

Perimeter = 56 cm

3. Find the value of 2πgl​​ when π=371​,1=98 and g=32

2πgl​​

2πgl​​ = 2*(371)(32)(98)

2πgl​​ = 1163456

4. I=R2+W2L2​E

-R2=-I+W2L2​E

-R= (-I+W2L2​E)/2

R= - (-I+W2L2​E)/2

R= (I-W2L2​E)/2