1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gogolik [260]
3 years ago
15

Simplify the complex fraction.

Mathematics
1 answer:
lilavasa [31]3 years ago
5 0

Given:

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}

To find:

The simplified fraction.

Solution:

Step 1: Simplify the numerator

$\frac{(4 r)^{3}}{15 t^{4}}=\frac{4^3 r^{3}}{15 t^{4}}=\frac{64 r^{3}}{15 t^{4}}

Step 2: Simplify the denominator

$\frac{16 r}{(3 t)^{2}}=\frac{16 r}{3^2 t^{2}}= \frac{16 r}{9 t^{2}}

Step 3: Using step 1 and step 2

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}} \right)}

Step 4: Using fraction rule:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}

$\frac{\left(\frac{64 r^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{9 t^{2}}\right)}=\frac{64r^3 \cdot 9t^2}{16 r \cdot 15 t^4}

Cancel the common factor r and t², we get

           $=\frac{64 r^{2} \cdot 9 }{16  \cdot 15 t^2 }

Cancel the common factors 16 and 3 on both numerator and denominator.

           $=\frac{4 r^{2} \cdot 3 }{  5 t^2 }

           $=\frac{12 r^{2}  }{  5 t^2 }

$\frac{\left(\frac{(4 r)^{3}}{15 t^{4}}\right)}{\left(\frac{16 r}{(3 t)^{2}}\right)}=\frac{12 r^{2}  }{  5 t^2 }

The simplified fraction is \frac{12 r^{2}  }{  5 t^2 }.

You might be interested in
Mario has a box of blocks 8 inches long, 6 inches wide, and 7 inches high.
Aleksandr [31]

Answer:

Volume = length× width× height

v=lwh

v=8×6×7

v=48×7

v= 336inches

3 0
3 years ago
How many solutions does the equation 6x-10=2(3x+8) have?
ivanzaharov [21]

Answer:

No solution

Step-by-step explanation:

As 6x on lhs and 2×3x on the rhs are equal and cancel each other

6 0
2 years ago
A sandwich shop offers a choice of 4 types of bread, 8 types of meat, and 4 types of cheese. How many different sandwiches could
Fantom [35]

4x8x4=

128

...............

7 0
3 years ago
Read 2 more answers
PLEASE HELP <3
quester [9]

Answer:

-403/40

or

-10 3/40

or

-10.075

3 0
2 years ago
Read 2 more answers
Can you help stuck on this question for a while ​
stepladder [879]

Answer:

Option B

Step-by-step explanation:

Length of the rectangular sand box is given by the function,

F(x) = 3x³ + 6x - 2

Width of the sand box is represented by the function,

W(x) = 2x² - 4

Area function for the sand box will be,

Area of a rectangle = Length × Width

F(x) × W(x) = (3x³ + 6x - 2)(2x² - 4)

                 = 2x²(3x³ + 6x - 2) - 4(3x³ + 6x - 2)

                 = 6x⁵+ 12x³ - 4x²- 12x³- 24x + 8

                 = 6x⁵- 4x²- 24x + 8

Therefore, Area function will be represented by a polynomial degree of 5.

Option B will be the answer.

3 0
2 years ago
Other questions:
  • A half-marathon 13 miles, how many kilometers is that?
    15·2 answers
  • A brick of mass 4 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is t
    12·2 answers
  • GEOMETRY QUESTION: PLEASE ANSWER FAST!
    10·1 answer
  • 1
    10·1 answer
  • Next question <br> lets keep going
    5·2 answers
  • 1 5/16 + 1 5/16=_____
    14·1 answer
  • Given the position of 2 points of a triangle with the lengths of all side and angle of each side how can you find the 3rd positi
    14·1 answer
  • 16 is what part of 96?
    14·2 answers
  • Find the volume of this triangular prism.<br> 6 cm<br> 7 cm<br> 10 cm
    15·1 answer
  • Inverse of f(x)=2 1/2-3 1/3x and what is its x intercept
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!