Question
upstudy study bank question image url

\( \frac { 6 c d ^ { 3 } - ( 10 c ) ^ { 2 } d + 8 c ^ { 4 } } { 2 c ^ { 2 } } = \frac { \square d } { c \square } - \square d + \square c \)

Ask by Evans French. in Canada
Mar 16,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\[ \frac{3d^3}{c} - 50d + 4c^2 \]

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Extra Insights

To solve the equation, let's start by simplifying the left-hand side step-by-step. The given expression is: \[ \frac { 6 c d ^ { 3 } - ( 10 c ) ^ { 2 } d + 8 c ^ { 4 } } { 2 c ^ { 2 } } \] First, simplify \( (10c)^2 \): \[ (10c)^2 = 100c^2 \] Now, substitute back into the expression: \[ \frac { 6 c d ^ { 3 } - 100c^2 d + 8 c ^ { 4 } } { 2 c ^ { 2 } } \] Now, we can divide each term in the numerator by \( 2c^2 \): 1. \( \frac{6cd^3}{2c^2} = \frac{6}{2} \cdot \frac{d^3}{c} = 3 \cdot \frac{d^3}{c} = 3\frac{d^3}{c} \) 2. \( \frac{100c^2 d}{2c^2} = \frac{100}{2}d = 50d \) 3. \( \frac{8c^4}{2c^2} = \frac{8}{2} \cdot c^{4-2} = 4c^2 \) Putting it all together, we have: \[ 3 \frac{d^3}{c} - 50d + 4c^2 \] We want to compare this with: \[ \frac {\square d } { c \square } - \square d + \square c \] Let’s express it in the same structure. We have: - \( 3 \frac{d^3}{c} \) suggests \( \square = 3d^2 \) and \( \square = 1 \). - From \( -50d \), it indicates the coefficient of \( d \) is \( -50 \), thus \( -\square d \rightarrow -50d \), leading to \( \square = 50 \). - Finally, from \( 4c^2 \), this suggests \( \square c = 4c^2 \) implies \( \square = 4 \). Gathering all the squares, we write: \[ \frac {3d^3}{c} - 50d + 4c^2 \] Thus, our solution can be filled as follows: The first square is `3`, the second `50`, and the third `4`. The final result can be expressed as: \[ \frac { 3 d^3 } { c } - 50 d + 4 c^2 \] So, the values to fill in are: \[ 3, 50, 4 \]

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy