Sophia Learning Milestone 5 Questions and Answers Already Passed

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You passed this Milestone 21 questions were answered correctly. 1 question was answered incorrectly. 1 Find the sum of the first 10 terms of the following geometric sequences: RATIONALE This is ... the formula to find the sum of a finite geometric sequence. We will use information from the given sequence to find values for , , and . Let's start by finding , the value of the first term. In the above sequence, the first term is . So we will substitute for in the sum of a geometric sequence formula. Next, let's determine the variable . To find , divide the value of any term by the value of the term before it to find the a subscript 1 r n a subscript 1 a subscript 1 r r 2/5/2021 Sophia :: Welcome https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7789171 2/29 common difference. For example, so . Finally, we need to review how many terms we want to consider, which will be . We are asked to find the sum of the first 10 terms, so . We can now substitute values in for , , and to solve for . Once the values for , , and have been plugged into the sum formula, we can simplify the numerator. to the power of is . Next, evaluate the subtraction in both the numerator and denominator. minus is and minus is . Then, divide the numerator and denominator. The negative values in the numerator and denominator cancel to result in a positive value of . Finally, multiply this by to find the sum. The sum of the first ten terms in the sequence is . CONCEPT Sum of a Finite Geometric Sequence 2 Suppose we have two functions: and . Find the value of . RATIONALE n n equals 10 a subscript 1 r n S subscript n a subscript 1 r n 2 10 1024 1 1 2/5/2021 Sophia :: Welcome https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7789171 3/29 To evaluate , evaluate and separately, and then multiply the values together. Start by evaluating first by substituting for in the given function. is plugged in for all instances of in the function . Next, evaluate the exponent. squared is . Then, add and together. plus is . Repeat this process for by substituting for in the given function. is plugged in for all instances of in the function . Next, evaluate the multiplication. times is . Then, add and together. plus is . Finally multiply the results of and together. We know that and . Multiply these values together. times is . CONCEPT Multiplying and Dividing Functions 3 Evaluate the following expression using the properties of logarithms. RATIONALE 2/5/2021 Sophia :: Welcome https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7789171 4/29 To evaluate this expression, recall that logarithmic expressions can be re-written as exponential expressions. We'll apply the following relationship to each individual term in the expression. If we have a logarithmic expression in the form it can be rewritten as . Let's apply this to the first term, . tells us that raised to some number, , equals . raised to the power of is , so is equal to . We can repeat this process with the next term, . tells us that raised to some number, , equals . raised to the power of is , so is equal to . Repeat this one more time for the last term, . tells us that raised to some number, , equals raised to the power of is , so is Substitute the calculated in for the log expressions to evaluate. Once the values are substituted, evaluate to addition. The expression evaluates to 7. CONCEPT Introduction to Logarithms 4 Consider the function . Find the formula for the inverse of this function. log subscript b open parentheses y close parentheses equals x b to the power of x equals y x x x 2/5/2021 Sophia :: Welcome https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7789171 5/29 RATIONALE To find the inverse of a function, you can write the function as , swap the variables and , and then rewrite the equation with on one side. First, start by swapping with . Here is the function written as an equation where . Next, we will swap the variables, and . Now that the variables are swapped, we will manipulate this equation to place on one side of the equation. We'll start by squaring both sides to undo the radical. When a square root is squared, the result is the expression under the radical. Next, we will add to both sides to undo the subtraction of . We have now isolated the variable to one side of the equation, which results in the inverse function. This is the inverse of . CONCEPT Finding the Inverse of a Function 5 Consider the function . What are the domain and range of this function? [Show More]

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