Answer:
7 17/49
Step-by-step explanation:
Convert mixed numbers to fractions:
= 90/7 ÷ 7/4
Apply the fraction rule:
= 90/7 * 4/7
Multiply fractions:
90 * 4 / 7 * 7
Simplify:
360/49
Convert improper fractions to mixed numbers:
= 7 17/49
Formula works when n=1
Assume the formula also works, when n=k.
Prove that the formula works, when n=k+1
Since the formula has been proven with n=1 and n=k+1, it is true.
Finding the distance between (-4,2) and (146,52)
Use the distance formula<span> to determine the </span>distance<span> between the two </span>points<span>.
</span><span>Distance= </span>√<span>(<span>x2</span>−<span>x1</span><span>)^2</span>+(<span>y2</span>−<span>y1</span><span>)^2
</span></span>Substitute the actual values of the points<span> into the </span>distance formula<span>.
</span>√<span>((146)−(−4)<span>)^2</span>+((52)−(2)<span>)^2
</span></span>Simplify the expression<span>.
</span>√19400<span>
</span>Rewrite 19400<span> as </span><span><span><span>10^2</span>⋅194</span>.
</span>√10^<span>2⋅194
</span>
Pull terms<span> out from under the </span>radical<span>.
</span>10√<span>194
</span>The approximate<span> value for the </span>distance<span> between the two </span>points<span> is </span><span>139.28389.
</span>
10√<span>194≈139.28389</span>
Answer:
Step-by-step explanation:
The Total Cost formula for the Dealership is
$24 + ($99/hr)h, where h represents the number of hours of labor performed.
That for the Local Mechanic is
$45 + ($89/hr)h
We equate these two formulas so as to determine h, the number of hours elapsed so that the total costs are the same:
24 + 99h = 45 + 89h
Combining like terms, we get:
21 = 188h
Solve for h by dividing both sides by 188:
h = 188/21 = 8.95
The two bills would be equal 8.95 hours after commencement of the work.
<em>Part b</em>:
Dealership: $24 + ($99/hr)h. Evaluate this at 8.95 hrs: $910.05.
The dealership's bill would be more expensive AFTER 8.95 hours, because the rate of change ($99/hr) is greater in that case.
The local mechanic's total bill would be less up until the time that the car has been worked on for 8.95 hours.
$24 + ($99/hr)(8.95 hr) =