All categories

3 years ago

The time t required to drive a certain distance varies inversely with the speed r. if it takes 4 hours to drive the distance at

35 miles per hour, how long it will take to drive the same distance at 45 miles per hour?
A. about 3.11 hours
B. 140 hours
C. about 5.14 hours
D. 393.75 hours

Mathematics

1 answer:

Aleksandr [31]3 years ago

4 0

$\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------$

$\bf \stackrel{\textit{time \underline{t} required to drive a certain distance varies inversely with the speed \underline{r}}}{t=\cfrac{k}{r}}
\\\\\\
\textit{we also know that }
\begin{cases}
t=4\\
r=35
\end{cases}\implies 4=\cfrac{k}{35}\implies 4(35)=k
\\\\\\
140=k\qquad therefore\qquad \boxed{t=\cfrac{140}{r}}
\\\\\\
\textit{now, when \underline{r} = 45, what is \underline{t}?}\qquad t=\cfrac{140}{45}$

You might be interested in

Determine the arithmetic sequence if the fourth term is negative six and the eleventh term is negative thirty four

ICE Princess25 [194]

An arithmetic sequence takes the form

$a_n=a_{n-1}+d$

where $d$ is the common difference between terms. You can solve for $a_n$ in terms of any of the previous terms of the sequence:

$a_n=a_{n-1}+d\implies~a_n=a_{n-2}+2d\implies~a_n=a_{n-3}+3d\implies\cdots\implies~a_n=a_{n-k}+kd$

for some integer $1\le k\le n-1$

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term $a_1$

$a_n=a_1+(n-1)d$

Given that the 4th term is $a_4=-6$ and the 11th term is $a_{11}=-34$ , you have the following system of equations.

$\begin{cases}-6=a_1+(4-1)d\\-34=a_1+(11-1)d\end{cases}$

Solving this system for the two unknowns yields $a_1=6$ and $d=-4$ .

So, the sequence is given explicitly by

$a_n=6+(n-1)(-4)=-4n+5$

3 0

3 years ago

Should i do my teast for 12th grade calculus

Salsk061 [2.6K]

Answer:

attempt it, if it's too hard, sleep

that's what I would do lol

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Please help and explain how to solve these! Thanks

spin [16.1K]

2. C
Slope = 40/8 = 5
Slope of graph c = 5/1 = 5

3. D
Slope = 9/3 = 3
Slope of graph d = 81/27 = 3

3 0

3 years ago

Read 2 more answers

Larry wants to enlarge a cube with edges of 3cm so that it's volume will be 8 times larger. How long must each edge of the enlar

Monica [59]

The answer is 6 inches, 3*3*3 equals 27, the current volume of the cube, 27*8 equals 216, the new volume, 6*6*6 equals 216, so the side lengths equal 6 inches.

6 0

3 years ago

An automated teller machine at a local bank is stocked with $10 and $20 bills. When a customer withdraws $40 from the machine, i

cestrela7 [59]

Answer:

There are 4 possibilities

Step-by-step explanation

Each customer has 2 ways to receive the money. For each way, the other customer has 2 option, giving a total of 2*2 = 4. Here are the possibilities, separating in 2 different cases.

Case 1: customer 1 withdraws 2 $20 bills

option 1.1: customer 1 withdraws 2 $20 bills AND customer 2 withdraws 2 $20 bills

option 1.2: customer 1 withdraws 2 $20 bills AND customer 2 withdraws 4 $10 bills

Case 2: customer 1 withdraws 4 $10 bills

option 2.1: customer 1 withdraws 4 $10 bills AND customer 2 withdraws 2 $20 bills

option 2.2: customer 1 withdraws 4 $10 bills AND customer 2 withdraws 4 $10 bills

options 1.1, 1.2, 2.1 and 2.2 give us a total of four ways for the customers to retrieve thier money.

5 0

3 years ago