Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Bridges have spaces between their sections to allow for expansion and contraction caused by temperature variation. This space is known as the gap width. The size of the gap width w(T), in inches, is a linear function of temperature T, in degrees Fahrenheit $open parentheses blank to the power of ring operator end exponent F close parentheses$ . For a certain bridge, the gap width is 2.875 inches at $40 to the power of ring operator end exponent F$ and is 1.875 inches at $100 to the power of ring operator end exponent F$ . Which of the following defines the relationship between temperature and gap width?

$w (T) = - \frac{1}{60} (T - 40) + 2.875$
$w (T) = - \frac{1}{60} (T + 40) - 2.875$
$w (T) = 60 (T - 40) + 2.875$
$w (T) = 60 (T + 40) - 2.875$

The correct answer is: $w left parenthesis T right parenthesis equals negative fraction numerator 1 over denominator 60 end fraction left parenthesis T minus 40 right parenthesis plus 2.875$

HINT: Find slope using the coordinates provided and thus define the relationship.
Complete step by step Solution
Given that the gap width is 2.875 inches at 40°F .
This can be represented as $left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis equals left parenthesis 402.875 right parenthesis$
Likewise the gap width is 1.875 inches at 100°F.
This can be represented as $left parenthesis x subscript 2 end subscript comma y subscript 2 end subscript right parenthesis equals left parenthesis 1001.875 right parenthesis$
We know that slope $m equals fraction numerator y subscript 2 end subscript minus y subscript 1 end subscript over denominator x subscript 2 end subscript minus x subscript 1 end subscript end fraction equals fraction numerator 1.875 minus 2.875 over denominator 100 minus 40 end fraction equals fraction numerator negative 1 over denominator 60 end fraction$
So, $m equals fraction numerator negative 1 over denominator 60 end fraction$
Since slope is $fraction numerator negative 1 over denominator 60 end fraction$ , option C and option D can be eliminated.
In option A,
if we substitute $T$ to be 40, we get w(T) = 2.875 which is one of the given points..
So, $w left parenthesis T right parenthesis equals fraction numerator negative 1 over denominator 60 end fraction left parenthesis T minus 40 right parenthesis plus 2.875 blank$ is the relationship between temperature and gap width.
Hence option A is the correct answer.

Related Questions to study

5x – y = 9
- 60x + 12y = - 108
How many solutions does the given system of equations have?

5x – y = 9
- 60x + 12y = - 108
How many solutions does the given system of equations have?

Which of the following is equivalent to the expression $x to the power of 4 end exponent minus 8 x to the power of 2 end exponent plus 16$ ?
I) $left parenthesis x plus 2 right parenthesis to the power of 2 end exponent left parenthesis x minus 2 right parenthesis to the power of 2 end exponent$
II) $open parentheses x to the power of 2 end exponent minus 4 close parentheses to the power of 2 end exponent$

Which of the following is equivalent to the expression $x to the power of 4 end exponent minus 8 x to the power of 2 end exponent plus 16$ ?
I) $left parenthesis x plus 2 right parenthesis to the power of 2 end exponent left parenthesis x minus 2 right parenthesis to the power of 2 end exponent$
II) $open parentheses x to the power of 2 end exponent minus 4 close parentheses to the power of 2 end exponent$

In the figure shown, point O is the center of the circle. One vertex of the square lies on the circle, and the opposite vertex is point O. If the area of the shaded region is $36 pi minus 18$ , what is the perimeter of the square?

In the figure shown, point O is the center of the circle. One vertex of the square lies on the circle, and the opposite vertex is point O. If the area of the shaded region is $36 pi minus 18$ , what is the perimeter of the square?

parallel

$3 x to the power of 2 end exponent plus x minus 2 equals 0$
The solutions to the quadratic equation above are a and b. What is the value of a + b ?

$3 x to the power of 2 end exponent plus x minus 2 equals 0$
The solutions to the quadratic equation above are a and b. What is the value of a + b ?

How many solutions does the equation $vertical line x plus 7 vertical line equals negative 4$ have?

How many solutions does the equation $vertical line x plus 7 vertical line equals negative 4$ have?

Triangle ABC and Triangle DEF each have an angle measuring $29 to the power of ring operator end exponent$ and an angle measuring $54 to the power of ring operator end exponent$ , as shown above. Which of the following statements is sufficient to prove triangle ABC is congruent to triangle DEF ?

Triangle ABC and Triangle DEF each have an angle measuring $29 to the power of ring operator end exponent$ and an angle measuring $54 to the power of ring operator end exponent$ , as shown above. Which of the following statements is sufficient to prove triangle ABC is congruent to triangle DEF ?

parallel

Dana is riding in a 100 -mile-long bicycle race. The function $f$ defined by f(x) = 100 - 18x models the number of miles that Dana has remaining $x$ hours after she starts the race. What is the best interpretation of f(2) = 64 ?

Dana is riding in a 100 -mile-long bicycle race. The function $f$ defined by f(x) = 100 - 18x models the number of miles that Dana has remaining $x$ hours after she starts the race. What is the best interpretation of f(2) = 64 ?

An advertising agency guarantees that its services will increase website traffic by 3.5% compared to each previous week. Which type of function best models the weekly guaranteed website traffic as the number of weeks increases?

An advertising agency guarantees that its services will increase website traffic by 3.5% compared to each previous week. Which type of function best models the weekly guaranteed website traffic as the number of weeks increases?

x + 2y = 10
2x – y = 5
The solution to the given system of equations is (x, y). What is the value of 3x + y ?

x + 2y = 10
2x – y = 5
The solution to the given system of equations is (x, y). What is the value of 3x + y ?

parallel

If 7x + 21 = - 2, what is the value of x + 3 ?

If 7x + 21 = - 2, what is the value of x + 3 ?

For the linear function f, f(2) = 10 and the graph of y = f(x) in the xy - plane has a slope of 3 . Which equation defines f ?

For the linear function f, f(2) = 10 and the graph of y = f(x) in the xy - plane has a slope of 3 . Which equation defines f ?

The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown.

What is an equation of the line of best fit?

The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown.

What is an equation of the line of best fit?

parallel

For the linear function, f, the table shows several values of x and their corresponding values of f(x). What is the y- intercept of the graph of y = f(x) in the $x y$ -plane?

For the linear function, f, the table shows several values of x and their corresponding values of f(x). What is the y- intercept of the graph of y = f(x) in the $x y$ -plane?

The frequency table above shows the distribution of the actual number of fluid ounces of water in a random sample of 8020 -ounce bottles of the water at a bottling plant. Bottles are only sold if they contain at least 19.8 but no more than 20.2 fluid ounces of water. If the proportion of bottles that can be sold is the same for the sample and the 16,000 20-ounce bottles produced at the plant each day, how many of the 16,000 bottles cannot be sold?

The frequency table above shows the distribution of the actual number of fluid ounces of water in a random sample of 8020 -ounce bottles of the water at a bottling plant. Bottles are only sold if they contain at least 19.8 but no more than 20.2 fluid ounces of water. If the proportion of bottles that can be sold is the same for the sample and the 16,000 20-ounce bottles produced at the plant each day, how many of the 16,000 bottles cannot be sold?

A local restaurant gives teachers a 20% discount on all their meals. If a teacher pays $14.00 for a meal after the discount was applied, what was the price of the meal before the discount?

A local restaurant gives teachers a 20% discount on all their meals. If a teacher pays $14.00 for a meal after the discount was applied, what was the price of the meal before the discount?

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.