Mathematics, 17.07.2020 16:01 any80

The distance needed for a car to stop depends on how fast the car is travelling. This distance can be calculated by adding the thinking distance and the braking distance. For example: at 30 miles per hour Here are the formulae to work out the thinking distance and the braking distance for a car travelling at miles per hour. Thinking distance = feet Braking distance = feet A car is travelling so that its braking distance is 125 feet. How fast is the car travelling? miles per hour

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Answer from: vaehcollier

Missing Parts

Here are the formulae to work out the thinking distance and the braking distance for a car traveling at V miles per hour.

Thinking distance = V feet

$\text{Braking distance = }\dfrac{V^2}{20}$ feet$

(a) A car is traveling at 70 miles per hour. What is the total stopping distance for this car? feet

(b) A different car is traveling so that its braking distance is 125 feet. How fast is the car traveling? miles per hour

(a)2520 feet

(b)50mph

Step-by-step explanation:

Total Stopping Distance = Thinking Distance + Braking Distance

Given that for a car traveling at V miles per hour:

Thinking distance = V feet

$\text{Braking distance = }\dfrac{V^2}{20}$ feet$

We have:

$\text{Total Stopping Distance=} (V+\dfrac{V^2}{20})$ feet$

(a)V=70 miles per hour

$\text{Total Stopping Distance=} 70+\dfrac{70^2}{20}$=2520 feet$

The total stopping distance for a car traveling at 70 miles per hour is 2520 feet.

(b)

Braking Distance = 125 feet

$\text{Braking distance = }\dfrac{V^2}{20}$ feet$

Therefore:

$\dfrac{V^2}{20}=125\\\\V^2=125\times 20\\V^2=2500\\V^2=50^2\\V=50$ miles per hour$

A car with a braking distance of 125 feet is traveling at a speed of 50mph.

Answer from: Quest

b: |12 – x| ≤ 0.25

step-by-step explanation:

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

Answer from: Quest

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,

b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,

and solve for the variable

* lets solve the problem

∵ $7^{x}=77$

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴ $ln(7^{x})=ln(77)$

- use the rule $ln(a^{n})= nln(a)$

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴ $x=\frac{ln(77)}{ln(7)}=2.23$

* the solution of the equation is 2.23 to the nearest 2 decimal places

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The distance needed for a car to stop depends on how fast the car is travelling. This distance can b...