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3 years ago

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A car can travel 300 miles on 10 gallons of gas. The ratio is 300 miles to 10 gallons.Write the ratio given in the problem. Divi

de both quantities in the ratio by the second quantity in the ratio and write the new ratio. What is this ratio called? Explain.

1 answer:

grin007 [14]3 years ago

8 0

Answer:

The new ratio is 30 miles : 1 gallon it called the unit rate

Step-by-step explanation:

* <em>Lets explain what is the unit rate</em>

- A unit rate describes how many units of the first type of quantity

equal to one unit of the second type of quantity

- Ex: 3 miles per hour

$100 per day

15 students per class

- A unit rate is a rate with 1 in the denominator

- Ex: $20 for 5 pens, the rate is 20 : 5 divide the two terms by the

denominator 5, then 20 : 5 = 4 : 1 then unit rate is $4 per pen

* <em>Lets solve the problem</em>

- A car can travel 300 miles on 10 gallons of gas

∴ The rate is 300 miles per 10 gallons

- To find the unit rate divide the two terms of the rate by 10

∴ 300 : 10 = 300/10 : 10/10

∴ 300 : 10 = 30 : 1

∴ <u><em>The unit rate is 30 miles per gallon</em></u>

* The new ratio is 30 miles : 1 gallon it called the unit rate

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Rajesh invested $30,000 into an account that compounds interest monthly at a rate of 2.16%. He has made arrangements to withdraw

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By Evaluating the Compound Interest, we come to know that Rajesh will have enough money in the account to cover all of the required loan payments.

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Now, we have

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3 years ago

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

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Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

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