Ask question

Ask question

All categories

3 years ago

5

Two cars left the city for a suburb, 480 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the

speed of the other, and that is why it arrived at the suburb 2 hour earlier than the other car. Find the speeds of both cars.

1 answer:

Alex_Xolod [135]3 years ago

4 0

The speed of both the cars are 80km/h and 60km/h

<u>Step-by-step explanation:</u>

Let the speed of one car be 'a' and the speed of other car be 'b'.

The total distance (d) = 480km

It is given that the speed of one car is 20km/h faster than the other.

We can write,

a = b+20

The slower car takes 2 hrs more to reach the suburb than the other car.

Let the time taken by the fastest car be t

Speed = distance/time

So,

a = 480/ t

b = 480/(t+2)

We got the values of a and b.

a = b+20

480/t = (480/(t+2)) + 20

Taking LCM on the right side.

480/t = (480 + 20t + 40) / (t+2)

480(t+2) = (480+20t+40) t

480t + 960 = 480t + 20t(t) + 40t

20t(t) + 40t - 960 = 0

Divide the whole equation by 20 to simplify the equation.

t(t) + 2t - 48 = 0

Solve the quadratic equation by splitting the middle terms.

t(t) + 8t - 6t - 48 = 0

t(t + 8) - 6(t + 8) = 0

(t- 6) (t+8) =0

t = 6 (or) -8

t is time and cannot be negative. So t= 6hrs

a = 480/t

a = 480/ 6 = 80

the speed of the fastest car is 80km/hr

a = b + 20

b = a - 20

b = 80 - 20

b = 60km/h

You might be interested in

show whether each equation has one solution, infinitely, many solutions or no solutions: 2x+7=-8x-9+10x

alexira [117]

Answer:

The statement is <em>false</em>
There is<em> no solution</em>

Step-by-step explanation:

Step 1: <em>Collect the like terms</em>

2x+7 = -8x-9+10x

2x+7 = 2x-9

Step 2: <em>Cancel</em><em> </em><em>equal</em><em> </em><em>terms</em><em> </em><em>of</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>equation</em>

2x+7 = 2x-9

7 = -9

Result: The statement is <em>false</em> and there is <em>no solution</em> as 7 is <em>not equal</em> to -9.

I hope this helped ! ;)

3 0

3 years ago

BaLLatris [955]

a) The polynomial in expanded form is $f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ .

b) The slant asymptote is represented by the linear function is $y = -x + 1$ .

c) There is a discontinuity at $x = 2$ with a slant asymptote.

a) In this question we are going to use the Factor Theorem, which establishes that polynomial are the result of products of binomials of the form $x-r_{i}$ , where $r_{i}$ is the i-th root of the polynomial and the grade is equal to the quantity of roots. Therefore, the polynomial $f(x)$ has the following form:

$f(x) = (x-6)\cdot (x+1)\cdot (x+3)$

And the expanded form is obtained by some algebraic handling:

$f(x) = (x-6)\cdot (x^{2}+4\cdot x +3)$

$f(x) = x\cdot (x^{2}+4\cdot x + 3)-6\cdot (x^{2}+4\cdot x +3)$

$f(x) = x^{3}+4\cdot x^{2}+3\cdot x -6\cdot x^{2}-24\cdot x -18$

$f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ (1)

The polynomial in expanded form is $f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18$ .

b) In this question we divide the polynomial found in a) (in factor form) by the polynomial $x^{2}-x -2$ (also in factor form). That is:

$g(x) = \frac{(x-6)\cdot (x+1)\cdot (x+3)}{(x-2)\cdot (x+1)}$

$g(x) = \frac{(x-6)\cdot (x+3)}{x-2}$ (2)

The slant asymptote is defined by linear function, whose slope ( $m$ ) and intercept ( $b$ ) are determined by the following expressions:

$m = \lim_{x \to \pm \infty} \frac{g(x)}{x}$ (3)

$b = \lim_{x \to \pm \infty} [g(x)-x]$ (4)

If $g(x) = \frac{(x-6)\cdot (x+3)}{x-2}$ , then the equation of the slant asymptote is:

$m = \lim_{x \to 2} \frac{(x-6)\cdot (x+3)}{x\cdot (x-2)}$

$m = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x^{2}-2\cdot x} \right)$

$m = 1$

$b = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x-2}-x \right)$

$b = \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x - 18-x^{2}+2\cdot x}{x-2}\right)$

$b = \lim_{n \to \infty} \left(\frac{-x-18}{x-2} \right)$

$b = -1$

The slant asymptote is represented by the linear function is $y = -x + 1$ .

c) The number of discontinuities in rational functions is equal to the number of binomials in the denominator, which was determined in b). Hence, we have a discontinuity at $x = 2$ with a slant asymptote.

We kindly invite to check this question on asymptotes: brainly.com/question/4084552

8 0

2 years ago

Please help soon!!! Will mark brainliest!!!

BartSMP [9]

REVISED ANSWER.

In the picture, I have drawn on the example given. the RC and PD are the same because They are across from each other perfectly. So the answer is still PD=400m but if there can be two answers then I would have to say another possiblity would be 200m for the diameter of the pond. The wording of this problem is tricky and the picture can throw you off a bit but I did my best to answer properly here.

So if you could mark brainliest that would be awesome.

4 0

3 years ago

What is the proportion for 105/280=x/8

saul85 [17]

Answer:

3

Step-by-step explanation:

we know that product do extreme is equal to the product of means

105:280::x:8

105*8=280x

840=280x

x=840/280

x=3

4 0

4 years ago

A country's population in 1993 was 72 million. In 1996 it was 76 million. Estimate the population in 2003 using exponential grow

miss Akunina [59]

We use the formula for exponential growth:
P = Po exp(kt)
Using the population data from 1993 to 1996, we can solve for the growth rate k
76 = 72 exp(k(3))
76/72 = exp(3k)
ln (76/72) = 3k
k = ln(76/72) / 3 = 0.0180

In 10 years (2003), the population will be:
P = Po exp(0.0180t)
P = 72 exp(0.0180(10))
P = 86.22 million

8 0

4 years ago

Read 2 more answers