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2 years ago

You have to pay 15p to park for every 8 minutes. How much would I pay to park for 90 minutes?

Mathematics

1 answer:

Ahat [919]2 years ago

3 0

Answer:

I am not exactly sure but it is around 170p

Step-by-step explanation:

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In a G.P the difference between the 1st and 5th term is 150, and the difference between the

liubo4ka [24]

Answer:

Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

$a$ ,
$a\cdot r$ ,
$a \cdot r^2$ ,
$a \cdot r^3$ ,
$a \cdot r^4$ .

First equation:

$a\, r^4 - a = 150$ .

Second equation:

$a\, r^3 - a\, r = 48$ .

Rewrite and simplify the first equation.

$\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}$ .

Therefore, the first equation becomes:

$a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150$ ..

Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

Therefore, the second equation becomes:

$a\, r\, \left(r^2 - 1\right) = 48$ .

Take the quotient between these two equations:

$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

$\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}$ .

$8\, r^2 - 25\, r + 8 = 0$ .

Either $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ or $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ .

Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}$ .

4 0

2 years ago

Three times a number, minus 5 is equal to two times the number, plus 7

vitfil [10]

3x - 5 = 2x + 7 i call the number "x"
3x = 2x + 12
1x = 12
x = 12 the number is 12

6 0

3 years ago

DONT SKIP URGENT , WILL GIVE BRAINLIEST

LekaFEV [45]

Answer:

The distance between C and D is 6 units

6 0

2 years ago

Read 2 more answers

The table below shows how much money Addison earns shoveling snow for

julia-pushkina [17]

Answer:

121

Step-by-step explanation:

Since the pattern is that for each 1 driveway, she makes $11, we multiply 11*11 and get 121. We determine that each driveway makes her $11 by dividing the amount earned by the driveways shoveled.

4 0

2 years ago

A cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to one-sixth its hei

Liono4ka [1.6K]

Answer:

1/216

Step-by-step explanation:

The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.

<h3>Linear scale factor</h3>

If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.

<h3>Volume scale factor</h3>

The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...

(1/6)³ = 1/216

The volume of the filled portion of the cup is 1/216 of the volume of the cup.

8 0

1 year ago