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3 years ago

9

Karabo is training by running for the Comrades Marathon,he starts his training by running 40km per week.Each week he increases t

he distance covered by 10km 1.Write down the formula to calculate the distance he runs in n-th week.

1 answer:

Maru [420]3 years ago

4 0

Answer:

40 + (n-1)10

Step-by-step explanation:

Correct me if im wrong but im pretty sure this is it.

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Scilla [17]

Answer:

63

Step-by-step explanation:

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3 years ago

Parallel lines t and u are cut by two transversals, r and s, which intersect line u at the same point.

Bezzdna [24]

Answer:

D

Step-by-step explanation:

it was right on edge

8 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

You must scuba dive to the entrance of your room at Jules' Undersea Lodge in Key Largo, Florida. The diver is 1 foot deeper than

liubo4ka [24]

Answer:

the elevation of the entrance is -21

Step-by-step explanation:

The computation of the elevation of the entrance is shown below;

-15 = -1 + 2 ÷ 3e

e = -21

Hence, the elevation of the entrance is -21

We simply applied the above equation so that we can determine the elevation of the entrance

5 0

3 years ago

(4,?) is on the line below. find the other half of the coordinate. y=2/7x+3

Savatey [412]

Since we have (4,?) we know x=4. Substitute this into the equation and solve for y.

y= 2/7*4+3

y= 2/7*4/1+3

y= 8/7+3

y= 8/7 + 3/1

y= 16/14 + 42/14

y= 58/14 or 4.14

8 0

3 years ago