Pleasee helpppㅤㅤㅤㅤㅤㅤㅤ

worty [1.4K]

Hey there!

According to our customary units of miles, 1 mile is equal to 5,280 feet - and 3 feet is a yard. That means, we have to divide 5,280 by 3 to figure out how many yards are in a mile:

5280/3 = 1760

That means that one mile is 1760 yards. But we're not finished yet. It says 1/5 miles, not one mile. Therefore, we take one half of the total distance in yards of a mile and add it to that 1760, because it's 1.5, or 1-and-a-half. Which, in technical terms means "1-plus-a-half".

We have:

1760 + 1760/2 = 1760 + 880 = 2640

Therefore, 1/5 miles, since it's 2640 yards, is greater than the 2500 yards specified in the question.

Hope this helps!

6 0

4 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

3 years ago

Help me for number 20 and 21 and also show work

Dmitrij [34]

32.4*0.69=22.149

...

45=3*3*5, 63=3*3*7 The greatest common factor is the product of shared primes of the numbers prime factorization. In this case 3*3=9 is the product of shared primes so the greatest common factor is 9

4 0

3 years ago

Christian is going to an amusement park. The price of admission into the park is $35, and once he is inside the park, he will ha

djyliett [7]

59 because if you do 3x8 that equals 24 and then you do 35+24 that equals 59

5 0

3 years ago

If ABCD is an isosceles trapezoid, what is the value of x

Grace [21]

Answer:

Since we know that ABCD is an isosceles trapezoid, we can also asume that its diagonals have the same length, which means:

AC = BD

=> 7x - 21 = 5x + 13

=> 7x - 5x = 21 + 13

=> 2x = 34

=> x = 34/2 = 17

So the answer is C.

4 0

3 years ago

Read 2 more answers