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4 years ago

Kevin paid $7.89 for 3 fruit salads. Each salad cost the same amount. How much did Kevin pay for each fruit salad?

Mathematics

2 answers:

olasank [31]4 years ago

4 0

He paid $2.63 for each salad

Sergeeva-Olga [200]4 years ago

3 0

Each salad costs $2.63

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Determine whether the following series converges. Summation from k equals 2 to infinity (negative 1 )Superscript k Baseline Star

Ket [755]

Answer:

$a_k=\left|\dfrac{k^2-3}{k^2+4}\right|;\text{ is nondecreasing for $k>2$}$

$\lim\limits_{k \to \infty} a_k =1$

The series does not converge

Step-by-step explanation:

Given ...

$S=\displaystyle\sum\limits_{k=2}^{\infty}{x_k}\\\\x_k=(-1)^k\cdot\dfrac{k^2-3}{k^2+4}\\\\a_k=|x_k|$

Find

whether S converges.

Solution

The (-1)^k factor has a magnitude of 1, so the magnitude of term k can be written as ...

$\boxed{a_k=1-\dfrac{7}{k^2+4}}$

This is non-decreasing for k>1 (all k-values of interest)

As k gets large, the fraction tends toward zero, so we have ...

$\boxed{\lim\limits_{k\to\infty}{a_k}=1}$

Terms of the sum alternate sign, approaching a difference of 1. The series does not converge.

7 0

3 years ago

Number 13. What is the value of x? Please help

Maru [420]

Both angles on the base are 72 which means X=36

8 0

3 years ago

Find m/ELM if m/ELM = 15x - 1, m/KLE = 20°, and m/KLM = 17x - 1.

Misha Larkins [42]

Answer:

∠ ELM = 149°

Step-by-step explanation:

∠ KLM = ∠ KLE + ∠ ELM , substitute values

17x - 1 = 20 + 15x - 1

17x - 1 = 15x + 19 ( subtract 15x from both sides )

2x - 1 = 19 ( add 1 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

Then

∠ ELM = 15x - 1 = 15(10) - 1 = 150 - 1 = 149°

6 0

3 years ago

Solve the equation 9b2 + 30b + 25 = 0.

jeka57 [31]

Factor the equation into...
(3b+5)(3b+5)=0
Each factor 3b+5=0 so 3b=-5 so b=-5/3

Check:
9(-5/3)^2+30(-5/3)+25=
9(25/9)-50+25=
25-50+25=0
It checks,

So answer is A.-5/3

5 0

3 years ago

The length of a rectangle is 45 inches and the width is 8 inches. a similar rectangle has a width of 24 inches. what is the peri

jenyasd209 [6]

If I'm correct t would be 135...

3 0

3 years ago