All categories

1 year ago

Can someone help will mark brainlist

Mathematics

1 answer:

Marina86 [1]1 year ago

3 0

Answer:

See below

Step-by-step explanation:

the common ratio, r <1 so it CONVERGES (r = 1/2 in this series)

sum = a1 ( 1-r^n) / (1-r) = 1000(1-.5^10)/(1-1/2) = ~1998

for n= 30 this results in ~~2000

As it continues, the terms get smaller and smaller and the SUM converges on 2000.

You might be interested in

Help pleaseeeeeeeeeeeeeeeeeeeeeee

statuscvo [17]

Number 1 is Rio Grande and number 2 is St. Lawrence River

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A healthy human heart beats about 1,533,000 times a year. A sparrow's heart beats about 241,776,000 times in a year. About how m

Galina-37 [17]

Answer:

About 158 times

Step-by-step explanation:

Represent the rate of human heart with H and sparrow's heart with S

$H = 1,533,000\ times$

$S = 241,776,000\ times$

Required

Determine how many times faster is S than H

To do this, we simply divide S by H i.e.

$Number = \frac{S}{H}$

$Number = \frac{241,776,000}{1,533,000}$

$Number = 157.714285714$

$Number = 158$ --- approximated

<em>Hence, the sparrow's heart beats about 158 times faster than the human hearts</em>

5 0

2 years ago

HELP ASAP NEEED THE CORRECT ANSWER

Tatiana [17]

The right answer is Option A.

Step-by-step explanation:

Given,

Amount in Jason's account = $300

Bills paid = $\frac{1}{4}$

Remaining balance after bills = -$50

Let,

x be the amount of bills.

Amount in account - Bills paid*Amount of bills = Remaining balance

$300-\frac{1}{4}x=-50\\-\frac{1}{4}x+300=-50$

The equation $-\frac{1}{4}x+300=-50$ can be used to find x.

The right answer is Option A.

Keywords: equation, subtraction

Learn more about subtraction at:

#LearnwithBrainly

5 0

3 years ago

Answer the following question: Melissa was collecting

emmasim [6.3K]

Answer:

1,280

Step-by-step explanation:

5 0

2 years ago

(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

2 years ago