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3 years ago

Consider the function represented by the

Mathematics

1 answer:

Jobisdone [24]3 years ago

8 0

Answer:

y -5×8=

3-40

setahu saya

Step-by-step explanation:

I hope you

i'm sorry ya kalo jawaban nya salah

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Find the arc length of the given curve between the specified points. x = y^4/16 + 1/2y^2 from (9/16), 1) to (9/8, 2).

lutik1710 [3]

Answer:

The arc length is $\dfrac{21}{16}$

Step-by-step explanation:

Given that,

The given curve between the specified points is

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

The points from $(\dfrac{9}{16},1)$ to $(\dfrac{9}{8},2)$

We need to calculate the value of $\dfrac{dx}{dy}$

Using given equation

$x=\dfrac{y^4}{16}+\dfrac{1}{2y^2}$

On differentiating w.r.to y

$\dfrac{dx}{dy}=\dfrac{d}{dy}(\dfrac{y^2}{16}+\dfrac{1}{2y^2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}\dfrac{d}{dy}(y^4)+\dfrac{1}{2}\dfrac{d}{dy}(y^{-2})$

$\dfrac{dx}{dy}=\dfrac{1}{16}(4y^{3})+\dfrac{1}{2}(-2y^{-3})$

$\dfrac{dx}{dy}=\dfrac{y^3}{4}-y^{-3}$

We need to calculate the arc length

Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4})^2+(y^{-3})^2+\dfrac{1}{2}}dy}$

$L=\int_{1}^{2}{\sqrt{(\dfrac{y^3}{4}+y^{-3})^2}dy}$

$L= \int_{1}^{2}{(\dfrac{y^3}{4}+y^{-3})dy}$

$L=(\dfrac{y^{3+1}}{4\times4}+\dfrac{y^{-3+1}}{-3+1})_{1}^{2}$

$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

Hence, The arc length is $\dfrac{21}{16}$

6 0

3 years ago

To begin a bacteria study, a petri dish had 2800 bacteria cells. Each hour since, the number of cells has increased by 7.2%. Let

Rudiy27

The function that models exponential growth is:

P(t) = P0*(1 + r)^t, where

P0 = P(0) is the initial value of P

r is the growth rate as a decimal

In our case we have:

P(0) = 2800

r = 0.035 or 3.5%

P(t) = 2800*(1 + 0.035)^t

P(t) = 2800*(1.035)^t

The same exponential function written using y and t is:

y = 2800*1.035^t.

Explanation: https://softmath.com/algebra-word-problems/to-begin-a-bacteria-study-a-petri-dish-had-2800-bacteria

7 0

3 years ago

A certain breed of mouse was introduced onto a small island with an initial population of 320 mice, and scientists estimate that

Viefleur [7K]

Y=2x+320
x being the number of years and 320 being the initial population of mice

7 0

3 years ago

What’s the volume will give brainliest

grigory [225]

I dont know but thanks for your points

6 0

3 years ago

Read 2 more answers

Perfect square trinomial conditions

aev [14]

Step-by-step explanation:

step 1. an example of difference of squares (dos) is (x + y)(x - y) = x^2 - y^2.

step 2. dos must have only 2 square rootable terms and a "-" between them.

step 3. 196x^2 - 121y^2 = (14x + 11y)(14x - 11y) works!

step 4. 5x^2 - 245 = 5(x^2 - 49) = 5(x + 7)(x - 7) works!

step 5. 27w^5 - 75w = 3w(9w^4 - 25) = 3w(3w^2 + 5)(3w^2 - 5) works!

step 6. x^4 - 100y^2 = (x^2 - 10y)(x^2 + 10y) works!

4 0

3 years ago