All categories

3 years ago

HURRY! What are all the possible rational solutions for x^4-3x^2+2x5=0

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

4 0

Answer: x = 1

x =(-3-√-15)/4=(-3-i√ 15 )/4= -0.7500-0.9682i

x =(-3+√-15)/4=(-3+i√ 15 )/4= -0.7500+0.9682i

x2 = 0

Step-by-step explanation:

You might be interested in

Kayla tutors for $20 per hour she spends $50 on transportation how much does she earn is she tutors for x hours

natima [27]

The equation to solve this is 20x-50

7 0

4 years ago

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

a bookstore took in$ 167 on the sale of 5 copies of a new cookbook and 3 copies of a new novel the next day it took in $ 89 on t

PSYCHO15rus [73]

I am going to use C to represent cookbook and N to represent N. I find that easier to remember which is which.

Day 1: 5C + 3N = 167

Day 2: 3C + 1N = 89

We need to solve one of these equation for either the C or N. I always choose the easiest one! Day 2 looks like the one.

3C + 1N = 89 (I am doing to solve for N because we won't have a fraction)

1N=89-3C

N=89-3C

Now we take this solution for N and put it into our first equation.

5C + 3(89-3C) = 167 (We need to distribute)

5C + 267 - 9C = 167 (Use subtraction to move C values to the right and numbers to the left)

267-167 = 9C-5C

100 = 4C

25 = C $25 for the Cookbooks.

Now, we have to go back and solve for N by putting $25 in for C in the second equation.

N=89-3(25)

N=89-75

N=14 dollars for each novel.

Check by putting both back into the first equation:

5C + 3N = 167

5(25) + 3(14) = 167. It checks out!

3 0

4 years ago

Avery prepares 2 equal-size oranges for the bats at the zoo. one dish has 3/8 of an orange. another dish has 1/4 of an orange. W

Scorpion4ik [409]

First you convert 1/4 so it would have the same denominator as 3/8:
1/4=2/8
Now you compare the fractions
2/8 ? 3/8
3/8 is more, so the dish with 3/8 of an orange has more.
Hope this helps!

8 0

4 years ago

An energy drink company claims that its product increases students' memory levels. To support its claims, the company issues adv

VMariaS [17]

Don’t know if the people surveyed were students or not

3 0

3 years ago