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3 years ago

Given the 3rd term =3.2 and d=-0.4, find the fourth term.

Mathematics

1 answer:

Marat540 [252]3 years ago

3 0

That is the solution

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Please help solve this system of equations

stepan [7]

Make a substitution:

$\begin{cases}u=2x+y\\v=2x-y\end{cases}$

Then the system becomes

$\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}$

Simplifying the equations gives

$\begin{cases}\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81}{182}\\\\\dfrac{4\sqrt[3]{v^4}}{u^2-v^2}=\dfrac1{182}\end{cases}$

which is to say,

$\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81\times4\sqrt[3]{v^4}}{u^2-v^2}$

$\implies\sqrt[3]{\left(\dfrac uv\right)^4}=81$

$\implies\dfrac uv=\pm27$

$\implies u=\pm27v$

Substituting this into the new system gives

$\dfrac{4\sqrt[3]{v^4}}{(\pm27v)^2-v^2}=\dfrac1{182}\implies\dfrac1{v^2}=1\implies v=\pm1$

$\implies u=\pm27$

Then

$\begin{cases}x=\dfrac{u+v}4\\\\y=\dfrac{u-v}2}\end{cases}\implies x=\pm7,y=\pm13$

(meaning two solutions are (7, 13) and (-7, -13))

8 0

2 years ago

What is the positive solution of x square minus 36 equals 5x

777dan777 [17]

Answer:

⇒x=9 (positive solution)

Explanation:

x2−36=5x

→x2−36−5x=0

Factor the expression:

We get:

(x−9)(x+4)=0

First solution:

⇒(x−9)=0x+4

⇒(x−9)=0

⇒x=9

3 0

3 years ago

Find the coordinates of k

marin [14]

If you plot the coordinates on a piece of graph paper your answer would come out too (1,-8)

4 0

2 years ago

Nancy was keeping track of how many miles she ran each month. In April, she ran 25 miles. In May, she ran 34 miles, and in June,

Elanso [62]

Answer:

She ran 101 miles within the 3 months. an estimate would be around 100

4 0

2 years ago

7227=7272+7272+7282=

Dmitriy789 [7]

Answer: Uhhhhhh

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers