Foam Play Structure

Help me please, also make sure its right

netineya [11]

The answer is D. trust me, i’m super good at math.

4 0

3 years ago

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

3 years ago

60 POINTS!!!! PLEASE HELP URGENT

sammy [17]

Using linear combination method to solve the system of equations 3x - 8y = 7 and x + 2y = -7 is (x, y) = (-3, -2)

<h3><u>Solution:</u></h3>

Given that, a system of equations are:

3x – 8y = 7 ⇒ (1) and x + 2y = - 7 ⇒ (2)

We have to solve the system of equations using linear combination method and find their solution.

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated. Addition or subtraction can be used to perform a linear combination.

Now, let us multiply equation (2) with 4 so that y coefficients will be equal numerically.

4x + 8y = -28 ⇒ (3)

Now, add (1) and (3)

3x – 8y = 7

4x + 8y = - 28

----------------

7x + 0 = - 21

7x = -21

x = - 3

Now, substitute "x" value in (2)

(2) ⇒ -3 + 2y = - 7

2y = 3 – 7

2y = - 4

y = -2

Hence, the solution for the given two system of equations is (-3, -2)

3 0

3 years ago

How much interest is earned on $300 at 6% for 6 years?

miskamm [114]

Answer:

108 dollars

Step-by-step explanation:

First, let's convert 6% to a decimal.

We get 0.06 because we multiplied (or divided by 100) it by 1/100.

Now, let's do 0.06 * 300 to get interest on one year. This equals to 18$

Let's now do 18 * 6 to get

108 dollars

7 0

3 years ago

A target at a shooting range is 60 yards away and 12 feet high. At what angle must the rifle be set to hit the target? Round to

Sunny_sXe [5.5K]

Answer:

The angle must be at 3.81°

Step-by-step explanation:

The horizontal distance of the shooting range is 60 yards

The height of the target is 12ft.

We'll have to convert the value of the height from ft to yards.

1 yards = 3 foot

X yards = 12ft

X = 4yards.

The height of the target is 4 yards.

Now, to find the angle at which the shooter makes with the zenith of the target(height), we'll have to use use SOHCAHTOA

To know which of the rules we'll follow, a pictorial illustration of the values will help

(See attached document for better illustration).

From the diagram, we can see we have values at both opposite and adjacent.

Opposite = 4

Adjacent = 60

Hence we can use Tanθ = opposite/ adjacent

Tanθ = 4 / 60

Tanθ = 0.067

θ = Tan⁻0.067

θ = 3.81°

The angle at which the rifle must be set to hit the target is 3.81°

5 0

3 years ago