## Question

Simplify: $-3 \\sqrt{18}-\\sqrt{8}+2 \\sqrt{8}+2 \\sqrt{8}$.

## Response

To simplify \( -3 \sqrt{18} - \sqrt{8} + 2 \sqrt{8} + 2 \sqrt{8} \):

1. Combine like terms involving \( \sqrt{8} \):
   \[
   -\sqrt{8} + 2\sqrt{8} + 2\sqrt{8} = (2 + 2 - 1)\sqrt{8} = 3\sqrt{8}.
   \]

2. Simplify \( \sqrt{18} \) and \( \sqrt{8} \) by factoring out perfect squares:
   \[
   \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}, \quad \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}.
   \]

3. Substitute back into the expression:
   \[
   -3\sqrt{18} + 3\sqrt{8} = -3(3\sqrt{2}) + 3(2\sqrt{2}) = -9\sqrt{2} + 6\sqrt{2}.
   \]

4. Combine terms:
   \[
   -9\sqrt{2} + 6\sqrt{2} = -3\sqrt{2}.
   \]

The simplified expression is:
\[
\boxed{-3\sqrt{2}}
\]

## Question

Find the angle measure to the nearest degree given $\\sin \\mathrm{Y}=0.6561$.

## Response

To find the angle \( Y \) where \( \sin Y = 0.6561 \), we use the inverse sine function (\( \arcsin \)).

1. Apply the inverse sine:
   \[
   Y = \arcsin(0.6561)
   \]

2. Calculate \( Y \) using a calculator:
   \[
   Y \approx 41^\circ
   \]

The angle measure is approximately:
\[
\boxed{41^\circ}
\]

## Question

Given $p(t)=-2 \\cdot 4^{2 t+1}+1$, find $p(-2)$.

## Response

To evaluate \( p(-2) \) given \( p(t) = -2 \cdot 4^{2t+1} + 1 \), follow these steps:

### Step 1: Substitute \( t = -2 \) into \( p(t) \):
\[
p(-2) = -2 \cdot 4^{2(-2) + 1} + 1
\]

### Step 2: Simplify the exponent:
\[
2(-2) + 1 = -4 + 1 = -3
\]
So:
\[
p(-2) = -2 \cdot 4^{-3} + 1
\]

### Step 3: Simplify \( 4^{-3} \):
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64}
\]

### Step 4: Substitute \( 4^{-3} \) into \( p(-2) \):
\[
p(-2) = -2 \cdot \frac{1}{64} + 1
\]

### Step 5: Simplify the multiplication:
\[
-2 \cdot \frac{1}{64} = -\frac{2}{64} = -\frac{1}{32}
\]

### Step 6: Add \( -\frac{1}{32} \) and \( 1 \):
\[
p(-2) = 1 - \frac{1}{32} = \frac{32}{32} - \frac{1}{32} = \frac{31}{32}
\]

### Final Answer:
\[
p(-2) = \boxed{\frac{31}{32}}
\]

## Question

Simplify the expression: $\\frac{4 m+36}{m+9} \\cdot \\frac{m-5}{5 m^{2}}$.

## Response

We are tasked with simplifying the expression:

\[
\frac{4m + 36}{m + 9} \cdot \frac{m - 5}{5m^2}.
\]

### Step 1: Factorize where possible
#### Factorize \( 4m + 36 \):
\[
4m + 36 = 4(m + 9).
\]

So the expression becomes:
\[
\frac{4(m + 9)}{m + 9} \cdot \frac{m - 5}{5m^2}.
\]

### Step 2: Simplify common terms
The \( m + 9 \) in the numerator and denominator cancels out, leaving:
\[
\frac{4}{1} \cdot \frac{m - 5}{5m^2}.
\]

This simplifies to:
\[
\frac{4(m - 5)}{5m^2}.
\]

### Final Answer:
\[
\boxed{\frac{4(m - 5)}{5m^2}}
\]

## Question

