To find the value of \( f(15) \) for the given function \( f(x) = \frac{1}{2} \cdot 3^{-x^2} \):
1. Substitute \( x = 15 \) into the function:
\[
f(15) = \frac{1}{2} \cdot 3^{-15^2}
\]
2. Calculate \( 15^2 \):
\[
15^2 = 225
\]
3. Substitute \( 225 \) for \( x^2 \) in the exponent:
\[
f(15) = \frac{1}{2} \cdot 3^{-225}
\]
4. Simplify the expression:
\[
f(15) = \frac{1}{2} \cdot \frac{1}{3^{225}} = \frac{1}{2 \cdot 3^{225}}
\]
Therefore, the value of \( f(15) \) is:
\[
f(15) = \frac{1}{2 \cdot 3^{225}}
\]
#17. Given fx= 1 23−x2, what is the value of f(15)?
11 answers
can you write the anwser in actual symbols please?
Sure! The value of \( f(15) \) given the function \( f(x) = \frac{1}{2} \cdot 3^{-x^2} \) can be written as:
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
i dont under the answer. can you example what are ther symbols because i need to copy this for my answer
Of course! Let's break it down step-by-step using the symbols to clarify:
Given the function:
\[ f(x) = \frac{1}{2} \cdot 3^{-x^2} \]
To find \( f(15) \), follow these steps:
1. **Substitute \( x = 15 \) into the function.**
\[ f(15) = \frac{1}{2} \cdot 3^{-15^2} \]
2. **Calculate \( 15^2 \):**
\[ 15^2 = 225 \]
3. **Substitute \( 225 \) into the exponent:**
\[ f(15) = \frac{1}{2} \cdot 3^{-225} \]
4. **Combine the terms:**
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
The answer in symbols is:
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Explanation of the symbols:
- \( \frac{1}{2} \) represents one half.
- \( 3^{-x^2} \) indicates 3 raised to the power of negative \( x^2 \).
- \( 15^2 \) means 15 squared, which equals 225.
- \( 3^{-225} \) means 3 raised to the power of negative 225.
- By multiplying \( \frac{1}{2} \) with \( 3^{-225} \), we get \( \frac{1}{2 \cdot 3^{225}} \).
This fraction is your final answer.
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Given the function:
\[ f(x) = \frac{1}{2} \cdot 3^{-x^2} \]
To find \( f(15) \), follow these steps:
1. **Substitute \( x = 15 \) into the function.**
\[ f(15) = \frac{1}{2} \cdot 3^{-15^2} \]
2. **Calculate \( 15^2 \):**
\[ 15^2 = 225 \]
3. **Substitute \( 225 \) into the exponent:**
\[ f(15) = \frac{1}{2} \cdot 3^{-225} \]
4. **Combine the terms:**
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
The answer in symbols is:
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
Explanation of the symbols:
- \( \frac{1}{2} \) represents one half.
- \( 3^{-x^2} \) indicates 3 raised to the power of negative \( x^2 \).
- \( 15^2 \) means 15 squared, which equals 225.
- \( 3^{-225} \) means 3 raised to the power of negative 225.
- By multiplying \( \frac{1}{2} \) with \( 3^{-225} \), we get \( \frac{1}{2 \cdot 3^{225}} \).
This fraction is your final answer.
\[ f(15) = \frac{1}{2 \cdot 3^{225}} \]
18. Suppose you are a solving a quadratic equation using the quadratic formula and this is your work so far: 2x2+7x−15=0 x= −7 ±72−42−15 22 x= −7 ±??? 4👈 What number goes in place of ???
To determine the number that goes in place of "???" in the given quadratic formula setup, we need to use the quadratic formula correctly.
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given the quadratic equation:
\[ 2x^2 + 7x - 15 = 0 \]
where \( a = 2 \), \( b = 7 \), and \( c = -15 \).
I'll show each step in detail:
1. **Identify \( a \), \( b \), and \( c \):**
- \( a = 2 \)
- \( b = 7 \)
- \( c = -15 \)
2. **Plug in the values into the quadratic formula:**
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
4. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
5. **Substitute back into the quadratic formula:**
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that goes in place of "???" is \( 13 \).
So the complete formula should look like this:
\[ x = \frac{-7 \pm 13}{4} \]
The quadratic formula is:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given the quadratic equation:
\[ 2x^2 + 7x - 15 = 0 \]
where \( a = 2 \), \( b = 7 \), and \( c = -15 \).
I'll show each step in detail:
1. **Identify \( a \), \( b \), and \( c \):**
- \( a = 2 \)
- \( b = 7 \)
- \( c = -15 \)
2. **Plug in the values into the quadratic formula:**
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
3. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
4. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
5. **Substitute back into the quadratic formula:**
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that goes in place of "???" is \( 13 \).
So the complete formula should look like this:
\[ x = \frac{-7 \pm 13}{4} \]
so what the answer
The number that goes in place of "???" is \( 13 \).
So, completing your quadratic formula setup correctly gives:
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the missing number (indicated by "???") is:
\[ 13 \]
So, completing your quadratic formula setup correctly gives:
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the missing number (indicated by "???") is:
\[ 13 \]
are you sure?
Let's re-check the steps to be absolutely certain.
The quadratic equation given is:
\[ 2x^2 + 7x - 15 = 0 \]
Using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given values:
\[ a = 2 \]
\[ b = 7 \]
\[ c = -15 \]
1. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - 4 \cdot 2 \cdot (-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
2. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
So, substituting this back into the quadratic formula,
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that replaces "???" is indeed:
\[ 13 \]
Thus, the correct answer is:
\[ x = \frac{-7 \pm 13}{4} \]
The quadratic equation given is:
\[ 2x^2 + 7x - 15 = 0 \]
Using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Given values:
\[ a = 2 \]
\[ b = 7 \]
\[ c = -15 \]
1. **Calculate the discriminant (\( b^2 - 4ac \)):**
\[ b^2 - 4ac = 7^2 - 4(2)(-15) \]
\[ = 49 - 4 \cdot 2 \cdot (-15) \]
\[ = 49 - (-120) \]
\[ = 49 + 120 \]
\[ = 169 \]
2. **Take the square root of the discriminant:**
\[ \sqrt{169} = 13 \]
So, substituting this back into the quadratic formula,
\[ x = \frac{-7 \pm \sqrt{169}}{2 \cdot 2} \]
\[ x = \frac{-7 \pm 13}{4} \]
Therefore, the number that replaces "???" is indeed:
\[ 13 \]
Thus, the correct answer is:
\[ x = \frac{-7 \pm 13}{4} \]