Math / Algebra

Question $\begin{array}{l}f(t)=\left\{\begin{array}{ll}t^{2}-5 t & , \quad t \leq-10 \\ t+19 & ,\end{array},-10<t<-2\right. \\ \frac{t^{3}}{t+9}\end{array}, \quad t \geq-2$ .

Studdy Solution

STEP 1

1. We are given a piecewise function $f(t)$ .
2. The function has three different expressions depending on the value of $t$ .
3. We need to find the value of $f(-10)$ .

STEP 2

1. Identify which piece of the piecewise function applies for $t = -10$ .
2. Substitute $t = -10$ into the appropriate expression.
3. Simplify the expression to find $f(-10)$ .

STEP 3

Identify the correct piece of the piecewise function for $t = -10$ :
- The first piece $f(t) = t^2 - 5t$ is defined for $t \leq -10$ .
Since $-10 \leq -10$ is true, we use the first piece of the function.

STEP 4

Substitute $t = -10$ into the expression $f(t) = t^2 - 5t$ :
$f(-10) = (-10)^2 - 5(-10)$

STEP 5

Simplify the expression:
$f(-10) = 100 + 50$ $f(-10) = 150$
The value of $f(-10)$ is:
$\boxed{150}$

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Question $\begin{array}{l}f(t)=\left\{\begin{array}{ll}t^{2}-5 t & , \quad t \leq-10 \\ t+19 & ,\end{array},-10<t<-2\right. \\ \frac{t^{3}}{t+9}\end{array}, \quad t \geq-2$ .

Studdy Solution

STEP 1

1. We are given a piecewise function $f(t)$ .
2. The function has three different expressions depending on the value of $t$ .
3. We need to find the value of $f(-10)$ .

STEP 2

1. Identify which piece of the piecewise function applies for $t = -10$ .
2. Substitute $t = -10$ into the appropriate expression.
3. Simplify the expression to find $f(-10)$ .

STEP 3

Identify the correct piece of the piecewise function for $t = -10$ :
- The first piece $f(t) = t^2 - 5t$ is defined for $t \leq -10$ .
Since $-10 \leq -10$ is true, we use the first piece of the function.

STEP 4

Substitute $t = -10$ into the expression $f(t) = t^2 - 5t$ :
$f(-10) = (-10)^2 - 5(-10)$

STEP 5

Simplify the expression:
$f(-10) = 100 + 50$ $f(-10) = 150$
The value of $f(-10)$ is:
$\boxed{150}$

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Questionf(t)={t2−5t,t≤−10t+19,,−10<t<−2t3t+9,t≥−2\begin{array}{l}f(t)=\left\{\begin{array}{ll}t^{2}-5 t & , \quad t \leq-10 \\ t+19 & ,\end{array},-10<t<-2\right. \\ \frac{t^{3}}{t+9}\end{array}, \quad t \geq-2f(t)={t2−5tt+19​,t≤−10,​,−10<t<−2t+9t3​​,t≥−2.

Studdy Solution

STEP 1

1. We are given a piecewise function f(t) f(t) f(t).2. The function has three different expressions depending on the value of t t t.3. We need to find the value of f(−10) f(-10) f(−10).

STEP 2

1. Identify which piece of the piecewise function applies for t=−10 t = -10 t=−10.2. Substitute t=−10 t = -10 t=−10 into the appropriate expression.3. Simplify the expression to find f(−10) f(-10) f(−10).

STEP 3

Identify the correct piece of the piecewise function for t=−10 t = -10 t=−10:- The first piece f(t)=t2−5t f(t) = t^2 - 5t f(t)=t2−5t is defined for t≤−10 t \leq -10 t≤−10.Since −10≤−10 -10 \leq -10 −10≤−10 is true, we use the first piece of the function.

STEP 4

Substitute t=−10 t = -10 t=−10 into the expression f(t)=t2−5t f(t) = t^2 - 5t f(t)=t2−5t:f(−10)=(−10)2−5(−10) f(-10) = (-10)^2 - 5(-10) f(−10)=(−10)2−5(−10)

STEP 5

Simplify the expression:f(−10)=100+50 f(-10) = 100 + 50 f(−10)=100+50 f(−10)=150 f(-10) = 150 f(−10)=150 The value of f(−10) f(-10) f(−10) is:150 \boxed{150} 150​

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Studdy solves anything!

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $\begin{array}{l}f(t)=\left\{\begin{array}{ll}t^{2}-5 t & , \quad t \leq-10 \\ t+19 & ,\end{array},-10<t<-2\right. \\ \frac{t^{3}}{t+9}\end{array}, \quad t \geq-2$ .

1. We are given a piecewise function $f(t)$ .
2. The function has three different expressions depending on the value of $t$ .
3. We need to find the value of $f(-10)$ .

1. Identify which piece of the piecewise function applies for $t = -10$ .
2. Substitute $t = -10$ into the appropriate expression.
3. Simplify the expression to find $f(-10)$ .

Identify the correct piece of the piecewise function for $t = -10$ :
- The first piece $f(t) = t^2 - 5t$ is defined for $t \leq -10$ .
Since $-10 \leq -10$ is true, we use the first piece of the function.

Substitute $t = -10$ into the expression $f(t) = t^2 - 5t$ :
$f(-10) = (-10)^2 - 5(-10)$

Simplify the expression:
$f(-10) = 100 + 50$ $f(-10) = 150$
The value of $f(-10)$ is:
$\boxed{150}$