Math / Algebra

Questionhave elapsed we use the first formula. If more than 3 hours and up to 5 hours have elapsed, we use the second formula.
Use the formula below to determine each of the following values. Pay attention to the value of to make sure you are using the correct formula! $d=\left\{\begin{array}{ccc} 2 t & \text { if } & 0 \leq t \leq 3 \\ 4(t-3)+6 & \text { if } & 3<t \leq 5 \end{array}\right.$ a. If $t=1.75$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches. b. If $t=4.25$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches. c. If $t=2.9$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches. d. If $t=3.1$ , then the total accumulated snowfall up to that point in the storm was $\square$ inches.
Submit Question 5. Points possible: 4 License Unlimited attempts. Message instructor about this question menes per hour for 1.5 hours $(4.5-3=1.5)$ . At $5: 00 \mathrm{pm}$ , th has only been falling at a rate of 4 inches per hour for 2 hours $5-3=2$ ). cements s. /Learning 47 alytics se Syllabus $d=4(t-3)+6$
Putting everything together we have so far, we get the following. This notation indicates that $d$ us represented differently dependin on how much time has passed. $d=\left\{\begin{array}{ccc} 2 t & \text { if } & 0 \leq t \leq 3 \\ 4(t-3)+6 & \text { if } & 3<t \leq 5 \end{array}\right.$
If between 0 and 3 hours nave elapsed we use the first formula. If more than 3 hours and up to 5 hours have elapsed, we use the sec formula.
Use the formula below to determine each of the following values. Pay attention to the value of to make sure you are using the correct formula!

Studdy Solution

STEP 1

What is this asking? Given a formula for snowfall accumulation that changes depending on how much time has passed, we need to calculate the total snowfall at different times. Watch out! We need to make sure we use the right formula based on the time t, and not mix them up!

STEP 2

1. Snowfall at $t = 1.75$
2. Snowfall at $t = 4.25$
3. Snowfall at $t = 2.9$
4. Snowfall at $t = 3.1$

STEP 3

Since our time $t = 1.75$ is between 0 and 3, we'll use the first formula: $d = 2 \cdot t$ .
It's the right one because $0 \leq 1.75 \leq 3$ is a true statement!

STEP 4

Substitute the value of $t$ : $d = 2 \cdot 1.75$

STEP 5

Calculate the result: $d = 3.5$

STEP 6

This time, $t = 4.25$ is between 3 and 5, so we're going with the second formula: $d = 4(t - 3) + 6$ .
This is because $3 < 4.25 \leq 5$ is true!

STEP 7

Substitute $t = 4.25$ : $d = 4(4.25 - 3) + 6$

STEP 8

Simplify inside the parentheses: $d = 4(1.25) + 6$

STEP 9

Multiply: $d = 5 + 6$

STEP 10

Add to find our answer: $d = 11$

STEP 11

With $t = 2.9$ , we're back to the first formula $d = 2 \cdot t$ since $0 \leq 2.9 \leq 3$ .

STEP 12

Substitute $t = 2.9$ : $d = 2 \cdot 2.9$

STEP 13

Calculate: $d = 5.8$

STEP 14

Here, $t = 3.1$ falls between 3 and 5, so we'll use $d = 4(t - 3) + 6$ because $3 < 3.1 \leq 5$ is true!

STEP 15

Substitute $t = 3.1$ : $d = 4(3.1 - 3) + 6$

STEP 16

Simplify the parentheses: $d = 4(0.1) + 6$

STEP 17

Multiply: $d = 0.4 + 6$

STEP 18

Add to get our final value: $d = 6.4$

STEP 19

a. If $t = 1.75$ , then $d = 3.5$ inches. b. If $t = 4.25$ , then $d = 11$ inches. c. If $t = 2.9$ , then $d = 5.8$ inches. d. If $t = 3.1$ , then $d = 6.4$ inches.

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Studdy Solution

STEP 1

What is this asking? Given a formula for snowfall accumulation that changes depending on how much time has passed, we need to calculate the total snowfall at different times. Watch out! We need to make sure we use the right formula based on the time *t*, and not mix them up!

STEP 2

1. Snowfall at t=1.75t = 1.75t=1.752. Snowfall at t=4.25t = 4.25t=4.253. Snowfall at t=2.9t = 2.9t=2.94. Snowfall at t=3.1t = 3.1t=3.1

STEP 3

Since our time t=1.75t = 1.75t=1.75 is between 0 and 3, we'll use the first formula: d=2⋅td = 2 \cdot td=2⋅t.It's the right one because 0≤1.75≤30 \leq 1.75 \leq 30≤1.75≤3 is a true statement!

STEP 4

**Substitute** the value of ttt: d=2⋅1.75d = 2 \cdot 1.75d=2⋅1.75

STEP 5

**Calculate the result**: d=3.5d = 3.5d=3.5

STEP 6

This time, t=4.25t = 4.25t=4.25 is between 3 and 5, so we're going with the second formula: d=4(t−3)+6d = 4(t - 3) + 6d=4(t−3)+6.This is because 3<4.25≤53 < 4.25 \leq 53<4.25≤5 is true!

STEP 7

**Substitute** t=4.25t = 4.25t=4.25: d=4(4.25−3)+6d = 4(4.25 - 3) + 6d=4(4.25−3)+6

STEP 8

**Simplify inside the parentheses**: d=4(1.25)+6d = 4(1.25) + 6d=4(1.25)+6

STEP 9

**Multiply**: d=5+6d = 5 + 6d=5+6

STEP 10

**Add to find our answer**: d=11d = 11d=11

STEP 11

With t=2.9t = 2.9t=2.9, we're back to the first formula d=2⋅td = 2 \cdot td=2⋅t since 0≤2.9≤30 \leq 2.9 \leq 30≤2.9≤3.

STEP 12

**Substitute** t=2.9t = 2.9t=2.9: d=2⋅2.9d = 2 \cdot 2.9d=2⋅2.9

STEP 13

**Calculate**: d=5.8d = 5.8d=5.8

STEP 14

Here, t=3.1t = 3.1t=3.1 falls between 3 and 5, so we'll use d=4(t−3)+6d = 4(t - 3) + 6d=4(t−3)+6 because 3<3.1≤53 < 3.1 \leq 53<3.1≤5 is true!

STEP 15

**Substitute** t=3.1t = 3.1t=3.1: d=4(3.1−3)+6d = 4(3.1 - 3) + 6d=4(3.1−3)+6

STEP 16

**Simplify the parentheses**: d=4(0.1)+6d = 4(0.1) + 6d=4(0.1)+6

STEP 17

**Multiply**: d=0.4+6d = 0.4 + 6d=0.4+6

STEP 18

**Add to get our final value**: d=6.4d = 6.4d=6.4

STEP 19

a. If t=1.75t = 1.75t=1.75, then d=3.5d = 3.5d=3.5 inches. b. If t=4.25t = 4.25t=4.25, then d=11d = 11d=11 inches. c. If t=2.9t = 2.9t=2.9, then d=5.8d = 5.8d=5.8 inches. d. If t=3.1t = 3.1t=3.1, then d=6.4d = 6.4d=6.4 inches.

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What is this asking? Given a formula for snowfall accumulation that changes depending on how much time has passed, we need to calculate the total snowfall at different times. Watch out! We need to make sure we use the right formula based on the time t, and not mix them up!

1. Snowfall at $t = 1.75$
2. Snowfall at $t = 4.25$
3. Snowfall at $t = 2.9$
4. Snowfall at $t = 3.1$

Since our time $t = 1.75$ is between 0 and 3, we'll use the first formula: $d = 2 \cdot t$ .
It's the right one because $0 \leq 1.75 \leq 3$ is a true statement!

Substitute the value of $t$ : $d = 2 \cdot 1.75$

Calculate the result: $d = 3.5$

This time, $t = 4.25$ is between 3 and 5, so we're going with the second formula: $d = 4(t - 3) + 6$ .
This is because $3 < 4.25 \leq 5$ is true!

Substitute $t = 4.25$ : $d = 4(4.25 - 3) + 6$

Simplify inside the parentheses: $d = 4(1.25) + 6$

Multiply: $d = 5 + 6$

Add to find our answer: $d = 11$

With $t = 2.9$ , we're back to the first formula $d = 2 \cdot t$ since $0 \leq 2.9 \leq 3$ .

Substitute $t = 2.9$ : $d = 2 \cdot 2.9$

Calculate: $d = 5.8$

Here, $t = 3.1$ falls between 3 and 5, so we'll use $d = 4(t - 3) + 6$ because $3 < 3.1 \leq 5$ is true!

Substitute $t = 3.1$ : $d = 4(3.1 - 3) + 6$

Simplify the parentheses: $d = 4(0.1) + 6$

Multiply: $d = 0.4 + 6$

Add to get our final value: $d = 6.4$

a. If $t = 1.75$ , then $d = 3.5$ inches. b. If $t = 4.25$ , then $d = 11$ inches. c. If $t = 2.9$ , then $d = 5.8$ inches. d. If $t = 3.1$ , then $d = 6.4$ inches.