QuestionCalculate $\frac{2.4^{3}}{\sqrt{5+\pi}-1}$ and round to the nearest thousandth.

Studdy Solution

STEP 1

Assumptions1. The value of $\pi$ is approximately3.14159. The operations should be performed according to the order of operations (PEMDAS/BODMAS)
3. The final answer should be rounded to the nearest thousandth

STEP 2

First, we need to calculate the value of $2.4^{}$ .
$2.4^{} =2.4 \times2.4 \times2.4$

STEP 3

Calculate the value of $2.^{3}$ .
$2.^{3} =13.824$

STEP 4

Next, we need to calculate the value inside the square root, which is $+ \pi$ .
$+ \pi = +3.14159$

STEP 5

Calculate the value of $5 + \pi$ .
$5 + \pi =8.14159$

STEP 6

Now, we need to calculate the square root of the result from the previous step.
$\sqrt{8.14159}$

STEP 7

Calculate the square root of $.14159$ .
$\sqrt{.14159} =2.85164$

STEP 8

Next, we need to subtract1 from the result from the previous step.
$2.85164 -1$

STEP 9

Calculate $2.85164 -$ .
$2.85164 - =.85164$

STEP 10

Now, we need to divide the result from step3 by the result from step9.
$\frac{13.824}{.85164}$

STEP 11

Calculate $\frac{13.824}{.85164}$ and round to the nearest thousandth.
$\frac{13.824}{.85164} \approx7.467$ So, $\frac{.4^{3}}{\sqrt{5+\pi}-} \approx7.467$ .

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QuestionCalculate $\frac{2.4^{3}}{\sqrt{5+\pi}-1}$ and round to the nearest thousandth.

Studdy Solution

STEP 1

Assumptions1. The value of $\pi$ is approximately3.14159. The operations should be performed according to the order of operations (PEMDAS/BODMAS)
3. The final answer should be rounded to the nearest thousandth

STEP 2

First, we need to calculate the value of $2.4^{}$ .
$2.4^{} =2.4 \times2.4 \times2.4$

STEP 3

Calculate the value of $2.^{3}$ .
$2.^{3} =13.824$

STEP 4

Next, we need to calculate the value inside the square root, which is $+ \pi$ .
$+ \pi = +3.14159$

STEP 5

Calculate the value of $5 + \pi$ .
$5 + \pi =8.14159$

STEP 6

Now, we need to calculate the square root of the result from the previous step.
$\sqrt{8.14159}$

STEP 7

Calculate the square root of $.14159$ .
$\sqrt{.14159} =2.85164$

STEP 8

Next, we need to subtract1 from the result from the previous step.
$2.85164 -1$

STEP 9

Calculate $2.85164 -$ .
$2.85164 - =.85164$

STEP 10

Now, we need to divide the result from step3 by the result from step9.
$\frac{13.824}{.85164}$

STEP 11

Calculate $\frac{13.824}{.85164}$ and round to the nearest thousandth.
$\frac{13.824}{.85164} \approx7.467$ So, $\frac{.4^{3}}{\sqrt{5+\pi}-} \approx7.467$ .

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QuestionCalculate 2.435+π−1\frac{2.4^{3}}{\sqrt{5+\pi}-1}5+π​−12.43​ and round to the nearest thousandth.

Studdy Solution

STEP 1

Assumptions1. The value of π\piπ is approximately3.14159. The operations should be performed according to the order of operations (PEMDAS/BODMAS)3. The final answer should be rounded to the nearest thousandth

STEP 2

First, we need to calculate the value of 2.42.4^{}2.4.2.4=2.4×2.4×2.42.4^{} =2.4 \times2.4 \times2.42.4=2.4×2.4×2.4

STEP 3

Calculate the value of 2.32.^{3}2.3.2.3=13.8242.^{3} =13.8242.3=13.824

STEP 4

Next, we need to calculate the value inside the square root, which is +π + \pi+π.+π=+3.14159 + \pi = +3.14159+π=+3.14159

STEP 5

Calculate the value of 5+π5 + \pi5+π.5+π=8.141595 + \pi =8.141595+π=8.14159

STEP 6

Now, we need to calculate the square root of the result from the previous step.8.14159\sqrt{8.14159}8.14159​

STEP 7

Calculate the square root of .14159.14159.14159..14159=2.85164\sqrt{.14159} =2.85164.14159​=2.85164

STEP 8

Next, we need to subtract1 from the result from the previous step.2.85164−12.85164 -12.85164−1

STEP 9

Calculate 2.85164−2.85164 -2.85164−.2.85164−=.851642.85164 - =.851642.85164−=.85164

STEP 10

Now, we need to divide the result from step3 by the result from step9.13.824.85164\frac{13.824}{.85164}.8516413.824​

STEP 11

Calculate 13.824.85164\frac{13.824}{.85164}.8516413.824​ and round to the nearest thousandth.13.824.85164≈7.467\frac{13.824}{.85164} \approx7.467.8516413.824​≈7.467So, .435+π−≈7.467\frac{.4^{3}}{\sqrt{5+\pi}-} \approx7.4675+π​−.43​≈7.467.

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QuestionCalculate $\frac{2.4^{3}}{\sqrt{5+\pi}-1}$ and round to the nearest thousandth.

Assumptions1. The value of $\pi$ is approximately3.14159. The operations should be performed according to the order of operations (PEMDAS/BODMAS)
3. The final answer should be rounded to the nearest thousandth

First, we need to calculate the value of $2.4^{}$ .
$2.4^{} =2.4 \times2.4 \times2.4$

Calculate the value of $2.^{3}$ .
$2.^{3} =13.824$

Next, we need to calculate the value inside the square root, which is $+ \pi$ .
$+ \pi = +3.14159$

Calculate the value of $5 + \pi$ .
$5 + \pi =8.14159$

Now, we need to calculate the square root of the result from the previous step.
$\sqrt{8.14159}$

Calculate the square root of $.14159$ .
$\sqrt{.14159} =2.85164$

Next, we need to subtract1 from the result from the previous step.
$2.85164 -1$

Calculate $2.85164 -$ .
$2.85164 - =.85164$

Now, we need to divide the result from step3 by the result from step9.
$\frac{13.824}{.85164}$

Calculate $\frac{13.824}{.85164}$ and round to the nearest thousandth.
$\frac{13.824}{.85164} \approx7.467$ So, $\frac{.4^{3}}{\sqrt{5+\pi}-} \approx7.467$ .