Calculus Examples

$\frac{\frac{2.378}{\cos (5)} - v ((\frac{{2.378}^{2}}{\cos^{2} (5)}) + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))}{- 9.8}$

Step 1

Evaluate $\cos (5)$ .

$\frac{\frac{2.378}{0.99619469} - v (\frac{{2.378}^{2}}{\cos^{2} (5)} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))}{- 9.8}$

Step 2

Raise $2.378$ to the power of $2$ .

$\frac{\frac{2.378}{0.99619469} - v (\frac{5.654884}{\cos^{2} (5)} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))}{- 9.8}$

Step 3

Simplify the denominator.

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Step 3.1

Evaluate $\cos (5)$ .

$\frac{\frac{2.378}{0.99619469} - v (\frac{5.654884}{{0.99619469}^{2}} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))}{- 9.8}$

Step 3.2

Raise $0.99619469$ to the power of $2$ .

$\frac{\frac{2.378}{0.99619469} - v (\frac{5.654884}{0.99240387} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))}{- 9.8}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $0.002$ out of $\frac{2.378}{0.99619469} - v (\frac{5.654884}{0.99240387} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))$ .

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Step 4.1.1

Factor $0.002$ out of $\frac{2.378}{0.99619469}$ .

$\frac{0.002 (\frac{1189}{0.99619469}) - v (\frac{5.654884}{0.99240387} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))}{- 9.8}$

Step 4.1.2

Factor $0.002$ out of $- v (\frac{5.654884}{0.99240387} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7))$ .

$\frac{0.002 (\frac{1189}{0.99619469}) + 0.002 (- 500 v (\frac{5.654884}{0.99240387} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7)))}{- 9.8}$

Step 4.1.3

Factor $0.002$ out of $0.002 (\frac{1189}{0.99619469}) + 0.002 (- 500 v (\frac{5.654884}{0.99240387} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7)))$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v (\frac{5.654884}{0.99240387} + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7)))}{- 9.8}$

Step 4.2

Simplify each term.

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Step 4.2.1

Divide $5.654884$ by $0.99240387$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v (5.69816798 + 4 \cdot 4.9 \cdot (23.78 \cdot \tan (5) + 0.7)))}{- 9.8}$

Step 4.2.2

Multiply $4$ by $4.9$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v (5.69816798 + 19.6 \cdot (23.78 \cdot \tan (5) + 0.7)))}{- 9.8}$

Step 4.2.3

Simplify each term.

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Step 4.2.3.1

Evaluate $\tan (5)$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v (5.69816798 + 19.6 \cdot (23.78 \cdot 0.08748866 + 0.7)))}{- 9.8}$

Step 4.2.3.2

Multiply $23.78$ by $0.08748866$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v (5.69816798 + 19.6 \cdot (2.08048041 + 0.7)))}{- 9.8}$

Step 4.2.4

Add $2.08048041$ and $0.7$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v (5.69816798 + 19.6 \cdot 2.78048041))}{- 9.8}$

Step 4.2.5

Multiply $19.6$ by $2.78048041$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v (5.69816798 + 54.4974162))}{- 9.8}$

Step 4.3

Add $5.69816798$ and $54.4974162$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 500 v \cdot 60.19558419)}{- 9.8}$

Step 4.4

Multiply $60.19558419$ by $- 500$ .

$\frac{0.002 (\frac{1189}{0.99619469} - 30097.79209659 v)}{- 9.8}$

Step 4.5

Divide $1189$ by $0.99619469$ .

$\frac{0.002 (1193.54178683 - 30097.79209659 v)}{- 9.8}$

Step 5

Simplify with factoring out.

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Step 5.1

Move the negative in front of the fraction.

$- \frac{0.002 (1193.54178683 - 30097.79209659 v)}{9.8}$

Step 5.2

Factor $9.8$ out of $9.8$ .

$- \frac{0.002 (1193.54178683 - 30097.79209659 v)}{9.8 (1)}$

Step 6

Separate fractions.

$- (\frac{0.002}{9.8} \cdot \frac{1193.54178683 - 30097.79209659 v}{1})$

Step 7

Simplify the expression.

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Step 7.1

Divide $0.002$ by $9.8$ .

$- (0.00020408 \frac{1193.54178683 - 30097.79209659 v}{1})$

Step 7.2

Divide $1193.54178683 - 30097.79209659 v$ by $1$ .

$- (0.00020408 (1193.54178683 - 30097.79209659 v))$

Step 8

Apply the distributive property.

$- (0.00020408 \cdot 1193.54178683 + 0.00020408 (- 30097.79209659 v))$

Step 9

Multiply.

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Step 9.1

Multiply $0.00020408$ by $1193.54178683$ .

$- (0.24357995 + 0.00020408 (- 30097.79209659 v))$

Step 9.2

Multiply $- 30097.79209659$ by $0.00020408$ .

$- (0.24357995 - 6.14240655 v)$

Step 10

Apply the distributive property.

$- 1 \cdot 0.24357995 - (- 6.14240655 v)$

Step 11

Multiply.

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Step 11.1

Multiply $- 1$ by $0.24357995$ .

$- 0.24357995 - (- 6.14240655 v)$

Step 11.2

Multiply $- 6.14240655$ by $- 1$ .

$- 0.24357995 + 6.14240655 v$