Basic Math Examples

$101 \cos (21) - w \sin (36) - \frac{0.0016 (w \sin (36) - 36.2) w}{9.8} \cdot 7.1$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Evaluate $\cos (21)$ .

$101 \cdot 0.93358042 - w \sin (36) - \frac{0.0016 (w \sin (36) - 36.2) w}{9.8} \cdot 7.1$

Step 1.2

Multiply $101$ by $0.93358042$ .

$94.29162307 - w \sin (36) - \frac{0.0016 (w \sin (36) - 36.2) w}{9.8} \cdot 7.1$

Step 1.3

Evaluate $\sin (36)$ .

$94.29162307 - w \cdot 0.58778525 - \frac{0.0016 (w \sin (36) - 36.2) w}{9.8} \cdot 7.1$

Step 1.4

Multiply $0.58778525$ by $- 1$ .

$94.29162307 - 0.58778525 w - \frac{0.0016 (w \sin (36) - 36.2) w}{9.8} \cdot 7.1$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Evaluate $\sin (36)$ .

$94.29162307 - 0.58778525 w - \frac{0.0016 (w \cdot 0.58778525 - 36.2) w}{9.8} \cdot 7.1$

Step 1.5.2

Move $0.58778525$ to the left of $w$ .

$94.29162307 - 0.58778525 w - \frac{0.0016 (0.58778525 w - 36.2) w}{9.8} \cdot 7.1$

Step 1.6

Cancel the common factor of $0.0016$ .

Tap for more steps...

Step 1.6.1

Move the leading negative in $- \frac{0.0016 (0.58778525 w - 36.2) w}{9.8}$ into the numerator.

$94.29162307 - 0.58778525 w + \frac{- 0.0016 (0.58778525 w - 36.2) w}{9.8} \cdot 7.1$

Step 1.6.2

Factor $0.0016$ out of $- 0.0016 (0.58778525 w - 36.2) w$ .

$94.29162307 - 0.58778525 w + \frac{0.0016 (- (0.58778525 w - 36.2) w)}{9.8} \cdot 7.1$

Step 1.6.3

Cancel the common factor.

$94.29162307 - 0.58778525 w + \frac{0.0016 (- (0.58778525 w - 36.2) w)}{9.8} \cdot 7.1$

Step 1.6.4

Rewrite the expression.

$94.29162307 - 0.58778525 w + \frac{- (0.58778525 w - 36.2) w}{9.8} \cdot \frac{7.1}{625}$

Step 1.7

Multiply $\frac{- (0.58778525 w - 36.2) w}{9.8}$ by $\frac{7.1}{625}$ .

$94.29162307 - 0.58778525 w + \frac{- (0.58778525 w - 36.2) w \cdot 7.1}{9.8 \cdot 625}$

Step 1.8

Multiply $7.1$ by $- 1$ .

$94.29162307 - 0.58778525 w + \frac{- 7.1 (0.58778525 w - 36.2) w}{9.8 \cdot 625}$

Step 1.9

Multiply $9.8$ by $625$ .

$94.29162307 - 0.58778525 w + \frac{- 7.1 (0.58778525 w - 36.2) w}{6125}$

Step 1.10

Move the negative in front of the fraction.

$94.29162307 - 0.58778525 w - \frac{(7.1 (0.58778525 w - 36.2)) w}{6125}$

Step 1.11

Factor $7.1$ out of $(7.1 (0.58778525 w - 36.2)) w$ .

$94.29162307 - 0.58778525 w - \frac{7.1 ((0.58778525 w - 36.2) w)}{6125}$

Step 1.12

Factor $6125$ out of $6125$ .

$94.29162307 - 0.58778525 w - \frac{7.1 ((0.58778525 w - 36.2) w)}{6125 (1)}$

Step 1.13

Separate fractions.

$94.29162307 - 0.58778525 w - (\frac{7.1}{6125} \cdot \frac{(0.58778525 w - 36.2) w}{1})$

Step 1.14

Divide $7.1$ by $6125$ .

$94.29162307 - 0.58778525 w - (0.00115918 \frac{(0.58778525 w - 36.2) w}{1})$

Step 1.15

Divide $(0.58778525 w - 36.2) w$ by $1$ .

$94.29162307 - 0.58778525 w - (0.00115918 ((0.58778525 w - 36.2) w))$

Step 1.16

Apply the distributive property.

$94.29162307 - 0.58778525 w - (0.00115918 (0.58778525 w \cdot w - 36.2 w))$

Step 1.17

Multiply $w$ by $w$ by adding the exponents.

Tap for more steps...

Step 1.17.1

Move $w$ .

$94.29162307 - 0.58778525 w - (0.00115918 (0.58778525 (w \cdot w) - 36.2 w))$

Step 1.17.2

Multiply $w$ by $w$ .

$94.29162307 - 0.58778525 w - (0.00115918 (0.58778525 w^{2} - 36.2 w))$

Step 1.18

Apply the distributive property.

$94.29162307 - 0.58778525 w - (0.00115918 (0.58778525 w^{2}) + 0.00115918 (- 36.2 w))$

Step 1.19

Multiply $0.58778525$ by $0.00115918$ .

$94.29162307 - 0.58778525 w - (0.00068135 w^{2} + 0.00115918 (- 36.2 w))$

Step 1.20

Multiply $- 36.2$ by $0.00115918$ .

$94.29162307 - 0.58778525 w - (0.00068135 w^{2} - 0.04196244 w)$

Step 1.21

Apply the distributive property.

$94.29162307 - 0.58778525 w - (0.00068135 w^{2}) - (- 0.04196244 w)$

Step 1.22

Multiply $0.00068135$ by $- 1$ .

$94.29162307 - 0.58778525 w - 0.00068135 w^{2} - (- 0.04196244 w)$

Step 1.23

Multiply $- 0.04196244$ by $- 1$ .

$94.29162307 - 0.58778525 w - 0.00068135 w^{2} + 0.04196244 w$

Step 2

Simplify by adding terms.

Tap for more steps...

Step 2.1

Add $- 0.58778525 w$ and $0.04196244 w$ .

$94.29162307 - 0.00068135 w^{2} - 0.5458228 w$

Step 2.2

Move $94.29162307$ .

$- 0.00068135 w^{2} - 0.5458228 w + 94.29162307$