Chemistry Examples

Solve for F1 F_1*cos(45)+F_2*cos(30)=500
Step 1
Simplify the left side.
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Step 1.1
Simplify each term.
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Step 1.1.1
The exact value of is .
Step 1.1.2
The exact value of is .
Step 2
Subtract from both sides of the equation.
Step 3
Multiply both sides of the equation by .
Step 4
Simplify both sides of the equation.
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Step 4.1
Simplify the left side.
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Step 4.1.1
Simplify .
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Step 4.1.1.1
Cancel the common factor of .
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Step 4.1.1.1.1
Cancel the common factor.
Step 4.1.1.1.2
Rewrite the expression.
Step 4.1.1.2
Cancel the common factor of .
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Step 4.1.1.2.1
Factor out of .
Step 4.1.1.2.2
Cancel the common factor.
Step 4.1.1.2.3
Rewrite the expression.
Step 4.2
Simplify the right side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Multiply by .
Step 4.2.1.2
Combine and simplify the denominator.
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Step 4.2.1.2.1
Multiply by .
Step 4.2.1.2.2
Raise to the power of .
Step 4.2.1.2.3
Raise to the power of .
Step 4.2.1.2.4
Use the power rule to combine exponents.
Step 4.2.1.2.5
Add and .
Step 4.2.1.2.6
Rewrite as .
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Step 4.2.1.2.6.1
Use to rewrite as .
Step 4.2.1.2.6.2
Apply the power rule and multiply exponents, .
Step 4.2.1.2.6.3
Combine and .
Step 4.2.1.2.6.4
Cancel the common factor of .
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Step 4.2.1.2.6.4.1
Cancel the common factor.
Step 4.2.1.2.6.4.2
Rewrite the expression.
Step 4.2.1.2.6.5
Evaluate the exponent.
Step 4.2.1.3
Cancel the common factor of .
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Step 4.2.1.3.1
Cancel the common factor.
Step 4.2.1.3.2
Divide by .
Step 4.2.1.4
Apply the distributive property.
Step 4.2.1.5
Move to the left of .
Step 4.2.1.6
Multiply .
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Step 4.2.1.6.1
Combine and .
Step 4.2.1.6.2
Combine using the product rule for radicals.
Step 4.2.1.6.3
Multiply by .
Step 5
Reorder and .