1. Solve for x: 4x−6=18
2. Calculate the area of a rectangle with a length of 12 cm and a width of 4 cm.
3. If cos(x)=0.5, what is the value of x in degrees? (Assume 0∘≤x≤90∘)
4. Factorize the quadratic expression: x2+7x+12
5. Find the length of the hypotenuse of a right-angled triangle with sides 5 cm and 12 cm.
6. Find the derivative of f(x)=2x3+3x2−x.
7. A bag contains 4 red balls and 6 blue balls. What is the probability of drawing a red ball?
8. Solve the following system of linear equations:
3x+y=19 x−y=2
9. Calculate the integral of (4x3−2x)dx.
10. In a triangle ABC, if side a=12, sin(A)=0.6, and sin(B)=0.9, what is the length of side b?
Get the complete, step-by-step math solution for: "1. Solve for x: 4x - 6 = 18 2. Calculate the area of a rectangle with a length of 12 cm and a width of 4 cm. 3. If cos(x) = 0.5, what is the value of ...". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Recall the Sine Rule
The Sine Rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. We will use this rule to find the unknown side b.
Step 2: Substitute known values into the Sine Rule
We are given the length of side a=12, sin(A)=0.6, and sin(B)=0.9. We substitute these values into the Sine Rule equation.
Step 3: Solve for side b
To find b, we rearrange the equation by multiplying both sides by 0.9. This isolates b on one side of the equation.
Step 4: Calculate the value of b
First, we simplify the fraction 00.9.6 to 1.5. Then, we multiply 12 by 1.5 to get the final value of b.