If sin ∅=2/3, then sec ∅ is?
The solution of the problem follows an easy procedure which can be divided in these steps: 1- The fundamental trigonometry formula follows the next expression : sin^2∅+cos^2∅=1 Where it express the ecuation of a circumference whose radius is equal 1 2-Considering the step 1 formula, replace the data into the ecuation: sin^2∅+cos^2∅=1→2/3^2+cos^2∅=1 3-Determine cos ∅ by organizing the expression : 4/9+cos^2∅=1→cos^2∅=1-4/9→(9-4)/9=5/9. Therefore, cos^2∅=5/9 → cos∅=√5/9 = (√5)/3 Next, determine the value of sec∅ based on the following expression that connects sec∅ and cos∅: sec ∅= 1/cos∅ then, sec ∅= 1/cos∅ →sec∅=1/((√5)/3) Finally, simplify the expression by eliminatiing the square root from the low part of the fraction… sec∅=1/((√5)/3)→3/(√5).(√5)/(√5)=(3√5)/〖√5〗^2 =(3√5)/5→sec∅=(3√5)/5
If the area of a certain triangle is 70 m^2 .Considering the base of 20 m, determine the value of its height.
The exercise can be solved in the following steps: First, if the area of a triangle follows the next expression : A= (base x height)/2. If A=70 and base= 20, then its height is the variable. Therefore, replace the value of the area and base to the formula → 70= (20 x height)/2. Then, determine the height by organizing and simplifying the expression 70= (20 x height)/2→70.2=20 x height→140/20= height →height = 7 m.
What is the value of X in the following expresion? 4^(-2)+3x=8^(-1)
The ecuation can be solved through the following steps: 1- First, simplify the negatives exponents by switching to fractions 4^(-2)+3x=8^(-1) → 1/4^(2 ) +3x=1/8 2- Second, apply CD in order to convert the expression from fraction to linear (LE) 1/16+3x=1/8 →CD(16,8)=16→ 1+48x=2 (LE) 3- Next, determine X by organizing and simplifying the expression (solving two-step ecuation) 1+48x=2→48x=2-1→48x=1→x=1/48