5. If find f(g(x)). 6. Write the slope-intercept form of the equation of the line containing the points (4,7) and 7. Write the equation of the line perpendicular to , passing through the point (6,1).
Begin by writing the corresponding linear equations, and then use back-substitution to solve your variables. 10–1301–8001 159–1 x,y,z=( , , ) 10–1301–8001 159–1 = x-13z=15y-8z=9z=-1 = x-13(-1)=15y-8(-1)=9z=-1 = x=2y=1z=-1 x,y,z=(2 , 1 , -1) Determinants and Cramer’s Rule: 2. Find the determinant of the given matrix. 8–2–12 8–2–12 = 8*2 - (-1)(-2) = 16 - 2 = 14 3. Solve the given linear system using Cramer’s rule.
Question: Proof of Hero’s formula for the area of triangle ABC with sides a, b and c and s being the semi-perimeter i.e. s=a+b+c/2, then Area A = [pic] Proof: Let a triangle ABC with sides a, b and c whose area is equal to A = [pic]. Let the triangle be as follows: Here, perimeter is the length of the sides, now as the sides are a, b & c, assume it is also the length of the sides, then the perimeter of this triangle is P = a+b+c And semi-perimeter i.e. half of the perimeter is S = a+b+c/2 If we draw a perpendicular from C to base and call it ‘h’ which divides the base into two parts i.e. x and c-x, then the diagram looks as follows: The perpendicular has divided the triangle into two right-angled triangles.
The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. This linear programming problem is a:Answer | | | | | | | Correct Answer: | minimization problem | | | | | Question 9 | | | The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. The equation for constraint DH is:Answer | | | | | | | Correct Answer: | X + 2Y ≥ 8 | | | | | Question 10 | | | The following is a
Because the resistors i n parallel have a combined resistance of 6 O, y o u f i n d the potential difference across the parallel branch as follows. Given: R = 6 7= 3A ft Unknoivn: V = ? Original equation: V = IR Solve: V = IR = i3 A)(6 ft) = 18 V Therefore, the potential difference across both the top and the bottom branches is 18 V. N o w use this 18-V drop to determine the current i n the 9-ft resistor. Given: F = 18 V R = 9 Unknoivn: 1=1 Original equation: V = IR ft Practice Exercises Exercise 16: Using the diagram, a) f i n d the total resistance i n the circuit, b) Find the total current through the circuit. i s j i loa (oA Answer: a.
Two real irrationals solutions Two real rationals solutions f(x) has two real rational solutions and and g(x) has two real irrational solutions. After matching these functions, explain to Professor McMerlock how you know these functions meet each condition. Remember, he is a professor, so use complete sentences. When the function crosses the x axis meaning f(x) = 0 there are two real numbers of x that satisfy the equation. Numbers where you can't write them as a fraction, and thus can't write them as a decimal which repeats are irrational.
This means the correlation is very strong since it is close to 1. The closer the correlation coefficient is to 1 or -1 the stronger it is. To find the quadratic regression I went to “Stat – Calc – QuadReg – Calc”. The formula was y = .06x + 1.1 and the correlation coefficient was 1. This means the quadratic regression fits the data perfectly.
What is x? The Pythagorean Theorem states that in every right triangle with legs the length a and b and hypotenuse c, these lengths have the relationship of a2 + b2=c2. a=x b=(2x+4)2 c=(2x+6)2 this is the binomials we will insert into our equation x2+(2x+4)2=(2x+6)2 the binomials into the Pythagorean Theorem x2+4x2+16x+16=24x36 the binomial squared. The 4x2can be subtracted out first x2+16x+16=24x+36 now subtract 24x from both sides x2+-8x+16=36 now subtract 36 from both sides x2-8x-20=0 this is a quadratic equation to solve by factoring and using the zero factor. (x- )(x+ ) the coefficient of x2 is one (1).
In order to understand what an integral is or how to take an integral one must understand the concept of a derivative or differentiation. A derivative is the instantaneous rate of change of y with respect to x. When a derivative is taken what we find is the slope of the tangent line to a graph at the point P. We can approximate the slope by drawing a line through the point P and another point nearby, and then finding the slope of that line, called a secant line. b-ya-x=∆y∆x=fx+∆x-f(x)∆x (Kline, 1967) Then we must choose a random interval to be ∆x. How does the size of ∆x affect our estimate of the slope of the tangent line?
* TASK Your task is to investigate the relationship between the discriminant and the nature of the roots of quadratic and cubic polynomials. Introduction This task looks at quadratic and cubic polynomials and the relationship between their roots and discriminants. By using a graphing package, it is possible to determine the axial intercepts, axis of symmetry and vertex coordinates of a polynomial. By using a, b and c values assigned to each individual, it can be shown that the discriminant directly affects the roots of a quadratic graph and the roots effect the discriminant. By determining a, b, c and d values for a cubic graph it is possible to find the cubic discriminant.