### Upward lift

An upward force of 47 N is sufficient to lift a window. What force must be exerted along a pole that makes an angle of 27 degrees with the wall in order to give the necessary upward lift?

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An upward force of 47 N is sufficient to lift a window. What force must be exerted along a pole that makes an angle of 27 degrees with the wall in order to give the necessary upward lift?

A. Convert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3". a) 16 3/2 = 64 b) ex = 5 B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25". a) log 3 27 = 3 b) log e 1 = 0 c) log 125 25 = 2/3 C. Use the

See attached file for full problem description. Please provide proof along with explanation. For integers n>= 1 and for all real numbers x>=-1, use mathematical induction to prove that 1 + nx =< (1 + x)^n

Heres my problem. Consider the group <R,+> (reals under addition) and its normal subgroups Z (integers) and Q (rationals0. (These are normal because R is abelian, of course.) (i) Find an element of Q/Z of order 350. (ii) Show that Q/Z is the torsion subgroup of R/Z. This problem is quite straightforward if you use the defini

What is the actual values for each one? 1. f(x) = e^x 2. f(x) = log x

In a polynomial space of degree {see attachment} is (p,q)=p(0)q(0)+Ap(1/2)q(1/2)+Bp(1)q(1) for A,B>0. Define the linear product.

Let A be an nxn symmetric matrix such that det {see attachment}. We know from the matrix algebra that the associated quadratic form {see attachment}, where x = (x1,...xn), is either positive-definite, negative- definite or indefinite. Now assume the diagonal entries of A are all zero. Explain why q(x) is indefinite. (Hint:

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Please see the attached file for the fully formatted problem. 2. (30 points) A thin, one-dimensional rod of heat-conducting material with length L = pi is internally and uniformly heated at a rate of alpha degrees per unit time. This means that the temperature of the rod, u(x, t), satisfies the inhomogeneous heat equation ..

Attached one absolute value equation

Matrix Algebra Investment Allocation Problem Donald Trump has some pocket change he wants to invest to make $3380. His stock broker suggested four (4) investment possibilities to accomplish this goal. The investments and their expected yields are listed in the table below. Investment Rate of Return Risk Level Magellan

Find the voltage V where V=V1+V2 using graphical addition and analytical methods, given that V1=3sin(theta+20 degrees) and V2=5sin(theta-40degrees).

1. Solve the following equation for the variable y. 5x - 3y + 9 = 0 2.Solve the following problem by identifying a variable, writing an equation that describes the situation, and then solving the equation. Find two consecutive even integers that have a sum of 450. 3.Solve the following problem by identifying a variable,

Please see the attached problem statement.

1.Solve the following equation 19 - 3n = - 2n 2.Solve the following equation 2(a - 4) + 4 = 5(9 - a) 3.Solve the following equation and check your answer. (1/2b)- (1/2)= 1/4b 4.Solve the following equation 0.6(x - 50) = 18 - 0.3(40 - 10x) 5.Solve the following equation for the variable x. t - 5x = 4x

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 3x y = log3x See attachment for Graph Plot the graphs of the following functions. Scan the graphs and plot them. 1. f(x)=7 2. f(x)=4 x - 3 3. f(x)=(1/5x 4. f(x)= 3 log x 5. f(x) = log x

Please see the attached file for the fully formatted problems. 1. Write the first four terms of the sequence an = 64(1/4)n , for n=0, 1, 2, 3,... a) 16, 4, 1, ¼ b) 60, 56, 52, 48 c) 64, 16, 4, 1 d) 256, 1024, 16384, 262144 2. Write the given series in expanded form without summation notation. a) -x2-x3

Please see the attached file for the fully formatted problems. 1. Can a graph be used to solve any quadratic equation? Why or why not? 2. Look at the graph below and comment on the sign of D or the discriminant. From the quadratic equation based on the information provided and find its solution. 3. Formulate two word

The solution can ONLY be accepted in Matlab. The problem is in the attachment file. Least Square Planetary orbit [2]. The expression z = a + bxy + cy + dx + ey + f is known as a quadratic form. The set of points (x, y) where z = 0 is a conic section. It can be an ellipse, a parabola, or a hyperbola, depending on the si

A system with two degrees of freedom has Hamiltonian (see attachment) ? Show that p2 and H will remain constant during the motion. ? If (see attachment), show that at other times (see attachment) ? Show that in the subsequent motion cannot reach the value (see attachment)

1. Rational Functions Graph the following function when a=3 and b=2. Develop a generic expression (i.e., as a function of "a" and "b") to find the "x" and "y" intercepts for this function (see attachment) 2. Exponential Functions Once a new automobile enters the market, the manufacturers try to estimate their residual valu

Write the 3rd term of the expression : (x+ y) to the seventh power. ( or (x+y)^7 )

(x+y)to the 16th power

Prove that for all odd integers n, (1^n)+(2^n)+(3^n)...+(n^n) is a proper multiple of 1+2+3+...n

If a,b,c are odd integers, show that all real roots of ax^2+bx+c=0 are irrational numbers.

Derive rationalized expressions for the admittances of the two parallel arms. Hence derive an expression for the total circuit admittance.

a) log y = 1.2x -1 b) ln y = 1.2x - 1

1. Solve the radical equation: {see attachment} 2. Find the equation of the line through the point (-2,-4) and perpendicular to the line {see attachment} 3. Complete the square, find the vertex, the axis of symmetry, all the intercepts, and graph the parabola: {see attachment} 4. ... Find the compositions {see attac

Please tell me whether or not the 2 correspondences are upper hemicontinuous and PLEASE (using the definition) justify why. 1)F:[2,3]->R^2, F(r)={(x,y):abs(x)+abs(y)<=r} 2)F:R^n{0}->R^n, F(x)=B(x;||x||), the closed ball centred at x with radius ||x||. Thanks Note: abs=absolute value is the complement ||x|| is d

(Algebraic continuity theorem): Assume f:A->R and g:A->R are continuous at a point c belong to A)then f(x)/g(x) is continuous at c, if both f and g are provided that the quotient is defined, show that if g is continuous at c and g(c) not= 0 then there exists an open interval containing c on which f(x)/g(x) is always defined.