Basic Math question and answers for October 26, 2024
- Q Select the correct answer.Rodrigo is tracking the number of visitors at two parks. He created these functions to model the total number of people visiting each park, wherex is the...
- Q A function is given.f(t) = /-;(a) Determine the net change between the given values of the variable.t = a, t = a + h(b) Determine the average rate of change...
- Q The average annual cost (in dollars) for health insurance in a country can be approximated by the function g(x)=1736.3 + 1661.3 In x, where x=6 corresponds to the year 2006.(a)...
- Q A chain-saw rental firm charges $21 per day or fraction of a day to rent a saw, plus a fixed fee of $9 for re-sharpening the blade. Additional portions of...
- Q Mrs. J bought a rare painting in 2000 for $150,000. The value of the painting increases at a rate of 3% per year. How much is the painting worth in...
- Q Evaluate the function f(x)=x + 8x + 7 at the given values of the independent variable and simplify,a. f(6) b. f(x+8) c. f(-x)
- Q The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of people she had invited the...
- Q In 2010, the population of Greenbow, AL was 1,200 people. The population has risen at at rate of 3% each year since. Let x = the number of years since...
- Q What is the equation for a cosecant function with vertical asymptotes found at x = pi/4 +pi/4 n, such that n is an integer?f(x) = 2cscxg(x) = 4csc2xh(x) = 2csc4xj(x)...
- Q The size P of a small herbivore population at time t (in years) obeys the function P(t)-900e0.15t if they have enough food and the predator population stays constant. After how...
- Q Find the average rate of change of f(x)=x - 4x + 4 over the following intervals.(a) From 3 to - 2(b) From 1 to 4(c) From 4 to 5(a) The...
- Q Given the toolkit function f(x) = x2, write the equation of the transformed function g(x) after a vertical STRETCH by a factor of 3.g(x) = 3xg(x) = (1/3)xg(x) = (3x)g(x)=x-3
- Q You notice that your 39 gallon aquarium is leaking 1.5 gallons of water per day. Write a function 'f(t)' to represent the amount of water in the aquarium asa function...
- Q For f(x) = (x ? 1) and g(x) = 1 - 8x, find the following.(a) (fog)(x)(b) (gof)(x)(c) f(f(x))(d) f(x) = (f. f)(x)
- Q Select the correct answer.The area of undeveloped land in a suburban town is decreasing at a rate of 17.3% annually. In 2016, there were 3,400 acres of undevelopedland. If t...
- Q Write a general formula to describe the variation.The square of T varies directly with the cube of a and inversely with the square of d; T = 3 when a...
- Q What is the transformation of the function f(x) = 2^(x-4) compared to the parent function f (x) = 2^x ?Shifted right 4 unitsShifted left 4 unitsShifted up 4 unitsShifted down...
- Q An object is dropped from 20 feet below the tip of the pinnacle atop a 920-ft tall building. The height h of the object after t seconds is given by...
- Q Consider the polynomial function.f(x) = x + 2x - 11x - 5x - 6Which statement correctly describes the number of possible positive zeros and the number of possible negative zeros?The...
- Q I am the only toolkit function that has a start and end number for the range. I am also the only that is cyclic, meaning I repeat over and over.Which...
- Q What is the inflection point of the graph of f(x) = -x + 24x - 27?
- Q Let f (x) = (x + 1) and g(x) = f- (x).What is the slope of the curve g(x) = f (x) at the point (8, 1)?g'(8) = -1g'(8) =...
- Q 3 points:Suppose a children's swimming pool is filled with 34 gallons of water, but it has a small leak and loses 1.3 gallons of water per hour.a) Write a function,...
- Q I am the only toolkit function whose domain contains no negative numbers but my range does.Which toolkit function am I?Exponential FunctionLogarithmic FunctionAbsolute Value FunctionQuadratic FunctionRational FunctionSquare Root FunctionLinear FunctionCubic FunctionConstant...
- Q Let f(x) be defined such that f(2) = 3 andf'(x) = cos(1/x + x) where 1 < x < 4.Part A: Find the tangent line approximation for f(2.1). (25 points)Part...
- Q Determine and classify the discontinuities, if any, of m.m(x) =6x/(7x-x^2)State the removable discontinuities, if any, of m. If multiple removable discontinuities exist, enter solutions using a comma-separated list.m has a...
- Q A ball bounces to a height of 6.1 feet on the first bounce. Each subsequent bounce reaches a height that is 82% of the previous bounce. What is the height,...
- Q f(x) = |x|g(x) = x + 1We can think of g as a translated (shifted) version of f.Complete the description of the transformation.Use nonnegative numbers.To get the function g, shift...
- Q While a function may not be one-to-one when defined over its "natural" domain, it may be possible to restrict the domain in such a way that it is one-to-one and...
- Q An employee at the bank notices an abandoned account with a balance of $360. The bank charges a monthly fee of $8 to maintain an account. The equation for thissituation...
- Q In simplest form, what is the ratio of the change in y to the change in x for this relationship? Fill in the following:y increases units for every units of...
- Q Given the functions (x) = 2x ? 3x + 4 and g(x) = ?3x 1 determine the value of ( + g)(?1).25119
- Q f(x) = 2xg(x)=x-3What is the domain of f(x)/g(x) = 2x / x-3 ?A. the set of all real numbersB. the set of all real numbers greater than 0OC. the set...
- Q Find the unit vector in the direction of 8 6 Write your answer in component form Do not approximate any numbers in your answer 0 0
- Q north positive y 1 the first hook origin Moving vertically up from the origin is movement in the direction of positive z The first hook will be hung at a...
- Q The magnitude and direction of vectors t u and v are shown in the table Vector Magnitude Direction 5 250 t u V 335 305 155 1 0213 6 What...
- Q A vector has a magnitude of 50 and a direction of 30 Another vector has a magnitude of 60 and a direction of 150 What are the magnitude and direction...
- Q Which of the below is are equivalent to the statement that a set of vectors v Vp in R is linearly independent Suppose also that A V V2 Vp A...
- Q Vector u PQ has initial point P 3 17 and terminal point Q 9 2 Vector v RS has initial point R 30 6 and terminal point S 8 18...
- Q Vectors t 6i 2j u 4i 8j and v 4i 12j are give Part A Find the angle between vectors t and u Show all necessary calculations 5 points Part...
- Q Given u 30 cos 60 sin 60 what are the magnitude and direction of 4u O 120 150 O 120 150 O 120 240 O 120 60
- Q Describe the transformations to the parent function. Check all boxes that apply.y = -(x - 5) +3Reflects across the x-axis (opens down)shifts right 5shifts left 5shifts up 5shifts down 5shifts...
- Q Find the angle 0 (in radians) between the vectors. (Round your answer to two decimal places.)u = 6i + 8jv = -2j
- Q Find the projection of u onto v.u = (4,8)v = (6,-3)Write u as the sum of two orthogonal vectors, one of which is projvu
- Q Determine whether u and v are equivalent. Explain.Vector Initial Point Terminal PointInterpret your results.u and v have the same magnitude and direction so they are equivalent.u and v have the...
- Q Let B =be any 2 x 2 matrix.and a such that(i) Show that there are real numbersas a scalar multiple of a unit vector, and hence find anexpression for u...
- Q Given the following vector v:v = (-2,-4)Step 2 of 2: Find the linear combination of i and i that is equivalent to v.
- Q Given the following vector v:Step 1 of 2: Find a unit vector pointing in the same direction as v.v = (-2,-4)
- Q Find the magnitude and direction angle (in degrees) of the following vector.Answer 5 Pointsv = 5(cos(37)i + sin(37")j)Recall that answers entered in degrees will require a degree symbol, which is...
- Q Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.u = 3i + 7j
- Q Consider the function f(x,y) = x - 2xy+3y +5 and the point P(-1,3).a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P.b. Find...
- Q A football was thrown into the air at a speed of 37 miles per hour at an angle of 50 from the horizontal. Express this velocity in vector form. Round...
- Q Determine the value of k such that the planes 2x-3y+kz=4 and ky-z+3=0 are perpendicular and the value of k such that the planes are parallel.k = 2, no such valuek...
- Q The area of the parallelogram whose adjacent sides are given by the vectors a = 3i + j + 4k and b = i - j +k (A) ?50(B)...
- Q Find the point that is symmetric to the point (0, -3) with respect to the x-axis, the y-axis, and the originThe point symmetric to (0, -3) with respect to the...
- Q Let u and u be two vectors in an inner product space so that ||u||= 6, |v||=2 and the angle between the two vectors is 30. Find the angle between...
- Q The vector PQ has initial point P(1, -3) and terminal point Q(4, -6). Find the magnitude and direction of PQ.Select the correct answer below:|PQ|=6?2; ?=315|PQ|=3?/2 ? = 225|PQ|-6?2; ?= 135|PQ|=3?2;...
- Q Let V be a vector space with dimension n. Consider the following statements.(i) Every independent set in V is a basis for V(ii) Every set in V that spans V...
- Q 4. X(-1, 2, 6) and Y(5, 5, 12) are two points in R.a). Determine the components of a position vector equivalent to YX.b). Determine the components of a unit vector...
- Q Which of the following represents vector u=RS in linear form, where R (-22, 6) and S(-35, 14)?v= 8i - 13jv= -8i +13jv = 131 + 8jv= -13i + 8j
- Q Given the following vectors, calculate - 9u +7v.u = {-9,-8}, v = {-1, -3}
- Q Given the vector u defined by the points: (3,4), (8, -7). Find the component form of the vector. Assume the first point is the initial point and the second point...
- Q Find the magnitude and the positive direction angle for u. u= (12,-5).
- Q Vector u has initial point at (4,8) and terminal point at (-12, 14). Which are the magnitude and direction of u?a)lull = 17.088; ? = 159.444b)|lull = 17.088; ? =...
- Q For the vectors M = (?3, -2, -3) and n = (2, ?3, -1), determine the following:a). the angle between these two vectors, to the nearest degreeb). the scalar projection...
- Q Find the vector w w of length 6 6 in the direction of v = 8 i +7j. v=8i+7j. (Give your answer using component form or standard basis vectors. Express...
- Q Find the angle between the vectors (7, 2) and (9, -3). Carry your intermediate computations to at least 4 decimal places. Round your final answer to the nearest degree.
- Q Find the angle between the vectors (-9, -8) and (-8, 7). Carry your intermediate computations to at least 4 decimal places. Round your final answer to the nearest degree.
- Q Let u = -5i +2j and v=-5i-5j. Decompose u into two vectors u1, and u?, where u1, is parallel to v and u2, is orthogonal to v.Write your answers in...
- Q Find the direction angle of the vector u = -3i+5j. That Is, find the angle between 0 and 360 that u makes with the positive x-axis (measured counterclockwise), when u...
- Q (a) An angle measures 26. What is the measure of its complement?(b) An angle measures 150. What is the measure of its supplement?
- Q Find the direction angle of the vector w=6i-4j. That is, find the angle between 0 and 360 that w makes with the positive x-axis (measured counterclockwise), when w is in...
- Q u =(-4,-5)Find the magnitude of .Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.
- Q A vector u has initial point (3, 4) and terminal point (5, 1).Write u in the form u = ai+bj.u=
- Q Find the direction angle of the vector v=-8i-7j. That is, find the angle between 0 and 360 that v makes with the positive x-axis (measured counterclockwise), when v is in...
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