Answers created by Yonas Yohannes
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How do you find the roots, real and imaginary, of #y= x^2 - 3x + 4-(x-1)^2 # using the quadratic formula?
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A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 7 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?
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The base of a triangular pyramid is a triangle with corners at #(2 ,6 )#, #(5 ,3 )#, and #(8 ,7 )#. If the pyramid has a height of #18 #, what is the pyramid's volume?
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A circle has a chord that goes from #( 3 pi)/2 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #121 pi #, what is the length of the chord?
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A line passes through #(5 ,0 )# and #(7 ,3 )#. A second line passes through #(3 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?
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Points #(6 ,2 )# and #(1 ,5 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
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Circle A has a center at #(2 ,3 )# and an area of #8 pi#. Circle B has a center at #(13 ,7 )# and an area of #54 pi#. Do the circles overlap?
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What formula is used to calculate the age of the universe?
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How are black holes related to galaxies?
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What is the parallax angle?
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How can we tell what the earth core is made of?
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A container with a volume of #14 L# contains a gas with a temperature of #160^o C#. If the temperature of the gas changes to #320 ^o K# without any change in pressure, what must the container's new volume be?
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Circle A has a center at #(1 ,-2 )# and a radius of #1 #. Circle B has a center at #(4 ,2 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?
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What is the orthocenter of the triangle formed by the intersection of the lines #x = 4# , #y = 1/2x + 7# , and# y = -x + 1#?
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What is the arclength of #f(x)=x^3-e^x# on #x in [-1,0]#?
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How many asteroids are in the solar system?
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How can parallax error be avoided?
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What evidence best supports the Milankovitch hypothesis?
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Why does opportunity cost include implicit costs?
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Why is any price above or below the clearing price inefficient?
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How does elasticity affect the profit maximizing price point?
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What was Aristotle's theory of the universe?
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How do we know there is such a thing as the strong nuclear force?
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What are the tree closest galaxies to the milky way galaxy and how far away are they?
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What defines a light year?
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Which blood vessels have an outer layer of elastic in their walls?
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The retina has two specialized cells, one gives you image resolution during the day and the other gives image resolution during the night, what are they called?
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An object with a mass of #120 g# is dropped into #640 mL# of water at #0^@C#. If the object cools by #48 ^@C# and the water warms by #8 ^@C#, what is the specific heat of the material that the object is made of?
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How do you find the inverse of #A=##((1, 3, -1), (2, 5, 1), (1, 4, -4))#?
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How do you use the rational roots theorem to find all possible zeros of #f(x)=x^3+x^2-8x-6 #?
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How do you long divide # (x^3 + 9x^2 + 7x + 3 ) div (x+2) #?
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Which biomes are suffering the most from climate change?
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Can someone list examples of ecological/environmental, social/economic and political effects of climate change?
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What is the perimeter of a triangle with corners at #(3 ,5 )#, #(1 ,6 )#, and #(4 ,3 )#?
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A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/12 #, and the triangle's area is #8 #. What is the area of the triangle's incircle?
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How do you name aromatic rings?
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What does hydrolysis of an amide using an acid catalyst produce?
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An object is at rest at #(4 ,7 ,1 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(3 ,1 ,6 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
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How can the Pythagorean Theorem be proved using a mean proportional in a 2-column format?
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How do you convert #2+(sqrt 3)i# to polar form?
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If #A= <7 , 2># and #B= <-7, -1 >#, what is #||A+B|| -||A|| -||B||#?
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How do you graph #y=2 sin 4(x+pi/4) #?
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How do you graph #r = sin(2θ)#?
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What is the angle between #<-3,2,0> # and #< 5,0,2 >#?
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How do you divide #( i+8) / (5i +5 )# in trigonometric form?
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How do you convert #(6, pi/4)# to rectangular form?
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The base of a triangular pyramid is a triangle with corners at #(6 ,8 )#, #(2 ,4 )#, and #(7 ,3 )#. If the pyramid has a height of #2 #, what is the pyramid's volume?
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How does a hydrolysis reaction separate a polymer into its monomers?
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Why was Ogelthorpe's prohibition of slavery reversed?
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Question #3eaec
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A triangle has corners A, B, and C located at #(1 ,8 )#, #(6 ,3 )#, and #(7 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
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A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #39 # and the height of the cylinder is #17 #. If the volume of the solid is #66 pi#, what is the area of the base of the cylinder?
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An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #14 # and the triangle has an area of #42 #. What are the lengths of sides A and B?
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What is the orthocenter of a triangle with corners at #(6 ,3 )#, #(2 ,5 )#, and (7 ,9 )#?
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A circle's center is at #(2 ,1 )# and it passes through #(3 ,1 )#. What is the length of an arc covering #(13pi ) /12 # radians on the circle?
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What is the perimeter of a triangle with corners at #(3 ,6 )#, #(1 ,5 )#, and #(8 ,1 )#?
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What does a z-test measure?
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What is an F-test?
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What is the variance of X if it has the following probability density function?:
f(x) = { 3x2 if -1 < x < 1; 0 otherwise}
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What type of data warrants the use of an augmented Dickey-Fuller?
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What are the mean and standard deviation of a binomial probability distribution with #n=100 # and #p=1/10 #?
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Let X and Y have joint density given by f(x,y) = 6(1-y) for 0 ≤ x ≤ y ≤ 1. What is Cov(X,Y)?
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What is a fixed effects model?
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How do you find the number of permutations of the first 13 letter of the alphabet taking 4 letters at a time?
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A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #5 #, #2 #, and #11 #, respectively. What is the rectangle's area?
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Point A is at #(1 ,-1 )# and point B is at #(-2 ,9 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
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A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/4 #, and the triangle's area is #3 #. What is the area of the triangle's incircle?
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A triangle has corners at #(-3 ,5 )#, #(7 ,6 )#, and #(1 ,-4 )#. If the triangle is dilated by a factor of #2/3 # about point #(-3 ,4 ), how far will its centroid move?
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Who was Mansa Musa? Why is he important?
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Why did the National Assembly declare war on Austria in April 1792?
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How might the rule of Wu Zhao have compared with the rule of men during that era?
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Question #57f13
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During World War II, which Allied nation suffered the most military deaths?
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How can fiscal policy affect inflation?
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What is the mathematical formula for how marginal revenue changes with quantity sold?
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How does marginal cost generally change with quantity?
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Why are price controls necessary in select markets or industries?
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Points #(5 ,2 )# and #(1 ,4 )# are #(5 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
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Two rhombuses have sides with lengths of #2 #. If one rhombus has a corner with an angle of #pi/3 # and the other has a corner with an angle of #(5pi)/8 #, what is the difference between the areas of the rhombuses?
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How do you solve #6x^2-8x-3=0# using the quadratic formula?
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How do you solve #x^2/(x^2-4) = x/(x+2)-2/(2-x)#?
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How do you solve #5x+12=x-4#?
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What is the difference between a Cournot and Bertrand competition?
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How does the BLS determine underemployment?
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What are sticky wages and what cause them to exist in an economy?
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How does Calcium Hypochlorite disinfect water?
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What experiments led to the development of the Bohr Model of the atom?
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Question #b1a9b
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What is the difference between london dispersion and van der waals forces?
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Question #a0a4c
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Question #027ed
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How do you write a polynomial in standard form given the zeros x=-9 and -i?
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What are the two most common elements in the sun? What three other elements are also produced in the sun?
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How do you write the equation #y+9= -3(x-2)# in standard form?
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How do you differentiate #g(x) = (2x^2 + 4e^x) ( 2x + 2)# using the product rule?
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What is the arclength of #f(t) = (te^(2t)-e^t-3t,-2t^2)# on #t in [1,3]#?
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What is the force, in terms of Coulomb's constant, between two electrical charges of #-1 C# and #-2 C# that are #4 m # apart?
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The force applied against an object moving horizontally on a linear path is described by #F(x)=x^3+ 3 #. By how much does the object's kinetic energy change as the object moves from # x in [ 3, 5 ]#?
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An object with a mass of #4 g# is dropped into #650 mL# of water at #0^@C#. If the object cools by #12 ^@C# and the water warms by #30 ^@C#, what is the specific heat of the material that the object is made of?
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Two small positively charged spheres have a combined charge of #5.0×10^-5 C#. If each sphere is repelled from the other by an electrostatic force of 1.0N when the spheres are 2.0m apart, what is the charge on each sphere?
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