Questions asked by Yonas Yohannes
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In the triangle embedded in the square what is the measure of angle, #theta#?
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A composite geometrical shape is made up of a square, equilateral and right triangles. Calculate the area of hatched triangle?
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For the composite geometric shapes given the semi circle has the same area measure as the right angle triangle, and the base of right triangle is congruent to the radius of the semicircle. Calculate the value of angle #theta#?
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Give a composite shape of quarter of circle and rectangle with a total area of #570 " square feet"# and and the diagonal angle of the rectangle equal to #18.43^0#, calculate the radius?
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Let #sqrt(1 + sqrt(3 + sqrt(5+ sqrt(x)))) = 2#
What x?
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Let #[(x_(11),x_(12)), (x_21,x_22) ]# be defined as an object called matrix. The determinant of of a matrix is defined as #[(x_(11)xxx_(22))-(x_21,x_12)]#. Now if #M[(-1,2), (-3,-5)]# and #N =[(-6,4), (2,-4)]# what is the determinant of #M+N# & #MxxN#?
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Given the right trapezoid calculate angle #theta# and the area of triangle #hat(EAD)#, provided #EA=4, AB=BC=CD=DA=2, AB_|_EC#?
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Simplify: #(12−5^2-:5)*4^2-:2^3+2^2−1+[(2^4-:2^3)^3+4^3-:4+2^5]-:7#?
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Solve for#x#, #=>(1− 5 /12)-:(5/6+1/3)=x-:(9/8
− 5/8)#?
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Draw in the cartesian coordinates the polygon having the following vertices #A(3, 2), B(10, 2), C(10, 7) and D(3, 7)#. What kind of geometric figure did you come up with? Upload your drawing?
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A isosceles triangular prism has a height of #15 cm#, the perimeter of the base is #32 cm# and the base of the triangle is #6/5# the side. Calculate the surface area of the prism?
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A right trapezoidal prism has base dimensions of #40 cm and 56 cm# and a height of #30 cm#. Calculate the volume, surface area and the weight of the prism, knowing it is #120 cm# high and has a density of #2.5 gm/cm^3#?
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Simplify the following expression: #101-{[(110 -: 2)-: 11]xx(10+4xx2) +7}+ [8xx(20 -: 5-1)-3xx3] -: 5#?
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Simplify: #{(6^6)^4 -: (6^7)^0 xx[(6^2)^3]^2}^2 -: {[(6^3)^5xx(6^2)^3]^3 : [(6^3)^3]^4}^2#?
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Simplify the aritmetic expression: #[3/4 ·1/4 ·(5− 3/2)-: (3/4 −
3/16)] -: 7/4 ·(2 + 1/2)^2 −(1 + 1/2)^2#?
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Simplify this expression: #[(−1/2)^2]^3-:2^-3 ·(−1/2)^-4 -: 2^11 =#?
Hint: #[(1/a)^n]^m= (1/a)^(n+m)#
#a^j xx a^k = a^(j+k)# this true for all power expression so long they have the same base
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A composite geometric shape of triangle and rectangle is given with the proportionate relation given in the figure. Find angle #alpha# and #theta#?
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A #5 cm# high prism has a right triangle base with cateti #6 cm and 8 cm# long. Calculate the surface area using a perimeter construct and a single formula. Calculate also the volume?
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Calculate x, y, Perimeter and area of the composite geometrical figure?
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The ancient Greeks struggled with three very challenging geometric problems. One of them, "Using only a compass, and a straightedge trisect an angle?". Research this problem and discuss it? Is it possible? If yes or no, explain?
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One of the Ancient Greeks famous problem entails, the construction of square whose area equals that of circler using only compass and straightedge. Research this problem and discuss it? Is it possible? If no or yes, explain providing clear rational?
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Ancient Greek's famous geometric problem is the doubling of the cube. It entail of constructing a cube with twice the volume as a given cube, using only a compass and straightedge. Using a mathematical approach to show it is impossible?
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Payton colored a composite shape made up semicircles whose diameters are the sides of a square. The result is a shape given below. Find the area of the shaded region (Petals) in terms of x? Calculate the area using the dimension in 2nd figure?
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In the diagram below, the small circle is centered at E, the large one is centered at O. The segments FC and OD have lengths as of 2.38 and 3 cm respectively. Find the length of CD and calculate shaded area?
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Find the area of the yellow shaded area govern the larger pentagon side #s=5.5# and area of the smaller pentagon (green) #A_(pentagon) = 7.59 cm^2#?
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Suppose that #lim_(xrarrc) f(x) = 0# and there exists a constant #K# such that #∣g(x)∣ ≤ K " for all " x nec# in
some open interval containing c. Show that# lim_(x→c)
(f(x)g(x)) = 0#?
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Suppose #lim_(x→0
+)f(x) = A and lim_(x→0
-)f(x) = B.# Determine
#a. lim_(x→0−)
f(x^2 − x)#
#b. lim_(x→0−)(f(x^2) − f(x))#
#c. lim_(x→0+)f(x^3 − x)#
#d. lim_(x→0−)(f(x^3) − f(x))#
#e. lim_(x→1−)f(x^2 − x)#?
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Find b, c and d so that the quadrilateral is a parallelogram with area equal to 80 square units?
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In the parallelogram find: the value of x, total perimeter and area of DEIK?
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Which triangles in the figure above are congruent and/or similar?
Find the value of x, angle #/_ACE# and the area #hat(AEC)#, and #BFDC#.
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In the figure given identify the congruent and/or similar triangles and find the value of x and y?
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Suppose you have a triangle measuring 3, 4, and 5, what type of triangle is that? Find it's perimeter and area?
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Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?:
1) #12, 16, 20#
2) #15, 17, 22#
3) #6, 16, 26#
4) #12, 12, 15#
5) #5,12,13#
6) #7,24,25#
7) #8,15,17#
8) #9,40,41#
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Suppose you have a traingle with sides: #a, b and c#. Using pythagorean theorem what can you deduce from the following inequality?
i) #a^2+b^2 = c^2#
ii) #a^2+b^2 lt c^2#
iii) #a^2+b^2 gt c^2#
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Use proportions to solve for x on the given triangular composite figure?
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Suppose #ΔDFG and ΔJKL# are both right and isosceles, which postulate
is sufficient to prove similarity?
a. Angle-Angle
b. Side-Side-Side
c. Side-Angle-Side
d. Angle-Side-Angle
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The ratio of my blue pens to my black pens is #7:2#; I add four more black pens to my collection. How many blue pens must I add to maintain the same ratio of blue to black?
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Name the following triangle: #ΔQRS#, where #m∠R = 94, m∠Q = 22 and m∠S = 90#?
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Check if the following are triangles? If yes name them?
1) #ΔTAR, ∠T= 184 and ∠A = 86#
2) #ΔDEZ, ∠D = 60 and ∠E = 60#
3) #ΔCHI, ∠C = 30, ∠H = 60 and ∠I = 90#
4)#ΔJMR, ∠J = 5, ∠M = 120 and ∠R = 67#
5) #ΔKLM, bar(KL) = bar(LM) = bar(MK)#
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Using the following figure, identify relationship of the angles or sum of the angles?
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Answer the following questions?
1) What the angle vertical to ∠NOM
2) What is the angle vertical to ∠TLK
3) Identify the pair of angles supplementary to ∠NOM
4) What the measurement of angles ∠1, ∠2, and ∠3
5) What is the measure of exterior ∠OPS?
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What are complementary, supplementary and vertical angles?
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An angle is twice as large as its complement, what is the measure of the angle and its complement?
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An angle is #50^0# less that its supplement. What is the measure of the angle and its supplement?
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Prove that given a line and point not on that line, there exactly one line that passes through that point perpendicular through that line? You can do this mathematically or through construction (the ancient Greeks did)?
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Prove that If two parallel lines are cut by a transversal then, any two angles are either congruent or supplementary?
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Show that the area of a triangle is #A_Delta = 1/2 bxxh# where b is the base and h the altitude of the traingle?
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Show the area of a trapezoid is #A_T = 1/2 (B+b)xxh# where #B= "Large base"#, #b= "is small base"# and #h= "altitude"#?
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Consider any triangle (see figure). Define #sin theta = h/c#, show that the area of triangle is #A_Delta = 1/2 (b*c) sintheta# where #b and c# are any two sides of the traingle that make the angle #theta#?
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Two overlapping circles with equal radius form a shaded region as shown in the figure. Express the area of the region and the complete perimeter (combined arc length) in terms of r and the distance between center, #D#? Let #r=4 and D=6# and calculate?
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A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?
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If the mean of numbers 28, x, 42, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x?
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The average of 5 numbers is 6. The average of 3 of them is 8. What is the average of the remaining two?
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Positive integers from 1 to 45, inclusive are placed in 5 groups of 9 each. What is the highest possible average of the medians of these 5 groups?
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Analysis on monthly incentive of 5 salesman shows the mean & median of the incentives is $7000. The mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest?
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Three friends Alice, Bond and Charlie divide $1105 among them. When $10, $20 and $15 are removed from the sums that Alice, Bond and Charlie received, the share of the sums that they receive is in the ratio of 11 : 18 : 24. What did Charlie receive?
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A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be C's share of the earnings?
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Mary and Mike enter invest $700 and $300 in a partnership. They divided their profits as follows: #1/3# is divided equally the remainder is split according to the investments. If Mary received $800 more than Mike, what was the profit made by the business?
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The area of a square field is #24,200 m^2#. How long will Maya take to cross the field diagonally at the rate of 6.6 km/hr?
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Sue the T-Rex grows cabbage in a square shaped garden. Each cabbage takes #1 ft^2# of area in the garden. This year, she increased her output by 211 cabbages compared to last year, If the shape remains a square how many cabbages did she grow this year?
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What values of 'x' will be the solution to the inequality #15x - 2/x > 1#?
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Yosief buys 10 apples for $1. At what price should he sell a dozen apples if he wishes to make a profit of 25%?
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By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What % profit will the merchant make if the article is sold at 95% of its marked price?
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There are 120 students waiting to go on field trip. The students are numbered 1 to 120, all even numbered students go on bus1, those divisible by 5 go on bus2 and those whose numbers are divisible by 7 go on bus3. How many students did not get in any bus?
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Out of 200 kids, 100 had a T-Rex, 70 had iPads and 140 had a cell phone. 40 of them had both, a T-Rex and a iPad, 30 had both, a iPad and a cell phone and 60 had both, a T-Rex and cell phone and 10 had all three. How many kids had none of the three?
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In a class of 40 students, 12 speak both English and German. 22 speak German. If the students of the class that speak at least one of the two subjects, then how many students speak only English and not German?
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In a class 40% of the students take Math and 70% take Spelling. If 15% of the students take both Math and Spelling, what % of the students did not take either of the two subjects?
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If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by what % should he reduce the quantity of petrol that he buys?
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In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
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In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
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What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?
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Prove the following statement. Let ABC be any right triangle, the right angle at point C. The altitude drawn from C to the hypotenuse splits the triangle into two right triangles that are similar to each other and to the original triangle?
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Given the similar right triangles in the figure. Find the exact values of x and y?
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Find the value of x in the figure?
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A person is standing 40ft away from a street light that is 30ft tall. How tall is he if his shadow is 10ft long?
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In a triangle ABC (figure) the points P and Q are selected in the sides AC and BC respectively in a way that PC is half of BC and QC is half of AC:#bar(PC)/bar(BC) = 1/2; bar(QC)/bar(AC)= 1/2#. Find #bar(PQ)# if the side #bar(Ab)# is 20?
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Papa is putting new concrete on a driveway. The driveway is 30' x 10' x 9" thick. Concrete is measured by the cubic yard. One sack of dry cement mix costs $7.30, and it takes four sacks to mix up 1 cubic yard of concrete. How much will it cost?
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A regulation baseball (hardball) has a great circle circumference of 9 inches; a regulation softball has a great circle circumference of 12 inches.
a. Find the volumes of the two types of balls. b. Find the surface areas of the two types of balls?
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A composite geometry is made up of cube and a square pyramid frustum. The slanted side AK stretch a side lengths of 5.62 forming an isosceles triangle. Calculate the volume, surface area and sketch the net of the surface area?
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A 6-foot spruce tree is planted 15 feet from a lighted streetlight whose lamp is
18 feet above the ground. How many feet long is the shadow of that tree?
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In the figure below, the lengths of DE , EF , and FG are given, in units. What is the
area, in square units, of ∆DEG ?
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From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is #57°#, as shown below. If the distance between the radio antenna and the library is #1.3 mls#, how many miles high is the balloon?
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Find an expression for the area of the shaded region? Now let r= 4 cm, calculate the area?
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The diameter for the smaller semicircle is #2r#, find the expression for the shaded area? Now let the diameter of the larger semicircle be 5 calculate the area of the shaded area?
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A rectangular prism with a height of 9 inches and a volume of 162 cubic inches, a triangular prism with the same height and volume.
a) State the area of the base of each b) If the height is "h" express the base of the triangle in terms of "h"?
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A pizza packages its circular pizzas in a cardboard box. The boxes are formed by folding in 1" squares from the corners of the cardboard. If the volume of the box is 324 cubic inches, what are the dimensions of the box, in inches? Draw it?
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When placed in the box, a large pizza can be described as being "inscribed" in a square box. If the pizza is 1" thick, find the volume of the pizza, in cubic inches given the volume of the box is 324 cubic inches?
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A baker is serving a new circular brownie pizza dessert (1" thick with a volume of 132.25 cubic inches). What are the dimensions of the open-topped cardboard box needed to serve the brownie pizza (assume the brownie to be inscribed in the box)?
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We have a circle with an inscribed square with an inscribed circle with an inscribed equilateral triangle. The diameter of the outer circle is 8 feet. The triangle material cost $104.95 a square foot. What is the cost of the triangular center?
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Yosief is 4 feet 9 inch boy. He stands in front of a tree and sees that it's shadow coincide with his. Yosief shadow measures 9 feet 6 inches. Yosief measures the distance between him and the tree to calculate its height, how does he do it?
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Given a circuit with resistors R1 = 10 W, R2 = 15 W, R3 = 20 and voltage, #V_b = 12V#, see figure, find the currents through all the resistors?
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The circuit in the figure has been in position a for a long time, then the switch is thrown to position b. With #Vb = 12 V, C = 10 mF, R = 20 W#. a.) What is the current through the resistor before/after the switch? b) capacitor before/after c) at t=3sec?
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Initially switch is open, no charge on the capacitor, (a) Close the switch, find #I_i, (i = 1, 2, 3) Q, & V_C# immediately after. (b) Switch is closed for long find #I_i, Q & V_C#. (c) Find #I_i, Q, & V_c# immediately reopened? d) Reopened for long?
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No initial current in the inductor, switch in open state find:
(a) Immediately after Close, #I_1, I_2, I_3, & V_L#?
(b) Close long #I_1, I_2, I_3, & V_L#?
(c) Immediately after Open, #I_1, I_2, I_3, & V_L#?
(d) Open Long, #I_1, I_2, I_3, & V_L#?
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Let M be a matrix and u and v vectors:
#M =[(a, b),(c, d)], v = [(x), (y)], u =[(w), (z)].#
(a) Propose a definition for #u + v#.
(b) Show that your definition obeys #Mv + Mu = M(u + v)#?
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Let M and N be matrices , #M = [(a, b),(c,d)] and N =[(e, f),(g, h)],#
and #v# a vector #v = [(x), (y)].#
Show that #M(Nv) = (MN)v#?
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Solve the differential equation: #(d^2y)/ (dx^2) −8 (dy)/(dx) =−16y#? Discuss what kind of differential equation is this, and when it may arise?
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Find #(d^2y)/(dx^2)∣_[(x,y)=(2,1)]# if y is a differentiable function of #x# satisfying the equation #x^3+2y^3 = 5xy#? Plot it?
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Determine how fast the length of an edge of a cube is changing at the moment when the length of the edge is #5 cm# and the volume of the cube is decreasing at a rate of #100 (cm^3)/sec#?
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A piston is connected by a rod of #14 cm# to a crankshaft at a point #5 cm# away from the axis of rotation. Determine how fast the crankshaft is rotating when the piston is 11 cm away from the axis of rotation and is moving toward it at 1200 cm/s?
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