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Two charged particles located at #(3.5, .5)# and #(−2, 1.5)#, have charges of #q_1 =3µC#, and #q_2=−4µC.# Find a) the magnitude and direction of the electrostatic force on q2? Locate a third charge #q_3= 4µC# such that the net force on #q_2# is zero?

Three identical point charges, each of mass m =0 .100kg and charge q hang from three strings. If the lengths of the left and right strings are L = 30 cm and the angle with vertical is θ = 45 .0◦, What is the value of charge q?

Why are the walls of arteries proportionally thicker than those of the corresponding veins?

An object having a net charge of 24µC is placed in a uniform electric ﬁeld of
610 N/C directed vertically. What is the mass of this object if it “ﬂoats” in the ﬁeld?

An electron is released from rest in a uniform electric of magnitude 2.00×104 N/C. Calculate the acceleration of the electron (Ignore gravitation)?

What is the magnitude of a point charge that would create an electric ﬁeld of 1.00 N/C at points 1.00m away?

Four charges are placed at the vertices of square with side of 5 cm. The charges are: #1, 1, 2 2 xx 10^(8) C#. What is the Electric field at the center of the circle?

A spherical water drop 1.20µm in diameter is suspended in calm air owing to a downward–directed atmospheric electric ﬁeld #E = 462 N/C#. (a) What is the weight of the drop? (b) How many excess electrons does it have?

What is the total charge of 75.0 kg of electrons?

(a) How many electrons would have to be removed from a penny to leave it with a charge of #1.0×10^7 C#? (b) To what fraction of the electrons in the penny does this correspond? [A penny has a mass of 3.11g; assume it is made entirely of copper.]

A point charge of #3.00×10^6 C# is #12.0cm# distant from a second point charge of #−1.50×10^6 C#. Calculate the magnitude of the force on each charge?

In ﬁssion, a nucleus of uranium–238, which contains 92 protons, divides into two smaller spheres, each having 46 protons and a radius of #5.9×10^15 m#. What is the magnitude of the repulsive electric force pushing the two spheres apart?

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?

An electron and a proton are each placed at rest in an electric ﬁeld of 520N/C. Calculate the speed of each particle 48ns after being released?

Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: #f(x)=33x^3245x^2+407x35#?

Use the Rational Zeros Theorem to find the possible zeros of the following polynomial function: #f(x)=2x^39^2+10x3#?

The electrons in a particle beam each have a kinetic energy of 1.60×10−17 J. What are the magnitude and direction of the electric ﬁeld that will stop these electrons in a distance of 10.0cm?

SImplify this expression: #{[(1+5/4)−(1+3/2)+(2+1/4)]−1/6+5/2}+(5/3+1)#?

When opening the kitty Yosief counted 700 coins from 1€ (one euro) and 2€. Knowing that the ratio of the 1€ coin to the 2€ coin is #3:2#, how many coins of 2€ does Yosief need to add to the kitty so he can have six 200 € banknotes (6 paper notes of 200)?

Calculates the Principal that produced an interest of $650 at the rate of 4 % per annum in 150 days? Calculate using simple interest rate assumption?

In a rightangled triangle the sum of the minor cathetus and the hypotenuse is #104cm#. The minor cathetus is #3/5# of hypotenuse. Calculate the perimeter and area of the triangle?

A cyclist takes part in a race with four stages. In the first stage he completes #5/12# of the entire course, in the second he complets #7/20# of the course #1/6# in the third . What fraction is the fourth stage?

Simplify this expression: #{[(2/5)^2xx(15/4)^2xx(1/9)]:(1/6)xx6}/{(2/3)^2xx(1)^2xx(3/2)^3}#?

I buy 5 notebooks and 3 albums spending $13.24, then I buy another 3 books and 6 albums spending $17.73. How much does each book and album cost?

Find the sum of the following number sequence:
#1+2+3+4+5+6+7+8+9+10#?

Find the sum of the following number sequence: #2+4+6+8+10#?

Find the sum of the following number sequence:
#3+5+7+9+11#?

The sum of eight consecutive (one after the other) numbers is 88. What are the numbers?

Find an easy way to evaluate the following series: #3+5+7+cdots+ 17+19+21#?

Fill each box of the magic square, with a number such that the number adds up to 18 horizontally, vertically and diagonally? #[(, ,), (, ,), (, ,)]#

Fill each box of the magic square, with a number such that the number adds up to 18 horizontally, vertically and diagonally? #[(, ,5), (,8 ,), (, ,9)]#

Maya was 6th in line. Yosief was 6th from the end of line and there were 3 children between Maya and Yosief. How many children were there in the line?

35 students took part in freestyle swimming event. 23 took part in the backstroke event and 10 students took part in both. How many students in total took part in the event?

A Captain, Quartermaster, First Mate in a pirate ship divide a loot of coins. The 1st gets 1,400 coins, the 2nd 700 more than the first and the 3rd 1/2 of the combined. How much coins do they have? How much does the captain gets?

Simplify the following expression: #2 + 2 ⋅{(14 + 6) 5: + (3⋅8):[12 − (3 + 2 ⋅3)]−15 :(2 + 2:6 )}− 2 ⋅ 9 =#?

Your father borrows $40 and agrees to 24% interest in a year? He decide that he wants to payoff what he owe in 1/2 a year. How much does he have to pay you in 1/2 a year? Yo convince him to keep the money for 2 years how much would he pay you in 2 years?

Simplify this expression: #[(12:4 + 9:1 + 15:5) · 2 – (1+1+8+16+1)] : 3 #?

Simplify this expression: #[(63/5)xx(1/4+2/95/12)+3/2xx(9/27/45/2)]xx2/27+1/4 #?

Simplify this expression: # [(17/319/4+5/24)+5/24]^2:(18/15+5/61/30)^3#?

Show that in the Denominator Addition/Subtraction Property of proportions: If #a/ b = c/ d#, then #( a + b)/ b = ( c + d)/ d# or #( a − b)/ b = ( c − d)/ d#?

What is x in the following ration equation # => x:(23/42 +x)=8/25 : 14/15#?

An urn contains 100 marbles: 20 white, 30 red, 50 green. Calculate the probability of selecting White, Red and Green marbles respectively. What is the probability of pulling a white, green, white and red marbles consecutively?

Calculate the probability of obtaining obtaining on rolling a fair dice: a) an even number, b) a number greater than 2, c) an odd number, d) a number divisible by 3?

Find the intersection point between #x^2+y^24x2y=0# and the line #y=x2# and then determine the tangent that those points?

Knowing the extreme points of a diameter in circle are #A(3,1) and D(2,5)#, find the canonical equation of a circle?

Solve the following system of equation:
#[((1), sqrt(2)x+sqrt(3)y=0),((2), x+y=sqrt(3)sqrt(2))]#?

Solve the following system of equations:
#(x^2+y^2=29),(xy=10)#
?

Solve the following system of equations #[((1) " ", (2x + y + 3z = 12)),((2) " ",(4y – z = 7)),((3) " ",(5x + 8z = 34))]#?

Grandfather is #15# time the age of his grandson today, in #10# years the grandson will be #3/17# the age of the grandfather. How old are the grandfather and grandson?

Grandfather is #15# time the age of his grandson today, in #10# years the grandson will be #3/17# the age of the grandfather. How old are the grandfather and grandson?

How do you solve the inequality: #x^29x+15>1 #?

How do you resolve the following inequality: #((x^24)(3x6))/(x7)>0#?

A right triangle with a hypotenuse of 34 cm and a minor cathetus 16 of cm rotates 360° about the major cathetus. What shape does it form? How do you calculate the surface area and volume of the shape it forms?

The sum of the altitude and the base radius of a cylinder is #63 cm#. The radius is #4/5# as long as the altitude. Calculate the surface area volume of the cylinder?

The sum of the altitude and the base radius of a cylinder is #63 cm#. The radius is #4/5# as long as the altitude. Calculate the surface area volume of the cylinder?

How do you simplify: #1/4x^2y^2z+25/4x^2z5/2x^2yz#?

The coefficients #a_2 and a_1# of a 2nd order polynomial #a_2x^2+a_1x+a_0=0# are 3 and 5 respectively. One solution of the polynomial is 1/3. Determine the other solution?

Solve the following algebraic equation: #2x^2x=2x^2x+8#?

Show that the diagonals of a trapezoid divide it into four triangles of which two have the same area? "equiextension"

Let #hat(ABC)# be any triangle, stretch #bar(AC)# to D such that #bar(CD)≅bar(CB)#; stretch also #bar(CB)# into E such that bar(CE)≅bar(CA). Segments #bar(DE) and bar(AB)# meet at F. Show that #hat(DFB# is isosceles?

An Isosceles Trapezium with a perimeter of 40cm is circumscribed in a circle with radius, r=#sqrt(21)#. Determine the lengths of its sides?

For what value of the parameter #k# does the curve function #y=x^3+kx+k^2−6k+5# passes through the origin?

A triangle #hat(ABC)# has vertices of #A(1,3);B(1/2,3/2);C(2,1)#. Verify that the triangle is isosceles and calculate the area and perimeter?

Solve the following equation: #(x^22)/3+((x^21)/5)^2=7/9(x^22)#?

Use limits to verify that the function #y=(x3)/(x^2x)#has a vertical asymptote at #x=0#? Want to verify that #lim_(x >0)((x3)/(x^2x))=infty#?

Prove Euclid's right traingle Theorem 1 and 2: #ET_1 =>\overline{BC}^{2} = \overline{AC}*\overline{CH};#
#ET'_1 =>bar(AB)^{2} =bar(AC)*bar(AH)#;
#ET_2 =>barAH^{2} = \overline{AH}*\overline{CH}#?
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Show that in rhombus the side,
1) #=>" "l = sqrt(d_min^2/4 + d_(maj)^2/4)#
Where #d_min = "minor diagonal" " " d_(maj) = "major diagonal"#
2) #=>" "r = (d_mind_(maj))/(4l) #
Where #l and r# are the side of rhombus and radius of inscribed circle?

A cone has a surface area of #600π cm^2# and a base area of #225π cm^2#. Calculate: the apothem and volume of the cone?

A solid is formed by a pyramid mounted on a cube, the base coinciding with cube's upper face. Side of cube is #16 cm# and the apothem of the pyramid is #17 cm#. Calculate: the total surface area, the volume and mass knowing is made wood #0.65 g/(cm^3)#?

A train covers 60 miles between 2 p.m. and 4 p.m. How fast was it going at 3 p.m.?

How high can a baseball player throw a ball in the air if he can throw it with initial velocity 160 km/h? What would that be standard units?

A car is accelerating at #12m/s^2# . What is the acceleration in #km/h^2#?

Yosief and his family went to San Diego for summer vacation. Yosief plotted the speed versus time on his note book see below. Estimate the distance to San Diego using Yosief's plot?

You bicycle 3.2 km east in 0.1 h, then 3.2 km at 15.0 degrees east of north in 0.21 h, and finally another 3.2km due east in 0.1 h to reach its destination. What is the average "velocity" for the entire trip?

An automobile traveling 90 km/h overtakes a 1.5kmlong train traveling in the same direction on a track parallel to the road. The train speed is 70 km/h,
 how long does it take the car to pass it
 how far will the car have traveled in that time?

The tallest spot on Earth is Mt. Everest, which is 8857 m above sea level. If the radius of the Earth to sea level is 6369 km, how much does the magnitude of g change between sea level and the top of Mt. Everest?

A person stands 40 m from a flagpole. With a protractor at eye level, he finds the angle at the top of the flag pole with the horizontal is 25.0 degrees. How high is the flag pole? The distance from his feet to his eyes is 1.8 m.

Yosief goes on adventure drive to Yellowstone with his family. The journey takes 17 hours and Yosief charts the speed of the RV from the Tachometer on notebook, see below. Use Yosief's chart to estimate the distance from Phoenix to Yellowstone?

A point object is moving on the cartesian coordinate plane according to:
#vecr(t)=b^2thatu_x+(ct^3−q_0)hatu_y#. Determine:
a) The equation of the trajectory of object on the cartesian plane
b) The magnitude and direction of the velocity?

A point object is moving on the cartesian coordinate plane according to:
#vecr(t)=b^2thatu_x+(ct^3−q_0)hatu_y#. Determine:
a) The equation of the trajectory of object on the cartesian plane
b) The magnitude and direction of the velocity?

A boat that can move 50 km/h, wants to cross a 2 Km wide river, with current of 20 Km/h. Discuss what direction should the boat go to for the shortest distance to the bank. Discuss now what route will result in shortest time?

Two motorcycles A and B depart simultaneously from opposite location toward one another 50km apart. The have 120km/h and 80km/h. Determine time the meet and distance travelled?

A truck is traveling at 90km/h when the driver sees an obstacle 85m away. The driver brakes and decelerates at #3.80m/s^2#.
Determine:
A) the time required to stop.
B) the distance required to stop.
C) the distance to reach half the initial speed?

What is the equation of the locus of points at a distance of #sqrt(20)# units from #(0,1)#? What are the coordinates of the points on the line #y=1/2x+1# at a distance of #sqrt(20)# from #(0, 1)#?

Describe and write an equation for the locus of points equidistant form #A(a_x, a_y) and B(b_x,b_y)#? Test what you derived for #P_A(2,5) and P_B(6,1)? #

Let #A(x_a,y_a)# and #B(x_b,y_b)# be two points in the plane and let #P(x,y)# be the point that divides #bar(AB)# in the ratio #k :1#, where #k>0#. Show that #x= (x_a+kx_b)/ (1+k)# and #y= (y_a+ky_b)/( 1+k)#?

If #P(x,y)# lies on the interval #A(x_1,y_1), B(x_2,y_2)# such that #AP : PB =a : b#, with a and b positive, show that #x= (bx_1+ax_2) /(b+a)# and #y=(by_1+ay_2)/(b+a)#?

Let A be #(−3,5)# and B be #(5,−10))#. Find:
(1) the length of segment #bar(AB)#
(2) the midpoint #P# of #bar(AB)#
(3) the point #Q# which splits #bar(AB)# in the ratio #2:5#?

Consider the angle sum formulas:
#sin(A+B)=sinA cosB+cosA sinB#
#cos(A+B)=cosA cosB−sinA sinB#
show that #tan(90^0+θ)=− 1/tanθ#.
and use this identity to prove that lines #y = mx and y = m_1x# are perpendicular iff #mm_1=−1#?

Let #l# be a line described by equation ax+by+c=0 and let #P(x,y)# be a point not on #l#. Express the distance, #d# between #l and P# in terms of the coefficients #a, b and c# of the equation of line?

Let #l# be a line described by equation ax+by+c=0 and let #P(x,y)# be a point not on #l#. Express the distance, #d# between #l and P# in terms of the coefficients #a, b and c# of the equation of line?

Express the area of a triangle given by vertices, #A(x_1,y_1), B(x_2,y_2), C(x_3,y_3)#. Show that it can be expressed as determinant of:
#det(Delta) = [(1, 1, 1 ),(x_1, x_2, x_3),(y_1, y_2, y_3) ]#.Calculate the area of A(3,6), B(7,8), & C(5,2)?

A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?

A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?

Find the area of the shaded region (green) knowing the side of square is #s = 25 cm#?

Calculate the area a brick region? The length from the base of the rectangle to the top of the arc is called "Sagita".

Calculate the radius and the area of the brick region?

Calculate the base of the rectangle?

Calculate the radius and the area of the brick region?

Calculate the area a brick region? The length from the base of the rectangle to the top of the arc is called "Sagita". The small side of the bridge into the sagita, #e=21#.

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