How do you find the vector equation of a line when given two points?
First we need the direction vector = (4,5,0)-(-4,-5,2)=(8,10,-2)Required vector equation r(t)=(4,5,0)+t(8,10,-2)=(4+8t, 5+10t, -2t)
Can anyone help me with these functions and inequalities and math stuff?
I need help with the following problems for test corrections. It's Algebra II stuff. Can anyone explain these to me? 1. I know the answer, but I copied it off someone who was helping me during class and don't really get it. ** Convert 20mph to ft/sec 5280ft = 1 mile 20mph/hr 1hr/60min 100min/3600sec 105600/3600 = 88/3 ft/sec 2. Solve 2/5x + 1/6 = 3/10x + 1/3 3. Solve for x: xy + xz = y 4. Tell whether the relation is a function. If not, why? (which it isn't because I said "yes" since I didn't know and didn't want to explain XD ) (-1, 3) (2, -6) (-1, 5) (4, -9) 5. For this problem, I just want to make sure you're only graphing a point, right? ** Solve for Y, then sketch a graph. 2x - 6y = 12. 2(0) - 6y = 12 -6y = 12 y = -2 2x - 6(0) = 12 2x = 12 x = 6 (6, -2) 6. I don't get if you're just finding a point or what... ** Solve for Y then graph the inequality in a coordinate plane: x - 4y < -12
Calc Q: ind a linear function that can be used to approximate the rate for holes that are close to 25 feet bel?
Torricelli's Theorem states: that if there is a hole in a container of liquid, then the liquid will flow out a a rate given by R(h) = squareroot (2gh) where g = 32 ft / sec^2. Find a linear function that can be used to approximate the rate for holes that are close to 25 feet below the surface of the water. Answer is f(h)=(4/5)h+20 explain please
A line makes an angle of 45 degrees with the x-axis. What is the slope of the line?
hey bro,I have assume that you don't know the meaning of slope, so let us find outslope: it is the change of something ( say y), with respect to some other thing ( say x). example: velocity is the rate of change of displacement with respect to time.in the same way if we take this knowledge and relate it with the graphical representation.we will get to know that the line ( say y) when is elevated from the origin to 45 degrees with respect to x axis, then slope is equal to the change in y divided by change in x. By using trigonometric ratios tanθ = change in y divided by change in x.hence we can conclude that tanθ = slope.in your case θ = 45 degrees.therefore, slope = tan45and slope = 1 ……………………………………………(tan45=1)hope you are totally satisfied with this contempt answer.this once is not for the person who asked question.the writer takes a deep breathe in and …….. submits the answer.
Find the range of f(x) =2-3x, x belongs to real numbers, x>0?
To find the range of the function f(x)= 2 - 3x, let's take f(x) = yi.e. f(x) = 2 - 3x = yi.e. 2 - y = 3xor x = 2 - y 3As x > 0, so 2 - y > 0 3 i.e. 2 - y > 0 or y < 2Hence range of this function is ( - infinity, 2)
A particle moves along a straight line and position at time t is given by s(t)=2t^3-21t^2+36t. Find velocity?
A) Differentiate s with respect to t: s' (t) = d/dt[2t^3-21t^2+36t] = 6t^2 - 42t +36 then find s'(0): s'(0) = 6(0)^2 - 42(0) +36 = 36 ------> you've just found the "starting velocity" of the particle B) Set the velocity equation to 0. The particle is at rest when the slope of the tangent is horizontal. 0 = 6t^2 - 42t +36 now factor and find solutions to t: 0 = 6(t-1)(t-6) (t-1)=0 and (t-6)=0 t=1 and t=6 C) "Position" is the original equation so solve for s when t= 14: s(14) = 2(14)^3-21(14)^2+36(14) = 5488 - 4116 + 504 = 1876 D) Because you know that the particle slows down when t= 1 and t = 6 (because it is changing direction) we know that it changes speeds along the way, so we need to calculate the velocity in intervals. [0, 1], [1, 6], and [6, 14] Distance is calculated using the position function. Use absolute value because distance can only be positive. from t=0 to t=1: |f(1) - f(0)| = |2(1)^3-21(1)^2+36(1) - 36| = | 2-21| = 19 feet from t=1 to t=6 |f(6) - f(1)| = |2(6)^3-21(6)^2+36(6) - 2(1)^3-21(1)^2+36(1) | = |-108 - 55| = 163 feet from t= 6 to t = 14 |f(14) - f(6)| = |2(14)^3-21(14)^2+36(14) - 2(6)^3-21(6)^2+36(6) | = | 1876- (-108)| = 1984 feet Add them all up for the total distance: 1984 + 163 + 19 = 2166 feet
Calculus question using a graph and asking to find points on a line?
A) y' = 1 - 2x/500 = 1 - x / 250 let Q be of coordinates (a , b) , then : the slope of n = 1 - a/250 = (b - 20) / a => a - a^2/250 = (a - a^2/500) - 20 so a^2/250 - a^2/500 - 20 = 0 mult by 500 u get : 2a^2 - a^2 - 10000 = 0 => a^2 = 10000 => a = 100 => b = a - a^2/500 = 100 - 20 = 80 so Q is (100 , 80) *********************************** B) the slope = 1 - 100/250 = 0.6 so y - 20 = 0.6 (x - 0) => y = 0.6x + 20 *********************************** C) ok , the top of the hill will be located at x = 250 , so the vertical line representing the tree has the eqn x = 250 , the hill's height = 250 - 250^2/500 = 125 ft now we need to show if line n and x = 250 intersect within the 50 ft range. =>y = 0.6 (250) + 20 = 170 ft since 170 ft lies within (125 ft - 175 ft) so the answer is yes the line n shines on the tree at pt(250 , 170)
Anyone for logarithms?
logx^4=log8 4logx=log8 logx=log8/4 logx= 0.225772497 x=10^ 0.225772497 x=1.68179283
A particle is moving along a circular path of radius 5 m with a uniform speed 5m/s. What will be average acceleration when it covers half revolution?
Centripetal accl. is equal to v^2/rac = 5^2/5 = 5m/s^2.Tangential accl.(at) is equal toChange in velocity/ time taken.Change in velocity = 5-(-5) =10.Time period =( 2*pi. R) /V = 2*pi sec.Time taken in half revolution is pi.at = 10/pi.Do rest of calculation hope you will find ans.