To prepare for a bake-off, Travis used 630 grams of flour each day for 3 weeks. How many kilograms did Travis use in those 3 wee
1 answer:
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Answer:
The spaceship will get to Alpha Centaur in time
Step-by-step explanation:
<u><em>The complete question in English is</em></u>
You're the commander of a spaceship. Your mission is to reach Alpha Centaur in five years. The distance from the sun to Alpha Centaur is 2.5 x 10^13 miles. The distance from Earth to Sun is approximately 9.3 x 10^7
miles. Your spaceship can travel at the speed of light. You know that light can travel a distance of 5.88 x 10^12 miles in a year. Can you get to Alpha Centaur in time?
step 1
Find the time it takes for the spaceship to travel from Earth to the Sun
The distance from the Earth to Sun is equal to
The spaceship can travel at the speed of light
The light can travel a distance of in a year
so
using a proportion
This time is very small in years
Convert to minutes
step 2
Find the time it takes for the spaceship to travel from the Sun to Alpha Centaur
The distance from the the Sun to Alpha Centaur is equal to
The spaceship can travel at the speed of light
The light can travel a distance of in a year
so
using a proportion
therefore
The spaceship will get to Alpha Centaur in time
9514 1404 393
Answer:
(2.27, 0.96)
Step-by-step explanation:
The orthocenter is the point of intersection of altitudes of the triangle. The equation for an altitude is the equation of a line through a vertex that is perpendicular to the opposite side.
For example, the line perpendicular to side AC can be found as ...
(∆x, ∆y) = C-A = (3, -1) -(-4, 2) = (7, -3)
∆x(x -h) +∆y(y -k) = 0 . . . . perpendicular through point (h, k)
For side AC, we want the point to be B(4, 5), so the equation is ...
7(x -4) -3(y -5) = 0
7x -3y -13 = 0
Similarly, the altitude to side AB can be written as ...
(∆x, ∆y) = B -A = (4, 5) -(-4, 2) = (8, 3)
8(x -3) +3(y +1) = 0
8x +3y -21 = 0
__
By the "cross multiplication method", the solution to these equations is ...
x = (-3(-21) -(3(-13))/(7(3) -8(-3)) = (63+39)/(21+24) = 102/45 = 2 4/15 ≈ 2.27
y = (-13(8) -(-21)(7))/45 = 43/45 ≈ 0.96
The orthocenter is near (2.27, 0.96).
__
A graphing application confirms this result.
_____
<em>Additional information about the cross multiplication method</em>
For the general form equations ...
- ax +by +c = 0
- dx +ey +g = 0
The "cross multiplication method" has you write the array ...
and form the "cross products" in groups of four coefficients:
D = ae -db, X = bg -ec, Y = cd -ga
Then the solution to the set of equations is ...
1/D = x/X = y/Y ⇒ x = X/D, y = Y/D
__
<em>Additional note</em>
Videos of this method show you writing the array as bcab/egde and using the final equation x/X=y/Y=1/D. The above gets the same result in a more straightforward manner.
