Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k
parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t
Step-by-step explanation: The vector equation is a line of the form:
r = 
+ t.v
where
is the position vector;
v is the vector;
For point (7,4,5):
= 7i + 4j + 5k
Then, the equation is:
r = 7i + 4j + 5k + t(3i + 2j - k)
<u><em>r = (7 + 3t)</em></u><u><em>i</em></u><u><em> + (4 + 2t)</em></u><u><em>j </em></u><u><em>+ (5 - 5t)</em></u><u><em>k</em></u>
The parametric equations of the line are of the form:
x = 
+ at
y = 
+ bt
z = 
+ ct
So, the parametric equations are:
<em><u>x = 7 + 3t</u></em>
<em><u>y = 4 + 2t</u></em>
<em><u>z = 5 - 5t</u></em>
Hi there! So the situation that we are talking about for this is compounding, because the population is growing.. The formula for compounding something is P(1 + r)^t, with P representing the initial amount, r representing the rate, and t representing the time in years. First off, let's add the rate into 1. 1.2% is 0.012 in decimal form. 1 + 0.012 is 1.012. Now, because we are looking for the population after 4 years. We raise 1.012 to the 4th power. 1.012^4 is 1.04887093274. It's a long decimal, but do not delete this number from your calculator. Now, we multiply that number by 38,300 in order to get 40,171.7567238 or 40,172 when rounded to the nearest whole number. There. The population of Huntersville will be 40,172 people in 4 years.
You can easily use online calculators for this.
Steps:
1) Find radius. 45 / 2 = 22.5
2) Substitute values (r) and (h) in the formula for surface area of a cylinder:
SA = 2πr² + 2πrh
3) Solve the formula.
You should end up with 9542.59 units². This answer is using π.
To get the answer with (3.14), do the steps above.
Gideon is painting all sides thus we find the overall area of the square pyramid given in the picture. A square pyramid is a polyhedron that consists of a square and 4 triangles. To solve the area that Gideon will have to paint, we can calculate the area of the square and the area of the triangles then add these two values of area. We proceed as follows:
Area of the square = s^2 where s is the measure of the side
Area of the square = 4^2 = 16 in^2
Area of the triangle= 1/2 bh where b is the base of the triangle and h is height of the triangle
Area of the triangle = 1/2 (4) (5) = 10 in^2
We multiply the area of the triangle to four in order to obtain the total area of the triangles.
Total area of the triangles = 4 x 10 = 40 in^2
We then add the two areas,
Total Area = 16 + 40 = 56 in^2
Thus the total area that Gideon will have to paint for one square pyramid is 56 in^2.
Answer:
9^2
so it is (m+9)^2
Step-by-step explanation:
i guess that is the correct answer
