Answer:
(4, -2) (see attached)
Step-by-step explanation:
Vector addition on a graph is accomplished by placing the tail of one vector on the nose of the one it is being added to. The negative of a vector is in the direction opposite to the original.
__
<h3>vector components</h3>
The components of the vectors are ...
u = (1, -2)
v = (-6, -6)
Then the components of the vector sum are ...
2u -1/3v = 2(1, -2) -1/3(-6, -6) = (2 +6/3, -4 +6/3)
2u -1/3v = (4, -2)
<h3>graphically</h3>
The sum is shown graphically in the attachment. Vector u is added to itself by putting a copy at the end of the original. Then the nose of the second vector is at 2u.
One-third of vector v is subtracted by adding a vector to 2u that is 1/3 the length of v, and in the opposite direction. The nose of this added vector is the resultant: 2u-1/3v.
The resultant is in red in the attachment.
Answer:
Actual volume: 150.8
Step-by-step explanation:
the equation to find the volume of a cylinder is:
V= pi (r)^2 (h)
r= radius
h= height
To get the radius, you divide the diameter by 2.
when you plug in the numbers is looks like this:
V= pi (2)^2 (12)
you'll get 150.8 ft^3
I'm not really sure which volume would be the closest, but it should be around the answer I provided
Answer:
a 70
Step-by-step explanation:
eanuts have a high oil content (45 percent to 52 percent) compared to several other oilseed crops. With a yield of 3,000 pounds per acre, a 70 grade (70 percent of the weight of the peanut in shell) and 50 percent oil content, peanuts could potentially produce 120 to 150 gallons of biodiesel per acre.
Answer:
- ∠CDE ↔ 50°
- ∠FEG ↔ 75°
- ∠ACB ↔ 55°
Step-by-step explanation:
To solve angle problems like this, you make use of three relations:
- linear angles have a sum of 180°
- angles in a triangle have a sum of 180°
- vertical angles have the same measure
The attached diagram shows the measures of all of the angles of interest in the figure. The ones shown in blue are the ones that have the measures and names on the list of answer choices.
__
A good place to start is with the linear angle pair at A. Since the sum of the two angles is 180°, the angle at A that is inside the triangle will be ...
180° -130° = 50°
Then the missing angle in that triangle at C will have the measure that makes the sum of triangle angles be 180°:
∠ACB = 180° -50° -75° = 55° . . . . . this is one of the angles on your list
Similarly, the angle at E inside triangle FEG will have a measure that makes those angles have a sum of 180°:
∠FEG = 180° -60° -45° = 75° . . . . . this is one of the angles on your list
__
The two angles whose measures we just found are vertical angles with the base angles in triangle CDE, so that triangle's angle D will have a measure that makes the total be 180°.
∠CDE = 180° -55° -75° = 50° . . . . . this is one of the angles on your list