Answer:
Step-by-step explanation:
Component form of a vector is given by 
, where 
represents change in x-value and 
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector 
, the magnitude is 
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being , and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that 
Therefore, the component form of this vector is 
Answer:
Therefore 200.96 ft.of fencing are needed to go around the pool path.
Step-by-step explanation:
Given, a circular swimming pool has a radius of 28ft. There is a path all the way around the pool. The width of the path 4 ft.
The radius of the outside edge the pool path is
= Radius of the pool + The width of the path
= (28+4) ft
= 32 ft.
To find the length of fencing, we need to find the circumference of outside the pool path.
Here r= 32 ft
The circumference of outside edge of the pool path
=
=200.96 ft.
Therefore 200.96 ft.of fencing are needed to go around the pool path.
Answer:
x = -1 and y = -1
Step-by-step explanation:
Solve 3x+3y=−6;−x+y=0
Steps:
I will solve your system by substitution.
−x+y=0;3x+3y=−6
Step: Solve−x+y=0for y:
−x+y+x=0+x(Add x to both sides)
y=x
Step: Substitutexforyin3x+3y=−6:
3x+3y=−6
3x+3x=−6
6x=−6(Simplify both sides of the equation)
6x
6
=
−6
6
(Divide both sides by 6)
x=−1
Step: Substitute−1forxiny=x:
y=x
y=−1
Answer:
x=−1 and y=−1
⓵
When multiplying several factors together, an even number of negative signs will result in a positive answer.
↠ Because when you multiply two negative signs together, the negative signs turn into a positive sign, giving you a positive answer.
↠ If you have an even number of negative signs to multiply, then all your negative signs will be turned into positive signs, giving you a positive answer!
⓶
When multiplying several factors together, an odd number of negative signs will result in a negative answer.
↠ Because when you multiply a negative sign by a positive sign, the negative sign always wins, giving you a negative answer.
↠ If you har an odd number of negative signs to multiply, this means that once you are done multiplying all of the negative signs together except for the last one, you will be multiplying a positive sign with a negative sign.
↠ Here’s another way to see it : if you have 5 negative signs to multiply together, you will start by multiplying the first 2, which will give you a positive result. Then you will multiply the third and the fourth negative signs together, which will also give you a positive result. By that time, you will have two positive signs and one negative sign left, which means you will have no choice but to multiply a positive sign by the last negative sign, resulting in a negative answer!
I hope this helps! If you need a visual example, just tell me, it will be my pleasure! ☻
Answer: the answer to lg is 18
