Answer:
a. Point S
b. Line segment PT and Line segment ST
c. PSQRU
d. Lines PR and SQ
e. Plane C and Plane QRS
Step-by-step explanation:
Answer:
Area of sector ≈ 15.6π (nearest tenth)
Step-by-step explanation:
Given:
radius = 5 cm
Central angle in radians = ∅ = 5π/4
Required:
Area of the sector
Solution:
Area of sector = ½*r²*∅
Plug in the values into the formula
Area of sector = ½*5²*5π/4
= ½*25*5π/4
= 12.5*5π/4
= (12.5*5π)/4
Area of sector = 15.625π ≈ 15.6π (nearest tenth)
Answer:
<11,33>
Step-by-step explanation:
If it is perpendicular to <3,-1> We can use <0,0> as the other point to get the slope
m = (y2-y1)/(x2-x2)
The slope of the vector is
(-1-0)/(3-0)
= -1/3
Then we want a vector perpendicular, so we take the negative reciprocal of the slope
- (-3/1) =3
So the perpendicular slope is 3
Our new vector y/x = 3/1
Using cross products
3x=y
The magnitude has to be 11 sqrt (10)
magnitude = sqrt( ((x)^2 + y^2) = 11sqrt(10)
magnitude = sqrt( ((x^2 + y^2) = 11sqrt(10)
Square both sides
x^2+y^2 = 11^2*10
x^2 + y^2 =1210
We have 2 equations and 2 unknowns
x^2 +y^2 =1210 and
3x=y
Replace y with 3x
x^2 + (3x)^2 =1210
x^2 +9x^2 =1210
10x^2 =1210
Divide both sides by 10
x^2 =121
Take the square root of each side
sqrt(x^2) = sqrt(121)
x=±11
But it problems states it has to be in the first quadrant so x=11
x =11
Now we can find y
y =3x
y =11*3
y =33
The vector is <11, 33>
r=98600/30 $/day
r=9860/3
debt=1200000-98600
d=1101400
Debt=r•days
1101400=9860/3•(days)
335.1=days
336 days because you can't have a partial day and 335 days would leave $367 of debt still.
It would take the company 336 more days to earn back it's investment.