recall the equation for a circle with center (h,k) and radius r At what point in the first quadrant does the line with equation
1 answer:
9514 1404 393
Answer:
≈ (3.578, 5.789)
Step-by-step explanation:
We can substitute for y and solve for x.
(x -h)^2 +(y -k)^2 = r^2 . . . equation of a circle with center (h, k), radius r
x^2 +(y -4)^2 = 4^2 . . . . . . the equation of the given circle
x^2 +((0.5x +4) -4)^2 = 16
(5/4)x^2 = 16
x = 8/5√5 . . . . multiply by 4/5 and take the square root
y = 0.5x +4
y = 4/5√5 +4
The point of intersection is (8/5√5, 4+4/5√5), approximately (3.578, 5.789).
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V=x^3+5x^2-57x-189
Width: W=(x+3) in = 15 in →x+3=15
Solving for x:
x+3-3=15-3→x=12
With x=12 the Volume would be:
V=(12)^3+5(12)^2-57(12)-189
V=1,728+5(144)-684-189
V=1,728+720-684-189
V=1,575
V=W*D*H
Depth: D
Height: H
with H>D
V=1,575; W=15
Replacing in the equation above:
1,575=15*D*H
Dividing both sides by 15
1,575/15=(12*D*H)/15
105=D*H
3*5*7=D*H
D<H
If D=5→H=3*7→H=21
If D=7→H=3*5→H=15
Answer: Option <span>C. height: 21 in. depth: 5 in.
</span>
Please, see the attached file for another form to solve the problem
Width: W=(x+3) in = 15 in →x+3=15
Solving for x:
x+3-3=15-3→x=12
With x=12 the Volume would be:
V=(12)^3+5(12)^2-57(12)-189
V=1,728+5(144)-684-189
V=1,728+720-684-189
V=1,575
V=W*D*H
Depth: D
Height: H
with H>D
V=1,575; W=15
Replacing in the equation above:
1,575=15*D*H
Dividing both sides by 15
1,575/15=(12*D*H)/15
105=D*H
3*5*7=D*H
D<H
If D=5→H=3*7→H=21
If D=7→H=3*5→H=15
Answer: Option <span>C. height: 21 in. depth: 5 in.
</span>
Please, see the attached file for another form to solve the problem