Answer:
Step-by-step explanation:
A=2B
AreaA= Area of a rectangle=Base* height = base (12-x)*height(4) = 48-4x
AreaB = Area of rectangle=base(x) *Height(x) =x^2
Since A=2B
48-4x =2x^2
Divide both sides of the equation by 2
24-2x=x^2
Put everything all on one side
X^2-2x-24=0
(x+4)(x-6)=0
X=-4 and x=6
Only x makes sense since it’s not negative or else your base or one of your sides would be negative
So x=6
Answer:
137.5 Miles
Step-by-step explanation:
Time driven=5/2 hours
Miles per hour=55
55 times 5/2= 137.5 miles
Triangles CPA and CPB are both right triangles. They share a leg, so that leg in one triangle is congruent to that leg in the other triangle. We are given that PA is congruent to PB by the hash marks on the diagram. Thus two legs and an included angle are congruent between the triangles.
... ∆CPA ≅ ∆CPB by the SAS postulate
Then side CA ≅ CB = 15 in, because corresponding parts of congruent triangles are congruent (CPCTC).
... CA is 15 in.
Answer:
A. 125
Step-by-step explanation:
the sum of the remote angles is equal to the exterior angle
90+35=125
Surface area of box=1200 cm²
<span>Volume of box=s²h </span>
<span>s = side of square base </span>
<span>h = height of box </span>
<span>S.A. = s² + 4sh </span>
<span>S.A. = surface area or 1200 cm², s²
= the square base, and 4sh = the four 'walls' of the box. </span>
<span>1200 = s² + 4sh </span>
<span>1200 - s² = 4sh </span>
<span>(1200 - s²)/(4s) = h </span>
<span>v(s) = s²((1200 - s²)/(4s)) </span>
<span>v(s) = s(1200 - s²)/4 . </span>
<span>v(s) = 300s - (1/4)s^3</span>
by derivating
<span>v'(s) = 300 - (3/4)s² </span>
<span>0 = 300 - (3/4)s² </span>
<span>-300 = (-3/4)s² </span>
<span>400 = s² </span>
<span>s = -20 and 20. </span>
again derivating
<span>v"(s) = -(3/2)s </span>
<span>v"(-20) = -(3/2)(-20) </span>
<span>v"(-20) = 30 </span>
<span>v"(20) = -(3/2)(20) </span>
<span>v"(20) = -30 </span>
<span>v(s) = 300s - (1/4)s^3 </span>
<span>v(s) = 300(20) - (1/4)(20)^3 </span>
<span>v(s) = 6000 - (1/4)(8000) </span>
<span>v = 6000 - 2000
v=4000</span>
