Last year a computer was $350. The computer company raise prices this year and the price has increased by 5%. What was the price
1 answer:
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Answer:
The dimension of the box is l×w×h = (2.274 × 2.274 × 1.934) ft³
Step-by-step explanation:
From the given information;
Let a be the cost of the box
Let b be one side of the square base ; &
h to be the height of the box
We know that the volume of the box = 10 cubic feet
Then;
a²h = 10
h = 10/a²
The base = (0.65)a²
The top = (0.2)a²
The side = (0.2) a × 25/a²
= 5/a
For the four sides of the box now ;
= (0.2) 4a × 25/a²
= 0.8 × 25/a
= 20 /a
The total cost of the box is:
b = 0.65a² + 0.2a² + 20 /a
b = 0.85 a² + 20 /a
Taking differential of b with respect to a ;we have:
db/da = 1.7a - 1/a²(20) = 0
1.7 a³ - 20 = 0
1.7 a³ = 20
a³ = 20/1.7
a³ = 11.77
a =
a = 2.274 ft
Thus; the cost for the base of the box = (0.65)a²
the cost for the base of the box =(0.65) × ( 2.274)²
the cost for the base of the box = 3.362
The top of the box = (0.2)a²
The top of the box = (0.2)× ( 2.274)²
The top of the box = 1.034
The four sides of the box = 20 /a
The four sides of the box = 20/2.274
The four sides of the box = 8.795
the total cost = b = 0.85 a² + 20 /a
the total cost = 0.85 (2.274)² + 20 /2.274
the total cost = 4.395 + 8.795
the total cost = 13.19
Recall that:
the volume of the box = 10 cubic feet
Then;
a²h = 10
h = 10/a²
h = 10/ 2.274²
h 1.934
The dimension of the box is l×w×h = (2.274 × 2.274 × 1.934) ft³
Answer:
angle NMP = 63°
angle LMP = 74°
Step-by-step explanation:
Let angle NMP be x° . It's given that angle LMP is 11° more than angle NMP. So, angle LMP = x° + 11°
But angle NML = 137°.
So,
angle NMP + angle LMP = 137°
=> x° + x° + 11° = 137°
=> 2x° + 11° = 137°
=> 2x° = 137° - 11°
= 126°
=> x° = 126/2 = 63°
angle NMP = 63°
angle LMP = 63 + 11 = 74°
The answers are 3.19 or -2.19.
In order to complete the square, you must first get the constant to the other side of the equation. WE do that by adding 7 to both sides.
x^2 - x - 7 = 0
x^2 - x = 7
Now we must take half of the x coefficient (-1), which would be -.5. Then we square it and add it to both sides. This is the second step to any completing the square problem.
x^2 - x = 7
x^2 - x + .25 = 7.25
Now that we have done that, the left side will be a perfect square so that, we can factor it.
x^2 - x + .25 = 7.25
(x - .5)^2 = 7.25
After having done that, we can take the square root of both sides
(x - .5)^2 = 7.25
x - .5 = +/-
Now we can take the value of that square root and solve.
x - .5 = +/-
x - .5 = +/-2.69
x = .5 +/- 2.69
And with the + and - both there, we need to do both to get the two answers.
.5 + 2.69 = 3.19
.5 - 2.69 = -2.19