Answer:
Step-by-step explanation:
What is the maximum volume in cubic inches of an open box to be made from a 10- inch by 20-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative.
Answer:
192.5 in³
Step-by-step explanation:
The cardboard is 10 by 20 before removing a square from each end. Assuming that the square is x inches wide. Therefore, the 20 in side gets reduced by x inches on both sides, or say it becomes 20 - 2x inches. On the other hand, the 10 in side is also reduced by 2x. The x value we get happens to be the height of the box when the sides are folded up.
Thus the volume V = lbh =
V = (20-2x)*(10-2x)*(x)
V = 4x³ - 60x² + 200x
On differentiating, we have dv/dx to be
dv/dx = 12x² - 120x + 200
Using general formula to find the roots of this equation, we can solve that x = 7.886 and x = 2.113
This roots we got are possible values of x, the square we cut. Since 7.886 * 2 = 15.772 inches, this is more than the 10 inch side, henceforth x = 2.113 inches.
You cut 2.113 inches from each corner to obtain the maximum volume.
The sizes of the cubes are
20 - (2 * 2.113) = 15.774
10 - (2 * 2.113) = 5.774
2.113
The volume of the cube is 15.774 * 5.774 * 2.113 = 192.5 cubic inches.
in parallelogram
abcd if b=50 find the other angles
Answer:
a is 130 c is 50 and d is 130 opposite angles are equal and corresponding angles sum equals 180
Which properties justify the steps taken to solve the system? {2a+7b=03a−5b=31 10a+35b=0; 21a−35b=217 31a = 217 a = 7 2(7)+7b=0 14 + 7b = 0 7b=−14 b=−2 what are each of the steps taken?
9514 1404 393
Explanation:
2a+7b=0 . . . . . . . . given [eq1]
3a−5b=31 . . . . . . . .given [eq2]
10a+35b=0 . . . . . . multiplication property of equality 5×[eq1] = [eq3]
21a−35b=217 . . . . .multiplication property of equality 7×[eq2] = [eq4]
31a = 217 . . . . . . . . addition/substitution properties of equality [eq3]+[eq4]
a = 7 . . . . . . . . . . . . division property of equality (÷31)
2(7)+7b=0 . . . . . . . .substitution property of equality; a=7 in [eq1]
14 + 7b = 0 . . . . . . . properties of real numbers
7b=−14 . . . . . . . . . . addition property of equality; add -14
b=−2 . . . . . . . . . . . . division property of equality (÷7)
how many cubes with a .25 inch side length will fit in a rectangular prism with a volume of 35.62
Answer:
142.48
Step-by-step explanation:
this i think is the answer
Can someone please check my answer for this function???
Answer:
You're wrong, it's the bottom left
Step-by-step explanation:
x^2-49 is a difference of squares so it factors into (x+7)(x-7) which obviously cancels out with the denominator leaving x-7 left. This is the line you should graph, but keep in that x+7 is still in the denominator so x cannot be equal to -7 which means that this point should be be on the line which leaves the answer to be the one on the bottom left.
X and Y
-5x+5y=-25
3x+2y=10
the X and Y is (4,-1) i need to know how to get the answer
Step-by-step explanation:
just substitute X and Y by their numerical values.
a) -5(4)+5(-1)=-25
-20-5= -25
-25= -25. true
b) 3(4)+2(-1) = 10
12 -2 =10
10=10. true
...what's
[tex]({1 + 2 } ) \div( 1 -2)[/tex]
Answer:
-3
Step-by-step explanation:
(1+2)/(1-2)
= 3/-1
= -3
Answer:
-3
Step-by-step explanation:
(1+2) ÷ (1-2) = 3 ÷ -1 = -3
Perimeter? =
Area? =
Answer:
Your answer is
Area = 16.23
perimeter = 24
Mark my answer as brainlist . I need that urgently . Folow me for more answer.
Step-by-step explanation:
the original pattern for dress is 33 3/4 inches long. kimmy needs her dress to be 32 1/2 inches long how much shorter than the pattern does kimmy need to make her dress
Answer: 1 1/4
Step-by-step explanation: 32 1/2 is the same as 32 2/4 so all you have to do is subtract 32 2/4 from 33 3/4 which leaves you with 1 1/4
The ratio of two number is 4:9.When 5 is subtracted from each of them,the new ratio becomes 3:8. Find the numbers.
Answer:
The numbers are 20 and 45
Step-by-step explanation:
Let the two numbers be a and b
The ratio of the two is 4:9
That means;
a/b = 4/9
9a = 4b •••••(i)
secondly;
Subtracting 5 from each gives a ratio of 3:8
(a-5)/(b-5) = 3/8
8(a-5) = 3(b-5)
8a - 40 = 3b - 15
3b - 15 + 40 = 8a
3b + 25 = 8a
a = (3b + 25)/8 •••(ii)
Insert this into 1
9(3b + 25)/8 = 4b
27b + 225 = 32b
32b - 27b = 225
5b = 225
b = 225/5
b = 45
From i;
9a = 4b
9a = 4 * 45
a = 4 * 45/9
a = 20
Is my answer correct???
Answer:
Yes! Great job!
Hope that helps!
Please help I don’t wanna add a bunch of points Bc nobody is helping me I’m just wasting them.
You want to determine the height of your
school building. The building casts a 6-foot
shadow at the same time you cast a 15-inch
shadow. If you are 5 feet tall, how tall is the
school building? Write an equation and solve,
showing ALL the work.
Answer:Cross multiply and solve for x.
x/6 = 5/1.25
let the height of building be h ft
h/6 = 60/15
h = 6(60/15) = 24
the building is 24 ft high
Step-by-step explanation:
Well first let’s covert the ft to in- 5ft is 60 in and 6ft is 72 in. Then we want to set up 2 fractions based on height and shadow, so we have 60/15=x/72 (we put x because that’s what we’re trying to find). Then we do cross multiplication so now we have 15x=4320. We divide 15, so now we have 4320/15=288. So the building is 288 in tall or 24ft tall! Glad to help! :)
17. Convert 37/6 to a mixed number.
A. 55/6
B. 6576
C. 6/6
D. 62/3
Answer:
6 1/6.
Step-by-step explanation:
That would be 6 1/6. Because 37/6 = 6 remainder 1, which is 1/6, so 6 1/6.
Enter an equation in the form y = mx + b that represents the function
Answer: no answer c
Step-by-step explanation:
1/2{x-1/6}+2/3=5/6+1/3 (1/2-3x)
Answer:
I think it's correct but tell me if I'm wrong
Construct quadrilateral with the measurements given below:
Quadrilateral ABCD with AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm
and AC = 7 cm
Answer:
Cevap A şkkı
İyi dersler
Each earbud is 4/7 of an inch long. If you put 8 earbuds end to end, how long would they be from beginning to end?
Answer:
4 4/7
Step-by-step explanation:
4/7x8/1
4x8/7x1
32/7
4 4/7
Answer:
The answer is 4 4/7.
Step-by-step explanation:
4/7 x 8 = 32/7
32/7 = 4 4/7
Picture is below...........................
Answer:
C or A
thats all i know hope it helps
A box of dried fruit has 80 calories in 5 servings. How many calories are there per serving?
Answer:
16 calories per serving
Step-by-step explanation:
80/5=16 calories per serving
Answer:
16 calories per serving. Hope this helps
Step-by-step explanation:
The sum of five-sixths of f, one-half of p, and 3
Answer:
The expression would look like this: [tex]\frac{5}{6}f + \frac{1}{2}p + 3[/tex]
A square cake sits on a circular cake stand. The circular cake stand has a diameter of 24 inches. The cake measures 16 inches on each side. How many square inches of the cake stand are visible?
Answer:
196.12 in^2
Step-by-step explanation:
circular cake stand area=(24/2)^2(3.14)=452.12 in^2
square cake=16x16=256 in^2
452.12-256=196.12 in^2
Calculate the area of the trapezoid
Answer:
180 in^2
Step-by-step explanation:
area = 5(sq rt 75) x (sq rt 27) - [5(sq rt 75)-5(sq rt 27)] x 3(sq rt 3) x 0.5
area = 180 in^2
...what's
[tex] \sqrt{169} [/tex]
Answer:
√169=13
Step-by-step explanation:
can also be understood by 13×13=169
Answer:
13
Step-by-step explanation:
√169 = 13
The height of a doorway is 7 yards. What is the height of the doorway in inches?
The height of the doorway is ____ inches.
How many degrees of rotational symmetry does the flower have
Answer:
It has 5-fold rotational symmetry (72 degrees). The Clematis shown has 8-fold rotational symmetry (45 degrees). It has 8 flower petals arranged around the center of the flower.
Step-by-step explanation:
Solve 2(x - 5) = 6(x - 1)
Answer:
60
Step-by-step explanation:
so first you multiply 2 times 5 =15 and the we do 15 times six which is 90 and then subtract one and keep subtracting util you get to 60
Answer:
x=-1
Step-by-step explanation:
2(x-5)=6(x-1)
2x-10=6x-6
-4x-10=-6
-4x=4
x=-1
Which pair of angles is congruent?
Answer:
Option 2
Step-by-step explanation:
Corresponding Angles Theorem
3 x 5 x 2 uygnkuhgkhgiyhbkhbkgy
Answer:
30 is the answer hope this helps!!
I need help with math if you don't know the answer get out of the question and don't answer it and give the wrong answer or some link or even say "I don't know" or anything like that it's not fair to me cause it a waste of my points I will report your if you do that :) have a nice day and stay safe
Answer:
Please do not report me if this is wrong but my friend beside me is giving me the answer and she said its 60
Step-by-step explanation:
Omg pls help in my math. It is 6th grade
Answer:
1. You have to shade 38/100 squares
2. You have to shade 65/100 squares
3. 3/5=15/25, 6/10, 9/15