Answer:
Box Dimensions:
L = 15.15 ul
W = 7.15 ul
h = x = 2.43 ul
V(max) = 263.22 cu
Step-by-step explanation:
We call x the length of the square to be cut in the corners then:
Are of the base of the box is:
(20 - 2*x) is the future length of the box and
(12 - 2*x) will be the width
The heigh is x then the volume of the box is:
V = ( 20 - 2*x )* ( 12 - 2*x ) * h
And the volume as a function of x is:
V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x or V(x) = (240 -40*x -24*x + 4*x²) * x
V(x) = 240*x - 64*x² + 4*x³
Taking derivatives on both sides of the equation we get:
V´(x) = 240 - 128*x + 12*x²
V´(x) = 0 240 - 128*x + 12*x² = 0 or 60 - 32*x + 3*x²
3*x² - 32*x + 60 = 0
Solving:
x₁,₂ = 32 ± √ (32)² - 4*3*60 ]/ 2*3
x₁,₂ = 32 ± √ 1024 - 720 )/6
x₁,₂ = ( 32 ± √ 304 )/6
x₁,₂ = ( 32 ± 17.44 )/6
x₁ = 8.23 ( we dismiss this solution because is not feasible 2*x > 12
x₂ = 2.43 u.l ( units of length)
Then
L = 20 - 2*x L = 20 - 4.85 L = 15.15 ul
W = 12 - 2*x W = 12 - 4.85 W = 7.15 ul
h = 2.43 ul
V = 2.43*7.15*15.15 cubic units
V = 263.22 cu
To see if when x = 2.43 function V has a maximum we go to the second derivative
V´´(x) = - 128 + (24)*2.43
V´´(x) = - 69.68 as V´´(x) < 0 then we have a maximum for V(x) in the point x = 2.43
Suppose 1757 grams of sugar is 31.69% of 5544 grams of jam. How much jam would there be if there were 2500 grams of sugar?
7889 grams of jam
Step-by-step explanation:
In 5544 grams of jam, 1757 grams of sugar ==> 31.69%
let x be the grams of jam
2500 grams of sugar ==> 31.69%
x grams of jam ==> 100%
[tex]x \times 31.69\% = 2500 \\ x = 2500 \div 31.69\% \\ x = 7888.92 \: grams \\ x = 7889 \: grams \: (nearest \: whole \: number)[/tex]
i’ll give you brainliest
Answer:
the answer you want is number 2
You want to nail your 4 championship plaques onto a wooden
plank. The plaques are each 5 inches wide, and the plank
measures 33 inches in length. If you have 2 inches of space on
both ends of the plank and want to space out your plaques
evenly, how much space should there be between each
plaque?
=============================================================
Explanation:
The overall plank is 33 inches long. Subtract 2 copies of 2 inches off to represent those left and right 2 inches of space at each end.
33 - 2*2 = 33 - 4 = 29
So we have 29 inches to work with.
There are 4 plaques to hang up, and each is 5 inches wide. So that accounts for 4*5 = 20 inches of space just for the plaques themselves. We have 29-20 = 9 inches left for the gaps between plaques.
Since we have 4 plaques, there are 4-1 = 3 gaps between the adjacent plaques. The gap width is 9/3 = 3 inches.
See the diagram below. The values in black are the widths of each championship (5 inches each). The values in red are the gaps either between the plaques or between the plaque and the edge of the plank.
As a check, the values in that diagram should add to 33.
2+5+3+5+3+5+3+5+2 = 33
So the answer is confirmed.
What is m angle A? Enter your answer in the box.
Answer:
ANSWER: 22
Step-by-step explanation:
hope it helps thankks
Answer:
I agree with the person above
The locksmith is 82.9 miles west of the bakery. The pet store is 44.5 miles west of the bakery. The toy store is 38.6 miles east of the bakery. The coffee shop is 71.5 miles east of the bakery. The library is 57.0 miles south of the bakery. The magic shop is 75.7 miles south of the bakery. How far apart are the toy store and the locksmith?
Answer:
82.9+38.6=121.5 miles far away.
Can someone help me with this.
Answer:
A' (-1, 1), B' (-2,1), C'(-2, 2), D'(-1, 3)
Step-by-step explanation:
Rotate all of the points 90 degrees clockwise and move them to the second quadrant.
In the circle shown below, The length of chord AB is 24 and the length of OC is 5. What is the radius of the circle with center O
Answer:
radius = 13
Step-by-step explanation:
OC is a perpendicular bisector of AB , then AC = 12
OA is the radius of the circle
Using Pythagoras' identity in right triangle OAC
OA² = OC² + AC²
OA² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )
OA = [tex]\sqrt{169}[/tex] = 13
The radius = 13 units
Answer:
13
Step-by-step explanation:
AB is bisected by perpendicular OC so AB is divided into intwo two equal halves.
if AB = 24
AC =[tex]\frac{1}{2} *AB[/tex]
=[tex]\frac{1}{2} *24[/tex]
=12
no join OA and name its length as x
OA = X
OC = 5
AC = 12
when u join O and A it forms a triangle . SO to find OA lets find pythagoras theorem
OC^2 + AC^2 = OA^2
5^2 + 12^2 = OA^2
25 + 144 = OA^2
169 = OA^2
[tex]\sqrt{169}[/tex] = OA
13 = OA
radius is the line joining the centre and any point on the circumference.So here since O is the centre and A is the points on the circumference and they are joined so the line can be named as radius of a circle.
Therefore radius of a circle is 13
Which expression is equivalent to 2^-3/2^-5
Answer:
2^2
Step-by-step explanation:
2^-3/2^-5
We know that a^b / a^c = a^(b-c)
2^-3/2^-5 = 2^( -3 - -5) = 2^(-3+5) = 2^2
In a community of 9,400 people the number of women exceeds the number of men by 1,500.Find the ratio of men to women in the community
Answer:
Step-by-step explanation:
x +(x+1500) = 9400
2x + 1500 = 9400
2x = 7900
x=3950 (men)
y = 5450 (woman)
5450 :3950
109:79
can you help answer these:
1) (-3 ) * ( + 3 ) = ___
2) ( - 3) * ( - 3)= ______
3) ( + 20 ) ( + 5) = ____
4) ( + 21 ) ( - 3 ) )= ___
5) (-2) * (+3) * (- 4) = ___
Answer:
1) -3 x 3=-9
2) -3x-3=9
3)20x5=100
4) 21x-3=-63
5) -2x3x-4=24
note: negative x positive= negative
negative x negative=positive
positive x positive= positive
Step-by-step explanation:
hope this is helpful
Step-by-step explanation:
(-3)*(1+3) = -9 (-3)*(-3) = 9(+20)(+5) =100(+21)(-3) = -63(-2)*(+3)*(-4) = 24
-y-22-13
6< X/2-2
I need help solving both
Answer: The first one is y≤11 and the second question is x>16 Hope that helps Goodbye!
Step-by-step explanation: 1. Add 22 to both sides.
-13+2
−y≥−13+2
2 Simplify -13+2−13+2 to -11−11.
-y\ge -11
−y≥−11
3 Multiply both sides by -1−1.
y\le 11
y≤11
1 Add 22 to both sides.
6+2<\frac{x}{2}
6+2<
2
x
2 Simplify 6+26+2 to 88.
8<\frac{x}{2}
8<
2
x
3 Multiply both sides by 22.
8\times 2<x
8×2<x
4 Simplify 8\times 28×2 to 1616.
16<x
16<x
5 Switch sides.
x>16
x>16
If the inverse of a function is also a function, then
The function is said to be ….?
Answer: Invertible
Step-by-step explanation:
If inverse of a function exists, then the function is said to be invertible. A unique value exits for each given input.
Inverse of a function can be obtained by expressing the given function in terms of y and then replace y by x.
find the outer perimeter of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate π.
Answer:
19.42 ft.
Step-by-step explanation:
The diameter of the semicircle is 6, so 3.14 x 6 = 18.84. Since it is a semicircle, we divide that by 2 to get 9.42.
The hypotenuse of the right triangles only matter for the perimeter. 5 + 5 = 10, and 9.42 + 10 = 19.42 ft.
The outer perimeter is 19.42 ft.
What is perimeter?Perimeter is the distance around the edge of a shape.
Given:
radius= 3 ft
height= 4 ft
slant height= 5 ft
diameter of the semicircle is 6 feet.
So,
= 3.14 x 6 = 18.84.
Since it is a semicircle,
=18.84/2
=9.42 feet
Now, the perimeter.
= 5 + 5 +9.42
= 19.42 ft.
Hence, the perimeter is 19.42 feet.
Learn more about perimeter here:
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22 - 8x = -5x - 14
Find x
Please help this is due today
Assignment - 3. Deductive Reasoning
State a true conclusion.
1) If two planes intersect, their intersection is a line.
2) Plane Rand plane S intersect.
Conclusion:
WRITER
Answer:
the answer is the intersection is a line
what’s 818*426 (multiplication)
Answer:
348468
Step-by-step explanation:
Answer:
348,468
Step-by-step explanation:
Hope it's help you !!!!:)
the gravitational acceleration on Earth is 9.8m/s^2 what is the weight of a car on earth if the mass is 1360
Answer:
13328 N
Step-by-step explanation:
9.8 m/s^2 • 1360 = X
13328 N = X
What is the next term in the sequence below?
0.25, 0.75, 2.25, 6.75, …
A. 6.25
B. 10.25
C. 20.25
D. 60.75
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {C. \:20.25}}}}}}[/tex]
[tex]0.25, 0.75, 2.25, 6.75,20.25,..[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]0.25, 0.75, 2.25, 6.75,20.25 \\ \\ ➺ \: 0.25 \times 3 = 0.75 \\ \\ ➺ \: 0.75 \times 3 = 2.25 \\ \\ ➺ \: 2.25 \times 3 = 6.75 \\ \\ ➺ \: 6.75 \times 3 = 20.25[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
Helpppppppppppppppp
if a triangle has one angle that measure 81 degrees and another that measures 47 degrees, what is the measure of the third angle?
Answer: 52
Step-by-step explanation:
81 + 47 is 128.
180 - 128 =52 degrees.
:)
Please answer quickly
Answer:
10
Step-by-step explanation:
given :
length WX ≅ (congruent means equal) length XY
therefore , WX = 3
WZ = WX + XZ
WZ = 3 + 7
WX = 10
What is the perimeter of the figure shown to the right.
Plss HELP MEE
Answer:
perimeter=a+b+c+d+e+f+g+h+I
x+13+3x+2+x+5+2+8+3x
CLT
x+x+3x+3x+13+2+5+2+8
8x+30
WILL MARK BRANLIEST
When describing a rotation, what
information must you include?
Answer:
The point you are rotating at (also called the centre of rotation)
The angle of rotation (usually in degrees but I don't know your school)
Direction of the turn
Step-by-step explanation:
Which of the following equations is of a parabola with a vertex at (0, 6)?
y = ( x + 6) 2
y = ( x - 6) 2
y = x2 + 6
y = x2 - 6
Answer:
y = x² + 6
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (0, 6) , let a = 1 , then
y = (x - 0)² + 6 , that is
y = x² + 6
How do I fill this out I need to pass this class to move up a grade
Answer: x = 8,-2
Step-by-step explanation:
x^2-6x-16=0
x =[ -(-6)+-sqrt(-6)^2 - 4x1x(-16)/2x1
x = [6+-sqrt 36+64]/2
x = 6+-sqrt 100/2
x = 6 +-10/2
x = 6+10/2, 6-10,2
x = 8, -2
Answer:
Step-by-step explanation:
This is the quadratic equation formula for the roots.
x^2 - 6x - 16 = 0
x = [- (-6) +/- √( (-6)^2 - 4*1*-16) / 2*1
x = (6 +/- √(36 + 64) / 2
x = (6 +/- √(100) / 2
x = (6 +/- 10) / 2
x = 16/2 = 8
x = -4/2 = -2
f(x) = x2. What is g(x)?
5
[ f(x)
g(x)
(3,3)
X
-5
5
x2
O A. g(x)=1
-02-G
B.
X
O c. g(x) = 3²
O D. g(x)=-* x2
Please help :/
The function g(x) = x²/3
Given that graph of the function f(x) = x²,
Since, the graph of f(x) is transformed to form the g(x).
We see that g(x) is passing by (3, 3)
Here, the scale factor is 1/3,
So, we can say that the equation of the function g(x) is g(x) = x²/3
Therefore, the required function is g(x) = x²/3
Learn more about function click;
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What is the factorization of 49b2 − 81?
(7b – 9)(7b – 9)
(7b – 9)(7b + 9)
(7b2 – 9)(7b2 – 9)
(7b2 – 9)(7b2 + 9)
Answer:
B. (7b – 9)(7b + 9)
Step-by-step explanation:
got 100% on my quiz
pls help me !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9.89 m
Step-by-step explanation:
AC is the hypotenuse (H)
x is the opposite (O)
O and H are in sine
sin=O/H
H=O/sin
H=7.9/sin(53)
=9.89187169943418
3 SF
9.89 m
Answer:
AC= 13.144
Step-by-step explanation:
cos ∅ = Adjacent/ Hypotenuse
cos (53°) = x/AC
cos (53°) = 7.9/AC
(0.601).(AC)=7.9
AC=(7.9)/(0.601)
AC= 13.144 (3 S.F)
Brainly to whomever solves for x and y. Will report scams and the unhelpful "what" answers!
Answer:
[tex]x=\frac{125}{6},\\y=11[/tex]
Step-by-step explanation:
The angles marked [tex]7x-15[/tex] and [tex]5x-5y[/tex] are co-interior angles. Since all co-interior angles are supplementary (add up to 180 degrees), we have the following equation:
[tex]7x-15+5x-5y=180[/tex]
The two angles marked [tex]4x+4y[/tex] and [tex]2x+y[/tex] are also co-interior angles, thus must also add to 180 degrees.
Therefore, we have the following system of equations:
[tex]\begin{cases}7x-15+5x-5y=180,\\4x+4y+2x+y=180\end{cases}[/tex]
Combine like terms:
[tex]\begin{cases}12x-5y-15=180,\\6x+5y=180\end{cases}[/tex]
Divide the first equation by -2 and add both equations to get rid of [tex]x[/tex]:
[tex]\begin{cases}-6x+2.5y=-97.5,\\6x+5y=180\end{cases},\\-6x+6x+2.5y+5y=82.5,\\7.5=82.5,\\y=\boxed{11}[/tex]
Now substitute [tex]y=11[/tex] into any equation with [tex]x[/tex]:
[tex]6x+5y=180,\\6x+5(11)=180,\\6x+55=180,\\6x=125,\\x=\boxed{\frac{125}{6}}[/tex]
Verify that these two solutions work:
[tex](7(\frac{125}{6})-15)+(5(\frac{125}{6})-5(11))=180\:\checkmark,\\\\(4(\frac{125}{6})+4(11))+(2(\frac{125}{6})+11)=180\:\checkmark[/tex]
expression of three power of five rational number with a negative exponent is?
answer with step by step explanation
Answer:
[tex]\frac{1}{243}\\[/tex]
Step-by-step explanation:
The expression of three power of five rational number with a negative exponent is;