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
Which equation has the least steep graph A. y = 2x + 1 B. y = -7x-2 C. y=-3/4x-9 D. y = 1/4x+6
Answer:
D. y = 1/4x + 6
Step-by-step explanation:
In the linear equation y = mx + b, m is the slope.
A graph will be steeper if it has a larger slope, and less steep if it has a smaller slope.
So, to find which equation has the least steep graph, find which one has the smallest slope.
Out of the 4 equations, the smallest slope is 1/4. Although -7 is the smallest number, it still has a steep slope. The negative sign just makes it go in the other direction.
So, the equation with the least steep graph is D. y = 1/4x + 6
Answer:D
Y= 1/4x +6
Step-by-step explanation:
HELP PLEASE I HAVE 15 MINS LEFT
In AABC median AM is drawn from vertex A to BC, BM = 14x and MC = 6x + 56. Determine and
state the value of x.
Answer:
x = 7
Step-by-step explanation:
A median bisects the opposite side length, therefore
14x = 6x+56
8x = 56,
x = 7
Answer:
x = 7
Step-by-step explanation:
given:
AM is the median
BM = 14x
MC = 6x + 5x
since the median is drawn fron vertex A to BC it bisects the BC into two equal halves. So,
14x = 6x + 54
14x - 6x = 54
8x = 54
x = 54/8
x = 7
. If XZ = 7x + 1 and PZ = 4x − 1, what is XP? 11
12 19 22
Answer:
XP = 11
Step-by-step explanation:
Given that XZ = 7x + 1 and PZ = 4x − 1
From the diagram, XZ = 2PZ
7x + 1 = 2(4x-1)
7x+1 = 8x - 2
7x - 8x = -2 -1
-x = -3
x = 3
Since XP = PZ
XP = 4x - 1
XP = 4(3) - 1
XP = 12-1
XP = 11
find the value of x and y, (3x - 2y, 7) = (11, x + y)
Answer:
Step-by-step explanation:
Given,(3x-2y,7)=(11,x+y)
So,3x-2y=11...............(i)
7=x+y
or,x+y=7................(ii)
Now,Multiplying eqn.(ii) by 2,we get,
2x+2y=14...........(iii)
Adding eqn(i) and eqn(iii),
3x-2y+2x+2y=11+14
or,5x=25
or,x=5
Substituting value of x in eqn(i),
5+y=7
or,y=2
Hence,the values of x and y are 5 and 2 respectively.
Determina la masa molar y el volumen que ocupa la siguiente sustancia CO2, si su masa es de 28 gr. *
Answer:
Para el CO₂ sabemos que:
densidad = 0,001976 g/cm³
Sabemos que:
densidad = masa/volumen
Entonces, si tenemos una masa de 28 g, podemos escribir:
volumen = masa/densidad
volumen = (28g)/(0,001976 g/cm³) = 14,170 cm^3
Para obtener la masa molar (es decir, la masa de un mol de esta sustancia) simplemente sumamos la masa de un mol de cada componente.
Carbono: tiene una masa molar de 12 g/mol
Oxígeno: tiene una masa molar de 16 g/mol (y tenemos dos oxígenos)
entonces la masa molar va a ser:
masa molar = 12g/mol + 2*16g/mol = 44 g/mol
Es decir, un mol de CO₂, pesa 44 gramos.
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in second, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of a second
10.17 seconds
hope this helps
Diane has $814 in her checking account. If she writes five checks for a total of $287, how much does she have left
in her account?
Answer:
$527
Step-by-step explanation:
Find how much she has left by subtracting 287 from 814:
814 - 287
= 527
So, she has $527 left in her account
What percent is represented by the shaded area?
plsssss help meeee ....i need the answerrrr
Answer:
20
Step-by-step explanation:
[tex] = \dfrac{ \sqrt[3]{125} \times \sqrt[3]{64} }{ \sqrt[3]{125} - \sqrt[3]{64} } [/tex]
[tex] = \dfrac{5 \times 4}{5 - 4} [/tex]
[tex] = \dfrac{20}{1} [/tex]
[tex] = 20[/tex]
La fórmula correcta para encontrar el valor del coseno de un ángulo agudo en un triángulo rectángulo dado es:
Answer:
El coseno del ángulo esta dado por:
[tex]cos(\theta)=\frac{CA}{H}[/tex]
Step-by-step explanation:
Si tenemos un triángulo recatángulo, el coseno del ángulo está dado por:
[tex]cos(\theta)=\frac{CA}{H}[/tex]
Donde:
CA es el cateto adyacenteH es la hipotenusa del triánguloEspero te haya sido de ayuda!
After a 20% discount the phone cost is $70.40. What was the original price?
Answer:
$84.48
Step-by-step explanation:
Multiply the price before discount by 1.2 (100% + 20%) to get 70.40 x 1.2 = 80.48; $80.48
Hope this helps!
:)
For the following set of data, find the percentage of data within 2
population standard deviations of the mean, to the nearest percent.
58, 77, 31, 54, 58, 54, 56, 58, 56
Answer:
58,+77,+31,+54+,58+,54+,46+,58+,56/9
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in a variation.
The data set is given below.
58, 77, 31, 54, 58, 54, 56, 58, 56.
Then the mean of the data set will be
Mean = (58 + 77 + 31 + 54 + 58 + 54 + 56 + 58 + 56) / 9
Mean = 502 / 9
Mean = 55.78
Then the standard deviation will be
[tex]\rm SD = \sqrt{\dfrac{(58 - 55.78)^2+(77-55.78)^2 + ..... + (56-55.78)^2 }{9}}\\\\SD = \sqrt { \dfrac{1085.5}{9}}\\[/tex]
On further solving we have
SD = 10.98
If the value of the mean is 55.78. Then the standard deviation will be 10.98.
More about the standard deviation link is given below.
https://brainly.com/question/12402189
#SPJ2
Which calculation shows the best method for estimating the result of 384 divided by three-sixteenths?
Answer:
the answer to this is 2048
Step-by-step explanation:
Answer: B
Step-by-step explanation: Just round
The diameter of a circle is 9 m. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer:
[tex]C=28.3m[/tex]
Step-by-step explanation:
From the question we are told that:
Diameter [tex]d=9m[/tex]
Radius[tex]r=4.5m[/tex]
Generally the equation for Circumference of a circle is mathematically given by
[tex]C=2\pi r\\\\\C=2*\pi*4.5m[/tex]
[tex]C=28.3m[/tex]
Answer:
Step-by-step explanation:
From the question we are told that:
Diameter
Radius
Generally the equation for Circumference of a circle is mathematically given by
Have a good day
Step-by-step explanation:
help help help due today
Answer:
sin 52°= AB/x
sin 52°=AB/7.7
AB= 6.06 m
Please help I’ll give brainliest
Answer:
285.214 cubic meters
Step-by-step explanation:
So I use this equation V=πr2h
All because this equation have a radius and so I put it in this form
V= π5.5^2 x 3
V=285
(I hope this help and if it’s wrong I am truly sorry)
The required volume of the given cylinder is 285.214 cubic meters. Option A is correct.
For a cylinder,
Height = 3m
Radius = 5.5m
Volume = ?
Volume is defined as the ratio of the mass of an object to its density.
Here,
The volume of the cylinder is given as,
Volume = πr²h
Substitute the value in the equation,
Volume = 3.14×5.5²×3
volume = 285.214 cubic meters.
Thus, the required volume of the given cylinder is 285.214 cubic meters. Option A is correct.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ2
Given(a*b)*c=a*(b*c) what property does this represent
Answer:
The associative property allows us to change groupings of addition or multiplication and keep the same value. (a+b)+c = a+(b+c) and (a*b)*c = a*(b*c).
Step-by-step explanation:
in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + (b + c) = (a + b) + c, and a(bc) = (ab)c; that is, the terms or factors may be associated in any way desired.
Answer:
Associative
Step-by-step explanation:
The volume of a cylinder is 1280pi cm cubed. The radius is 8cm. Find the missing length.
If Albert owns x model airplanes and Maxim owns x + 13 model airplanes, then Albert and Maxim own___ model airplanes together. Albert owns ___ less model airplanes than Maxim.
Answer:
2x + 13
13
Step-by-step explanation:
Albert and Maxim own
x + (x + 13) = 2x + 13 model airplanes together
Albert owns
(x + 13) - x = 13 less model airplanes than Maxim.
Answer:
They own 2x+13 model airplanes together
Albert owns 13 less model airplanes than Maxim
You have $9 and earn $0.75 for each cup of orange juice you sell. Write an equation that represents the total amount $A (in dollars) you have after selling $j cups of orange juice. $A
Answer:
I believe it's A = 0.75j + 9
Step-by-step explanation:
If x or j is the amount of cups of OJ you sell, and you earn $0.75 per cup.
0.75x
The b = 9 which adds to the total amount of money you have
0.75x+9
A is the total money you earn after you sell j cups.
I hope this helps!
Determine the value of a so that x1-3x3=-3 2x1+ax2-x3=-2 (i)unique solution(ii)no solution(iii)many solutions
Answer:
(i)unique solution
Explanation:
We solve for x1 thus in the first equation:
x1-3x3=-3
x1-9=-3
x1=-3+9
x1= 6
We solve for a thus in the second equation:
2x1+ax2-x3=-2
2+a2-x3=-2
a2-x3=-4
a2=-4+x3
Brenya Estate produces a high quality tea branded Super by blending three types of tea coded A, B and C in the ration 1: 5:1. Originally Type A tea costs GHS 1,600 type B costs GHS 800 and type C costs GHS 1,700 per kg to produce. Brenya Tea Estate packs Super tea in packets of 825g each. Blending and packing costs are 40 per kg. Determine the production cost for a packet of Super tea,
Solution :
Cost of 1 kg super tea mixture
[tex]$=\frac{1(1600)+5(800)+1(1700)}{1+5+1}$[/tex]
[tex]$=\frac{1600+4000+1700}{7}$[/tex]
[tex]$=\frac{7300}{7}$[/tex]
= 1042.8
≈ 1043
Include of cost blending and packaging.
So, cost of 1 kg is 1043 + 40 = 1083
Cost of packaging of 825 gram super tea = [tex]$\frac{825}{1000} \times 1083$[/tex]
= 893.47
The price of a technology stock has risen to $9.66 today. Yesterday's price was $9.59. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
% increase = 100 x [(new price) - (original price)] / (original price)] = 100 (9.67 - 9.56) / 9.56
% increase ≅ 1.2% (to the nearest tenth)
What is another word for zeros?
Answer:
nothing
Step-by-step explanation:
Zero is a number without a value so nothing could be another word for it
Question 2 of 10
A rectangle's width is 5 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
O A. A(1) = lw
B. A(1)=12 + 51
C. All) = w(w+5)
O D. All) = 12 - 51
A rectangle's width is 5 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
O A. A(1) = lw
B. A(1)=12 + 51
C. All) = w(w+5)
O D. All) = 12 - 51
Help me with this one plz
Answer:
-1 is the only number there that is an integer as all the rest of them are mixed fractions.
Answer:
- 1
Step-by-step explanation:
the coordinates of three vertices of a rectangle are -2, 3, -2, -1, and 3, -1. what are the coordinates of the fourth vertex
Answer:
(3,-5)
Step-by-step explanation:
We first cal ulate the distance
a.)Would the equation be sine or cosine if the situation was someone being on a roller coaster that starts 15 ft above ground level, goes up to 45 feet above ground level, and goes down 20 feet under ground level?
b.) What would the equation be? ford monition and the terminal is in the third quadrant
75 mm
a
60 mm
What is the length of the missing leg?
Answer:
a = 45 millimeters
Step-by-step explanation:
In order to solve this, we need to know that for right-angled triangles the following is true:
[tex]c^{2} = a^{2} + b^{2}[/tex] (where c is the hypotenuse and "a" and "b" are the legs)
From the formula above we can conlude that...
[tex]a = \sqrt{c^{2} - b^{2} }[/tex]
Now we just substitute the variable that we know and get that...
[tex]a = \sqrt{c^{2} - b^{2} }\\a = \sqrt{75^{2} - 60^{2} } \\a = \sqrt{5,625 - 3600} \\a = \sqrt{2025} \\a = 45[/tex]
Therefore a = 45millimeters.
The points A, B, C and D lie on a circle centre O.
Angle AOB = 90° angle COD= 50° and angle BCD= 1239
The line DT is a tangent to the circle at D.
Find
(a) angle OCD
The measure of angle OCD from the given figure is 58°.
Given that, the points A, B, C and D lie on a circle Centre O.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here, OC and OB are radius of a circle, then BOC is isosceles triangle
Now, ∠BOC+∠OBC+∠OCB=180°
50°+∠OBC+∠OBC=180°
⇒ 2∠OBC=130°
⇒ ∠OBC=65°
Here, ∠OCD=∠BCD-65°
⇒ x=123-65=58°
Hence, the measure of angle OCD from the given figure is 58°.
To learn more about the circle visit:
https://brainly.com/question/11833983.
#SPJ2
