Answer:
Dimensions to minimize surface are is 28 ft x 28 ft x 14 ft
Step-by-step explanation:
The Volume of a box with a square base of say;x cm by x cm and height
h cm is;
V = x²h
Now, the amount of material used is directly proportional to the surface area, hence we will minimize the amount of material by minimizing the surface area.
The formula for the surface area of the box described is given by;
A = x² + 4xh
However, we need A as a function of
only x, so we'll use the formula;
V = x²h
V = x²h = 10,976 ft³
So,
h = 10976/x²
So,
A = x² + 4x(10976/x²)
A = x² + 43904/x
So, to minimize the area, it will be at dA/dx = 0.
So,
dA/dx = 2x - 43904/x² = 0
Factorizing out, we have;
2x³ = 43904
x³ = 43904/2
x³ = 21952
x = ∛21952
x = 28 ft
since, h = 10976/x²
h = 10976/28² = 14 ft
Thus,dimension to minimize surface are is 28 ft x 28 ft x 14 ft
What is the volume of the following rectangular prism? the height is 5 and 1/4 and the base is 8
Answer:
V = 42 units ^3
Step-by-step explanation:
The volume of a rectangular prism is
V =Bh
V = 8*5 1/4
Changing to a mixed number
V = 8* ( 5*4+1) /4
=8*21/4
= 42 units^3
Answer:
[tex]\huge\boxed{V=42\ u^3}[/tex]
Step-by-step explanation:
Th formula of a volume of a prism:
[tex]V=BH[/tex]
B - base
H - height
We have
[tex]B=8;\ H=5\dfrac{1}{4}=\dfrac{5\cdot4+1}{4}=\dfrac{20+1}{4}=\dfrac{21}{4}[/tex]
Substitute:
[tex]V=(8)\left(\dfrac{21}{4}\right)[/tex] simplify 8 and 4
[tex]V=(8\!\!\!\!\diagup)\left(\dfrac{21}{4\!\!\!\!\diagup}\right)=(2)(21)=42[/tex]
Which phrase refers to the legal act of lowering an individual’s tax liability?Which phrase refers to the legal act of lowering an individual’s tax liability?
Answer:
Tax avoidance - legal
Tax evasion - illegal
Which is the definition of a rhombus?
a. A quadrilateral with four right angles
b. A quadrilateral with four congruent sides
c. A quadrilateral with interior angles that sum to 360°
d. A quadrilateral with two pairs of opposite congruent sides
Answer:
a) A quadrilateral with 4 right angles
Answer:
I think the answer is b
I'm sorry if I'm not correct
first correct answer gets best marks
Answer:
x ≤5
Step-by-step explanation:
Pointing to the left means less than or less than or equal to
x ≤5
Answer:
[tex]\boxed{x \leq 5}[/tex]
Step-by-step explanation:
[tex]\sf Arrow \ pointing \ to \ the \ left \ on \ a \ number \ line \ means \ that[/tex]
[tex]\sf \ the \ value \ is \ either \ less \ than \ or \ less \ than \ or \ equal \ to.[/tex]
[tex]\sf{Graph}[/tex] [tex]x\leq 5[/tex] [tex]\sf{on \ the \ number \ line.}[/tex]
Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister (i.e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answer:
The larger canister has 8 times the volume and 4 times the volume of the smaller one.
Step-by-step explanation:
The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.
The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.
The canisters are in the shape of a cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
The surface area of a cylinder is given as:
A = 2πr(r + h)
SMALLER CANISTER
Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres
Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres
LARGER CANISTER
Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres
Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres
By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.
Answer:
Yeah, what they said above.
Step-by-step explanation:
How many Real Solutions
Answer:
D.0
Step-by-step explanation:
Our system of equations is
y= x²+1y=xthen we can conclude that
x²+1 = xx²+1-x = 0x²-x+1 = 0This is a quadratic equation so we will use the dicriminant method:
Let Δ be our dicriminant
a= 1b= -1c= 1Δ = (-1)²-4*1*1 = 1-4 = -3 < 0The dicriminant is negative so this equation has no real solutions
the the system has no real solutions
Find the value of
x in the triangle shown below.
Answer:
69.7° (corrected to 3 significant figures)
Step-by-step explanation:
Use the cosine formula to solve for x.
[tex]cosA=\frac{(b^2+c^2-a^2)}{2bc} \\cos x =(3.5^2+ 3.5^2 -4^2)}/[2(3.5)(3.5)]cos x =0.346939\\x=69.7[/tex]
Which phrase matches the expression p+7? A. 7 minus p B. the difference of 7 and p C. the quotient of p and 7 D. the sum of p and 7
Answer:
the sum of p amd 7
hopefully this helped :3
Answer:
D
Step-by-step explanation:
Since addings answer is a sum
p+7
D
Can anyone answer this?
Answer:
Because the triangle is isosceles, the base angles are congruent. Since the sum of angles in a triangle is 180° we can write:
24 + x + x = 180
24 + 2x = 180
2x = 156
x = 78°
Answer:
[tex]\boxed{x=78}[/tex]
Step-by-step explanation:
The triangle is an isosceles triangle.
The two base angles are equal.
Angles in a triangle add up to 180 degrees.
x + x + 24 = 180
Combine like terms.
2x + 24 = 180
Subtract 24 on both sides.
2x = 156
Divide both sides by 2.
x = 78
The graph of f(x)=4x^3-13x+9x+2 is shown below. How many roots of f(x) are rational numbers? Quick Please!!!!
Answer:
All three are rational numbers.
Step-by-step explanation:
I used Desmos (a graphing calculator online) and the roots were all able to be written with fractions.
how to do this question plz
Answer:
Depth of the milk = 4 cm
Step-by-step explanation:
In the figure attached,
Milk carton is in the shape of a cuboid having length = 8 cm, Width = 5 cm and Height = 15 cm
Depth of the milk in the carton = 12 cm
Milk inside the carton will have the same shape of cuboid, having same length and width but a different height.
Volume of the milk = volume of the cuboid shape of the milk
= Length × width × height
= 8 × 5 × 12
= 480 cm³
Now the carton is turned with its base on the shaded region.
By changing the base, dimensions of the milk inside the carton will change but the volume of the milk will remain the same.
New dimensions of the milk inside the carton will be,
Length = 15 cm
Width = 8 cm
Height = d cm (unknown side)
By using the formula of volume again,
V = l × b × h
480 = 15 × 8 × d
480 = 120d
d = [tex]\frac{480}{120}[/tex]
d = 4 cm
Therefore, depth of the milk in the carton will be 4 cm.
PLEASEEEEE I don't understand this question.
Answer:
262°
Step-by-step explanation:
The relationship between the angle at B (82°) and the arcs of the circle, CGF and CDF, is that the angle is half the difference of those arcs. Of course the sum of those arcs is 360°, since together they make a full circle. So. we have ...
CGF +CDF = 360
(CGF -CDF)/2 = 82
We need to solve this system of equations to find CGF.
__
Multiplying the second equation by 2 and adding the first, we get ...
2((CGF -CDF)/2) +(CGF +CDF) = 2(82) +(360)
2CGF = 524 . . . . . simplify
CGF = 262 . . . . . . divide by 2
The measure of arc CGF is 262°.
_____
Alternate solution
Here's another way to get there. Arc CDF is the supplement to angle B, so is ...
CDF = 180° -∠CBF
Of course, arc CGF is 360° minus arc CDF, so ...
CGF = 360° -(180° -∠CBF)
CGF = 180° +∠CBF . . . . . simplify . . . please note this is a general solution
Then ...
arc CGF = 180° +82° = 262°.
On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike? if possible, I would like a clear equation.
Answer:
He hiked 10 miles.
Step-by-step explanation:
rate x time = distance
The distance up and the distance down are equal
3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours
3h + 2 = 5h
2 = 2h
h = 1 hour
3mi/hr x 1 2/3 hr = 5 miles
5 mi/hr x 1 hr = 5 miles
Choose the equivalent system of linear equations that will produce the same solution as the one given below 4x-y=-11 2x+3y=5
Answer: x = -2 , y = 3
Step-by-step explanation:
4x-y=-11
2x+3y=5
Solve 4x-y=-11 for y
Add -4x to both sides
4x-y+-4x=-11+-4x
-y=-4x-11
Divide both sides by -1
-y/-1=-4x-11/-1
y=4x+11
Substitute 4x+11 for y in 2x +3y=5
2x+3y=5
2x+3(4x+11)=5
Simplify both sides of the equation
14x+33=5
Add -33 to both sides
14x+33+-33=5+-33
14x=-28
Divide both sides by 14
14x/14=-28/14
x=-2
Substitute -2 for x in y= 4x+11
y=4x+11
y=(4)(-2)+11
Simplify both sides of the equation
y=3
Ted and three of his friends went out to eat. They decided to split the bill evenly. Each person paid $16.88. What was the total bill?
Answer:
Total bill = $67.52
Step-by-step explanation:
Ted + 3 = 4
$16.88 × 4 = $67.52
hopefully this helped you :3
Answer:
16.88*4= 67.52 dollars
Step-by-step explanation:
Ted and 3 friends split the bill evenly, each person paid 16.88:
16.88*4= 67.52 dollars
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a
Answer:
Unknown side = 28tan B = 7/24Step-by-step explanation:
The question is incomplete. Here is the complete question.
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.
Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.
From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;
c² = a²+b²
100² = 96² +b²
b² = 100² - 96²
b² = 10,000 - 9216
b² = 784
b = √784
b = 28
Hence, the unknown length is 28.
To get tanB, we will use the SOH, CAH, TOA trigonometry identity
According to TOA, tan B = opposite/adjacent
tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)
Given b = 28 and a = 96
tan B = 28/96
tan B = 4*7/4*24
tan B = 7/24
Given ADC ACB and BDC BCA prove a squared + b squared = c squared. Use the two Column proof.
Answer:
a² + b² = c · (e + d) = c × c = c²
a² + b² = c²
Please see attachment
Step-by-step explanation:
Statement, Reason
ΔADC ~ ΔACB, Given
AC/AD = BA/AC, The ratio of corresponding sides of similar triangles
b/e = c/b
b² = c·e
ΔBDC ~ ΔBCA, Given
BC/BA = BD/BC, The ratio of corresponding sides of similar triangles
a/c = d/a
a² = c·d
a² + b² = c·e + c·d
a² + b² = c · (e + d)
e + d = c, Addition of segment
a² + b² = c × c = c²
Therefore, a² + b² = c²
Write 5x^2 - 10x + 4 in vertex form.
Answer:
y=5(x-1)^2-1
Step-by-step explanation:
Answer:
5(x - 1)² - 1
Step-by-step explanation:
Given
5x² - 10x + 4
Using the method of completing the square
The coefficient of the x² term must be 1 , so factor out 5 from the first 2 terms
= 5(x² - 2x) + 4
add/ subtract ( half the coefficient of the x- term )² to x² - 2x
= 5(x² + 2(- 1)x + 1 - 1 ) + 4
= 5(x - 1)² - 5 + 4
= 5(x - 1)² - 1 ← in vertex form
An educational researcher used school records to determine that, in one school district, 84% of children living in two-parent homes graduated high school while 75% of children living in single-parent homes graduated high school. Determine the parameter of interest.
Answer:
Your parameter of interest is the thing that your research is focusing on. For example, if you want to find the weight of an average goat, your parameter of interest will be the weight of an average goat.
In this case, you will have two parameters of interest: percentages of children in a school district living in two-parent homes that graduated high school, and percentages of children living in single-parent homes that graduated from high school.
Hope this helps!
8x + 5y=-22
-3x - 5y = 2
Answer:
(-4, 2).
Step-by-step explanation:
8x + 5y=-22
-3x - 5y = 2 Adding the 2 equations:
5x = -20
x = -4.
Substitute x = -4 in the first equation:
8(-4) + 5y = -22
5y = -22 + 32
5y = 10
y = 2.
Answer:
[tex]x=-4,\:\\y=2[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}8x+5y=-22\\ -3x-5y=2\end{bmatrix}\\\mathrm{Multiply\:}8x+5y=-22\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:24x+15y=-66\\\mathrm{Multiply\:}-3x-5y=2\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:-24x-40y=16\\\\\begin{bmatrix}24x+15y=-66\\ -24x-40y=16\end{bmatrix}\\\\-24x-40y=16\\+\\\underline{24x+15y=-66}\\-25y=-50\\\begin{bmatrix}24x+15y=-66\\ -25y=-50\end{bmatrix}\\-25y=-50\\\mathrm{Divide\:both\:sides\:by\:}-25\\\frac{-25y}{-25}=\frac{-50}{-25}\\y=2\\[/tex]
[tex]\mathrm{For\:}24x+15y=-66\mathrm{\:plug\:in\:}y=2\\24x+15\times\:2=-66\\24x+30=-66\\24x+30-30=-66-30\\24x=-96\\\frac{24x}{24}=\frac{-96}{24}\\x=-4\\\\\\x=-4,\:y=2[/tex]
When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. Results. What is the value of ?
Answer:
0Step-by-step explanation:
Given the expression after 4 has been subtracted from both sides as
1/2 x = - 1/2 x, the original expression will be gotten by adding back 4 to both sides of the resulting expression as shown;
1/2 x + 4 = - 1/2 x + 4
x/2 + 4 = -x/2 + 4
Find the LCM of both equation;
(x+8)/2 = (-x+8)/2
Multiplying both sides by 2 will give;
x+8 = -x+8
Collecting the like terms;
x+x = 8-8
2x = 0
x = 0/2
x = 0
Hence, the value of x is 0
Answer:
0
Step-by-step explanation:
what is the value of 24% of 800?
Question of mathematics
Answer:
[tex] \huge \boxed{192}[/tex]Step-by-step explanation:
[tex]24\% \: of \: 800[/tex]
By definition of p% = p/100
[tex] = \frac{24}{100} \times 800[/tex]
Reduce the numbers with Greatest Common Factor 100
[tex] = 24 \times 8[/tex]
Multiply the numbers
[tex] = 192[/tex]
Hope I helped!
Best regards!!
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 and is the least intense sound a human ear can hear. What is the approximate loudness of a dinner conversation with a sound intensity of 10–7?
Answer:
The loudness of the dinner conversation is 40 dB
Step-by-step explanation:
Loudness in dB = 10[tex]Log_{10}[/tex] [tex](\frac{I}{I_{o} })[/tex]
where [tex]I_{0}[/tex] is the least intense sound a human can hear = [tex]10^{-12}[/tex] W/m^2
For a dinner conversation with sound intensity of [tex]I[/tex] = [tex]10^{-7}[/tex] W/m^2
Loudness = 10[tex]Log_{10}[/tex] [tex](\frac{10^{-7} }{10^{-12} })[/tex] = 10[tex]Log_{10}[/tex] [tex]( 10^{4} )[/tex] = 40 dB
Answer:
50 Db
Step-by-step explanation:
Find the angle measures given the figure is a rhombus. m=
Answer:
74°
Step-by-step explanation:
A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.
According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.
The remaining angle of the rhombus will be calculated as thus;
= 360° - (32°+32°)
= 360° - 64°
= 296°
This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°
This means that each obtuse angles of the rhombus will be 148°.
To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.
m° = 148°/2
m° = 74°
Hence the angle measure if m(1) is 74°
PLEASE HELP
A hire purchase agreement offers gym equipment, with a marked price
$897, for $87 deposit and $46.80 a month payable over 2 years.
Calculate :
a) the total hire-purchase price
b) the amount of
amount of interest charged
Answer: a) $1,210.20 b) $313.20
Step-by-step explanation:
a) $87 down + $46.80(24 months) = $1,210.20 total paid
b) $1,210.20 - $897.00 = $313.20 interest paid
4) Solve the problem for the compound events.
A bank has a special vault for valuable items. It has 3 dials that operate the combination. The
first dial has the numbers from 1 to 100, the second and third each have the 26 letters of the al-
phabet. In order to open the vault, the bank manager must correctly set each dial. How many
possible combinations are there for this vault?
Answer:
i think its 67600
Step-by-step explanation:
100*26=2600
2600*26=67600
We have 9 balls, numbered 1 through 9, and 27 bins. How many different ways are there to distribute these 9 balls among the 27 bins? Assume the bins are distinguishable (e.g., numbered 1 through 27).
Answer:
7625597484987 ways
Step-by-step explanation:
Given the following :
Number of ball(k) = 9
Number of bins (n) = 27
How many different ways are there to distribute these 9 balls among the 27 bins.
Here, the balls have different labels (1 to 9)
The bins are also distinguishable, therefore each ball can go into any of the 27 distinct bins.
Therefore, the different ways are there to distribute these 9 balls among the 27 bins equals = n^k
27^9 = 7625597484987 ways.
hellpp plzzzzz.......
Answer:
120Step-by-step explanation:
Given
u = 14 , a = 8 , t = 4
Now, let's find the value of s
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
plug the values
[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]
Reduce the numbers with G.C.F 2
[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]
Multiply the numbers
[tex] = 56 + 4 \times {4}^{2} [/tex]
Calculate the product
[tex] = 56 + {4}^{3} [/tex]
Evaluate the power
[tex] = 56 + 64[/tex]
Add the numbers
[tex] = 120[/tex]
Hope this helps..
best regards!!
Polygon CCC has an area of 404040 square units. K 2ennan drew a scaled version of Polygon CCC using a scale factor of \dfrac12 1 2 start fraction, 1, divided by, 2, end fraction and labeled it Polygon DDD. What is the area of Polygon DDD?
Answer:
Area of polygon D = 10 square units
Step-by-step explanation:
Given:
Polygon C has an area of 40 square units.
It is scaled with a scale factor of [tex]\frac{1}2[/tex] to form a new polygon D.
To find:
The area of polygon D = ?
Solution:
When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.
And the area becomes one-fourth of the original polygon.
Let us consider this by taking examples:
First of all, let us consider a right angled triangle with sides 6, 8 and 10 units.Area of a right angled triangle is given by:
[tex]A = \dfrac{1}{2} \times Base \times Height\\\Rightarrow A = \dfrac{1}{2} \times 6 \times 8 = 24\ sq\ units[/tex]
If scaled with a factor [tex]\frac{1}{2}[/tex], the sides will be 3, 4 and 5.
New area, A':
[tex]A' =\dfrac{1}{2} \times 3 \times 4 = 6\ sq\ units = \dfrac{1}4\times A[/tex]
i.e. Area becomes one fourth.
Let us consider a rectangle now.Sides be 8 and 10 units.
Area of a rectangle, A = [tex]Length \times Width[/tex] = 8 [tex]\times[/tex] 10 = 80 sq units.
Now after scaling, the sides will be 4 and 5 units.
New Area, A' = 4 [tex]\times[/tex] 5 =20 sq units
So, [tex]\bold{A' = \frac{1}4 \times A}[/tex]
Now, we can apply the same in the given question.
[tex]\therefore[/tex] Area of polygon D = [tex]\bold{\frac{1}{4}}[/tex][tex]\times[/tex] Area of polygon C
Area of polygon D = [tex]\bold{\frac{1}{4}}[/tex][tex]\times[/tex] 40 = 10 sq units
Answer:
Step-by-step explanation:
10
WILL GIVE BRAINLEST ANSWER IF ANSWERED IN THE NEXT 24 HRS Express the complex number in trigonometric form. -5i
Answer:
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Step-by-step explanation:
If a complex number is z=a+ib, then the trigonometric form of complex number is
[tex]z=r(\cos \theta +i\sin \theta)[/tex]
where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].
The given complex number is -5i.
It can be rewritten as
[tex]z=0-5i[/tex]
Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.
[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]
[tex]\tan \theta=\dfrac{-5}{0}[/tex]
[tex]\tan \theta=\infty[/tex]
[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex] [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]
[tex]\theta=\dfrac{3\pi}{2}[/tex]
So, the trigonometric form is
[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]
Answer:
in degrees the answer is 5 (cos 270 + i sin 270)
in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))
Step-by-step explanation: