[tex](3-9i)(6-i)=18-3i-54i+9i^2=18-57i-9=\boxed{9-57i}[/tex].
Hope this helps.
La población de Colombia para el 2018 es de 49 821 512 Si 25'228.444 es la cantidad de mujeres ¿Que porcentaje representan del total de la población?
Answer:
Las mujeres representan el 50.63% de la población.
Step-by-step explanation:
Este problema es un problema de proporciones el cual puede resolverse usando una regla de tres.
El problema nos dice que la población total de Colombia es de 49,821,512 y nos pide calcular qué porcentaje representa el total de mujeres que es igual a 25,228,444. Si llamamos x al porcentaje de mujeres podemos representar esto de la siguiente manera mediante una regla de tres:
Población Porcentaje
49, 821,512 100%
25,228,444 x%
Resolviendo para x tenemos que:
[tex]x=\frac{25,228,444(100)}{49,821,512}=\frac{2,522,844,400}{49,821,512}= 50.6376[/tex]
Por lo tanto, las mujeres representan el 50.63% de la población.
Please answer it now in two minutes
Answer:
m<x = 60
Step-by-step explanation:
This triangle seems to be a 30-60-90 triangle, therefore m<x will be 60 degrees.
In the figure, OM is perpendicular to AB. Prove that M is the the midpoint of AB.
we know by looking at the picture that m is the midpoint of AB since O to M doted lines had half into two equal parts.so M is in the midpoints of AB.
Step-by-step explanation:
to prove: M is the midpoint of AB
given: OM is perpendicular to AB
construction: joint AO and BO
proof: in the given fig,
OA and OB are joined
In Δ AOM and ΔBOM
AO = BO ( two sides of Δ AOB )
OM = OM ( common )
∴ Δ AOM ≅ Δ BOM ( by SAS rule )
∴ AM = BM ( by CPCT ) -------- 1
∴ M is the midpoint of AB ( from 1 )
⇒hence proved
HOPE THIS HELPED and PLEASE MAKE ME AS THE BRAINLIEST
Six different books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right. How many possible arrangement are there?
Answer:
720 ways
Step-by-step explanation:
At first their are six books, that means that there are six different positions to put them. The first book to be placed would have 6 position, when the first book is placed, to place the second book there would be 5 position since one position has been used by the first book. After placing the second book, to place the third book there would 4 available position, and it follows this manner i.e for the fourth book 3 available position, for the fifth book 2 available position and for the sixth book, one available position.
Therefore the number of ways to arrange the books on the shelf from left to right = 6 × 5 × 4 × 3 × 2 × 1 = 6! = 720 ways
Let u and v be the solutions to 3x^2 + 5x + 7 = 0. Find (u/v) + (v/u)
Answer:
=-0.809
Step-by-step explanation:
3x^2+5x+7=0 complete the square
3x^2+5x=-7 divide both sides by 3
x^2+5/3 x = -7/3 to complete the square add term(b/2)^2=((5/3)/2)²=25/36
X^+5/3 x+25/36=-7/3 +25/36 factorize
(x+5/6)²= -59/36
x+5/6= + or - √59/36
solution for x= -5/6-√59/6i (u) OR -5/6+√59/6i (v)
u/v + v/u=(-5/6-√59/6i)/(-5/6+√59/6i) +(-5/6+√59/6i)/(-5/6-√59/6i)=-17/21
=-0.809
Answer:
[tex]\large \boxed{\sf \ \ \ -\dfrac{17}{21}=-0.80952... \ \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all we can verify that 0 is not a solution of the equation so that we can divide by u or v
[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{u^2+v^2}{uv}=\dfrac{(u+v)^2-2uv}{uv}=\dfrac{(u+v)^2}{uv}-2[/tex]
And we know that
[tex]u+v=-\dfrac{5}{3}\\\\uv=\dfrac{7}{3}\\\\\\as \ \ (x-u)(x-v)=x^2-(u+v)x+uv[/tex]
So it comes
[tex]\dfrac{v}{u}+\dfrac{u}{v}=\dfrac{5^2*3}{7*3^2}-2=\dfrac{25-42}{21}=-\dfrac{17}{21}=-0.80952...[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
In training for a distance cycling event, Milicent bikes 23 miles to the park. Then, she bikes 42 miles to the beach before cycling 29 miles from the beach back to her house. How many total miles does Millicent cycling her bike? Give the numeric value only, without units.
Answer:
94
Step-by-step explanation:
Add the three distances.
23 + 42 + 29 = 94
94 miles
[tex]\text{We need to get the total miles Milicent cycled}\\\\\text{To do this, we would add up all the distances she travelled}\\\\\text{Add:}\\\\23+42+29=94\\\\\boxed{\text{94 miles}}[/tex]
9/4n = 1.5/7 Please Explain
Answer:
9/4n= 1.5/7
right now to find this equation it is a proportion so you cross multiply and you gonna get 63=6n and divide 6 on both sides and u get 10.5.
Check 9/4n= 9/42 and to simply u will get 1.5/7
Step-by-step explanation:
The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2. What is the lateral area of the smaller cylinder? 17.1π mm2 33.6π mm2 60π mm2 84π mm2
Answer: Step 1
Find the scale factor
we know that
If the two cylinders are similar
then
The ratio between the circumference of the larger cylinder to the circumference of the smaller cylinder is equal to the scale factor
Step 2
Find the lateral area of the smaller cylinder
we know that
If the two cylinders are similar
then
The ratio between the lateral area of the larger cylinder to the lateral area of the smaller cylinder is equal to the scale factor squared
Let
x--------> the lateral area of the larger cylinder
y-------> the lateral area of the smaller cylinder
z--------> the scale factor
In this problem we have
substitute in the formula and solve for y
therefore
the answer is
33.6π mm2
The correct option is Option D: the lateral area of the smaller cylinder is 84π mm².
What is the lateral area of the cylinder?The lateral area of the cylinder is the area of the curved surface which can be calculated by the formula given below
lateral area of the cylinder= 2πrl
where r is the radius of the cylinder and l is the length of the cylinder.
Here given that the two cylinders are similar.
The larger cylinder has base of circumference = 60π mm
As we know the circumference of base of cylinder= 2πR
⇒60π= 2πr
⇒2πR= 60π
Given the lateral area of the larger cylinder is 210π mm²
From above formula, it is clear that the lateral area of the cylinder= 2πrl
⇒ 210π = 2πrl
⇒2πRl= 210π
⇒60πl= 210π (as from above it is derived that 2πr= 60π)
⇒l= 210π/ 60π= 7/2
⇒l= 3.5 mm
the smaller cylinder has base of circumference = 24π mm
⇒ 2πr= 24π mm
then the lateral area of the smaller cylinder is= 2πrl= 24π*3.5= 84π mm²
Therefore the correct option is Option D: the lateral area of the smaller cylinder is 84π mm².
Learn more about the lateral area of the cylinder
here: https://brainly.com/question/2292413
#SPJ2
Every bottle of Supercharge vitamins contains 50 vitamins. Let v be the total number of vitamins and let b be the number of bottles. Which equation represents the situation? B=50v or v=b+50 or b=v+50 or v=50b
Answer:
v = 50b / v = 50 × b
Step-by-step explanation:
1 bottle of subercharge = 50 vitamins
v = the total number of vitamins
b = number of bottles
For getting the answer of the total number of vitamins (v) you need to multiply the whole number of bottles (b) with the amount of vitamins present in a one bottle (50 vitamins). So , the answer is v = 50 × b / v =50b..Don't get confused both are the same.
Hope this helps and pls mark as brainliest : )
Answer: V=50b
Step-by-step explanation:
I got it right.
Look at triangle ABC
A (4.5)
5
4
3
2
1
B (2.2)
C (4.2)
1
5 -4 -3 -2 -1 0
1
23
4
5
-1
N
-3
-4
5
What is the length of side AB of the triangle?
A) 3
B) 5
C) square root of 6
D) square root of 13
Answer:
[tex] \sqrt{13} [/tex]Option D is the correct option.
Step-by-step explanation:
Given,
A ( 4, 5 ) , B ( 2 , 2 ) , C ( 4 , 2 )
Let,
A ( 4 , 5 ) → ( x1 , y1 )
B ( 2 , 2 ) → ( x2 , y2 )
Now, finding the length of AB
Use the distance formula to find the length of AB
[tex] = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
plug the values
[tex] = \sqrt{ {(2 - 4)}^{2} + {(2 - 5)}^{2} } [/tex]
Calculate the difference
[tex] = \sqrt{ {( - 2)}^{2} + {( - 3)}^{2} } [/tex]
Evaluate the power
[tex] = \sqrt{4 + 9} [/tex]
Add the numbers
[tex] = \sqrt{13} [/tex]
Hope this helps..
Best regards!!
Calculate the area of the regular hexagon ABCDEF.
A. 150 u^2
B. 259.8 u^2
C. 300 u^2
D. 519 u^2
Answer:
B. 259.8 u²
Step-by-step Explanation:
The area of a regular hexagon is given as:
[tex] Area = \frac{3\sqrt{3} }{2} a^{2} [/tex]
Where a = side length of the hexagon
Thus, the area of the regular hexagon with a given side length, a = 10, is calculated as follows:
[tex] Area = \frac{3\sqrt{3} }{2} a^{2} [/tex]
[tex] Area = \frac{3\sqrt{3} }{2}* 10^{2} [/tex]
[tex] = \frac{3\sqrt{3} }{2}* 100 [/tex]
[tex] = \frac{3*1.7321 }{2}* 100 [/tex]
[tex] = \frac{5.1963 }{2}* 100 [/tex]
[tex] = \frac{519.63 }{2} [/tex]
[tex] Area = 259.815 [/tex]
The area of the regular hexagon ≈ 259.8 u²
What are the coordinates of the image of vertex D after
a reflection across the x-axis?
(5.3)
O (-5.–3)
O (-3.5)
(3-5)
Answer: A 5,3
Step-by-step explanation:
I just took the test
The coordinates of the image of vertex D after a reflection across the x-axis is (5.3).
The correct option is (A).
what is reflection over x- axis?A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
For example,
when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P’, the coordinates of P’ are (5,-4). Notice that the x-coordinate for both points did not change, but the value of the y-coordinate changed from 4 to -4.
The given coordinates of D is (5, -3).
Now, to get the reflection over x- axis we have negate the value of y- coordinate and no changes in x- coordinate.
Hence, the coordinate of vertex D is (5, 3).
Learn more about reflection here:
https://brainly.com/question/3480959
#SPJ2
PLEASE PLEASE HELP IM BEING TIMED The two-way table represents data from a survey asking students whether they plan to attend college, travel, or both after high school. A 4-column table with 3 rows. The first column has no label with entries travel, not travel, total. The second column is labeled college with entries 43, 24, 67. The third column is labeled not college with entries 10, 5, 15. The fourth column is labeled total with entries 53, 29, 82. Which is the marginal relative frequency for students who plan to attend college? Round the answer to the nearest percent. 18% 22% 35% 82%
Answer: 82%
Step-by-step explanation:
- - - - - - - - college - - not college - - - - total
Travel - - - - 43 - - - - - - - 10 - - - - - - - - 53
Not travel - 24 - - - - - - - 5 - - - - - - - - - 29
Total - - - - 67 - - - - - - - 15 - - - - - - - - - 82
Marginal relative frequency of students who plan to attend college:
(Number of students who plan to attend the college / Total number of the students)
Number of students who plan to attend college = 67
total number of students = 82
Marginal relative frequency = 67/82
= 0.8170731
= (0.8170731) * 100%
= 81.7% = 82%
Answer:
a: 14/50
b: 15/50
c: 21/50
Step-by-step explanation:
on edge
In the International Grandmaster Championship, a total of 105 games were played where each team played exactly one game with all the other teams. How many teams were participating in the Championship?
Answer: 15 teams
Step-by-step explanation:
Total number of games played in the tournament = 105
Number of participating teams = p
Each team plays against every other team , then the total number of games played by each team = (p - 1) , since a team can't play itself
To obtain total number of games played =
(Number of teams × number of games played) [p × (p-1)]
However, the teams played against each other only once :
Therefore, total number of games played:
[p × (p-1)] / 2
Since we've been given the total number of games played :
[p × (p-1)] / 2 = 105
p × (p-1) = 105 × 2
p × (p-1) = 210
p^2 - p = 210
p^2 - p - 210 = 0
p^2 - 15p + 14p - 210 = 0
p(p - 15) +14(p-15) = 0
(p - 15) = 0 or (p + 14) = 0
p = 15 or p = - 14
Number of teams can't be negative
Therefore p = 15
Number of teams = 15
Felicia had $80 when she went to a music store that charges $18 for each CD. She needs to have no less than $20 in her wallet when she leaves the store so she has enough money to buy gas for the ride home. Which shows a possible number of CDs she could buy? Select three options. 1 2 3 4 5
Answer:
The amount of CD's she could buy would be 3.
Step-by-step explanation:
80-20=60
60÷18 = 3 CD's
Answer:
1,2,3
Step-by-step explanation:
Two similar cylindrical cans hold 2 litres and 6.75 litres of liquid. If the diameter of the smaller can is 16cm, find the diameter of the larger can.
Step-by-step explanation:
It is given that,
Volume of the cylindrical can 1 is 2 litres and that of cylindrical can 2 is 6.75 litres. The diameter of the smaller can is 16 cm. We need to find the diameter of the larger can.
The formula of the volume of a cylinder is given by :
[tex]V=\pi r^2h[/tex]
So,
[tex]\dfrac{V_1}{V_2}=\dfrac{r_1^2}{r_2^2}[/tex]
Diameter, d = 2r
[tex]\dfrac{V_1}{V_2}=\dfrac{(d_1/2)^2}{(d_2/2)^2}\\\\\dfrac{V_1}{V_2}=(\dfrac{d_1^2}{d_2^2})[/tex]
V₁ = 2 L, V₂ = 6.75 L, d₁ = 16 cm, d₂ = ?
[tex]\dfrac{2}{6.75}=(\dfrac{16^2}{d_2^2})\\\\d_2=29.39\ cm[/tex]
So, the diameter of the larger can is 29.39 cm.
PLZ HELP!! In the following figure, triangle ABC is a right triangle, and mA = 42°. Find the value of n°. Note: the figure is not drawn to scale. n =____a0°
Answer:
n = 132
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
n is an exterior angle of the triangle, thus
n = 90 + 42 = 132
Answer:
n = 132
Step-by-step explanation:
Which of the following statements are true?
I believe it is C, as the graphs do look the same.
How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution
Answer:
One
Step-by-step explanation:
It is given that,
y = 3x-5 ....(1)
y = -x+4 .....(2)
We can solve the above equations using substitution method. Put the value of y from equation (1) to equation (2) such that,
[tex]3x-5 = -x+4\\\\3x+x = 5+4\\\\4x = 9\\\\x=\dfrac{9}{4}[/tex]
Put the value of x in equation (1) we get :
[tex]y = 3x-5\\\\y = 3\times \dfrac{9}{4}-5\\\\y=\dfrac{7}{4}[/tex]
It means that the value of x is [tex]\dfrac{9}{4}[/tex] and the value of y is [tex]\dfrac{7}{4}[/tex]. Hence, the given equations has only one solution.
Answer:
1
Step-by-step explanation:
Multiply using distributive property.
(2m-5)(3m+8)
PLEASE HELP!!! ASAP!!!
Answer: 6m^2 +m -40
Step-by-step explanation: Distributing binomials calls for the FOIL method.
Multiply the First times the First: 3m×2m= 6m^2. (^2 means squared when we can't use superscript for exponents.)
Then multiply and combine the Outside and Inside terms: 2m ×8=16m. and -5 ×3m= -15m
16m - 15m = m
Then multiply the Last terms: -5×8= -40
You end up with
6m^2 + m -40
Answer:
6m^2 + m - 40.
Step-by-step explanation:
(2m - 5)(3m + 8)
= (2m * 3m) + (-5 * 3m) + (2m * 8) + (-5 * 8)
= 6m^2 - 15m + 16m - 40
= 6m^2 + m - 40.
Hope this helps!
A student earned grades of Upper B, Upper F, Upper B, Upper B, and Upper C. Those courses had the corresponding numbers of credit hours 4, 2, 1, 2, and 2. The grading system assigns quality points to letter grades as follows: Aequals4; Equals3; Equals2; Equals1; Alphaequals0. Compute the grade point average (GPA) as a weighted mean and round the result with two decimal places. If the Dean's list requires a GPA of 3.00 or greater, did this student make the Dean's list
Answer:
the grade point average (GPA) of the student is 2.27
If the Dean's list requires a GPA of 3.00 or greater, the student did not make the Dean's list.
Step-by-step explanation:
Given that:
A student grade are as follows:
B --- 3
F --- 0
B ---- 3
B ----- 3
C ------- 2
Those courses had the corresponding numbers of credit hours 4, 2, 1, 2, and 2.
The grading system assigns quality points to letter grades as follows:
A = 4; B=3; C=2; D=1; F=0
The sample mean simply implies the sum of the products of the value and the weights divided by the total weights;
i.e
[tex]\overline x = \dfrac{\sum xf}{n }[/tex]
[tex]\overline x = \dfrac{3(4)+0(2)+3(1)+3(2)+2(2)}{4+2+1+2+2 }[/tex]
[tex]\overline x = \dfrac{12+0+3+6+4}{11 }[/tex]
[tex]\overline x = \dfrac{25}{11 }[/tex]
[tex]\overline x =[/tex] 2.27
the grade point average (GPA) of the student is 2.27
If the Dean's list requires a GPA of 3.00 or greater, the student did not make the Dean's list.
The equations 2 x minus y = negative 2, 3 x + 2 y = 5, 4 x minus y = 2, and 22 x + 10 y = 7 are shown on the graph below. Which system of equations has a solution of approximately (–0.3, 1.4)? 2 x minus y = negative 2 and 22 x + 10 y = 7 3 x + 2 y = 5 and 4 x minus y = 2 4 x minus y = 2 and 22 x + 10 y = 7 2 x minus y = negative 2 and 3 x + 2 y = 5
Answer:
The correct option is;
(2·x - y = -2 and 22·x + 10·y = 7)
2 x minus y = negative 2 and 22 x + 10 y = 7
Step-by-step explanation:
2x - y = -2.........(1)
3x + 2y = 5.......(2)
4x - y = 2..........(3)
22x + 10y = 7...(4)
Given that the solution of the system of equation is (-0.3, 1.4), we have;
The system of equations consist of those equations that pass through the point (-0.3, 1.4)
We check as follows;
Equation (1)
2×(-0.3) - 1.4 = -2
Therefore, equation (1) passes through the point (-0.3, 1.4) and is one of the equations
Equation (2)
3×(-0.3) + 2×1.4 = 1.9 ≠ 5
Equation (2) is not part of the system of equations
Equation (3)
4×(-0.3) - 1.4 = -2.6 ≠2
Equation (3) is not part of the system of equations
Equation (4)
22×(-0.3) + 10×1.4 = 7.4 ≈ 7
Therefore, equation (4) approximately passes through the point (-0.3, 1.4) and is one of the equations
The correct option is A. [tex]2x - y = -2\ and 22x + 10y = 7.[/tex]
Given equations,
[tex]2x - y = -2.........(1)[/tex]
[tex]3x + 2y = 5.......(2)[/tex]
[tex]4x - y = 2..........(3)[/tex]
[tex]22x + 10y = 7...(4)[/tex]
Since the solution of the system of equation is [tex](-0.3, 1.4),[/tex] Hence the system of equation satisfy the above point.
Now check all the equations,
Equation (1),
[tex]2\times(-0.3) - 1.4 = -2\\-0.6-1.4=-2\\-2.0=-2[/tex]
Hence, equation (1) passes through the point[tex](-0.3, 1.4)[/tex] and is one of the equations.
Similarly, Equation (2)
[tex]3\times (-0.3) + 2\times1.4 = 5\\-0.9+2.8=5\\1.9=5\\[/tex]
Hence the above equation does not satisfy the solution, so it is not the other system of equation.
Now, Equation (3)
[tex]4\times(-0.3) - 1.4 = -2.6 \neq 2[/tex]
Hence Equation (3) is not part of the system of equations.
Now, Equation (4)
[tex]22\times (-0.3) + 10\times1.4 = 7.4[/tex]
Hence the above equation approximately passes through the solution[tex].(-0.3, 1.4)[/tex] and is one of the equations.
Hence the required system of equation is [tex]2x - y = -2[/tex] and [tex]22x + 10y = 7[/tex].
Therefore the correct option is A.
For more details follow the link:
https://brainly.com/question/2263981
The Goodsmell perfume producing company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to hold at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and the corresponding surface area and volume. This cylindrical perfume bottle needs to be boxed in a prism for sale on store shelves. The Goodsmell perfume producing company would like a box with the smallest possible surface area which will hold your design for the perfume bottle. Report the dimensions of the box and the corresponding area and volume. The pretty perfume company, Goodsmell’s competition, has also designed a new perfume bottle. The bottle is to be a spherical shape with a diameter of 7cm. Determine the volume and surface area of this bottle. The spherical bottle has a conical shaped lid with a diameter of 5cm and a height of 4.5cm. Given this information, calculate the volume and surface area of the lid of the spherical shaped bottle. Determine the dimensions of the smallest possible box which could be used to package Pretty Perfume’s new bottle with its spherical bottle and conical-shaped lid. However, this box is not shaped like a rectangular prism. Pretty Perfume would like to have unique packaging and have chosen to have a box shaped like a pyramid. Calculate the volume and surface area of this pyramid shaped box. The Final Product: Prepare a written report that includes: A clear and concise explanation of the process that you used to solve the problem. The calculations that you made, presented in an organized fashion. A rationale (reason) for your selection of values.
Answer:
1. r = 2.82 cm
h = 5.6 cm
The maximum volume possible to the nearest 10 mL = 140 mL
2. Size side of square base of box is 5.64 cm
Height of box = 5.6 cm
The surface area of the box is 189.96 cm²
The volume of the box is 178.13 cm³
3. The procedure for solving the problem was through noting that the shape of the cross-section of the pyramid is an isosceles triangle ans also that smallest possible box for the pretty perfume is one which fits the angle of inclination of the lid. This was found out by initially using the combined height of the perfume and the lid (placed to fit the spherical outline of the bottle) to calculate the dimensions of the pyramid, from which it was observed that the angle of inclination of the lid is larger than that of the calculated dimension, such that the lid outline would be visible and could eventually tear the perfume box
With the inclination angle, β, which is the base angle of the isosceles triangle, the angle at the top of the pyramid cross-section is calculated and the following relations are used to calculate the triangular cross-section of the pyramid
h = a·cos(α/2)
b = 2·a·cos(β)
[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]
[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]
With the calculated dimensions, a, b, and h the area, A, of the square pyramid is calculated as 2×b×a + b² and the volume, V, as 1/3×b²×h
The attached diagram shows the the cross-section of the perfume in the pyramid box.
Step-by-step explanation:
1. The surface area of the cylinder = 2πr² + 2πrh = 150 cm².........(1)
The volume of the cylinder, V = πr²h = 100 mL = 100 cm³..............(2)
From equation (2), h = 100/(π·r²)
Substituting the value if h in equation (1), we have;
2πr² + 2πr100/(π·r²) = 150
2πr² + 200/r = 150
(2πr³ + 200)/r = 150
2πr³ + 200 = 150×r
2πr³ -150·r+ 200 = 0
150 = 2πr² + 2πrh
h = (150 - 2πr²)/(2πr)
h = (75- πr²)/(πr)
Substituting the value of h in the equation for the volume, we have;
V = πr²h = πr²(75- πr²)/(πr)
V = 75·r - π·r³
At maximum volume, dV/dr = 0, we have
d(75·r - π·r³)/dr = 75 - 3·π·r²= 0
3·π·r²= 75
π·r² = 25
r = 5√π/π
h = (75- πr²)/(πr) = (75- π(5√π/π)²)/(π(5√π/π)) = (75 -25)/(5·√π)
h = 50/(5·√π)= 10·√π/π
The maximum volume = πr²h = π×25/π×10·√π/π = 250·√π/π = 141.05 cm³
The maximum volume possible = 141.05 cm³ = 141.05 mL
The maximum volume possible to the nearest 10 mL = 140 mL
The dimensions of the bottle are;
r = 2.82 cm
h = 5.6 cm
The surface area of the bottle = 2π(2.82)² + 2π×2.82 ×5.6 = 149.2 cm
2
Given that the cylindrical bottle has r = 2.82 cm and h = 5.6 cm, we have;
Size side of square base of box = 2 × 2.82 = 5.64 cm
Height of box = 5.6 cm
The surface area of the box = 2 × Area of base + 4 × Area of side
The surface area of the box = 2 *5.64^2 + 4 * 5.6 * 5.64 = 189.96 cm²
The volume of the box = Area of base × Height = 5.64^2*5.6 = 178.13 cm³
3. Diameter of spherical bottle = 7 cm = 2×r
Volume of the sphere bottle = 4/3πr³ = 4/3*3.5^3*π = 343/6·π = 179.6 cm³
The surface area of the sphere bottle = 4πr² = 4*(7/2)^2*π = 49·π = 156.94 cm²
3 i. The volume of a cone = 1/3πr²h = 1/3*(5/2)^2*4.5 = 9.385·π = 29.45 cm³
The surface area of a cone = πrS
S = √(4.5^2 + (5/2)^2) = 5.15
The surface area of a cone = π*2.5*5.15 = 40.43 cm²
3 ii. The depth of fitness of the lid on the bottle = 7/2 - √(7/2)^2 - 2.5^2) = 1.05
The total height of the spherical bottle with the conical lid = 7 + 4.5 - 1.05 = 10.45 cm
3 iii. Given that the box is shaped like a pyramid we have;
Width of the box at middle of the height of the spherical bottle = 7 cm
Height of the box = 10.45 cm
[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]
[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]
With the aid of a graphing calculator, the width of the square pyramid is found to be 12.12 cm
The volume = 1/3*12.12^2*10.45 = 511.68 cm²
The surface area = 2*12.12*√(12.12/2)^2 + 10.45^2) +12.12²= 439.7 cm²
The angle of inclination of the lid = tan⁻¹ (4.5/2.5) = 60.95°
The angle of inclination of the calculated box is tan⁻¹ (10.45/6.06) = 59.88
Since the lid is steeper, we make use of the angle of the lid
The base angles are thus = 60.95°
The angle at the top is thus 180 - 60.95*2 = 58.11°
Therefore, by the formula, we find that
a = 12.25 cm
b = 11.897 cm
h = a·cos(α/2)
h = 10.707 cm
The volume = 1/3*11.897^2*10.707 = 505.15 cm³
The surface area = 2*11.897*√(11.897/2)^2 + 10.707^2) +11.897²= 432.98 cm²
The angle at the top of the box = 2
Given that:
r = 2.82 cmh = 5.6 cmThen the maximum volume possible to the nearest 10 mL =
140 mLGiven that:
The size side of square base of box is 5.64 cmHeight of box = 5.6 cmHence, the surface area of the box is
189.96 cm²The volume of the box is :
178.13 cm³What is Surface Area?This refers to the measure of the total area of an object.
The written report:The procedural method used to solve the problem was to identify the shape of the pyramid, then finding out the smallest possible box for the pretty perfume and then using the calculated dimensions, found the answers.
Read more about surface area here:
https://brainly.com/question/76387
What is the value of x?
A. 60°
B. 155
C. 25°
D. 35°
Answer:
D. 35°
Step-by-step explanation:
1. The bottom right angle and 95° add up to 180°. Solve for that angle.
95 + y = 180
y = 85
2. Triangles have a total of 180°. Set up the equation.
60 + 85 + x = 180°
3. Simplify
145 + x = 180
4. Solve for x by subtracting 145 from both sides
x = 35°
Answer:
x = 35
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
60+x = 95
Subtract 60 from each side
60 +x-60 = 95-60
x = 35
what does 9! mean in math?
Answer:
9! means 9 factorial
Step-by-step explanation:
9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Find volume of cylinder if its
radius
height
5.5m and
height 9 m?
Answer:
855.298 m^3
Step-by-step explanation:
The volume of a cylinder equation is piR^2H.
So pi5.5^2×9
855.298 m^3
A game is played using one die. if the die is rolled and shows 6, the player wins $20. if the die shows any number other than 6, the player wins nothing.
a. if there is a charge of $4 to play the game, what is the game's expected value?
$______(round to the nearest cent)
b. choose the statment below that best describes what this value means.
Choose one!
a. over the long run, the player can expect to lose about this amount for each game played
b. over the long run, the player can expect to win about this amount for each game playedc. over the long run, the player can expect to break even.
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a charge of $1 to play the game, what is the game's expected value?
--------------------
Let random variable "x" be a count of player gain.
X-values are: 4, -1
P(x=4) = 1/6; P(x= -1) = 5/6
---------------------------------
E(x) = (1/6)(4) + (5/6)(-1)
E(x) = [4-5]/6
E(x) = -1/6 = -17 cents
=============================
Cheers,
(i) Write the expansion of (x + y)² and (x - y)². (ii) Find (x + y)² - (x - y)² (iii) Write 12 as the difference of two perfect square.
Answer:
1a (x + y)² = x² + 2xy + y²
1b. (x - y)² = x² - 2xy + y²
2. (x + y)² - (x - y)² = 4xy
3. 4² – 2² = 12
Step-by-step explanation:
1a. Expansion of (x + y)²
(x + y)² = (x + y)(x + y)
(x + y)² = x(x + y) + y(x + y)
(x + y)² = x² + xy + xy + y²
(x + y)² = x² + 2xy + y²
1b. Expansion of (x - y)²
(x - y)² = (x - y)(x - y)
(x - y)² = x(x - y) - y(x - y)
(x - y)² = x² - xy - xy + y²
(x - y)² = x² - 2xy + y²
2. Determination of (x + y)² - (x - y)²
This can be obtained as follow
(x + y)² = x² + 2xy + y²
(x - y)² = x² - 2xy + y²
(x + y)² - (x - y)² = x² + 2xy + y² - (x² - 2xy + y²)
= x² + 2xy + y² - x² + 2xy - y²
= x² - x² + 2xy + 2xy + y² - y²
= 2xy + 2xy
= 4xy
(x + y)² - (x - y)² = 4xy
3. Writing 12 as the difference of two perfect square.
To do this, we shall subtract 12 from a perfect square to obtain a number which has a perfect square root.
We'll begin by 4
4² – 12
16 – 12 = 4
Find the square root of 4
√4 = 2
4 has a square root of 2.
Thus,
4² – 12 = 4
4² – 12 = 2²
Rearrange
4² – 2² = 12
Therefore, 12 as a difference of two perfect square is 4² – 2²
A drone is monitoring the atmospheric conditions above a farm field. The drone hovers 5 meters above the crop line. Suddenly, it rises to approximately 5.9 meters (which takes 1.9 seconds) to avoid colliding with the sprinkler system. Based on this information, which equations could model the height, y, of the drone as a function of time, x?
Answer:
The correct options are;
g(x) = -0.27·x² + x + 5
h(x) = 2·㏒(x + 1) + 5
Step-by-step explanation:
To answer the question, we substitute x = 1.9 seconds into the given options as follows;
1) For f(x) = √(1.6·x) + 5
When x = 1.9 seconds, we have;
y = f(1.9) = √(1.6×1.9) + 5 = 6.74 which is not equal to the given height of 5.9 meters
Therefore, f(x) = √(1.6·x) + 5 does not model the height of the drone y as a function of time, x
2) For g(x) = -0.27·x² + x + 5
When x = 1.9 seconds, we have;
y = g(1.9) = -0.27×1.9^2 + 1.9 + 5 = 5.93 meters, which is approximately 5.9 meters to one place of decimal
Therefore, the function, g(x) = -0.27·x² + x + 5, approximately models the height of the drone y as a function of time, x
3) For h(x) = 2·㏒(x + 1) + 5
When x = 1.9 seconds, we have;
y = h(1.9) = 2·log(1.9 + 1) + 5 = 5.92 meters,
The function, h(x) = 2·㏒(x + 1) + 5, approximately models the height of the drone y as a function of time, x
4) For j(x) = -∛(-1.4·x - 1) + 5
When x = 1.9 seconds, we have;
y = j(1.9) = -∛(-1.4×1.9 - 1) + 5 = 6.54 meters
The function j(x) = -∛(-1.4·x - 1) + 5 does not model the height of the drone y as a function of time, x
5) For k(x) = -1.2·x³ + 2.6·x² - 0.5·x + 5
When x = 1.9 seconds, we have;
y = k(1.9) = -1.2×1.9^3 + 2.6×1.9^2 - 0.5×1.9 + 5 = 5.21 meters
Therefore, the function, k(x) = -1.2·x³ + 2.6·x² - 0.5·x + 5, does not model the height of the drone y as a function of time, x
Molly was curious if quadrilaterals ABCDABCDA, B, C, D and EFGHEFGHE, F, G, H were congruent, so she tried to map one figure onto the other using transformations
Answer:
The answer is below
Step-by-step explanation:
A transformation of a point is the movement of an point from an initial position to a new position. If an object is transformed, all the point of an object is transformed. Two figures are said to be congruent if they have the same shape and the measure of each of their sides are the same.
An object is congruent to another object if the object can be mapped to the other object when transformed.
Answer:
The answer is c
Step-by-step explanation:
It is the correct solution because you are able to map circle m onto m