Answer:
Don Abel debe construir un cuadrado con lados de 25 metros de longitud.
Step-by-step explanation:
Geométricamente hablando, el área y el perímetro del rectángulo rodeado por el cerco son representadas por las siguientes fórmulas:
[tex]A = w\cdot l[/tex] (1)
[tex]p = 2\cdot (w+l)[/tex] (2)
Donde:
[tex]A[/tex] - Área, en metros cuadrados.
[tex]p[/tex] - Perímetro, en metros.
[tex]w[/tex] - Ancho, en metros.
[tex]l[/tex] - Longitud, en metros.
Puesto que el área a cercar debe ser la máxima posible y la longitud disponible de malla es de 100 metros, cabe despejar el ancho en (2):
[tex]w = \frac{p}{2}-l[/tex]
Ahora, aplicamos esta expresión en (1) y expandimos la expresión resultante:
[tex]A = \left(\frac{p}{2}-l\right) \cdot l[/tex]
[tex]A = \frac{p\cdot l}{2} -l^{2}[/tex] (3)
A continuación, obtenemos la primera y segunda derivada de (3):
[tex]A' = \frac{p}{2}-2\cdot l[/tex] (4)
[tex]A'' = -2[/tex] (5)
Igualando (4) a cero, tenemos que el valor crítico de la longitud del rectángulo es:
[tex]\frac{p}{2}-2\cdot l = 0[/tex]
[tex]2\cdot l = \frac{p}{2}[/tex]
[tex]l = \frac{p}{4}[/tex]
Por (5), sabemos que ese valor crítico está asociado al área máxima.
Si sabemos que [tex]p = 100\,m[/tex], entonces la longitud del rectángulo es:
[tex]l = 25\,m[/tex]
Ahora, tenemos el ancho de la figura por (2):
[tex]w = \frac{p}{2}-l[/tex]
[tex]w = 25\,m[/tex]
En consecuencia, don Abel debe construir un cuadrado con lados de 25 metros de longitud.
PLS HELPPP !! BRAINLIEST!!
Each cube in this figure is a 1/2 -centimeter cube. What is the total volume of the prism?
A. 4 1/2cm3
B. 1 1/2cm3
C. 6cm3
D. 18cm3
Micki bought 4 gallons of apple cider. How many quarts did she buy?
Answer:
16
Step-by-step explanation:
There are four quarts in a gallon. 4x4=16.
Answer:
4 quarts per gallon
4 quarts times 4 gallons= 16 quarts
License plates in the tiny country of Venn follow a unique pattern. The first character is one of 41 Egyptian hieroglyphs, the second is one of 39 emojis, and the third character is one of 10 polygons. How many 3 character license plates are available to the people of Venn?
Answer:
12710 license plates
Step-by-step explanation:
Given that :
First character = one of 41 different hieroglyphs
Second character = one of 31 emojis
Third character = one of 10 polygons
A license plate consists of 3 characters
Number of 3-character license plates available :
Number of hieroglyphs * Number of emojis * number of polygons
41 * 31 * 10 = 12710 license plates.
happy april fools day you nerds now take my points
Answer:
WOW THANK YOU SO MUCH!
Step-by-step explanation:
I'm more of a dog lover and not a nerd, but hey I'll take what I can get!
If your like dogs, can you guess what kind of dog this is?
(yes they are all the same breed just different coat colors)
URGENT: Find the value of X
Answer:
72x
Step-by-step explanation:
Help, Help, Please
[tex] \sf find \: the \: value \: of \: \theta \: when \: \theta \: is \: acute\: angle[/tex]
[tex] \sf \cos^{2}(\theta) - \sin^{2}(\theta) =2-5 \cos(\theta) [/tex]
[tex]\text{note:explanation is a must}[/tex]
Answer:
θ = [tex]\frac{\pi }{3}[/tex] (60° )
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cos²θ - sin²θ = 2 - 5cosθ
cos²θ - (1 - cos²θ) = 2 - 5cosθ
cos²θ - 1 + cos²θ = 2 - 5cosθ
2cos²θ - 1 = 2 - 5cosθ ( subtract 2 - 5cosθ from both sides )
2cos²θ + 5cosθ - 3 = 0 ← in standard form
(cosθ + 3)(2cosθ - 1) = 0 ← in factored form
Equate each factor to zero and solve for θ
cosθ + 3 = 0
cosθ = - 3 ← not possible as - 1 ≤ cosθ ≤ 1
2cosθ - 1 = 0
cosθ = [tex]\frac{1}{2}[/tex] , so
θ = [tex]cos^{-1}[/tex] ([tex]\frac{1}{2}[/tex] ) = [tex]\frac{\pi }{3}[/tex] ( or 60° )
Answer:
[tex] \huge \boxed{ \boxed{\blue{ { \theta = 60}^{ \circ} }}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASlet's solve:[tex] \sf \: rewrite \: \sin ^{2} ( \theta) \: as \: 1 - \cos ^{2} ( \theta) : \\ \sf \implies \: \cos ^{2} ( \theta) - (1 - \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: remove \: parentheses \: and \: change \: its \: sign : \\ \sf \implies \: \cos ^{2} ( \theta) - 1 + \cos ^{2} ( \theta)) = 2 - 5 \cos( \theta) [/tex][tex] \sf \: add : \\ \sf \implies \: 2\cos ^{2} ( \theta) - 1 = 2 - 5 \cos( \theta) [/tex][tex] \sf \: move \: left \: hand \: sides \: expression \: to \: right \: hand \: sides \: : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 5 \cos( \theta) - 1 -2 = 0[/tex][tex] \sf \: rewrite \: 5\cos( \theta) \: as \: 6 \cos( \theta) - \cos( \theta) : \\ \sf \implies \: 2\cos ^{2} ( \theta) + 6 \cos( \theta) - \cos( \theta) - 3 = 0[/tex][tex] \sf \:factor \: out \: 2 \cos( \theta) \: and \: - 1 : \\ \sf \implies \: 2\cos ( \theta)( \cos( \theta) + 3 ) -1( \cos( \theta) + 3) = 0[/tex][tex] \sf \: group: \\ \sf \implies \: (2\cos( \theta) - 1) ( \cos( \theta) + 3 ) = 0[/tex][tex] \sf \: rewrite \: as \: two \: seperate \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) - 1 = 0\\ \cos( \theta) + 3 = 0 \end{cases} [/tex][tex]\sf add \: 1 \: to \: the\: first \: equation \: and \: substract \: 3 \: from \: the \: second \: equation: \\ \sf \implies \: \begin{cases}2\cos( \theta) = 1\\ \cos( \theta) = - 3 \end{cases} [/tex][tex] \sf the \: second \: eqution \: is \: false \: \\ \sf because \: - 1 \leqslant \cos( \theta) \leqslant 1 \: \\ \sf but \: we \: can \: still \: work \: with \: the \: second \: equation[/tex]
[tex] \sf substract \: both \: sides \: by \: 2 : \\ \implies\frac{ 2\cos( \theta) }{2} = \frac{1}{2} \\ \implies\cos( \theta) = \frac{1}{2} \\ \therefore \: \theta \: = {60}^{ \circ} [/tex]slope of 1/2 and y-intercept is -5.
Answer:
Y= 1/2x-5
Step-by-step explanation:
Find the total surface area of this cone.
Leave your answer in terms of .
4ft
3ft
SA = [?] ft2
Enter
Total surface area is: 21 ft²
Lateral area is: 12π ft²
The total surface area of this cone is 21π square feet.
What is the total surface area of the cone?The total surface area of the cone is given by the following formula;
[tex]\rm Surface \ area=\pi r(r+l)[/tex]
Where h denotes the height of the cone and r is the radius and l is the slant height.
The radius of the cone = 3
The height of the cone = 4
Substitute all the values in the formula
[tex]\rm Surface \ area=\pi r(r+l)\\\\\rm Surface \ area=\pi 3(4+3)\\\\\rm Surface \ area=3\pi \times 7\\\\\rm Surface \ area=21\pi[/tex]
Hence, the total surface area of this cone is 21π square feet.
Learn more about the surface area here;
https://brainly.com/question/20759327
#SPJ2
what is the sum of -4/7 and 6/7
Answer:
2/7
Step-by-step explanation:
Since the denominators are the same, we need to add the numerators and place it over the common denominator
-4+6 = 2
so
-4/7 + 6/7 = 2/7
2/7
Answer:
B
Step-by-step explanation:
Ab and cd intersects at e, aec=5x+12 and deb=8x-3
Answer:
x = 5
Step-by-step explanation:
Angles DEB and AEC are vertical angles, so they are congruent, and their measures are equal.
8x - 3 = 5x + 12
3x = 15
Carlos has 2.6 meters of wire. He has 3 projects for which he needs 0.9 meters each. Does carlos have enough wires?
Answer: Carlos does not have enough wires by 0.1 meters
Step-by-step explanation:
To determine if Carlos has enough wires, you need to find out the total amount of wires needed and then compare this to the amount of wires that Carlos has already.
= 0.9 + 0.9 + 0.9
= 2.7 meters
Carlos has 2.6 meters of wire but needs 2.7 meters.
Carlos therefore, does not have enough wires.
What is the value of y in the equation below?
4y + 8 = 6y + 2
3/5
1
3
5
Answer:
y=3
Step-by-step explanation:
good luck
QUESTION 6 / 10
Which of the following is not a source of income?
A. Your monthly student loan payment.
B. The stipend you receive for doing an internship.
C. Your annual salary for doing your job.
D. The wages you receive after a work shift.
Answer:
b. The stipend you receive.
Step-by-step explanation:
It would say paid intern if they were paid.
find the slope of the line that passes through the two given points of (-3, 4) and (-3, -8)
Answer:
it is not express because the line is parallel at y axis
Step-by-step explanation:
Please answer the question above.
Answer:
∠2 = 80°
Step-by-step explanation:
∠1 and ∠2 are supplementary angles (their sum is 180°)
Find the apothem or height of the triangle. Round your answer at the end to the nearest tenth.
Answer:22.4
Step-by-step explanation:
Yea I'm bad at explaining
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
not sure but i think c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Together Mike and Sara ran 42 laps on the
track. Sara ran twice as many laps as
Mike did. Write a system of equations and
solve it to see how many laps they each ran.
Answer:
i dont know the system of equations since i only calculated it until i got the right answer but sara did 28 laps and mike did 14
Plz, answer this question plz!
What is the value of n in the equation below?
StartFraction a Superscript n Over a cubed EndFraction = a Superscript 9
Answer:
ok ok it it 12
Step-by-step explanation:
stay safe 2021
Answer:
12
Step-by-step explanation:
Edge
can someone help please
half of the triangle is a right angle triangle, so we use the phythagoras theorem and multipy our answer by 2
3/5-the square root of 5
Answer:
1.341
Step-by-step explanation:
I'm smart at maths
The base of a 14-foot ladder is 2 feet from a building. If the ladder reaches the flat roof , how tall is the building
Answer:
Step-by-step explanation:
The height of the building is 8 rad 3
Approximately 13.9 ft
32 oz = _______ lb
Please answer the question
Answer:
2 lb
Step-by-step explanation:
1lb = 16 pounds.
plz help me I only have 5 minutes left winner gets brainliest
In what year did the Apartheid Laws in South Africa end?
1990
1972
1994
1958
Answer:1994.
Step-by-step explanation:I need brainliest I helped with your other questions in comments pls
PLZZZZ HAAALLLPPPP!!!!!
Answer:
0
Step-by-step explanation:
-9x -3(2) = 6
-9x + 6 = 6
-9x + 6 -6 = 6-6
-9x/ -9= 0/-9
x=0
A survey was conducted on 800 students regarding the number of automobiles in their household. The population mean is 2.7 automobiles with a standard deviation of 0.7.
Which statement is true?
A.
There is a 95% certainty that the sample mean will fall within the interval 2.68 to 2.72.
B.
There is a 95% certainty that the sample mean will fall within the interval 2.67 to 2.73.
C.
There is a 95% certainty that the sample mean will fall within the interval 2.62 to 2.77.
D.
There is a 95% certainty that the sample mean will fall within the interval 2.65 to 2.75.
1. What is the decimal equivalent of 3/
9? 0.2 0.3 0.4 0.5
If a car has tires with a diameter of 28 inches and is traveling at 55 mph, how fast are its tires spinning, in rpm^ prime s (revolutions per minute)? [There are 63,360 inches in 1 mile) Round your final answer to 2 decimal places .
Answer:
The tires are spinning at 660.49 revolutions per minute.
Step-by-step explanation:
The speed of the tires (v) is the same that the speed of the car, so to find the angular velocity of the tires we need to use the equation:
[tex] \omega = \frac{v}{r} [/tex]
Where:
r: is the radius of the tires = d/2 = 28 inches/2 = 14 inches
[tex]\omega = \frac{55 mph}{14 inches*\frac{1 mile}{63360 inches}} = 2.49 \cdot 10^{5} \frac{rad}{h}*\frac{1 h}{60 min}*\frac{1 rev}{2\pi rad} = 660.49 rpm[/tex]
Therefore, the tires are spinning at 660.49 revolutions per minute.
I hope it helps you!
Which expressions are equivalent to this exponential expression?
6-10
6-4
06-6
0 66
0
1
0
O
1
36
Answer:
6*6=36
Step-by-step explanation:
6*6. 6 with exponent of 2=36