What is the equation of the line that passes through the point (1,3) and is perpendicular to the line 2x+3y=15?
Answers
Answer:
3x -2y = -3
Step-by-step explanation:
The perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. The constant in its equation will ensure the line goes through the desired point.
__
form of the equationThe equation for the given line is in standard form:
ax +by = c . . . . . where a>0 and a, b, c are mutually prime
The equation of the perpendicular line can be written ...
bx -ay = c' . . . . . where c' is a new constant
For a=2, b=3, the equation of the perpendicular will be ...
3x -2y = c'
constantThe constant is chosen so the given (x, y) values satisfy the equation.
3(1) -2(3) = c' = -3
equationThen the equation of the perpendicular line through point (1, 3) is ...
3x -2y = -3
_____
Additional comment
For the standard-form equation shown, the slope of the line is ...
m = -a/b
The negative reciprocal slope is ...
-1/m = -1/(-a/b) = b/a
This is the original slope equation with a and b swapped, and one of them negated.
__
The graph confirms the new equation.
Related Questions
Please help???????????????
Answers
Answer:
A
Step-by-step explanation:
if you dont feel right dont pick my answer
HELPP!!!
The area of the figure is ____ square units.
Answers
Answer:
The answer is 132 square units
Step-by-step explanation:
Cutting the shape
we have two trapeziums
A=(area of small +Area of big)Trapezium
A=1/2(3+9)8 + 1/2(9+12)8
A=1/2×12×8 + 1/2×21×8
A=12×4 + 4×21
A=48+84
A=132 square units
What is the equation of the graph below? y=1/2sinx y=1/2cosx y=1/2sin2x
Answers
9514 1404 393
Answer:
(d) y = 1/2sin(2x)
Step-by-step explanation:
The sin(x) function will have a maximum value of 1 and a period of 360°. The function plotted is a sine function with a maximum value of 1/2 and a period of 180°.
For a function g(x) = a·f(b·x), the vertical scale factor is 'a', and the horizontal compression factor is 'b'. Our sine function has a vertical scale factor of 1/2, and a horizontal compression of 360/180 = 2, so the transformed function is ...
y = 1/2sin(2x)
PLEASE HELP
A busy candy stores going to replace their current gumball machine with a giant gumball machine. The globe on the current gumball machine is 22 inches in diameter and the volume is 5575 in.³ compared to what has been ordered the current gumball machines volume is 532 in.³ less than 1/4 of the volume of the globe of the giant gumball machine.
3. Carry out your plan from question to what is the volume of the globe on the new gumball machine you can round your final answer to the nearest whole number. Be sure to check your work.
4. Is your answer to question through the real solution or an extraneous solution explain how you?
Answers
3. The volume of the new gumball machine is of 861.75 in³.
4. This is a real solution, as it is a positive number.
How to obtain the volume of the new machine?The volume of the old machine was of:
5575 in.³
(as stated in the problem)
The volume of the new machine is obtained as follows:
532 in.³ less than 1/4 of the volume of the globe of the giant gumball machine.
One fourth of the volume of the old machine is obtained as follows:
1/4 x 5575 in³ = 1393.75 in³.
532 in.³ less than that is obtained as follows:
1393.75 - 532 = 861.75 in³.
An extraneous volume is a negative value to the volume, as the volume cannot be negative. Since the number is positive, it represents a real solution.
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classify the following differential equation s given in both standard and differential form. Q5 only
Answers
y' = 2xy + x
Rewriting it in differential form, we get:
(2xy + x)dx - dy = 0
This is a first-order linear differential equation, which can be written in the form:
y' + P(x)y = Q(x)
where P(x) = -2x and Q(x) = x.
Therefore, the differential equation is a first-order linear differential equation.
Use factoring to solve the polynomial equation. Check by substitution or by using a graphing utility and identifying
x-intercepts.
8x4-32x² = 0
Rewrite the equation in factored form.
(Blank)=0
Then what is the solution pair?
Answers
The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2
Using factoring to solve the polynomial equationTo solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:
8x²(x² - 4) = 0
Now we can use the difference of squares identity to factor the quadratic expression:
8x²(x + 2)(x - 2) = 0
Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.
Therefore, we can set each factor equal to zero and solve for x:
8x² = 0 or x + 2 = 0 or x - 2 = 0
Solving for x, we get:
x = 0 or x = -2 or x = 2
So the solution set for the equation is {0, -2, 2}.
To check the solution, we can substitute each value into the original equation and verify that it equals zero.
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Annette has 3 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 9mph and walks back at a speed of 3mph , how long should she plan to spend walking back?
Answers
Answer:
Annette should plan to spend 2.25 hours walking back.
Step-by-step explanation:
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume the distance of the race is D miles.
Annette spends her time running the distance of the race, which takes:
Time running = D / 9 hours
She then walks back the same distance, which we need to find the time for:
Time walking = D / 3 hours
Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:
D / 9 + D / 3 = 3
To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:
D + 3D = 27
Combining like terms:
4D = 27
Dividing both sides of the equation by 4:
D = 6.75
So, the distance of the race is 6.75 miles.
To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:
Time walking = D / 3 = 6.75 / 3 = 2.25 hours
Therefore, Annette should plan to spend 2.25 hours walking back.
What is the image point of (3,-4) after a translation left 2 units and up 5 units?
Answers
Answer:
(1,1)
Step-by-step explanation:
3-2=1
-4+5=1
The image point of (3,-4) after a translation left 2 units and up 5 units is (1,1).
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
We are given that;
Point= (3,-4)
Now,
To find the image point of a translation, we can use the following rule:
To translate a point left or right, add or subtract the horizontal distance to the x-coordinate of the point.
To translate a point up or down, add or subtract the vertical distance to the y-coordinate of the point.
In this case, we have a translation left 2 units and up 5 units. This means that we need to subtract 2 from the x-coordinate and add 5 to the y-coordinate of the point (3,-4). Therefore, the image point is:
(3−2,−4+5)
(1,1)
Therefore, by the graph the answer will be (1,1)
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Which numerical pattern is linear?
A.3, 5, 7, 8, 10, 12, 13, . . .
B.4, 7, 10, 13, 16, 19, . . .
C.2, 4, 8, 16, 32, . . .
D.3, 5, 4, 6, 5, 7, . . .
Answers
Step-by-step explanation:
I believe the answer is A and B
Find the area of a rectangle whose length is 14cm and breadth is 6cm
Answers
Answer:
Ellos dan las pistas de algunos problemas se pueden resolver de forma automática, los valores numéricos tienen ninguna importancia en los distintos ejemplos.
Traza 1
Uno de los lados de un rectángulo es 20 cm de largo; un segundo lado del rectángulo es de 0,85 m de largo. Calcular el perímetro y el área del rectángulo.
Traza 2
Calcular el área de un rectángulo cuyas dimensiones son 85 cm de largo y 20 cm respectivamente.
Traza 3
La base de un rectángulo es 20 cm de largo; la área es de 300 cm². Calcular la altura del rectángulo.
Traza 4
La altura de un rectángulo es 15 cm de largo; la área es de 300 cm². Calcula la base del rectángulo.
Traza 5
Un rectángulo tiene la altura que es de 3/8 de la base; la suma de las longitudes de los dos segmentos es 44 cm. Determinar el área del rectángulo y el perímetro.
Traza 6
La base de un rectángulo es de 0,40 m de largo; La altura del rectángulo es 30 cm. Calcular la diagonal.
Traza 7
Un tamaño de un rectángulo es un medio del lado de un cuadrado que tiene el perímetro de 20 cm. Sabiendo que los dos polígonos tienen el mismo perímetro, calcula la medida del tamaño del rectángulo.
Traza 8
La diagonal de un rectángulo es de 50 cm; la base es de 3/4 de la altura. Calcular el perímetro y el área del rectángulo.
Traza 9
La diagonal de un rectángulo mide 50 cm; ella es 5/3 de altura. Calcular el perímetro y el área del rectángulo.
Traza 10
Una mesa rectangular tiene lados de 180 cm y 90 cm respectivamente. Cuál es el perímetro y el área de un mantel que cuelga de 20 cm alrededor de la mesa?
Traza 11
Calcular el área de un rectángulo que tiene la altura 10 cm de largo, sabiendo que la medida de la base es el doble de la altura.
Traza 12
La diferencia entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo
Traza 13
La suma entre el tamaño de un rectángulo es 12 cm y una es el triple de la otra. Calcular el área del rectángulo
Traza 14
La suma de la base y la altura de un rectángulo es 50 cm; la base es superior a la altura de 4 cm. Calcular el área del rectángulo.
Traza 15
El semi-perímetro de un rectángulo es 32 cm y una dimensión es de 3/5 de la otra. Calcular el área del rectángulo.
Traza 16
El semi-perímetro de un rectángulo es 30 cm y una dimensión es igual a los sus 2/5. Calcular el área del rectángulo.
Traza 17
Un rectángulo tiene una base de 20 cm y una altura igual a 2/5 de la base. Calcular el perímetro y el área del rectángulo.
Traza 18
Un rectángulo tiene el área de 600 cm² y la base es 20 cm de largo. Cuál es su perímetro ?
Traza 19
Un rectángulo tiene un perímetro de 100 cm y la base es 30 cm de largo. Calcula su área.
Traza 20
Un rectángulo tiene un perímetro de 120 cm. Sabiendo que un tamaño es tres veces la otra, calcula el área del rectángulo.
Traza 21
La diferencia entre el tamaño de un rectángulo es 10 dm. Sabiendo que el perímetro es 100 dm, calcula el área del rectángulo.
Traza 22
Un rectángulo tiene un perímetro de 100 cm. Calcula su área sabiendo que la medida de la base es superior a la de la altura de 10 cm.
Traza 23
En el perímetro de un rectángulo es de 100 cm y la altura es de 20 cm de largo. Calcular el perímetro de un rectángulo equivalente a el mismo y que tiene su base de 40 cm de largo.
Traza 24
Un rectángulo es formado por dos cuadrados congruentes que tienen cada uno el perímetro de 24 cm. Calcular el perímetro y el área del rectángulo.
Traza 25
Un rectángulo es formado por tres cuadrados congruentes con cada lado 20 cm de largo. Calcular el perímetro y el área del rectángulo.
Traza 26
Un rectángulo es formado por dos cuadrados congruentes. Sabiendo que el perímetro del rectángulo es de 180 cm, calcular su área.
Traza 27
Un rectángulo y un cuadrado tienen el mismo perímetro. El lado de un cuadrado de 45 cm y las dimensiones del rectángulo son una 1/2 de la otra. Calcular el área del rectángulo.
Traza 28
Dos rectángulos son equivalentes. Sabiendo que las dimensiones de el primero miden respectivamente 30 cm y 20 cm, y que la base del segundo rectángulo es 40 cm de largo, calcula la diferencia entre los dos perímetros.
Traza 29
Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:
Traza 30
Calcular el perímetro de la figura y el área de la parte interior con la obtención de las medidas a partir del dibujo:
Traza 31
Un constructor ha comprado un terreno que tiene la planta mostrada en el dibujo y las dimensiones en metros se indican en la figura. Calcula el área y el perímetro de la tierra.
Traza 32
Una parcela de tierra tiene una forma rectangular con unas dimensiones de 50 m y de 30 m de largo. En el interior se ha construido una casa que ocupa una superficie rectangular de longitud 20 m y de 8 m de ancho. Calcular el área de la tierra permanecida libre.
Traza 33
Step-by-step explanation:
Answer:
A= 84cm
Step-by-step explanation:
length x width= area
plug in the given information.
14cm x 6cm = A
A=84
with a length of 14cm and a width of 6cm multiply them for an area of 84cm.
A car is driving away from El Paso with constant velocity. At 1 p.m., it is 145 miles away from El Paso. At 3 p.m., it is 275 miles away from El Paso.
Part A: Write a linear function that describes the distance (in miles) the car is from El Paso in terms of time (in hours after 12:00 p.m.).
Answers
The linear function that describes the distance (in miles) is therefore y = 65x + 80
How to solve for the linear functionWe have to find the slope and the intercept in other to get the linear function
The data points are:
(1, 145) and (3, 275).
m = (y2 - y1) / (x2 - x1)
fixing the data points we have
m = (275 - 145) / (3 - 1)
= 130 / 2
= 65
y = mx + b
(1, 145):
145 = 65(1) + b
b = 145 - 65
= 80
y intercept is 80
The linear function is therefore y = 65x + 80
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Daniel is thinking of a 2-digit number that is less than 50. When it is divided by 2, there is no remainder. When it is divided by 3, there is a remainder of 1 When it is divided by 5, there is a remainder of 3 What number is Daniel thinking of?
Answers
Answer:
28
Step-by-step explanation:
The two digit numbers less than 50 that when divided by 5 have a remainder of three are: 13, 18, 23, 28, 33, 38, 43, and 38.
Since the number must be evenly divisible by 2, you can remove the odd answers which leaves you with 18, 28, 38, and 48.
The only one that has a remainder of 1 when divided by 3 is 28.
ANSWER:
28
28÷2=14
28÷3=9 with remainder of 1
28÷5=5 with a remainder of 3
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Vince is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $51 for the meal, plus $5 per kilogram for the lobster he picks. At the second restaurant, Vince would pay $8 per kilogram for the lobster, in addition to $33 for the meal. Vince realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Vince pay for his dinner? What is the weight?Dinner would cost $ at either restaurant if Vince's lobster weighed kilograms.
Answers
Based on the given situation, if x is number of kilograms of lobster, you can write the following expressions:
51 + 5x cost in the first restaurant
33 + 8x cost in the second restaurant
In order to determine the value of x which makes the cost the same in both restaurants, equal the previous expressions and solve for x:
51 + 5x = 33 + 8x subtract 33 both sides and 5x subtract both sides
51 - 33 = 8x - 5x simplify
18 = 3x divide by 3 both sides
18/3 = x
6 = x
x = 6
Hence, the weight of the lobster is 6 kg.
The cost of the dinner is:
51 + 5(6) = 51 + 30 = 81
Hence, the cost of the dinner is $81
Triangle ABC is reflected over the line y = x. Triangle ABC has points A (-6, -1), B (-2, -1), and C (-5, -6). What is the A' coordinate?
Answers
Answer:
(1,6)
Step-by-step explanation:
Because reflecting to x axis u change the position
I need help finding the domain and range for both graphs , I’ve tried but I am a little confused
Answers
Given:
graph of the functions are given.
Find:
we have to find the Domain and Range of the graphs.
Explanation:
From the first graph, x varies from 0 to 18 and y=f(x) varies from 200 to 2000 depending upon the values of x.
Domain = [0,18]
Range=[200,2000]
From the second graph, x varies from 0 to 4 and y=f(x) varies from 0 to 160 depending upon the values of x.
Therefore,
Domain=[0,4]
Range=[0,160]
en
please answer this using the foil method\( {9x}^{2} + 60x + 100\)
Answers
Answer
Given expression
\(9x^2+60x+100\)By factorization, we have
\(\begin{gathered} 9x^2+30x+30x+100 \\ 3x(3x+10)+10(3x+10) \\ (3x+10)(3x+10) \end{gathered}\)Now to check, using FOIL method, we have
F = First, i.e 3x(3x) = 9x²
O = Outer = 3x(+10) = +30x
I = Inner = +10(3x) = +30x
L = Last = +10(+10) = +100
![please answer this using the foil method[tex] {9x}^{2} + 60x + 100[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/GReVo5H5usvfvYg2jz64zJJOAOcHXncd.png)
The Venn diagram below shows the events A and B, and the probabilities p, q and r.
It is known that P(A)=0.43 , P(B)=0.62 and P(A∩B)=0.27 .
Calculate the value of p
Calculate the value of q
Calculate the value of r
Find the value of P (A given NOT B)
Answers
The value of q is 0.35.
The value of p is 0.16.
The value of r is 0.27.
The value of P(A given NOT B) is approximately 0.4211.
To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.
Given:
P(A) = 0.43
P(B) = 0.62
P(A∩B) = 0.27
Calculating the value of p:
The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.
We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:
p = P(A) - P(A∩B)
= 0.43 - 0.27
= 0.16
Therefore, the value of p is 0.16.
Calculating the value of q:
The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.
We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:
q = P(B) - P(A∩B)
= 0.62 - 0.27
= 0.35
Therefore, the value of q is 0.35.
Calculating the value of r:
The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.
We are given that P(A∩B) = 0.27, so the value of r is 0.27.
Therefore, the value of r is 0.27.
Finding the value of P(A given NOT B):
P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.
To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.
P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)
We can calculate the value of P(A given NOT B) using the provided probabilities:
P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))
= 0.43 - 0.27 / (1 - 0.62)
= 0.16 / 0.38
≈ 0.4211
Therefore, the value of P(A given NOT B) is approximately 0.4211.
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14:56 in simplest form?
Answers
Answer:
4
Step-by-step explanation:
Hope this helps:)
Answer:
No
Step-by-step explanation:
Simplest form is
1:4
14/14 = 1
56/14 = 4
Suppose that you borrow $13,000 for 5 years at 7% toward the purchase of a car.
The monthly payment is $
The total interest for the loan is $
Answers
The total interest for the loan is $4,550. This means that over the course of 5 years, you will pay back the original loan amount of $13,000 plus $4,550 in interest for a total of $17,550.
To calculate the total interest for this loan, we need to use the simple interest formula:
Monthly EMI formula :
Interest = Principal x Rate x Time
In this case, the principal (amount borrowed) is $13,000, the rate is 7%, and the time is 5 years.
So,
Interest = $13,000 x 0.07 x 5
Interest = $4,550
It's important to keep in mind that this calculation assumes that the interest rate remains constant over the entire 5-year period.
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A local health clinic surveys its patients about their waterdrinking habits. It found the data is normally distributed,the mean amount of water consumed daily is 62 ounces, andthe standard deviation is 5.2. How much water, in ounces,do approximately 95% of the patients drink each day?A: 56.8 to 67.2B: 54.2 to 69.8C: 51.6 to 72.4D: 41.2 to 62.0
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
water drinking habits:
mean = 62 ounces
standard deviation = 5.2 ounces
Step 02:
normally distribution:
95% ===> 2 SD
(62 + 5.2 + 5.2) ounces = 72.4 ounces ==> + 2 SD
(62 - 5.2 - 5.2) ounces = 51.6 ounces ==> - 2 SD
The answer is:
51.6 ounces - 72.4 ounces
16.468>16.4 or < or =
Answers
Answer:
The answer is not that clear: But for 16.4 it isn't correct because you need to round it from 16.468 to 16.5. so therefore the answer is <
How long would it take to fill up 480cm3 pool at 25litres a min
Answers
Answer:
the answer is 8cm i think
What is the answer to Y=30x+25
Answers
Answer:
x=1/30y + -5/6
Step-by-step explanation:
help. use the figure shown to the right to find the value of x
Answers
Answer:
\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)
Step-by-step explanation:
We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:
\(a^2 + b^2 = c^2\)
↓ plugging in the given values
\(a^2 + 2^2 = 14^2\)
↓ subtracting 2² from both sides
\(a^2 = 14^2 - 2^2\)
\(a^2 = 196 - 4\)
\(a^2 = 192\)
↓ taking the square root of both sides
\(a = \sqrt{192\)
↓ simplifying the square root
\(a = \sqrt{2^6 \cdot 3\)
\(a = 2^{\, 6 / 2} \cdot \sqrt3\)
\(a = 2^3\sqrt3\)
\(a = 8\sqrt3\)
Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.
\(a = \dfrac{1}{2}x\)
↓ plugging in the a-value we solved for
\(8\sqrt3 = \dfrac{1}2x\)
↓ multiplying both sides by 2
\(\boxed{x = 16\sqrt3}\)
The sum of the age of a girl and her brother is 34. The girl is 8 years older than her heather, how old is her brother
Answers
Answer:
26
Step-by-step explanation:
if she is 8 years older, then is just 34-8 which is 26
What is the solution for x in the equation
-4+5x-7=Okay 0+3x-2x
Answers
Answer:
X = 2.75 or 2 3/4 in fraction form
Step-by-step explanation:
We know that the variable X has to make both equations equal.
It is really just crossing out the options.
2.75 can fit in the X variable because if 2.75 was in both equations, the answer would be the same.
So the answer is 2.75
Hope this helps! :)
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Last week Henry loaned a friend $15 from his wallet. This week Henry loaned the friend
another $7. In dollars, what is the change to Henry's wallet balance?
Answers
Answer: its real answer is -22
Step-by-step explanation:
Help me please!!!!!!!
Answers
Answer:
I am not sure on the first one but this is what I think:
False
False
True
Step-by-step explanation:
Sorry if it's wrong!!
As part of a survey, 2400 people were asked to name their favorite sport to watch. The table below summarizes their answers. This information is also presented
as a circle graph.
Find the central angle measure, x, for the Baseball slice in the circle graph. Do not round.
Sport
Football
Soccer
Baseball
Basketball
Hockey
Other
Percentage
of People
29%
9%
14%
8%
8%
Soccer
Baseball
Basketball
Football
Other
Hockey
Answers
The central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.
Given that, a survey was conducted in which 2400 people were asked to name their favorite sport to watch and the table below shows their answers: Sport percentage of people are:
Football 29%
Soccer 9%
Baseball 14%
Basketball 8%
Hockey 8%
Other 32%
We need to find the central angle measure, x, for the Baseball slice in the circle graph.
For this, we need to use the formula that gives the central angle measure in degrees for a sector of a circle:
Central angle measure = (Percentage/100) × 360°
Now, using the above formula, we can calculate the central angle measure for each sport as shown below:
Football: (29/100) × 360° = 104.4°
Soccer: (9/100) × 360° = 32.4°
Baseball: (14/100) × 360° = 50.4°
Basketball: (8/100) × 360° = 28.8°
Hockey: (8/100) × 360° = 28.8°
Other: (32/100) × 360° = 115.2°
The sum of all central angle measures should be 360°, which is the measure of a full circle.
So we can check if the calculations are correct: 104.4° + 32.4° + 50.4° + 28.8° + 28.8° + 115.2° = 360°
We see that the sum is indeed 360°, so the calculations are correct. The central angle measure for the Baseball slice is 50.4°.
Therefore, the central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.
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A box with a square base and open top must have a volume of 318028 cm^3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = ______ Preview Next, find the derivative, A?(x) A'(x) = ___________ Preview Now, calculate when the derivative equals zero, that is, when A?(x) = 0. [Hint: multiply both sides by x^2.] A'(x) = 0 when x = ____________ We next have to make sure that this value of x gives a minimum value for the surface area. Let?s use the second derivative test. Find A? (x). A''(x) = _____________ Preview Evaluate A''(x) at the x-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x). (Your boss is happy now)
Answers
At x = 86 gives minimum value of surface area and the dimensions of the box that minimize the amount of material used.
What is Surface Area ?The surface area of an object refers to the overall space filled by its surfaces. Different 3D shapes in geometry have various surface areas, which may be quickly estimated using the formulas we shall learn in this lesson. Two categories are used to classify the surface area:
Curved surface area or Lateral surface area
Surface area in total
V = x²h = 318028
h = 318028 / x²
∴ A( x ) = x² + 4ah = x² + 1272112 / x .
Derivative of A(x)
= 2x - 1272112 / x² = 0
After solving
x³ = 636056
x= 86
After doing double derivative we get the point as Positive,
A''(x) = 2 + 2544224 / x³
A''(86)= 6
Hence at x = 86 gives minimum value of surface area.
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