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Trigonometric Ratios
The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.
Related Questions
a= 8 in, b= ? C= 14 in.using pythagorean theorem
Answers
by Pythagorean theorem'
[tex]8^2+b^2=14^2[/tex][tex]\begin{gathered} 64+b^2=196 \\ b^2=196-64 \end{gathered}[/tex][tex]\begin{gathered} b^2=132 \\ b=\sqrt[]{132} \\ b=11.48 \end{gathered}[/tex]b = 11.48
How do you determine a relation is function on a GRAPH?
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To Determine: How to determine a relation is function on a GRAPH
In other to achieve this, we will use the vertical test
If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function
Check the image below for a better clarification
With the use of the vertical line test, the graph in OPTION C and OPTION D are functions and the graph in OPTION A and B are not functions
In summary, you determine a relation is a function on a graph by using a vertical line test
drag and drop the matching inequality from the left into the box on the right
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The first problem is modeled by the following inequality:
[tex]40+5x\ge95-4x[/tex]The second problem is represented by
[tex]95+4x<40+5x[/tex]The third problem is represented by
[tex]95-4x<40+5x[/tex]Observe that, "spending" refers to subtraction, "earnings" refers to addition. Also, the variables represent time. Additionally, "less than" is expressed as "<", "as much as or more than" is expressed as >=.
Write an equation of the line that passes through (-4,-5) and is parallel to the line defined by 4x +y = -5. Write the answer inslope-intercept form (if possible) and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot bewritten" button, if applicable.The equation of the line in slope-intercept form:
Answers
Answer: y = -4x - 21 OR 4x + y = -21
The given line is 4x + y = -5
Given point = (-4, -5)
Step 1: find the slope of the line
The slope intercept form of equation is given as
y = mx + b
Re -arrange the above equation to slope - intercept form
4x + y = -5
Isolate y
y = -5 - 4x
y = -4x - 5, where m = -4
Since the point is parallel to the equation
Therefore, m1 = m2
m2 = -4
For a given point
(y - y1) = m(x - x1)
Let x1 = -4, and y1 = -5
[(y - (-5)] = -4[(x - (-4)]
[y + 5] = -4[x + 4]
Open the parentheses
y + 5 = -4x - 16
y = -4x - 16 - 5
y = -4x - 21
The equation is y = -4x - 21 or 4x + y = -21
A scientist needs 270 milliliters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. How many milliliters of the 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution?
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Given:
A scientist has 5% and a 10% acid solution in his lab.
He needs 270 milliliters of a 20% acid solution.
To find the amount of 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution:
Here,
The dearer percentage is 25%.
The cheaper percentage is 10%.
The mean percentage is 20%.
Using the mixture and allegation method,
The ratio of the litters of cheaper (10% solution) to dearer value (25% solution) is,
[tex]\begin{gathered} (\text{Dearer value-mean): (Mean-Ch}eaper\text{ value)} \\ (25-20)\colon(20-10) \\ 5\colon10 \\ 1\colon2 \end{gathered}[/tex]So, the number of liters to be taken from 10% solution is,
[tex]\frac{1}{3}\times270=90\text{ liters}[/tex]So, the number of liters to be taken from 25% solution is,
[tex]\frac{2}{3}\times270=180\text{ liters}[/tex]Hence, the answer is
Select three equations that could represent a step in solving this system using the substitution method. 4x+y = 6 x = 8 0.00 0:52 9 1x 2 4(8)+y=6 o y = 18
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the first step is replacing x=8 on the first equation, so
[tex]4(8)+y=6[/tex]the second step is do the multiplication
[tex]\begin{gathered} 32+y=6 \\ y+32=6 \end{gathered}[/tex]and the last step is place the 32 on the other side substracting
[tex]\begin{gathered} y=6-32 \\ y=-26 \end{gathered}[/tex]I need help with the work question Find area of regular polygon.Round to nearest tenth
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Given:
The number of sides in a given polygon is n = 5.
The length of each side is s = 8
The length of the apothem is a = 5.5
To find:
The area of the regular polygon
Explanation:
The formula of the area of the regular polygon is,
[tex]\begin{gathered} A=\frac{1}{2}\times n\times s\times a \\ A=\frac{1}{2}\times5\times8\times5.5 \\ A=110\text{ units}^2 \end{gathered}[/tex]Thus, the area of the given regular polygon is 110 square units.
Final answer:
The area of the regular polygon is 110 square units.
If triangle JKL = triangle TUV , which of the following can you NOT conclude as being true? __ ___JK = TU
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If two triangles are said to be congruent, then they must have equal side lengths and equal angle measures.
See a sketch of triangles JKL and TUV below:
As shown in the sketch above:
- The side JK is equal in length as with the side TU
- The angle L is equal in measure as with the angle V
- The side LJ is equal in length as with the side VT
- The angle K is equal in measure as with the angle U
Therefore, we can NOT conclude that the angle J is equal in measure as with the angle V: Option B
A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 4, 0, B prime at 2, negative 2, C prime at 2, negative 5, D prime at 4, negative 3.
Part B: Are the two figures congruent? Explain your answer.
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The two figures ABCD and A'B'C'D' are congruent .
In the question ,
it is given that the coordinates of the figure ABCD are
A(-4,4) , B(-2,2) , C(-2,-1) , D(-4,1) .
Two transformation have been applied on the figure ABCD ,
First transformation is reflection on the y axis .
On reflecting the points A(-4,4) , B(-2,2) , C(-2,-1) , D(-4,1) on the y axis we get the coordinates of the reflected image as
(4,4) , (2,2) , (2,-1) , (4,1) .
Second transformation is that after the reflection the points are translated 4 units down .
On translating the points (4,4) , (2,2) , (2,-1) , (4,1) , 4 units down ,
we get ,
A'(4,0) , B'(2,-2) , C'(2,-5) , D'(4,-3).
So , only two transformation is applied on the figure ABCD ,
Therefore , The two figures ABCD and A'B'C'D' are congruent .
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Take a look at the graph below. In the text box provided, describe to the best of yourability the following characteristics of the graph:Domain & RangeIs it a function?InterceptsMaximum/Minimum• Increasing/Decreasing intervals
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we know that
The domain is the set of all possible values of x and the range is the set of all possible values of y
so
In this problem
The domain is the interval {-6,5}
[tex]-6\leq x\leq5[/tex]The range is the interval {-2,1}
[tex]-2\leq y\leq1[/tex]Intercepts
we have
x-intercepts (values of x when the value of y is equal to zero)
x=-5,x=0 and x=3
y-intercepts (values of y when the value of x is equal to zero)
y=0
Maximum value y=1
Minimum value y=-2
Increasing intervals
{-6,4}, {2,3}
Decreasing intervals
{-1,2} and {3,5}
Find du and v. Treat a and n as constants.
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Stated that;
[tex]u=x^n[/tex]Then, differentiating u with respect to x using the power rule where n is a constant is;
[tex]\begin{gathered} du=(n\times1)x^{n-1} \\ du=nx^{n-1} \end{gathered}[/tex]Also,
[tex]dv=e^{ax}[/tex]Then, we can find v by integrating, we have;
[tex]\begin{gathered} \int dv=\int e^{ax}dx \\ v=\frac{1}{a}e^{ax} \\ \end{gathered}[/tex]
How do you solve this??
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A mathematical statement comprehended as an equation exists created up of two expressions joined together by the equal sign.
If the equation be 12 - 2x = x - 3 then the value of x = 5.
What is meant by an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
A mathematical phrase with two equal sides and an equal sign is called an equation. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Let the equation be 12 - 2x = x - 3
Subtract 12 from both sides
12 - 2x - 12 = x - 3 - 12
Simplifying the above equation, we get
-2x = x - 15
Subtract x from both sides
-2x - x = x - 15 - x
Simplifying the above equation, we get
-3x = -15
Divide both sides by -3
[tex]$\frac{-3 x}{-3}=\frac{-15}{-3}[/tex]
Therefore, the value of x = 5.
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Find the maximum and minimum values of the function g(theta) = 2theta - 4sin(theta) on the interval Big[0, pi 2 Bigg\
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Hello there. To solve this question, we have to remember some properties about polar curves and determining maximum and minimum values.
In this case, we have the function in terms of the angle θ:
[tex]g(\theta)=2\theta-4\sin(\theta)[/tex]We want to determine its minimum and maximum values on the closed interval:
[tex]\left[0,\,\dfrac{\pi}{2}\right][/tex]We graph the function as follows:
Notice on the interval, it has a maximum value of 0.
We can determine its minimum value using derivatives, as follows:
[tex]g^{\prime}(\theta)=2-4\cos(\theta)[/tex]Setting it equal to zero, we obtain
[tex]\begin{gathered} 2-4\cos(\theta)=0 \\ \Rightarrow\cos(\theta)=\dfrac{1}{2} \\ \\ \Rightarrow\theta=\dfrac{\pi}{3} \end{gathered}[/tex]Taking its second derivative, we obtain
[tex]g^{\prime}^{\prime}(\theta)=4\sin(\theta)[/tex]And notice that when calculating it on this point, we get
[tex]g^{\prime}^{\prime}\left(\dfrac{\pi}{3}\right)=4\sin\left(\dfrac{\pi}{3}\right)=2\sqrt{3}[/tex]A positive value, hence it is a minimum point of the function.
Its minimum value is then given by
[tex]g\left(\dfrac{\pi}{3}\right)=2\cdot\dfrac{\pi}{3}-4\sin\left(\dfrac{\pi}{3}\right)=\dfrac{2\pi}{3}-2\sqrt{3}[/tex]Of course we cannot determine that 0 is a maximum value of this function using derivatives because it is a local maxima on a certain interval, and derivatives can only gives us this value when the slope of the tangent line is equal to zero.
A ladder resting on a vertical wall makes an angle whose tangent is 2.5 with the ground of the distance between the foot of the ladder and the wall is 60cm what is the length on the ladder
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If AC denote the ladder and B be foot of the wall the length of the ladder AC be x metres then the length of the ladder exists 5 m.
What is meant by trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
Let AC denote the ladder and B be foot of the wall. Let the length of the ladder AC be x metres.
Given that ∠ CAB = 60° and AB = 2.5 m In the right Δ CAB,
cos 60° = AB / AC
simplifying the above equation, we get
⇒ AC = AB / (cos 60°)
x =2 × 2.5 = 5 m
Therefore, the length of the ladder exists 5 m.
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The width of a rectangle measures (4.3q - 3.1) centimeters, and its length
measures (9.6q-3.6) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
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The expression that represents the perimeter and the of the rectangle is: 14.6q - 13.4.
What is the Perimeter of a Rectangle?A rectangle's perimeter if the length of its surrounding borders. Thus, the perimeter of a rectangle is the sum of all the length of the sides of the rectangle which can be calculated using the formula below:
Perimeter of a rectangle = 2(length + width).
Given the following:
Width of the rectangle = (4.3q - 3.1) centimetersLength of the rectangle = (9.6q - 3.6) centimetersTherefore, substitute the expression for the width and length of the rectangle into the perimeter of the rectangle formula:
Perimeter of rectangle = 2(9.6q - 3.6 + 4.3q - 3.1)
Combine like terms
Perimeter of rectangle = 2(7.3q - 6.7)
Perimeter of rectangle = 14.6q - 13.4
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factor the following by taking on the greatest common factor 14a^3 + 35a^2 +42a
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Let's break apart each term into its factors:
[tex]\begin{gathered} 14a^3=2\cdot7\cdot a\cdot a\cdot a \\ 35a^2=5\cdot7\cdot a\cdot a \\ 42a=2\cdot3\cdot7\cdot a \end{gathered}[/tex]The common factors are
7 * a
That is,
[tex]7\cdot a=7a[/tex]Now, factorizing the expression, we have:
[tex]\begin{gathered} 14a^3+35a^2+42a \\ =7a(2a^2+5a+6) \end{gathered}[/tex]Answer[tex]7a(2a^2+5a+6)[/tex]los números que faltan.
What comes after
3.0
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Answer:
3.1? 4.0? 3.0000001?
I did not know what are you mean sorry but uf i correct say me it
Need some help with table 2.Fill up tables of proportional relationships with missing Values.
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Proportional Relationships
If the variables x and y are in a proportional relationship, then:
y = kx
Where k is the constant of proportionality that can be found as follows:
[tex]k=\frac{y}{x}[/tex]If we are given a pair of values (x, y), we can find the value of k and use it to fill the rest of the table.
For example, Table 1 relates the cost y of x pounds of some items. We are given the pair (2, 2.50). We can calculate the value of k:
[tex]k=\frac{2.50}{2}=1.25[/tex]Now, for each value of x, multiply by this factor and get the value of y. For example, for x = 3:
y = 1.25 * 3 = 3.75
This value is also given and verifies the correct proportion obtained above.
For x = 4:
y = 1.25 * 4 = 5
For x = 7:
y = 1.25 * 7 = 8.75
For x = 10:
y = 1.25 * 10 = 12.50
Now for table 2, we are given the pair (3, 4.5) which gives us the value of k:
[tex]k=\frac{4.5}{3}=1.5[/tex]Apply this constant for the rest of the table.
For x = 4:
y = 1.5 * 4 = 6
For x = 5:
y = 1.5 * 5 = 7.50
For x = 8:
y = 1.5 * 8 = 12
The last column doesn't give us the value of x but the value of y, so we need to solve for x:
[tex]y=k\cdot x\text{ }=>\text{ }x=\frac{y}{k}[/tex]For y = 15:
[tex]x=\frac{15}{1.5}=10[/tex]Victoria, Cooper, and Diego are reading the same book for theirlanguage arts class. The table shows the fraction of the bookeach student has read. Which student has read the leastamount? Explain your reasoning.
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Given:
Completion of reading in fractions:
[tex]\text{Victoria}=\frac{2}{5};\text{Cooper}=\frac{1}{5};\text{Diego}=\frac{3}{5}[/tex]Since the denominators,
[tex]\text{The least value of the three given values is }\frac{1}{5}[/tex]Therefore, Cooper has read the least amount.
To verify the identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.
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ANSWER:
Separate the quotient in two terms
STEP-BY-STEP EXPLANATION:
We have the following:
[tex]\begin{gathered} \tan x=\frac{\sin x}{\cos x} \\ \tan x=\frac{1}{\cos x}\cdot\sin x \end{gathered}[/tex]Therefore, the step shown in the image is to separate the quotient in two terms
if you copy a page on a machine at 60%, you should get a similar copy of the page. What is the corresponding setting to obtain the original from the copy? The corresponding setting to obtain the original from the copy is _______%
Answers
Answer:
The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]Explanation:
Let c and x represent the copy and original respectively;
[tex]c=60\text{\% of x}[/tex]making x the subject of formula;
[tex]\begin{gathered} c=0.6x \\ x=\frac{c}{0.6} \\ x=1\frac{2}{3}c \\ in\text{ percentage;} \\ x=1\frac{2}{3}c\times100\text{\%} \\ x=166.67\text{\% of c} \end{gathered}[/tex]Therefore, The corresponding setting to obtain the original from the copy is 166.67%
[tex]166\frac{2}{3}\text{\%}[/tex]Johnathan works on IXL 5 nights per week. One week, he masters 7 skills. If he makes the sameamount of progress each night, how many skills does he master per night?Linear Equation:Solve:
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In this problem
Divide total skills by the total night per week
so
7/5=1.4 skills per night
therefore
Let
x ----> number of night
y ----> total skills
so
y=(7/5)x ------> y=1.4xIf f(x)3(=- Vx-3, complete the following statement:x + 2f(19) ==Answer here
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This exercise is about evaluating a function at a particular argument. To do that, we replace the variable with the argument in the formula of the function, and simplify.
Let's do that:
[tex]\begin{gathered} f(19)=\frac{3}{19+2}-\sqrt[]{19-3}, \\ \\ f(19)=\frac{3}{21}-\sqrt[]{16}, \\ \\ f(19)=\frac{1}{7}-4, \\ \\ f(19)=\frac{1-28}{7}, \\ \\ f(19)=-\frac{27}{7}\text{.} \end{gathered}[/tex]Answer[tex]f(19)=-\frac{27}{7}\text{.}[/tex]help 25 points
A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
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Answer:
y = (-1/8)x + (29/4)
Step-by-step explanation:
(10, 6), (2, 7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 7 - 6 1 -1
m = ------------ = ----------- = ----------- = ---------
x₂ - x₁ 2 - 10 -8 8
y - y₁ = m(x - x₁)
y - 6 = (-1/8)(x - 10)
y - 6 = (-1/8)x + (5/4)
+6 +6
-------------------------------
y = (-1/8)x + (29/4)
I hope this helps!
Find the surface area of the solid. Use 3.14 for T. Round final answer to the nearest hundredth.
Answers
Answer:
Given:
Radius of the sphere is 26 mi.
To find the surface area of a given sphere.
We know that,
Surface area of a sphere is,
[tex]4\pi r^2[/tex]where r is the radius of the sphere.
Substitute the values we get, (pi=3.14)
[tex]=4\times3.14\times(26)\placeholder{⬚}^2[/tex][tex]=4\times3.14\times676[/tex][tex]=8,490.56\text{ mi}^2[/tex]The required surface area is 8,490.56 mi^2.
Wilson paints 40% of a bookcase in 20 minutes.How much more time will it take him to finish the bookcase?1. Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase. 2 Use your equation to find the amount of time it will take Wilson to paint the whole bookcase. Explain how you found this answer. 3. How much time will it take Wilson to finish painting the bookcase? Explain.
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We can start that, by rewriting 40% as a fraction:
[tex]\frac{40}{100}=\frac{2}{5}[/tex]So let's find how long it will take to finish this painting, by writing the following fractions, and from them an equation:
1)
[tex]\begin{gathered} \frac{2}{5}---20 \\ \frac{3}{5}---x \\ \frac{2}{5}x=\frac{3}{5}\cdot20 \\ \frac{2}{5}x=12 \end{gathered}[/tex]So this is the equation, let's find the time to complete the painting:
[tex]\begin{gathered} \frac{2}{5}x=12 \\ 5\times\frac{2}{5}x=12\times5 \\ 2x=60 \\ \frac{2x}{2}=\frac{60}{2} \\ x=30 \end{gathered}[/tex]So it will take plus 30 minutes for to Wilson finish the bookcase. Note that
5/5 is equivalent to the whole bookcase or 100%
2) The amount of time to paint this whole bookcase, is found taking the initial 20 minutes and adding to them the 30 minutes we can state that the painting overall takes 50 minutes
3) Sorting out the answers:
[tex]\begin{gathered} 1)\frac{2}{5}x=\frac{3}{5}\cdot20 \\ 2)50\min \\ 3)30\min \end{gathered}[/tex]
You go to a candy store and want to buy a chocolate
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To find the amount of servings, we just need to divide the entire bar weight by the serving weight. Solving this calculation, we have
[tex]\frac{14.8}{2.4}=\frac{37}{6}=6.166666666..\text{.}[/tex]write the equation of a line in y = mx + b form that passes through the given pair of points (1,-2) (3,2)
Answers
The formula for the equation of a line given two points is,
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Given that
[tex]\begin{gathered} (x_1,y_1)=(1,-2) \\ (x_2,y_2)=(3,2) \end{gathered}[/tex]Substituting the given points to the equation and expressing it in the form, y = mx+b
[tex]\begin{gathered} \frac{y--2}{x-1}=\frac{2--2}{3-1} \\ \frac{y+2}{x-1}=\frac{2+2}{3-1} \\ \frac{y+2}{x-1}=\frac{4}{2} \\ \frac{y+2}{x-1}=2 \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} y+2=2(x-1) \\ y+2=2x-2 \\ y=2x-2-2 \\ y=2x-4 \\ \therefore y=2x-4 \end{gathered}[/tex]Hence, the equation of a line in slope in y = mx+b is
[tex]y=2x-4[/tex]
please try to answer quickly because my brainly app keeps crashing before i get the answer.
Answers
Answer:
Explanations:
The formula for calculating the surface area of a sphere is given as:
[tex]SA=4\pi r^2[/tex]Determine the radius of the sphere given the Circumference 4cm. Recall that;
[tex]\begin{gathered} C=4cm \\ 2\pi r=4 \\ r=\frac{4}{2\pi} \\ \end{gathered}[/tex]Substitute the resulting radius into the sphere's surface area
[tex]\begin{gathered} SA=4\pi\cdot(\frac{4}{2\pi})^2 \\ SA=4\pi\cdot\frac{16}{4\pi^2} \\ SA=\frac{16}{\pi} \\ SA=\frac{16}{3.14} \\ SA=5.096\approx5cm^2 \end{gathered}[/tex]Hence the surface area of the spherical object is 5 squar
use the second derivative test to classify the relative extrema if the test applies
Answers
Answer
The answer is:
[tex](x,f(x))=(0,256)[/tex]SOLUTION
Problem Statement
The question gives us a polynomial expression and we are asked to find the relative maxima using the second derivative test.
The function given is:
[tex](3x^2+16)^2[/tex]Method
To find the relative maxima, there are some steps to perform.
1. Find the first derivative of the function
2. Equate the first derivative to zero and solve for x.
3. Find the second derivative of the function.
4. Apply the second derivative test:
This test says:
[tex]\begin{gathered} \text{ If }a\text{ is one of the roots of the equation from the first derivative, then,} \\ f^{\doubleprime}(a)>0\to\text{There is a relative minimum} \\ f^{\doubleprime}(a)<0\to\text{There is a relative maximum} \end{gathered}[/tex]5. Find the Relative Minimum
Implementation
1. Find the first derivative of the function
[tex]\begin{gathered} f(x)=(3x^2+16)^2 \\ \text{Taking the first derivative of both sides, we have:} \\ f^{\prime}(x)=6x\times2(3x^2+16) \\ f^{\prime}(x)=12x(3x^2+16) \end{gathered}[/tex]2. Equate the first derivative to zero and solve for x.
[tex]\begin{gathered} f^{\prime}(x)=12x(3x^2+16)=0 \\ \text{This implies that,} \\ 12x=0\text{ OR }3x^2+16=0 \\ \therefore x=0\text{ ONLY} \\ \\ \text{Because }3x^2+16=0\text{ has NO REAL Solutions} \end{gathered}[/tex]This implies that there is ONLY ONE turning point/stationary point at x = 0
3. Find the second derivative of the function:
[tex]\begin{gathered} f^{\prime}(x)=12x(3x^2+16) \\ f^{\doubleprime}(x)=12(3x^2+16)+12x(6x) \\ f^{\doubleprime}(x)=36x^2+192+72x^2 \\ \therefore f^{\doubleprime}(x)=108x^2+192 \end{gathered}[/tex]4. Apply the second derivative test:
[tex]\begin{gathered} f^{\doubleprime}(x)=108x^2+192 \\ a=0,\text{ which is the root of the first derivative }f^{\prime}(x) \\ f^{\doubleprime}(a)=f^{\doubleprime}(0)=108(0)^2+192 \\ f^{\doubleprime}(0)=192>0 \\ \\ By\text{ the second derivative test,} \\ f^{\doubleprime}(0)>0,\text{ thus, there exists a relative minimum at }x=0\text{ } \\ \\ \text{ Thus, we can find the relative minimum when we substitute }x=0\text{ into the function }f(x) \end{gathered}[/tex]5. Find the Relative Minimum:
[tex]\begin{gathered} f(x)=(3x^2+16)^2 \\ \text{substitute }x=0\text{ into the function} \\ f(0)=(3(0)^2+16)^2 \\ f(0)=16^2=256 \\ \\ \text{Thus, the minimum value of the function }f(x)\text{ is }256 \\ \\ \text{The coordinate for the relative minimum for the function }(3x^2+16)^2\text{ is:} \\ \mleft(x,f\mleft(x\mright)\mright)=\mleft(0,f\mleft(0\mright)\mright) \\ \text{But }f(0)=256 \\ \\ \therefore(x,f(x))=(0,256) \end{gathered}[/tex]Since the function has ONLY ONE turning point, and the turning point is a minimum value, then THERE EXISTS NO MAXIMUM VALUE
Final Answer
The answer is:
[tex](x,f(x))=(0,256)[/tex]