Answers
Consider the following function:
[tex]f(x)=\text{ }\tan(x)\text{ cot\lparen x\rparen}[/tex]First, let's find the derivative of this function. For this, we will apply the product rule for derivatives:
[tex]\frac{df(x)}{dx}=\tan(x)\cdot\frac{d}{dx}\text{ cot\lparen x\rparen + }\frac{d}{dx}\text{ tan\lparen x\rparen }\cdot\text{ cot\lparen x\rparen}[/tex]this is equivalent to:
[tex]\frac{df(x)}{dx}=\tan(x)\cdot(\text{ - csc}^2\text{\lparen x\rparen})\text{+ \lparen sec}^2(x)\text{\rparen}\cdot\text{ cot\lparen x\rparen}[/tex]or
[tex]\frac{df(x)}{dx}=\text{ -}\tan(x)\cdot\text{ csc}^2\text{\lparen x\rparen+ sec}^2(x)\cdot\text{ cot\lparen x\rparen}[/tex]now, this is equivalent to:
[tex]\frac{df(x)}{dx}=\text{ -2 csc \lparen2x\rparen + 2 csc\lparen2x\rparen = 0}[/tex]thus,
[tex]\frac{df(x)}{dx}=0[/tex]Now, to find the slope of the function f(x) at the point (x,y) = (1,1), lug the x-coordinate of the given point into the derivative (this is the slope of the function at the point):
[tex]\frac{df(1)}{dx}=0[/tex]Notice that this slope matches the slope found on the graph of the function f(x), because horizontal lines have a slope 0:
We can conclude that the correct answer is:
Answer:The slope of the graph f(x) at the point (1,1) is
[tex]0[/tex]
Related Questions
what is the value of the expression below when w=2 8w+10
Answers
Given the expression:
8w + 10
To find the value when w = 2, we need to substitute 2 for w in the expression.
Therfore, we have:
[tex]8(2)\text{ + 10}[/tex][tex]16\text{ + 10 = 26}[/tex]Therefore, the value of the expression when w = 2 is 26
ANSWER:
26
Simplify the following sum of polynomials completely ( - 12s raise to power 2 + 10s - 3) + ( 2s raise to power 2 - 12s - 2)
Answers
ANSWER
[tex]-10s^2-2s-5[/tex]EXPLANATION
Given
[tex]\mleft(-12s^2+10s-3\mright)+\mleft(2s^2-12s-2\mright)[/tex]removing the brackets, we have;
[tex]-12s^2+10s-3+2s^2-12s-2[/tex]collecting like terms, we have
[tex]\begin{gathered} -12s^2+2s^2+10s-12s-3-2 \\ \end{gathered}[/tex]adding similar terms, we have;
[tex]-10s^2-2s-5[/tex]The solution is
[tex]-10s^2-2s-5[/tex]5. What is the range of the graph?8all real numbers{y 1-1 sys1)(XI-15x51){x | xs-1 or x 21)
Answers
The correct option is option D
For more comprehension,
Option D is :
[tex]undefined[/tex]find the value or measure. Assume all lines that appear to be tangent are tangent. mPM=
Answers
Segments that crosses around a circle
MN ^2 = OP • ON
mm
then 59° = (
Graph a right triangle with the two points forming the hypotenuse. Using the sides,find the distance between the two points in simplest radical form.
Answers
Answer:
Explanation:
Given the points:
[tex](7,-5)\text{ and }(2,-7)[/tex]The graphed right triangle is given below:
Using the sides, we then find the distance between the two points, d.
By the Pythagorean theorem:
[tex]\begin{gathered} d^2=[5-(-7)]^2+[7-2]^2 \\ d^2=[5+7]^2+5^2 \\ d^2=12^2+5^2 \\ d^2=144+25 \\ d^2=169 \\ d^2=13^2 \\ \implies d=13 \end{gathered}[/tex]The distance between the two poi
Consider the following relation: (1,12) ,(3, 8) , (3, 11) , (6, 9) , (7, 11) . Whichordered pair could be removed so thatthe relation is a function?Group of answer choices
Answers
Answer: Rajesh Kumar
Step-by-step explanation I took the wok to poland
You deposit $400 into a savings account that earns interest annually. The function g(x) = 400(1.05)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[0, 400]
[0, ∞)
[400, ∞)
Answers
Answer:
Step-by-step explanation:
The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits.
Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.
Principal - $400
rate of interest is compounded annually
g(x) = 400( 1.03)ˣ equation 1.
Formula used
A = P( 1 + r )ⁿ
here n = x
Solution:
Putting the value of n, and principal in the formula
A = P( 1 + r )ⁿ ................... equation 2
now comparing both equation 1 and equation 2,
400( 1.05)ˣ = 400( 1 + r )ˣ
( 1.05)ˣ = ( 1 + r )ˣ
1.05 = 1 + r
r = 1.05 - 1
r = 0.05
r % = 0.05 × 100
r % = 5 %
thus, the constant percent rate of change = 5 %
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Using f(x) = 2x - 3 and g(x) = 5, find f(g(3)).7530None of the choices are correct.I don’t think my answer is right please help me thank you
Answers
As per given by the question,
There are given that function,
[tex]\begin{gathered} f(x)=2x-3,\text{ } \\ g(x)=5 \end{gathered}[/tex]Now,
Find the value of f(g(3)).
Then,
There are given that,
[tex]g(x)=5[/tex]And,
According to question, value of x is 3, that means g(3).
So,
Put the value of x in g(x).
Then,
[tex]\begin{gathered} g(x)=5 \\ g(3)=5 \end{gathered}[/tex]Now,
For find the value f(g(3));
Put the value of g(3) in the above condition,
f(g(3)).
So,
[tex]f(x)=2x-3[/tex]Instead of x in f(x), put the g(3).
Then,
[tex]\begin{gathered} f(g(3))=2x-3 \\ f(5)=2\times5-3 \\ f(5)=10-3 \\ f(5)=7 \end{gathered}[/tex]So, the value of f(g(x)) is 7.
Hence, the option first is correct.
Triangle ABC is similar to triangle DEF. Find the measure of side DE. Round youranswer to the nearest tenth if necessary.C7BF27E15DAD
Answers
Given:
Triangle ABC is similar to triangle DEF.
[tex]\frac{DE}{AB}=\frac{EF}{BC}[/tex][tex]\begin{gathered} \frac{DE}{15}=\frac{27}{7} \\ DE=\frac{27}{7}\times15 \\ DE=57.9 \end{gathered}[/tex]Graph v (standard position) and find its magnitude. Show all work.
Answers
EXPLANATION
[tex]\mathrm{Computing\: the\: Euclidean\: Length\: of\: a\: vector}\colon\quad \mleft|\mleft(x_1\: ,\: \: \ldots\: ,\: \: x_n\mright)\mright|=\sqrt{\sum_{i=1}^n\left|x_i\right|^2}[/tex][tex]=\sqrt{2^2+5^2}[/tex][tex]=\sqrt{4+5^2}[/tex][tex]=\sqrt{4+25}[/tex][tex]=\sqrt{29}[/tex]Now, we need to graph the vector as shown as follows:
Identify the minimum from the tableType your answer as an ordered pair (x,y)
Answers
By definition, a function is a relation in which each input value has one and only one output value.
The input values are also known as x-values and the output values are also called y-values.
By definition, the Minimum is the lower point of the function.
Having the table shown in the exercise, you can identify the following points:
[tex]\begin{gathered} (-2,10) \\ (-1,8) \\ (0,6) \\ (1,4) \end{gathered}[/tex]You can identify that the lower y-value of all those points is:
[tex]y=4[/tex]Therefore, you can determine that the lower point of the function is:
[tex](1,4)[/tex]The answer is:
[tex](1,4)[/tex]Operations in Scientific NotationWrite two numbers in scientificnotationFind their sum, difference, product& quotient
Answers
Solution:
Let the two numbers be
[tex]20\text{ and 10}[/tex]In scientific notation, the numbers are
[tex]\begin{gathered} 20=2\times10^1 \\ 10=1\times10^1 \end{gathered}[/tex]The sum of the numbers will be
[tex]=(2\times10^1)+(1\times10^1)=10^1(2+1)=10^1(3)=3\times10^1[/tex]Hence, the sum is
[tex]3\times10^1[/tex]The difference between the two numbers will be
[tex]=(2\times10^1)-(1\times10^1)=10^1(2-1)=10^1(1)=1\times10^1[/tex]Hence, the difference is
[tex]1\times10^1[/tex]The product of the numbers will be
[tex]=(2\times10^1)\cdot(1\times10^1)=(2\times1)(10^{1+1})=2(10^2)=2\times10^2[/tex]Hence, the product is
[tex]2\times10^2[/tex]The quotient of the numbers will be
[tex]=\frac{2\times10^1}{1\times10^1}=\frac{2}{1}\times(10^{1-1})=2(10^0)=2\times10^0[/tex]Hence, the quotient is
[tex]2\times10^0[/tex]n=39; i = 0.039; PMT = $196; PV =?
Answers
Given the Present Value (PV) formula
[tex]PV=PMT\times\frac{1-(\frac{1}{(1+i)^n})}{i}[/tex]Write out the parameters
[tex]\begin{gathered} PV=\text{?} \\ n=39 \\ i=0.039 \\ \text{PMT=\$196} \end{gathered}[/tex]Substitute the following values in the present value formula to find the PV
[tex]PV=196\times\frac{1-(\frac{1}{(1+0.039)^{39}})}{0.039}[/tex][tex]PV=196\times\frac{1-0.2249021697}{0.039}[/tex][tex]PV=196\times\frac{0.7750978303}{0.039}[/tex][tex]\begin{gathered} PV=196\times19.87430334 \\ PV\approx3895.36 \end{gathered}[/tex]Hence, the Present Value (PV) is approximately $3895.36
hello can you help me with this question and this a homework assignment
Answers
Problem
Solution
For this case we can use the Cosine law and we have:
[tex]\cos (c)=\frac{a^2+b^2-c^2}{2ab}=\frac{35^2+56^2-33^2}{2\cdot35\cdot56}=0.8346938776[/tex][tex]\cos (b)=\frac{a^2+c^2-b^2}{2ac}=\frac{35^2+33^2-56^2}{2\cdot35\cdot33}=-0.356[/tex][tex]\cos (a)=\frac{c^2+b^2-a^2}{2cb}=\frac{33^2+56^2-35^2}{2\cdot33\cdot56}=0.8116883117[/tex]And then we can find the angles with the arcos like this:
[tex]<\gamma=ar\cos (0.8346938776)=33.42[/tex][tex]<\beta=ar\cos (-0.356)=110.85[/tex][tex]<\alpha=ar\cos (0.8116883117)=35.74[/tex]Can you see the new values for gamma and alfa
Find the circumference of each circle .(use 22/7 as an approximation for PI
Answers
Let us find the circumference of each circle.
The circumference of a circle is given by
[tex]C=2\pi r\: \: or\: \: C=\pi D[/tex]Where r is the radius and D is the diameter of the circle.
Circle 1:
Here we are given the diameter of the circle
D = 21 cm
[tex]C=\pi D=\frac{22}{7}\cdot21=22\cdot3=66\operatorname{cm}[/tex]So, the circumference of the circle is 66 cm.
Circle 2:
Here we are given the diameter of the circle
D = 91 ft
[tex]C=\pi D=\frac{22}{7}\cdot91=286\: ft[/tex]So, the circumference of the circle is 286 ft.
Circle 3:
Vernon mixed 2 1/3 cups of water with 2 1/3 of white vinegar to make a cleaning solution.how much cleaning solution did he make
Answers
SOLUTION
Write out the information given
[tex]\begin{gathered} \text{Quantity of water=2}\frac{1}{3}cups\text{ } \\ \\ \text{Quantity of white vinegar=2}\frac{1}{3}cups \end{gathered}[/tex]The quantity of the cleaning solution will the sum of the quantity above
The number model will be
[tex]2\frac{1}{3}cups+2\frac{1}{3}\text{cups }[/tex]Then
[tex]\begin{gathered} 2\frac{1}{3}+2\frac{1}{3}=2\times(2\frac{1}{3})=2\times(\frac{7}{3})=\frac{14}{3} \\ \text{then} \\ \frac{14}{3}=4\frac{2}{3} \end{gathered}[/tex]hence the cleaning solution will be
[tex]4\frac{2}{3}[/tex]Answer: 4 2/3
I will attach a picture to this question so you can understand it better.
Answers
Here are the given information:
1. 7 red beads for every 4 blue beads
2. total of 44 beads (red and blue)
Find: the number of red beads
Solution:
We can solve this in two ways. We can solve this using proportion or we can solve this by counting.
Let's start counting first. Let's say 7 red beads and 4 blue beads is 1 set. So, for every set, we already have 7 + 4 = 11 beads in total.
First set = 7 red bead + 4 blue beads = 11 beads
Second set = 7 red bead + 4 blue beads = 11 beads
Third set = 7 red bead + 4 blue beads = 11 beads
Fourth set = 7 red bead + 4 blue beads = 11 beads
If we add all the 4 sets, we have a total of 44 beads. If we add all the RED beads only, we get 7 red beads x 4 sets = 28 red beads.
Therefore, Lily used 28 red beads.
Now, using proportion, we can have this equation:
[tex]\frac{7\text{red beads}}{4\text{blue bead}}=\frac{x\text{ red beads}}{(44-x\text{ red)blue beads}}[/tex]where x = the total number of red beads and we got 44 - x as the number of blue beads.
The next thing that we need to do here is to solve for x.
1. To solve for x, do cross multiplication first.
[tex]7(44-x)=4x[/tex]2. Multiply 7 to the numbers inside the parenthesis.
[tex]308-7x=4x[/tex]3. Add 7x on both sides of the equation.
[tex]\begin{gathered} 308-7x+7x=4x+7x \\ 308=11x \end{gathered}[/tex]4. Lastly, divide both sides by 11.
[tex]\begin{gathered} \frac{308}{11}=\frac{11x}{11} \\ 28=x \end{gathered}[/tex]As we can see, the value of x = 28. Lily used 28 red beads.
Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary.5,−2,45,...5,−2, 54 ,...Sum of a finite geometric series:Sum of a finite geometric series:Sn=a1−a1rn1−rS n = 1−ra 1 −a 1 r n
Answers
Solution:
Given:
[tex]5,-2,\frac{4}{5},\ldots[/tex]To get the sum of the first 7 terms, the formula below is used;
[tex]S_n=\frac{a_1-a_1r^n}{1-r}[/tex]where;
[tex]\begin{gathered} n=7 \\ a_1\text{ is the first term = 5} \\ r\text{ is the co}mmon\text{ ratio=}\frac{-2}{5} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} S_n=\frac{a_1-a_1r^n}{1-r} \\ S_7=\frac{5-5(-\frac{2}{5})^7}{1-(-\frac{2}{5})} \\ S_7=\frac{5-5(-0.4)^7}{1+\frac{2}{5}} \\ S_7=\frac{5-5(-0.0016384)}{1+0.4} \\ S_7=\frac{5+0.008192}{1.4} \\ S_7=\frac{5.008192}{1.4} \\ S_7=3.57728 \end{gathered}[/tex]Therefore, the sum of the first 7 terms is 3.57728
The director of an alumni association for a small college wants to determine whether there is any type of relationship between an alum’s contribution (in dollars) and the number of years the alum has been out of school. The data follow.
Answers
----------------------------
b)
[tex]\begin{gathered} X=4 \\ \hat{y}(4)=-50.43919(4)+453.17568 \\ \hat{y}(4)=-201.75676+453.17568 \\ \hat{y}(4)=251.41892 \end{gathered}[/tex]Takashi is driving to his grandmother's house. he is driving at a constant speed and will not make any stops along the way. Takashi’s distance in miles from his grandmother’s house h hours after leaving can be described by equationA. Identify and interpret the independent variable? B. Identify and interpret the coefficient? C. Identify and interpret the constant term ?D. Identify and interpret the dependent variable?
Answers
Let's begin by listing out the information given to us:
To calculate Takashi's distance from his grandmother's house is given by the formula:
[tex]\begin{gathered} distance=speed\cdot time \\ h=v\cdot t \end{gathered}[/tex]Independent variable refers to the variable that stands by itself and whose value is not affected by the other
Dependent variable refers to the variable whose value is affected by the value of another variable
A. The distance (h) does not change irrespective of Takashi's speed, hence it is the independent variable
B. The coefficient is the speed (v)
C. The constant is time (t)
D. The speed (v) changes with variation in time, hence it is the dependent variable
1. Abby baked 2-dozen brownies. She took 1 dozen to her scout meeting. Her family ate 8, and she put the rest in a container in the refrigerator. How can Abby find the number of brownies left in the refrigerator?
Answers
The number of brownies left in the refrigerator is 4.
How to calculate the value?It's important to note that 1 dozen = 12
In this case, Abby baked 2-dozen brownies, she took 1 dozen to her scout meeting and her family ate 8, and she put the rest in a container in the refrigerator.
Therefore, the remaining amount will be:
= 2 dozens - 1. dozen - 8
= (2 × 12) - 12 - 8
= 24 - 12 - 8
= 4
There'll be 4 left. This illustrates the concept of subtraction.
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5 1/7 * 4 2/3 equals
Answers
We have to solve this operation with mixed numbers.
We can solve this applying the distributive property or by converting the mixed numbers into fractions.
We will solve this converting the numbers into fractions:
[tex]\begin{gathered} (5+\frac{1}{7})\cdot(4+\frac{2}{3}) \\ \frac{5\cdot7+1}{7}\cdot\frac{4\cdot3+2}{3} \\ \frac{35+1}{7}\cdot\frac{12+2}{3} \\ \frac{36}{7}\cdot\frac{14}{3} \\ \frac{36}{3}\cdot\frac{14}{7} \\ 12\cdot2 \\ 24 \end{gathered}[/tex]Answer: 24
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units. Where has the point moved to?
Answers
Given
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units.
To find:
Where has the point moved to?
Explanation:
It is given that,
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units.
That implies,
Since starting at 0 on a number line, a point is moved 21 units.
Then,
[tex]0+21=21[/tex]Also, then 53 units.
Then,
[tex]21+53=74[/tex]Also, then 721 units.
Then,
[tex]74+721=795[/tex]And, finally negative-50 units.
Then,
[tex]\begin{gathered} 795+(-50)=795-50 \\ =745 \end{gathered}[/tex]Hence, the point is moved to 745.
It is question 16 pls help
Answers
Answer: yes it is 16 i did my work let me know if you want me to show my work
Step-by-step explanation:
In 2012 the total population of individuals in the
United States who were between 14 and 17 years old
(inclusive) was about 17 million. If the survey results
are used to estimate information about summer
employment of teenagers across the country, which
of the following is the best estimate of the total
number of individuals between 16 and 17 years old in
the United States who had a summer job in 2012?
Answers
Answer:
Its B I'm not to good at explaining but I've done my math
Step-by-step explanation:
and its b just trust me
Convert each slope-intercept or point slope equation into standard form.
y - 3 = 1/5(x + 6)
Answers
The Standard form of the equation will be as x - 5y = -21
What is Standard form of equation?The standard form of the equation is defined as; Ax + By = C
Where, A, B and C are integers.
Given that the equation in slope - intercept form is;
⇒ y - 3 = 1/5 (x + 6)
Now,
We need to convert the equation in standard form as;
⇒ y - 3 = 1/5 (x + 6)
Now Change into standard form as;
⇒ y - 3 = 1/5 (x + 6)
Then Multiply by 5 both side, we get:
⇒ 5( y - 3) = (x + 6)
⇒ 5y - 15 = x + 6
⇒ 5y = x + 21
Now Subtract 21 both side, we get:
⇒ 5y - 21 = x + 21 - 21
⇒ 5y - 21 = x
⇒ - 21 = x - 5y
⇒ x - 5y = -21
Therefore,
The Standard form of the equation will be as x - 5y = -21
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9 - 6 - 19 c) y - 12 OC p = b) y 24 c) = 9
Answers
x=70, y= -50 and x=80
1) Let's solve each equation, plugging in the given value for x
y=5x -300
a) y=50
y=5x -300 Plug y=50
50=5x -300 Add 300 to both sides
50+300=5x
350 = 5x Divide both sides by 5
x=70
b) x = 50
y=5x -300 Plug x=50
y=5(50) -300 Distribute the factor
y= 250 -300
y= -50
c) y=100
y=5x -300 Plug y=100
100 = 5x -300 Add 300 to both sides
400 = 5x
x =80
Hence, the answer is
x=70, y= -50 and x=80
The force of gravity is 6 times greater on the earth than it is on the moon. What is the weight of a 150-pound man on the moon?
Answers
The force of gravity on the Earth is equal to 9.8m/s².
Now, if the force of gravity on the moon is 6 times lesser than Earth's gravity.
Then,
The weight of a 150-pound man on the moon is:
150-pound/ 6
= 25-pounds
Hence, the weight of the man is 25-pounds
A father is buying cheeseburgers for his children. Each cheeseburgercosts $3.50. He spends $17.50 on cheeseburgers. Which equation canyou use to determine how many cheeseburgers he bought?O 17.50 = 3.50cO 3.50 = 17.500O 3.50 + 17.50 =cO 17.50 -3.50 = C« PreviousNext
Answers
Each cheese burger costs $3.50
c reprsents the number of cheese burgers
$17.50 is the total cost spent on c cheeseburgers
If you multiply the value of each cheeseburger by the number bought, you'll obtain the total cost:
3.50c=17.50
The correct option is number 1
Look at the first Model It. In the first place-value chart, why is the thousandths column for the decimal 5.67 empty?
Answers
The thousandths column for the decimal 5.67 is empty because there's no thousandth value in the decimal.
What is a place value?Place value is the value provided by a digit in a number based on its place in the number. For example, 7 hundreds or 700 is the place value of 7 in 3,743. Place value is the value provided by a digit in a number based on its place in the number.
In this case, the decimal that's given is illustrated as 5.67. It should be noted that 6 is the tenths value and 7 is the hundredth value. Therefore, there is no thousandth value. This is why it's empty.
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