Answers
Given:
[tex]y=tan\left(2x+4\right)[/tex]To find:
The differential when x = 4 and dx = 0.1.
Explanation:
Differentiating with respect to x we get,
[tex]\begin{gathered} \frac{dy}{dx}=sec^2\left(2x+4\right)\cdot(2) \\ \frac{dy}{dx}=2sec^2\left(2x+4\right) \\ dy=2sec^2\left(2x+4\right)dx.............(1) \end{gathered}[/tex]Substituting x = 4 and dx = 0.1 in equation (1), we get
[tex]\begin{gathered} dy=2sec^2(2(4)+4)\cdot(0.1) \\ dy=0.2sec^2(12) \end{gathered}[/tex]Therefore, the differential is,
[tex]dy=0.2sec^{2}(12)[/tex]Final answer:
The differential is,
[tex]dy=0.2sec^{2}(12)[/tex]
Related Questions
Find the values of 2x2 by completing this chart.xx22x2−248−11200011224Fill in the blank text field 1
Answers
Solution
Step 1:
Draw and complete the chart
Explanation
[tex]\begin{gathered} \text{For x = -2, x}^2\text{ = \lparen-2\rparen}^2\text{ = 4 , 2x}^2\text{ = 2}\times4\text{ = 8} \\ For\text{ x = -1 , x}^2\text{ = \lparen-1\rparen}^2\text{ = 1, 2x}^2\text{ = 2}\times\text{ 1 = 1} \\ For\text{ x = 0, x}^2\text{ = 0}^2\text{ = 0 , 2x}^2\text{ = 2}\times\text{ 0 = 0} \\ For\text{ x = 1, x}^2\text{ = 1}^2\text{ = 1, 2x}^2\text{ = 2 }\times\text{ 1 = 2} \\ For\text{ x = 2 , x}^2\text{ = 2}^2\text{ = 4, 2x}^2\text{ = 2}\times\text{ 4 = 8} \end{gathered}[/tex][tex]\begin{gathered} \text{y = 3x}^2+\text{ 12x - 4} \\ To\text{ find the minimum value, find the first derivative} \\ \frac{dy}{dx}\text{ = 6x + 12} \\ 6x\text{ + 12 = 0} \\ 6x\text{ = -12} \\ x\text{ = }\frac{-12}{6}\text{ = -2} \end{gathered}[/tex]Substitute x = -2, to find the minimum value.
[tex]\begin{gathered} \text{y = 3x}^2+12x-4 \\ \text{y = 3}\times(-2)^2\text{ + 12}\times(-2)\text{ - 4} \\ \text{y = 12 - 24 - 4} \\ \text{y = -16} \end{gathered}[/tex]The minimum value is (-2, -16)
Can you help me figure out the answer for 135 and -65?
Answers
135
For letter S, we have
x/3 + 10 = 55
Subtracting 10 from both sides of the equation, we have
x/3 + 10 - 10 = 55 - 10
x/3 = 45
x = 45 * 3
x = 135
Therefore,
What is the volume of the following prism?A. 189 m³B. 42 m³C. 126 m³D. 63 m³
Answers
Given the figure of a prism
The volume of the prism = area of triangular base times the height of the prism
As shown:
The area of the triangular base =
[tex]\frac{1}{2}\cdot6\cdot3=3\cdot3=9m^2[/tex]The height of the prism = 7 m
So, the volume = 9 * 7 = 63 squared meter
So, the answer will be option D) 63 m^3
19.02 M)Which equation could be used to solve for the measure of angle O?(1 point)
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Given the cyclic quadilateral below,
In a cyclic quadilateral, the sum of angles is 360°
The sum of the opposite angles of a cyclic quadilateral is 180° i.e,
[tex]\begin{gathered} x^0_{_{_{_{}}}}+z^0=180^0_{_{}} \\ w^0+y^0=180^0 \\ (\text{Sum of the opposite angles of a cyclic quadilateral)} \end{gathered}[/tex]Hence, the equation to find the measure of angle O i.e x° is,
[tex]x^0_{_{_{_{}}}}+z^0=180^0_{_{}}[/tex]Graph the line with a y-intercept of (0, 2) whose slope is m=3/5
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We must plot the line with:
• y-intercept (0, 2) ⇒ b = 2,
,• slope m = 3/5.
The equation of the line is:
[tex]y=m\cdot x+b=\frac{3}{5}x+2.[/tex]Replacing the value x = 5, we get the point:
[tex](5,\frac{3}{5}\cdot5+2)=(5,5).[/tex]We must plot a line that passes through the points (0, 2) and (5, 5). Plotting this line, we get the following graph:
AnswerFind a formula for the nth termof the arithmetic sequence.First term -17Common difference 5an=[? ]n +Enter
Answers
The nth term of a sequence is given by the formula:
[tex]T_n_{}=a+(n-1)d[/tex]Where
[tex]\begin{gathered} T_n=\text{nth term} \\ a=\text{ first term} \\ n=\text{ number of terms} \\ d=\text{ common difference} \end{gathered}[/tex]From the question given
We are told that the first term is -17
the common difference is 5
We will simply substitute these values into the formula
[tex]T_n=-17+(n-1)\times5[/tex]Simplifying
we will have
[tex]\begin{gathered} T_n=-17+5n-5 \\ T_n=5n-17-5 \end{gathered}[/tex]Simplifying further, we will have
[tex]T_n=5n-22[/tex]So If we compare the answer above with what is required in the question, we will have
[tex]a_n=5n-22[/tex]Therefore we will have
In the figure below line de is parallel to line gg with transversal ag
Answers
From the problem with the information given we will have:
[tex]5y-18=x[/tex]&
[tex]2x+2y=360[/tex]Now, we will replace the value of "x" from the first equation into the second one and we will solve for "y", that is:
[tex]2(5y-18)+2y=360\Rightarrow10y-36+2y=360[/tex][tex]\Rightarrow12y=396\Rightarrow y=33[/tex]Now, we replace this value of "y" in the first equation or the second one to obtain "x", We will replace in the first equation in this case:
[tex]5(33)-18=x\Rightarrow x=147[/tex]So, the values of x & y are respectively 147 & 33.
Which inequality represents the graph? -20 -15 -10 -5 0 5 10 5 10 15 20
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EXPLANATION:
We can see in the graph that the value of -15 appears on the negative axis,
What we observe in the graph is that a closed circle is used, that means that the inequality is "less than or equal to" q
[tex]\begin{gathered} ANSWER\colon \\ q\leq-15 \end{gathered}[/tex]the following table shows a proportional realashonship between m and n write an equation to describe the realashonship between m and n
Answers
From a review of the table,
when m = 3, n = 21
this means that m was multiplied by
= 21/3 = 7
By 7 to get n
A similar trend was noted through the table
Hence the relationship between m and n may be stated as
n = 7m
Songhee leisurely rides her bicycle at 10 miles per hour. In about 675 revolutions of the wheel, Songhee travels one mile. Use a unit multiplier to convert 10 miles per hour to revolutions per hour.
Answers
Since in about 675 revolutions of the wheel, Songhee travels one mile, then in about:
[tex]675\times10\text{ revolutions}[/tex]Songhee travels 10 miles.
Then:
[tex]10\text{mi}\leftrightarrow6750\text{ revolutions.}[/tex]Now, we know that Songhee rides her bicycle at 10 miles per hour, substituting 10mi=6750revolutions we get that Songhee rides her bicycle at:
[tex]6750\text{revolutions per hour.}[/tex]Answer: 6750 revolutions per hour.
In a circle of radius 6 miles, the length of the arc that subtends a central angle of 2 radians.....
Answers
Given the word problem, we can deduce the following information:
Radius = 6 miles
Central angle = 2 radians
To determine the length of the arc, we use the formula:
[tex]s=r\theta[/tex]where:
s= arc length
r= radius
θ= central angle in radians
We plug in what we know:
[tex]\begin{gathered} s=r\theta \\ s=(6)(2) \\ \text{Calculate} \\ s=12\text{ miles} \end{gathered}[/tex]Therefore, the length of the arc is 12 miles.
Which of the following is the graph of the quadratic function y=x+4x-12?-20-20A.20-20-20B.20C.-6D.
Answers
Given
The quadratic function,
[tex]y=x^2+4x-12[/tex]To find;
The graph representing the above function.
Explanation:
It is given that,
[tex]y=x^2+4x-12[/tex]That implies,
[tex]y=x^2+4x-12[/tex]Ralph is planning to use the same indoor rock climbing facility that his friend Trina did. Trina can'tremember how long she climbed, but she spent a total of $21.25 on her session. She paid a $5entrance fee and $3.25 for every hour she climbed. If Ralph wants to spend the same amount ofmoney, write an equation to help him figure out how long he should plan on climbing. Highlightyour equation in green. Then, solve the equation.
Answers
Let's generate an equation from the relationships found in the given scenario,
We get,
[tex]\text{ 5 + 3.25x = 21.25}[/tex]This equation reflects Trina's expenses during her indoor rock climbing. She spent an entrance fee of $5 and a rate of $3.25 per hour climb with a total expense of $21.25.
Where,
x = the number of hours Trina climbed.
Let's now compute how long did Trina use the indoor rock climbing facility.
[tex]\text{ 5 + 3.25x = 21.25}[/tex]Applying the Rule of Additive Inverse Property, we get,
[tex]\text{ 5 + 3.25x - 5 = 21.25 - 5}[/tex][tex]\text{ 3.25x = 16.25 }\rightarrow\text{ x =}\frac{16.25}{3.25}[/tex][tex]\text{ x =5}[/tex]Therefore, Trina spent 5 hours in the indoor rock climbing facility.
If Ralph wants to spend the same amount of money, he must use the indoor rock climbing facility for 5 hours.
If oats cost $0.02is the cost of theoats if thecontainer is full?
Answers
Given the cost of an oats = $0.02
Pre-Algebra: Find the slope of the line passing through the pair of points
Answers
We have to find the slope of the line that passes thorugh points (19/2, -8/3) and (-7/2, -1/15).
We can find the slope m as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-\frac{1}{15}-(-\frac{8}{3})}{-\frac{7}{2}-\frac{19}{2}} \\ \\ m=\frac{-\frac{1}{15}+\frac{8}{3}\cdot\frac{5}{5}}{\frac{-7-19}{2}} \\ \\ m=\frac{-\frac{1}{15}+\frac{40}{15}}{\frac{-26}{2}} \\ \\ m=-\frac{2}{26}(\frac{39}{15}) \\ \\ m=-\frac{1}{13}(\frac{13\cdot3}{5\cdot3}) \\ \\ m=-\frac{1}{5} \end{gathered}[/tex]We can check the result with a graph as:
Answer: the slope is m = -1/5.
Solve for x2x - 7 = -3x + 18
Answers
Given the following equation:
[tex]2x-7=-3x+18[/tex]You can solve it as follows:
1. Apply the Addition Property of Equality by adding this term to both sides of the equation:
[tex]3x[/tex]Then:
[tex]\begin{gathered} 2x-7+(3x)=-3x+18+(3x) \\ 5x-7=18 \end{gathered}[/tex]2. Apply the same property. Add 7 to both sides of the equation:
[tex]\begin{gathered} 5x-7+(7)=18+(7) \\ 5x=25 \end{gathered}[/tex]3. Finally, you can apply the Division Property of Equality by dividing both sides of the equation by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{25}{5} \\ \\ x=5 \end{gathered}[/tex]Therefore, the answer is:
[tex]x=5[/tex]Use the sum-to-product identities to rewrite the following expression as a product.sin(x) – sin(3x)
Answers
Given:
[tex]\sin x-\sin 3x[/tex]Sol:.
Formula of sin3A is:
[tex]\sin 3A=3\sin A-4\sin ^3A[/tex]Put the value of sin3x in given function:
[tex]\begin{gathered} =\sin x-\sin 3x \\ =\sin x-(3\sin x-4\sin ^3x) \\ =\sin x-3\sin x+4\sin ^3x \\ =-2\sin x+4\sin ^3x \\ =2\sin x(2\sin ^2x-1) \end{gathered}[/tex]Find a pH for a substance with the hydronium ion [H3O^+] concentration of 1.3x10^-4.
Answers
A substance with a hydronium ion [H3O+] concentration of 1.00× [tex]10^{-4}[/tex] has a pH of 4.
What is meant by hydronium ion?Protonated water, also known as the hydronium ion (H3O+), is present in all acidic aqueous solutions. It can form when an acid is present in water or simply when pure water is present. It has the chemical formula H3O+. It can also be formed by combining an H+ ion and an H2O molecule. The hydronium ion is made up of three hydrogen atoms and one oxygen atom and has a trigonal pyramidal geometry.Therefore,
Use the equation to calculate the pH of a solution.
p H = - log[ [tex]H}_3 \mathrm{O}^{+}\right[/tex]]
Because we have been given the hydronium ion [tex]H}_3 \mathrm{O}^{+}\right[/tex] We can plug the concentration of the solution into the formula.
[tex]&p H=-\log \left[1.00 \times 10^{-4} M\right] \\[/tex]
[tex]&p H=4[/tex]
The pH of this solution is 4.
Added notes:
[tex]$p H=p H_3 \mathrm{O}^{+}$[/tex] because hydrogen ions attach to water molecules for form hydronium ions.
Some other key things to remember for pH calculations include:
[tex]&\mathrm{pH}+\mathrm{pOH}=14 \\[/tex]
[tex]&\mathrm{pH}=-\log \left[H^{+}\right] \\[/tex]
[tex]&\mathrm{pOH}=-\log \left[O H^{-}\right][/tex]
[tex]&{\left[H^{+}\right]=10^{-p H}} \\[/tex]
[tex]&{\left[O H^{-}\right]=10^{-p O H}}[/tex]
The video below explains how to use all of this information to perform these types of calculations.
The complete question is:
What is the pH of a solution that has a hydronium ion concentration of 1.00× [tex]10^{-4}[/tex] M?
To learn more about hydronium ion, visit:
https://brainly.com/question/27586088
#SPJ1
sara is packing for a trip. she has 16 pairs of shoes. if she has room to pack 5 pairs, how many ways can she choose which shoes to take
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It i given that n = 16, which is the total number of shoes and r = 5.
The number of ways she can choose which shoes to take is determined by combination.
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Substitute the values,
[tex]^{16}C_5=\frac{16!}{5!11!}=\frac{16\times15\times14\times13\times12\times11!}{5\times4\times3\times2\times1\times11!}[/tex]Hence the answer is 4368. The number of ways she
You have two ways to drive home from work: Route A is usually quicker; Route B is scenic but slower. You choose Route A on 80% of your days and this gets you home by 6:00 PM 90% of the time. When you choose Route B you get home by 6:00 PM only 60% of the time. What is the probability that you choose Route B and get home by 6:00 PM?
Answers
According to the information the probability of choosing the route B would be 20% (Since the probability of the other option is 80%). Then we multiply it by the probability of getting home at 6 PM through the route B, which is 60%.
P = 20/100*(60/100)
P=1200/10000 (Multiplying fractions)
P=3/25 (Simplifying)
The answer is 3/25 or 12% (converted to percentage)
The rocket is at ground level at ( ) seconds and ( ) seconds.
Answers
Given the equation:
[tex]h=-16t^2+48t[/tex]Where (h) represents the height of the rocket, and (t) is the time
We will find when the rocket will be at the ground level
The ground will be at the ground level when (h=0), which means the x-intercepts of the given graph
As shown: the graph has two points of x-intercepts
The points are (0, 0) and (3, 0)
So, the answer will be:
The rocket is at ground level at ( 0 ) seconds and ( 3 ) seconds.
CoursesStandard Normal DistributionCatalog and Study ToolsRental OptionsMasoStandard Devletion 10College Success TipsCareer Success Tips0 Help5000-500001 Give Feedback-2.0-1.00:00.00001.02.0P(Z > 2.00)P(Z > -1.00) =p(Z < 0.50) =p(z < 1.75) -Grade It NowSave & ContinueContinue without saving
Answers
From z table:
For P(Z > 2.00)
[tex]P(Z>2.00)=1-P(Z<2.00)=1-0.9772=0.0228[/tex]Answer: 0.0228
For P(Z > -1.00)
[tex]P(Z>-1.00)=1-P(Z<-1.00)=1-\text{0}.1587=0.8413[/tex]Answer: 0.8413
For p(Z < 0.50)
[tex]P(Z<0.50)=0.6915[/tex]Answer: 0.6915
For p(z < 1.75)
[tex]P(Z<1.75)=0.9599[/tex]Answer: 0.9599
4 with an exponent of -4 as a fraction
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Supply the missing reasons to complete the proof.
Given: Q=T and QR=TR
Prove: PR=SR
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3. ASA theorem as two of the angles and one side of the triangle is congruent to those of another triangle.
4. Since ΔPRQ≅ΔSRT
what does it mean when it says identity the variable 10x +4
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first 10 is the coefficient of x
and 4 is a constant term
variable is x
a. 1. A large corporation wants to find out which benefits plan its employees would prefer. Which procedure would be most likely to obtain a statistically unbiased sample? survey a random sample of employees from a list of all employees b. invite all employees to indicate their choices by e-mail place suggestion boxes at random locations in the company's plant and offices d. assemble a group with one member from each department and record the preferences of these employees thom proportional to the number of C.
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ANSWER:
In order to obtain an unbiased sample for the purpose of this type of research, the most appropriate option would be option C.
(C) Place suggestion boxes at random locations in the company's plant and offices.
Note that, the other suggested options would yield results but these might not be free from bias since it does not guarantee anonymity. However, with the use of option C, each participant in the survey can protect their identity as much as he/she chooses.
2 One fluid ounce is approximately 30 milliliters. A water bottle holding 20 fluid ounces would holdmany milliliters (ml)?A 1.5 mLB 66.7 mlC 150 mLD 600 mL
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answer:600mL
one fluid ounce holds 30mL
20 fluid ounces will hold 20*30ml
therefore, a water bottle will hold 600mL
The exact area of a circle is 2106.811 square miles.What is the radius?1mi
Answers
Answer:
[tex]r=26\text{ miles}[/tex]Step-by-step explanation:
The area of a circle is represented by the following equation:
[tex]\begin{gathered} A_o=\pi\cdot r^2 \\ \end{gathered}[/tex]If the exact area is 2106.811, plug it into the equation and solve for r(radius);
[tex]\begin{gathered} 2106.811=\pi\cdot r^2 \\ r=\sqrt[]{\frac{2106.811}{\pi}} \\ r=25.89 \\ \text{ Rounding:} \\ r=26\text{ miles} \end{gathered}[/tex]Find the vertical asymptotes and holes for the graph of the rational function. y = (x+2)(x-5) / (x-5)(x+3)Identify any vertical asymptotes for the graph of the function. Select all that apply.
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To find out the vertical asymptotes, you must find out which value equals the denominator to 0.
In this case will be:
x=5 and x -3 because:
[tex]\begin{gathered} Y=\text{ }\frac{(x\text{ -2\rparen\lparen x+5\rparen}}{(x\text{ -5\rparen \lparen x + 3\rparen}} \\ y=\frac{(x-2)(x+5\rparen}{(5\text{ -5\rparen \lparen x+3\rparen}} \\ y=\text{ }\frac{(x-2\rparen(x+5\rparen}{0} \\ y=\text{ undefined} \\ \\ y=\frac{(x-2\rparen(x+5\rparen}{(x\text{ -5\rparen\lparen-3 + 3\rparen}} \\ y=\text{ }\frac{(x-2\rparen(x+5\rparen}{0} \\ y=undefined \end{gathered}[/tex]The answers are:
x=5 and x= -3
Write an equation in slope intercept form of a line passing through the given point and perpendicular to the given line(0, -6);3x-2y=5
Answers
Answer:
y = -2 /3 x - 6
Explanation:
Here we remind ourselves that if we have an equation of the form
[tex]y=mx+b[/tex]then the equation of a line perpendicular to the above line is
[tex]y=-\frac{1}{m}x+c[/tex]where c is the y-intercept.
Now for our case, the equation we have is
[tex]3x-2y=5[/tex]which isn't helpful since we cannot use it to find the equation of the perpendicular line.
Therefore, to make it useful, we first convert it to the slope-intercept form: y = mx + b.
Now, subtracting 3x from both sides gives
[tex]3x-2y-3x=5-3x[/tex][tex]-2y=5-3x[/tex]dividing both sides by -2 gives
[tex]\frac{-2y}{-2}=\frac{5-3x}{-2}[/tex][tex]y=\frac{3}{2}x-5[/tex]Now that our equation is in slope-intercept form, we can find the equation for the perpendicular line.
The equation of the line that is prependicular to the above line is
[tex]y=-\frac{1}{3/2}x+b[/tex][tex]y=-\frac{2}{3}x+b[/tex]Now, we are told that this line must pass through (0, -6). Therefore, we have to find a value of b such that the above line passes through (0, -6). To find b, we put x = 0 and y = -6 into the above equation to get
[tex]-6=-\frac{2}{3}(0)+b[/tex][tex]-6=b\text{.}[/tex]The value of b is -6.
Therefore, the equation of a line perpendicular to 3x - 2y = 5 line passing through (0, -6) is
[tex]\boxed{y=-\frac{2}{3}x-6.}[/tex]