Need help #3. The answer is shown, but I don’t know how to get to the answer. Please teach and show steps.
Answers
Answer:
A
Step-by-step explanation:
We are given a right triangle with a base of x feet and a height of h feet, where x is constant and h changes with respect to time t.
The angle in radians is defined by:
[tex]\displaystyle \tan(\theta)=\frac{h}{x}[/tex]
And we want to find the relationship that describes dθ/dt and dh/dt.
So, we will differentiate both sides with respect to t where x is a constant:
[tex]\displaystyle \frac{d}{dt}[\tan(\theta)]=\frac{d}{dt}\Big[\frac{h}{x}\Big][/tex]
Differentiate. Apply the chain rule on the left. Again, remember that x is just a constant, so we can move it outside the derivative operator. Therefore:
[tex]\displaystyle \sec^2(\theta)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]
Since we know that tan(θ)=h/x, h is the opposite side of our triangle and x is the adjacent. Therefore, by the Pythagorean Theorem, our hypotenuse will be:
[tex]\text{Hypotenuse}=\sqrt{h^2+x^2}[/tex]
Since secant is the ratio of the hypotenuse to adjacent:
[tex]\displaystyle \sec(\theta)=\frac{\sqrt{h^2+x^2}}{x}[/tex]
So:
[tex]\displaystyle \sec^2(\theta)=\frac{x^2+h^2}{x^2}[/tex]
By substitution, we have:
[tex]\displaystyle \Big(\frac{x^2+h^2}{x^2}\Big)\frac{d\theta}{dt}=\frac{1}{x}\frac{dh}{dt}[/tex]
By multiplying both sides by the reciprocal of the term on the left:
[tex]\displaystyle \frac{d\theta}{dt}=\frac{1}{x}\Big(\frac{x^2}{x^2+h^2}\Big)\frac{dh}{dt}[/tex]
Therefore:
[tex]\displaystyle \frac{d\theta}{dt}=\frac{x}{x^2+h^2}\frac{dh}{dt}[/tex]
Our answer is A.
Related Questions
Use the drawing tool to form the correct answer on the provided graph plot the x-intercept y-intercept and axis of symmetry for the function below g(x) = x2+4x+3
Answers
Answer:
x-intercepts: x =-1, x=-3 when y=0
y-intercept, y=3, when x =0
axis of symmetry x = -2
Step-by-step explanation:
We are given the function: [tex]g(x) = x^2+4x+3[/tex]
We need to draw the graph for
x-intercept y-interceptaxis of symmetryof the given function.
x-interceptFor finding x-intercept put y=0, in the given function, we will put g(x) =0
We know that: g(x)=y
[tex]y=x^2+4x+3[/tex]
Putting y=0, we get:
[tex]0=x^2+4x+3[/tex]
Now, we need to solve the equation by factorization, to find value of x
[tex]0=x^2+4x+3\\We\:can\:write\\x^2+4x+3=0\\x^2+3x+x+3=0\\x(x+3)+1(x+3)=0\\(x+1)(x+3)=0\\x+1=0\:or\:x+3=0\\x=-1\:or\:x=-3[/tex]
So, we get x-intercepts: x =-1, x=-3 when y=0
y-interceptFor, finding y-intercept, put x =0
Putting x=0
[tex]g(x)=x^2+4x+3\\We\:know\:g(x)=y\\y=x^2+4x+3\\y=(0)^2+4(0)+3\\y=3[/tex]
So, we get y-intercept, y=3, when x =0
Axis of symmetryThe formula used to calculate axis of symmetry is: [tex]x = \frac{-b}{2a}[/tex]
We have b=4 and a = 1
Putting values and finding axis of symmetry
[tex]x =-\frac{b}{2a} \\x=-\frac{4}{2(1)}\\x=-2[/tex]
So, we get axis of symmetry x = -2
We will also be requiring vertex of the function:
We can find h = -b/2a (same as axis of symmetry) we get h =-2
k can be found as k=f(h)
Put h=-2 in the function:
g(-2)=(-2)^2+4(-2)+3
g(-2)=4-8+3
g(-2)=-1
So, we get k = -1
The vertex (h,k) is (-2,-1)
Now, the graph is attached in figure below.
Hamda and Layla get paid per project.
Hamda is paid a project fee of AED 25 plus AED 10.50 per hour.
Layla is paid a project fee of AED 18 plus AED 14.25 per hour.
Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.
Show your steps
Answers
Answer:
[tex]Company: 43 + 24.75h[/tex]
Step-by-step explanation:
Given
Hamda:
[tex]Project\ Fee = 25[/tex]
[tex]Hourly\ Rate = 10.50[/tex]
Layla:
[tex]Project\ Fee = 18[/tex]
[tex]Hourly\ Rate = 14.25[/tex]
Required
Derive an expression for total pay
Represent the number of hours with h.
For Hamda and Layla, their pay for h hours is:
[tex]Pay = Project\ Fee + Hourly\ Rate * h[/tex]
For Hamda, we have:
[tex]Hamda : 25 + 10.50 * h[/tex]
[tex]Hamda : 25 + 10.50 h[/tex]
For Layla, we have:
[tex]Layla: 18 + 14.25 * h[/tex]
[tex]Layla: 18 + 14.25 h[/tex]
For h hours, the company will pay:
[tex]Company: Hamda + Layla[/tex]
[tex]Company: 25 + 10.50h + 18 + 14.25h[/tex]
Collect like terms
[tex]Company: 25 + 18 + 10.50h + 14.25h[/tex]
[tex]Company: 43 + 24.75h[/tex]
5/8 - 1/2 =
1/8
2/3
1/2
Answers
5/8 - 1/2 = 1/8
John is putting together Christmas gift bags. If he has 20 Kit Kats and 35 bracelets, what is the greatest number of bags he can make in order to have the equal number of KitKats and bracelets in each bag? Hint: Find the GCF
Answers
Answer:5
Step-by-step explanation: the gcf for both number are 5, 20: 5*4. 35: 5*7
Solve 72 = 3v^2, where v is a real number
Answers
Answer:
v is equal to 6
Step-by-step explanation:
Answer: v=2√6 or v=−2√6
Step-by-step explanation:
A number y has a minimum of -2.5
a.>
b.<
c.≥
d.≤
Answers
Answer:
c.≥
Step-by-step explanation:
Minimum of means the number y can be -2.5 and higher, but it cannot be lower than -2.5.
≥ means more than or equal to.
> means more than only.
< means less than only.
≤ means less than or equal to.
how is the graph of f(x)=-3x^2-4 different from the graph of f(x)=-3x^2 ?
Answers
Answer:
B
Step-by-step explanation:
rules:
add outside the function : f(x) ± a; will shift a + up / a- down
add inside the function: f(x ± a); will shift a + left / a- right
so if
f(x) becomes f(x) -4 will be shifting down 4 units
2% as a decimal plssssssssssss help brainliest!
Answers
i need help plz
State the coordinates of the point.
Answers
Answer:
(-5,8)
Step-by-step explanation:
Hope this helps ;)
Evaluate if a = 2 , b = 3, and c = -4 :
ab +3c-b
Answers
Answer:
Evaluate if a = 2 , b = 3, and c = -4 :
Step-by-step explanation: that the answer
-2v3 + v75
How do I solve this and what would be the answer
Answers are either
3 √3
25 √3
-25 √3
-3 √3
Answers
Answer:
a) [tex]3\sqrt{3}[/tex]
Step-by-step explanation:
Step(i):-
Given - 2 √3 + √75
we know that 25 × 3 = 75
- 2 √3 + √75
= -2 √3 + [tex]\sqrt{25 X 3}[/tex]
By using
[tex]\sqrt{ab} = \sqrt{a} \sqrt{b}[/tex]
= [tex]-2\sqrt{3} + \sqrt{25} X \sqrt{3}[/tex]
= [tex]-2\sqrt{3} + 5 \sqrt{3}[/tex]
= [tex](-2 + 5 ) \sqrt{3}[/tex]
= [tex]3\sqrt{3}[/tex]
i don't really understand, please help!!
Answers
Step-by-step explanation:
the proof is given above
Step-by-step explanation:
In Triangle ICU,
Angle 2 = 180° - Angle 1 (Angles on a straight line)
CR = CU - RU
In Triangle ISR,
Angle 3 = 180° - Angle 4(Angles on a straight line)
SU = RS - RU
Angle 1 = Angle 4
Therefore, Angle 2 is equal to Angle 3
CU = RS
Therefore, CR is equal to SU
Triangle ICR and Triangle ISU
IC = IS
Angle 2 = Angle 3
CR = SU
Therefore, Triangle ICR and Triangle ISU are congruent (SAS congruency).
As the two triangles are congruent, Angle CIR = Angle SIU
An understanding of statistics is necessary in any job. The use of statistics can help provide answers to many questions. Write a question you think that statistics may help you answer and explain why statistics can help provide an accurate answer.
Answers
Answer:
Statistics can help solving data quantitative analysis data.
Step-by-step explanation:
Statistics can help solving data quantitative analysis data.
Examples of questions, that statistics can help provide answers to
What is the measure of central tendency, that is representative of entire statistical data.Ans : It can be found out by calculating mean , median , mode
How widely dispersed or spread off is the dataAns : It can be found out by calculating standard deviation, variance
An example of a question statistics can help you answer is: What is are the socio-economic characteristics of people living in Texas?
Using frequency count and percentage, we can determine the gender, age distribution, occupation and other demographics of the population of people living in Texas.
What is Statistics?Statistics involves the collection, collation, analysis, and interpretation of data to form valid conclusions about problems and give answers to questions raised.We have descriptive and inferential statistics as the two types of statistics.For descriptive statistics, frequency count and percentage can be used to describe the socio-economic characteristics of a population.Therefore:
An example of a question statistics can help you answer is: What is are the socio-economic characteristics of people living in Texas?Using frequency count and percentage, we can determine the gender, age distribution, occupation and other demographics of the population of people living in Texas.Learn more about statistics on:
https://brainly.com/question/12150562
The sum of four times a number and fifteen is forty-seven. Find the number.
Answers
Answer:
8 is the number
Step-by-step explanation:
I don't know why it took me so long to figure it out, 4 x 8 = 32 32 + 15 = 47
It probably took me a really long time because I am tired, and I am not using a calculator.
An airplane makes a 2,748-mile flight in 6 hours. What is the airplane's average rate of speed in miles per hour?
Answers
Answer:
speed=16,480 miles per hour or 16,480/hour.
Step-by-step explanation:
Distance=speed ×time
In ΔVWX, x = 160 cm, v = 150 cm and ∠W=77°. Find the length of w, to the nearest centimeter. PLEASE HURRY
Answers
Answer:
193
Step-by-step explanation:
according to the question
w²=x²+v²-2xv.cos(<w)
w=√160²+150²-2.160.150.cos(77)°
w=√48100-48000cos(77°)
w=193
Answer:
193
Step-by-step explanation:
delta math
so I really need help. you have to set fractions equal to each other and try and find out how many prefer sweaters and whatnot. Also, the answer isn't supposed to be a fraction, it's supposed to be a whole number, you find the answer by using fractions with the information provided in the word problem above ^
I hope that makes sense. lol, thank you :)
Answers
The distance in feet that Karina swims in a race is represented by 5d -5, where d is the distance for eac
What is an expression equivalent to 5d -5?
Choose the correct answer below.
A. 5d - 5 = 5(-5)
B. 5d -5 = -5 + 5d
C. 5d - 5 = 5-5d
D. 5d - 5 = -5(d+5)
Answers
Answer:
C. 5d - 5 = 5-5d
Step-by-step explanation:
Find the value of this expression if x=-9.
Answers
Answer:
if x = -9
then, (-9)×(-9) + 3
= 81 +3
= 84
(-9) + 6
= -3
so, ans is = 84/(-3)
= (-84)/3
Please help ASAP! Will give brainlist
Answers
2x-3x=-12
-x=-12
x=12
A 24-foot by 72-foot rectangular dance floor is completely tiled with 1-foot by 1-foot square tiles. Two opposite corners of the dance floor are connected by a diagonal. This diagonal passes through the interior of exactly how many tiles
Answers
Answer:
do do do do to stop do so at to do do d
The diagram shows a square.
(7x + 3) cm
Find the length of the side of the square.
(5x + 8) cm
Answers
The length of each side of the square is; 20.5cm
Squares and equal sidesSince, all sides of a square have equal lengths;
We can assume that the the sides given are equal so that we have;7x +3 = 5x +8
2x = 8 -3
2x = 5
x = 5/2
x = 2.5
By substituting x into either of the expressions! we have;
7x + 37(2.5) + 3 = 17.5 + 3 = 20.5Read more on squares;
https://brainly.com/question/2279006
Factor.
x^2−8x+16
(x−4)2
(x+8)^2
(x−8)^2
(x+4)^2
Answers
Answer:
A
Step-by-step explanation:
Solve for s.
3 = s - 2
s=
Answers
Answer:
3 = s - 2
s = 3 - 2
s = 1
what was hard lol
7/y = 3x make y the subject
Answers
Answer:
7/y=3x
(3x)y=7
y=7/3x
I will give brainiest to whoever answers correctly !!
Answers
Answer:
it is not clear .... please add the question and send the link of the question
Answer:
$712.79
Step-by-step explanation:
PLZ HELP!!
What quadrant is (0, 4)
A.1
B.2
C.3
D.4
E.x-axis
F.y-axis
Answers
Answer:
F.y-axis
Step-by-step explanation:
y axis is the answer because 0 is starting.
The given point
(0,4)
is on the positive segment of the y-axis.
3+(-4) on a number line iready
Answers
Answer:
it minus one or -1
Step-by-step explanation:
because 4 has more minus than 3 plus
how many hours and minutes are there between 9:30 and 1:50
Answers
Answer:
4 hours and 20 minutes!
Answer:
Step-by-step explanation:
PM or AM?
If it is 9:30 AM to 1:50 PM, it is 4 hours and 20 minutes.
if it is 9:30 PM to 1:50 AM, it is also 4 hours and 20 minutes.
If it is 9:30am to 1:50 AM, it is 16 hours and 20 minutes.
how do you simplify this radical (4x^2y)^1/3 and have no negative exponents?
Answers
Answer:
4^(1/3) x^(2/3) y^(1/3)
Step-by-step explanation:
why would you expect negative exponents? Just pultiply powers