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
so which one is it? a, b, c, or d? I NEED HELP ASAP NO STEP BY STEP NEEDED
THANKS SO MUCH :)
Answers
Answer:
The answer would be B. With equations, what you do to one side you have to do to the other.
Need help asap please!!!
Answers
Answer:15
Step-by-step explanation: 7 and a half times 2 is 15
the answer to that question is 15.
32) Write a compound inequality that represents the given graph:
A. 6≤x 10
D. 6
Answers
Answer:
6 < x ≤ 10
Step-by-step explanation:
The graph given shows that the possible value of x greater 6 (does not include 6 because the circle is not full) and also is less than or equal to 10 (includes 10 because the circle is full).
That is: x > 6 and x ≤ 10
This can be written as: 6 < x ≤ 10
Enter the decimal represented by the shaded square.
Answers
Have a great day :)
Because 32 of the 100 squares are filled we know the fraction is 32/100 and if you long divide you get 0.32
A 5x5 table is filled with numbers (one number per cell). It is known that the product of 5 numbers in each column is negative. Is it possible that the product in each row is positive?
Answers
Answer:
Yes
Step-by-step explanation:
A negative multiplied by another negative will turn into a positive. A positive multipled by a negative will stay as a negative.
The ratio of red to blue counters
in a bag is 1 : 4 The ratio of blue to
green counters is 2:3
If there are 20 red counters how
many green counters are there?
Answers
What is the slope of the line through (2, 10) and (-2, 17)?
Answers
A circle has a diameter of 18
m. Find the area of the sector
whose central angle is 135º
Answers
Answer: i think i would be half of it
Step-by-step explanation:
Are these triangles similar?
Answers
pretty sure its no, the number on the outside arent the same meaning both areas wont add up.
Use the following sets to answer the following:
Y: The set of yellow attribute pieces
H: The set of hexagonal attribute pieces
SY: The set of small yellow attribute pieces
SB: The set of small blue attribute pieces
L: The set of large attribute pieces
1. Which pairs of sets, if any, can be put into one-to-one correspondence?
2. Which pairs of sets, if any, are equal?
3. Which pairs of sets, if any, are disjoint?
4. Which set is a proper subset of another?
5. Which attribute pieces are in Y ∩ L?
6. Which attribute pieces are in Y UL?
Answers
Answer:
i have no clue
Step-by-step explanation:
tbh
halona walks 1.93 kilometers in 23 minutes, assuming constant speed write a proportion that represents how many kilometers in x minutes
Answers
In one online store, 12% of the orders are placed by new customers. Let N be the number of orders
placed in a day to reach the store's first new customer. Assume each order's customer status is
independent
Find the mean and standard deviation of N.
Round your answers to one decimal place.
Mean:
orders
Standard deviation:
orders
Answers
Answer:
Mean= 8.3
Standard deviation=7.8
Step-by-step explanation:
i need help with finding area whats the area of a 11ft an 6ft rectangle
Answers
Hello!
[tex]\large\boxed{A = 66ft^{2}}[/tex]
Formula for the area of a rectangle:
A = b × h where:
b = base
h = height
We are given the base and height as 11 ft and 6 ft, so use the equation above to solve for the area:
A = 11ft × 6ft
A = 66ft²
15-[14/(15-8)+13-14]•
10
Answers
Answer:
5
Step-by-step explanation:
15-(2+13-14)×10 (beacuse 14÷7=2)
15-(15-14)×10
15-1×10
15-10
5 ans
Trignometery: Sin Cos and Tan
Answers
Answer:
766m (3 s.f.)
Step-by-step explanation:
Please see the attached picture for the full solution.
What is the measure of 21?
13
126°
A
54°
B.
440
36°
126°
Answers
Answer:
<1 =126
Step-by-step explanation:
<2 = 126 since they are vertical angles
<1 = <2 since they are alternate interior angles
<1 =126
A committee is to consist of two members. If there are seven people
available to serve on the committee, how many different committees can
be formed
Answers
Answer:
2
Step-by-step explanation:
Common Sense
The number of different ways committees can be formed will be 21.
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
A committee is to consist of two members.
If there are seven people available to serve on the committee.
If two people are selected from the group of seven people.
Then the number of different ways committees can be formed will be
⇒ ⁷C₂
⇒ 7! / [(7 – 2)! x 2!]
⇒ 7! / [5! x 2!]
⇒ 7 x 6 x 5! / [5! x 2 x 1]
⇒ 7 x 6 / 2
⇒ 7 x 3
⇒ 21
Thus, the number of different ways committees can be formed will be 21.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
#SPJ2
What's 10.08 rounded to the nearest one?
Answers
Answer:
10
Step-by-step explanation:
Television screens are usually described by the length of their diagonal measure. What would the diagonal measure be for a television whose dimensions are 54 inches by 28 inches?
A) 61 inches
B) 71 inches
C) 81 inches
D) Unable to determine with given data.
Answers
Answer:
A
Step-by-step explanation:
61 inches
Step-by-step explanation:
61inches is answer.. .. ..
A swimming pool and deck are built in a rectangle with length 40 ft and width 18 ft. If the pool itself is
320 square feet, what is the area of the deck itself?
A. 320 square feet
B. 400 square feet
C. 480 square feet
D. 560 square feet
Answers
Explanation:
40 x 18 = 720
720 - 320 = 400
How do I write this expression in fewer terms?
9m + k - (3m-2k)
Answers
since a negative x positive is a negative, and a negative x negative is a positive, we get
9m + k - 3m + 2k
let's simplify
9m - 3m + 2k + k
ANSWER
6m + 3k
Replace the values of A, b, x, and y to write an exponential equation that represents the number of cells present at h hours.
Answers
Answer:
100(2)^h =6,400
Step-by-step explanation:
For an equation in the form A(b)^x=y , A represents the initial amount, and b represents the growth rate. At 0 hours, there were 100 cells, so A=100 .
Between 0 hours and 1 hour, the number of cells doubled from 100 to 200, or 100(2). Between 1 and 2 hours, the number of cells again doubled from 200 to 400, or 100(2)^2 . So the growth rate, or b, is 2.
The table shows that at h hours, there were 6,400 cells. Therefore, the equation that represents the number of cells at h hours is 100(2)^h =6,400.
what is 117 ÷12 equal
Answers
Answer:
9.75
Step-by-step explanation:
Easy math (17 points))
Answers
Answer:
A-8.25 B-43.2 C-248.5
Step-by-step explanation:
Answer:
A-8.25
B-43.2
C-248.5
Step-by-step explanation:
Evaluate -2 - 6y when x=5 and y =-3
Answers
Answer:
-10-6.(-3)
-10+18
=8
Step-by-step explanation:
Please find x....................
Answers
Answer:
x = 14.1
Step-by-step explanation:
Reference angle = 62°
Side opposite to reference angle = x
Hypotenuse = 16
Applying trigonometric ratio, thus:
Sin 62 = x/16
Multiply both sides by 16
16*sin 62 = x
14.1271615 = x
x = 14.1 (nearest tenth)
Rational numbers are fractions or their opposites. is a rational number. Show this by writing it in the form , where a and b are integers.
plz help
Answers
Answer:
Explained below
Step-by-step explanation:
A rational number is one that can be expressed in form a of a fraction whereby both the numerator and the denominator are integers.
Also, if it results in a recurring decimal it is still a rational number but if the decimal is not recurring, then it is not a rational number.
Now, for example let's consider the number 5.
It is a rational number because it can be expressed as; 5/1; 10/2; 20/4; -5/-1 e.t.c
Now, the opposite of these fractions like we are told to check in the question results in;
1/5; 2/10; 4/20; -1/-5;
The opposite will give us still a rational number because both numerator and denominator are still integers and also the value of the division is 0.2 which is a definite decimal and also can be expressed as an integer.
use a number line to show the following operations (a) -5+7-2 (b) -4×3 (c) 3.5+4.5
Answers
Hey there!
• A.
–5 + 7 – 2 = ?
–5 + 7 = 2
2 – 2 = 0
Answer: 0 ☑️
• B.
–4 * 3 = ?
“Guide”
• Negative & Negative = Positive
• Positive & Positive = Positive
• Negative & Positive = Negative
• Positive & Negative = Negative
• So, in this particular equation your answer will most likely have a NEGATIVE result because you have a NEGATIVE number & a POSITIVE number!
–4 * 3 = –12
Answer: –12 ☑️
• C.
3.5 + 4.5 = ?
5 + 5 = 10
• CARRY your 1
3 + 4 + 1 = ?
3 + 4 = 7
7 + 1 = ?
Answer: 8 ☑️
You basically had to do ORDER OF OPERATIONS / PEMDAS
(Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction)
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
I will give brainiest to whoever answers correctly !!
Answers
Answer:
14.0
Step-by-step explanation:
14.096 rounded to the nearest tenth
Sharif stared a new job working 15 hours a week after how many weeks will he have worked a total of 75 hours ?
Answers
Answer: 5 weeks
Step-by-step explanation: Please give me brainliest
