Answer:
13,101,108
as in Thirteen million ,hundred and one thousand, one hundred and eight
For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 20 ft/sec, starting at time t = 0, where t is time in seconds. Let θ be the angle between the line of your horizon and your line of sight to the elevator. 4 (a) Find a formula for h(t), the elevator's height above the ground as it descends from the top of the hotel. h(t) = (b) Using your answer to part (a), express θ as a function of time t. θ(t) = Find the rate of change of θ with respect to t. dθ dt = (c) The rate of change of θ is a measure of how fast the elevator appears to you to be moving. At what time does the elevator appear to be moving fastest? time = seconds At what height does the elevator appear to be moving fastest?
9514 1404 393
Answer:
a. h(t) = -20t +400
b. θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)
c. 15 seconds; 100 ft
Step-by-step explanation:
a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...
h(t) = -20t +400
__
b. The tangent of the angle above the line of sight is "opposite"/"adjacent":
tan(θ) = (h(t) -100)/(150) = -2/15t +2
θ(t) = arctan(2 -2/15t) . . . . radians
The derivative of the angle function is ...
dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)
dθ/dt = -30/(1125 -120t +4t^2)
__
c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)
The elevator appears to be moving fastest at t=15 seconds.
The height at that time is ...
h(15) = 400 -20(15) = 100
The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.
Find a polynomial f (x) of degree 4 that has the following zeros.
6 (multiplicity 2), –1, 0
Leave your answer in factored form.
Step-by-step explanation:
The polynomial with given zero's is:
f(x) = a(x - 6)(x - 6)(x - (-1))(x - 0)Or simplified:
f(x) = ax(x + 1)(x - 6)², here a is the coefficient we don't knowDraw a square and its diaginals
Answer:
you cant draw......................
Step-by-step explanation:
What is the key difference between simple interest and compound interest, and how does this difference affect the
effectiveness of each?
Answer:
the answer is
Step-by-step explanation:
The simple interest is calculated only on the principal amount of a loan so it is relatively easier to calculate than the compound interest. The compound interest is calculated on the principle amount plus the interest that the amount gets per compounding period up to the period of the loan.
If the principal is $3,200.00 and the rate of interest is 8%, what is the final account balance after 3 years
Answer:
i think it would round to 4031.08
Step-by-step explanation:
3200.00 * 1.08^3
=4032.0784
Need help with thissss!!
Answer:
f(5) = 38
Step-by-step explanation:
f(a) = 7(a + 1) - 4
f(5) = 7(5 + 1) - 4
f(5) = 7(6) - 4
f(5) = 42 - 4
f(5) = 38
1. Two linear functions are shown below. Which function has the greater rate of change? Function A Function B 10 у y 4 32 8 8 6 44 12 4 56 2 16 68 Х 0 20 80 0 2 4 6
Answer:
I don't understand clear ur question
Find the missing length of each triangle and round to the nearest tenth.
Answer: 5 inches
Step-by-step explanation: We must use the Pythagorean theorem to solve this. Since the hypotenuse is always opposite of the right angle, we know that the hypotenuse is 13 and we can substitute the values into this formula: a^2 + b^2 = c^2
12^2 + b^2 = 13^2
144 + b^2 = 169
169 - 144 = 25 (this is b^2)
[tex]\sqrt{25}[/tex] = 5
Thus, the value of x is 5 inches.
Would appreciate brainliest <3
What is the answer to, one half of 9?
A rectangular field is ten times as long as it is wide. If the perimeter of the field is 1100 feet, what are the dimensions of the field?
Answer:
Length = 500, Width = 50
Step-by-step explanation:
EQUATION:
2(10x) + 2x = 1100
20x + 2x = 1100
22x = 1100
x=50
Find the slope of the line that goes through the points (4,-3) and (5,0)
Answer:
the slope of the points (4,-3) and (5,0) is 3
Step-by-step explanation: I used the formula y2-y1 over x2-x1 will give you the answer hope this helped!
Answer:
[tex]\boxed {\boxed {\sf m=3}}[/tex]
Step-by-step explanation:
We are asked to find the slope of the line that passes through (4, -3) and (5,0).
The slope is the number that tells us the steepness and direction of a line. It is the rise over run, or the change in y over the change in x.
[tex]m= \frac{ \Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}[/tex]
In the slope formula, (x₁, y₁) and (x₂, y₂) are the points the line passes through. The points we are given are (4, -3) and (5,0). If we match the value with its corresponding value, we see that:
x₁ = 4 y₁ = -3x₂ = 5 y₂ = 0Substitute the values into the formula.
[tex]m= \frac{0 - -3}{5-4}[/tex]
Solve the numerator. Remember that 2 back to back subtraction signs become an addition sign.
0--3 = 0+3=3[tex]m= \frac{3}{5-4}[/tex]
Solve the denominator.
5-4 =1[tex]m= \frac{3}{1}[/tex]
Divide.
[tex]m=3[/tex]
The slope of the line is 3.
There are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen
Answer:
45
Step-by-step explanation:
This is a combination question: how many ways can you pick 2 people from a group of 10?
Using the notation C(10, 2) for the number of combinations of 10 things chosen 2 at a time...
[tex]C(10, 2)=\frac{10!}{2!(10-2)!}=\frac{10!}{2!\cdot 8!}=\frac{10\cdot 9}{2\cdot 1}=45[/tex]
It is 9 kilometers from Charlie's house to the nearest mailbox. How far is it in meters?
Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
9,000 meters
What’s the answer need in 20 minutes
Clayton Burrington purchased the following school supplies on s
$2.79 notebook for $1.99, a $1.49 ballpoint pen for $0.99, a $1.99 p
notebook paper for $0.99, and a $3.49 automatic pencil for $2.79.
Clayton estimated the total savings to be $7.00. (a) Is the answer
reasonable? (b) If not, what error was made?
Answer:
The answer is not reasonable.
The error that Clayton made was that he accidentally added all of the products that had a saved price tag on it, he did not find the difference between the old price and the new, sales price.
Step-by-step explanation:
Hope this helps :) Mark me brainliest if anyone else answers this question.
Find the values of x, y, and z angle measurements
Someone, please help me with this. I will give Brainliest
Explanation:
What we need to do here is to take the ratio of the distances of the planets to determine how much farther Neptune is from the sun compared to Mercury:
[tex]\dfrac{D_N}{D_M} = \dfrac{4.503×10^9\:\text{km}}{5.791×10^7\:\text{km}} = 7.776×10^1[/tex]
This means that Neptune is 77.76 times farther from the sun than Mercury is.
During a snowstorm, Noah tracked the amount of snow on the ground. When the
storm began, there was 1 inch of snow on the ground. For the first 4 hours of the
storm, snow fell at a constant rate of 3 inches per hour. The storm then stopped for 2
hours and then started again at a constant rate of 2 inches per hour for the next 6
hours. Make a graph showing the inches of snow on the ground over time using the data that Noah created
data that Noah collected.
Click twice to plot a segment.
Click a segment to delete it.
25
24
23
22
ow on the Ground (Inches)
20
19
18
17
16
15
14
13
12
9
Answer:
ss the question
Step-by-step explanation:
A game designer is creating a computer animation of a rectangle with sides that vary in size. The length of the rectangle in centimeters after t seconds is given by the expression 2t-9, while the width is given by the expression 1 + t. After how many seconds is the rectangle a square?
Answer:
Step-by-step explanation:
Squares have equal length and widths
2t - 9 = 1 + t
2t - t - 9 + 9 = 1 + 9 + t - t
t = 10 s
Which of the functions below have period pie check all that apply
3.
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms.
f(x) = 6x2 + x − 12
A. quadratic function; quadratic term: 6x2; linear term: x; constant term: −12
B. linear function; linear term: 6x2; constant term: −12
C. quadratic function; quadratic term: −12x2; linear term: −6x; constant term: −12
D. linear function; linear term: x; constant term: −12
Answer:
A. quadratic function; quadratic term: 6x2; linear term: x; constant term: −12
Step-by-step explanation:
We have been given the equation
The degree of the given polynomial is 2.
Hence, the function is quadratic.
The term with exponent 2 on x is called the quadratic term. The term with exponent 1 on x is called linear and the term without any variable is a constant term.
Therefore, we have
Quadratic term= 6x^2
Linear term= x
Constant term= -12
9514 1404 393
Answer:
A. quadratic function; quadratic term: 6x²; linear term: x; constant term: −12
Step-by-step explanation:
The squared term (6x^2) is also called the "quadratic" term. The term with x to the first power (no exponent) is the "linear" term. The term with no variable at all is the "constant" term.
It should be no mystery that the quadratic term is 6x^2; the linear term is x; and the constant term is -12.
_____
Additional comment
As with much of algebra, this is about vocabulary and pattern recognition.
Which equation has no solution?
A)
2x=5
B)
X + 12 = 3x - 2
C)
3x + 4 = 3x + 3
D)
- 2x + 5 = -2x + 5
If you subtract 3x from both sides of that equation, you'll go from
3x+4 = 3x+3
to
4 = 3
which is a false statement. No matter what you plug in for x, the original equation is always false as well. This is why it has no solutions.
Which is the slope of the line that passes through the points (2,10) and (5,8)?
Answer:
Slope = (Y2 - Y1) / (X2 -X1)
Slope = (8 -10) / (5 -2)
Slope = -2 / 3
Which of the following statements about resale price maintenance is correct? Resale price maintenance _______.
A. is considered by some economists to be efficient and by other economists to be inefficient
B. is also called horizontal price fixing
C. is legal under the Sherman Act
D. occurs when a manufacturer prints the price of its good directly on the packaging
Answer:
A. is considered by some economists to be efficient and by other economists to be inefficient
Step-by-step explanation:
In fast will give brainly
= 1 × ⅔ × 5/3
= ⅔ × 5/3
= 10/9
= 1 1/9 ft³ (D.)
A shadow 12 meters long is cast by a water tower that is 16 meters tall. What is the length of the shadow cast by a nearby utility pole that that is 12 meters tall?
A. 6
B. 9
C. 13
D.16
perdón xbdkdbsjjznsNxnznxn
Find the product of 4v22 and 4v4 in simplest form. Also, determine whether the result is rational or irrational and explain your answer. Result: V The result is because it integers and its decimal expansion be written as the ratio of two terminate or repeat.
Answer:
32[tex]\sqrt{22}[/tex]
irrational
cannot be written as a ratio
does not repeat or terminate
Step-by-step explanation:
[tex]\sqrt{4}[/tex] = 2
4[tex]\sqrt{22}[/tex] · 4(2) = 4[tex]\sqrt{22}[/tex] · 8 = 32[tex]\sqrt{22}[/tex]
Will someone PLEASSSSSSEEEEEEEE help me
Answer:
C
Step-by-step explanation:
i did the math she needs to wake up at 8:00
Frank had 42 rocks that he wanted to share with his friends. If he gave each friend the same number of rocks(and kept the same number of rocks for himself), how many rocks did each person get ?
Answer:6. 42 split 7 ways is 6
Step-by-step explanation:
Which equations are true? Select all that apply.
A.
66
÷
10
1
=
6
.
6
B.
660
÷
10
0
=
66
C.
6
,
600
÷
1
,
000
=
0
.
66
D.
0
.
66
÷
10
1
=
0
.
066
E.
6
÷
100
=
0
.
06
Answer:
a b d e
Step-by-step explanation:
i just took the test and got a hundred
Equations A, B, and E are true, i.e 66: 10 = 6.6, 660: 10° = 66, 6: 100 = 0.06.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Make sure your equation is correct by comparing the values on either side of the equals sign to create a true equation. A true equation must have the same numerical values on both sides of the "=" sign. One real equation is, for instance, 9 = 9. A valid equation is 5 + 4 = 9.
As a result, the true equations are,
66: 10 = 6.6
660: 10° = 66
6: 100 = 0.06
Thus, equations A, B, and E are true, i.e 66: 10 = 6.6, 660: 10° = 66, 6: 100 = 0.06.
Learn more about the equation here,
https://brainly.com/question/10413253
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