An observer stands 400 ft away from a launch pad to observe a rocket launch. The rocket blasts off and maintains a velocity of 300 ft/sec. Assume the scenario can be modeled as a right triangle. How fast is the observer to rocket distance changing when the rocket is 300 ft from the ground?
Answers
Let's draw the scenario to understand it better:
From the figure, the information given are:
[tex]\frac{dy}{d\text{t}}=\text{ 300 ft./sec}[/tex]Question:
[tex]\text{What is }\frac{dD}{dt}\text{ at y = }300\text{ ft.}[/tex]Step 1: We write a function that relates the quantities in the diagram using Pythagorean
Theorem.
[tex]\text{ 400}^2\text{ + }y^2=D^2[/tex]Step 2: Differentiate with respect to t.
[tex]2y\frac{dy}{dt}=\text{ }2D\frac{dD}{dt}[/tex]Now we wish to plug in specific numbers for every quantity in the above equation except for dD/dt. However, we notice that we don’t have a specific value for D at y = 400 ft. So first we need to find D at y = 400 ft. using the Pythagorean Theorem.
[tex]400^2\text{ + }300^2=D^2[/tex][tex]D\text{ = }\sqrt[]{400^2+300^2}[/tex][tex]D\text{ = 500 ft.}[/tex]Step 3: Finish the problem by plugging in numbers for every quantity in the equation
containing dD/dt.
[tex]2(300)(300)\text{ = 2(500)}(\frac{dD}{dt})[/tex][tex]\frac{dD}{dt}=\text{ }\frac{2(300)(300)}{2(500)}[/tex][tex]\frac{dD}{dt}=\text{ }\frac{180,000}{1000}[/tex][tex]\frac{dD}{dt}=180[/tex]Conclusion: When the rocket is 300 ft. feet from the ground, the distance between the observer and the rocket is increasing at a rate of 180 ft./sec.
Related Questions
what is the answer to number 9 and how do i solve?
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Given:
[tex]T=\frac{1}{r}\frac{N_{\infty}-N_0}{N_0}[/tex]From question (1)
[tex]r=2[/tex]and given:
[tex]\begin{gathered} N_{\infty}=3.3 \\ N_0=10 \end{gathered}[/tex]we will find the daily cases beak as follows:
[tex]undefined[/tex]A school sells adult tickets and student tickets for a play. It collects $1,400 in total The graph shows the possible combinations of the number of adult tickets sold and the number of student tickets sold. What does the vertical intercept (0.200) tell us in this situation? O (1 Point) It tells us the decrease in the sale of adult tickets for each student ticket sold It tells us that if no adult tickets were sold, then 200 student tickets were sold It tells us that is no students tickets were sold, then 200 adult tickets were sold It tells us the decrease in the sale of student tickets for each adult ticket sold.
Answers
In the graph, the horizontal axis represents the number of adult tickets sold
And the vertical axis represents the corresponding number of student tickets sold.
The vertical intercept, as we are indicated is at (0,200)
That point is at 0 in the horizontal axis and at 200 on the vertical axis, comparing with what each axis represents:
(0,200) represents that when 0 adult tickets are sold, 200 student tickets are sold.
Answer:
it tells us that if no adult tickets were sold, 200 student tickets were sold
I know to solve its y over x (y/x) but it comes out to 0.25 and that’s not one of the answer choices? And I think it might me B. but I’m not sure? Also please provide an explanation
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since the statement gives values of y and x, find the value of k
[tex]\begin{gathered} k=\frac{y}{x} \\ k=\frac{1.5}{6} \\ k=0.25=\frac{1}{4} \\ \text{the function is } \\ y=\frac{1}{4}x \end{gathered}[/tex]Can you pls help me with this question thank you
Answers
1) In this problem, we need to make use of the order of operations.
2) Notice that we have divisions, so let's prioritize the division inside the parentheses, we can also rewrite another one, like this:
[tex]\begin{gathered} 10\div(-6--6\div6) \\ 10\div(-6-(-6)\div6) \\ 10\div(-6-(-1)) \\ 10\div(-6+1) \\ 10\div(-5) \\ -2 \end{gathered}[/tex]Notice that minus outside the parentheses work like a product (-1) x
2) Thus the answer is -2
emeline can type at a constant rate of 1/4 pages/minute.c emeline has to type a 7 page article. How much time will it take her?
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Step 1. Since Emeline can type at a constant rate of 1/4 pages per minute, she will write 1 page in
[tex]\frac{1}{4}\text{pages in 1minute }\longrightarrow\frac{1}{4}\cdot4=1page\text{ in }1\cdot4=4\text{ minutes}[/tex]She writes 1 page in 4 minutes.
Step 2. Now that we know how much it takes Emeline to write one page, we multiply that by the number of pages that she has to write for the article:
[tex]4\text{ minutes }\cdot7=28\text{ minutes}[/tex]It will take her 28 minutes.
Answer: 28 minutes
Homework: 6.3 HWQuestion 8, 6.3.17ОРAn employee makes $14.41 per hour but is getting a 4% increase. What is his new wage per hour to the nearest cent?His new wage per hour is $(Type an integer or decimal rounded to two decimal places as needed.)
Answers
The employee's original wage is $14.41 per hour.
If the wage increases by 4%, the percentage increase will be:
[tex]\Rightarrow\frac{4}{100}\times14.41=0.58[/tex]Therefore, the new wage per hour will be:
[tex]\Rightarrow14.41+0.58=14.99[/tex]The new wage is $14.99.
A landscaper's truck is filled with ton of gravel.The gravel is shared equally among 3 projects.3. Write and solve a division equation to find how muchgravel each project will get. Explain your reasoning.
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Step 1
Let n represent the weight of tons of gravel.
Step 2
The gravel is shared equally among the 3 projects.
Step 3
Write the division equation
Each project will get
[tex]=\text{ }\frac{n}{3}\text{ tons of gravel}[/tex]which statement best describes the association between the energy and light output of these light bulbs?
Answers
As we can see from the graph, we can see that we could have two populations of lightbulbs in the graph. If we draw or try to approximate a line to these two different populations of lightbulbs, we end up with the next graph:
Then, we can conclude that, for most cases, as the energy increases, the light output increases too. Of course, there are some exceptions like the point (18, 800), but the tendency is in this way.
Therefore, the statement that best describes the association between the energy and light output is statement F: As the energy increases, the light output increases.
brainliest if you can answer this math question
Answers
y=-5x+8
EXPLANATION:
slope is -5
y intercept is 8
Angles A and B are supplementary. If m∠A=67°, find m∠B.
Answers
Two Angles are Supplementary when they add up to 180 degrees, in this case we have:
[tex]67^o+m\angle B=180^o[/tex][tex]m\angle B=180^o-67^o[/tex][tex]m\angle B=113^o[/tex]Solve 3 x − 5 = 2 − 6 x for x
Answers
Answer:
[tex]\boxed{\sf \boxed{\sf x=\frac{1}{3}}\; or\;\boxed{\sf x=0.333...}}[/tex]
Step-by-step explanation:
[tex]\sf 3x-5=2-6[/tex]
Subtract numbers:-
[tex]\sf 2-6=\bf -4[/tex]
[tex]\sf 3x-5=-4[/tex]
Add 5 to both sides:-
[tex]\sf 3x-5+5=-4+5[/tex]
Simplify:-
[tex]\sf 3x=1[/tex]
Divide both sides by 3:-
[tex]\sf \cfrac{3x}{3}=\cfrac{1}{3}[/tex]
Simplify:-
[tex]\sf x=\cfrac{1}{3}[/tex]
__________________
Hope this helps!
Have a great day! :)
Answer:
x = 7/9
Step-by-step explanation:
Given equation,
→ 3x - 5 = 2 - 6x
Now the value of x will be,
→ 3x - 5 = 2 - 6x
→ 3x + 6x = 2 + 5
→ 9x = 7
→ [ x = 7/9 ]
Hence, value of x is 7/9.
write out the steps for graphing a piecewise function with 3 equations and sketch a graph
Answers
Given the piecewise function below:
[tex]h(x)=\begin{cases}2x,x\le-2 \\ x^2-1,-2For the first equation: h(x)=2x[tex]\begin{gathered} At\text{ }x=-4,h(-4)=2(-4)=-8\implies(-4,-8) \\ At\text{ }x=-2,h(-2)=2(-2)=-4\implies(-2,-4) \end{gathered}[/tex]Join the point
50 points!
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer: x = 1
Step-by-step explanation:
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of drawing a queen ? Question content area bottomPart 1The probability of drawing a queen is enter your response here .(Type an integer or a simplified fraction.)
Answers
Given:
Total number of cards = 52
Number of cards drawn = 1
Then:
Number of ways of drawing a card from 52 cards
[tex]\begin{gathered} =^{52}C_1 \\ =52 \end{gathered}[/tex]Number of queens in a deck of cards = 4
Number of ways that one card is a queen
[tex]\begin{gathered} =^4C_1 \\ =4 \end{gathered}[/tex]Probability of drawing a queen
[tex]\begin{gathered} =\frac{\text{ Number of favorable cases}}{\text{ Total number of cases}} \\ =\frac{4}{52} \\ =\frac{1}{13} \end{gathered}[/tex]Final answer: 1/13
Really need help with 11 and 12 just started learning this today and I don't quite understand it would really appreciate it
Answers
11.
Given:
[tex]y=x^2[/tex]Differentiate with respect to x, we get
[tex]\frac{dy}{dx}=2x[/tex]The given point is (3,9)
Substitute x=3 in the derivative, we get
[tex]\frac{dy}{dx}=2\times\times3=6[/tex]Hence the slope is 3.
12.
Given:
[tex]y=x^2+4[/tex]Differentiate with respect to x, we get
[tex]\frac{dy}{dx}=2x+0[/tex]The given point is (0,4)
Substitute x=0 in the derivative, we get
[tex]\frac{dy}{dx}=2(0)+0=0[/tex]Hence the slope is 0.
which of these is an example of a proportional relationship
Answers
A proportional relationship is essentially a function where the output is a direct product of the input and the coefficient. Any relationship that has another constant term is not a proportional relationship because the final product is offset by the constant term.
The final answer where Samuel earns $20 for each lawn he mows can be expressed as 20x. This is a proportional relationship because the total money he earns is a product of the rate and x-value.
Which of the following phrases represents n ÷ 5?the sum of five and a numbera number decreased by fivethe quotient of a number and fivefive divided by a number
Answers
Answer:
The quotient of a number and five
Explanation:
Given:
[tex]n\div5[/tex]To find:
The phrase that represents the above expression
The below phrase represents the given expression;
The quotient of a number and five
The Senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High school A Rented and Filled 6 vans and 7 buses with 471 students. High School B rented and Filled 5 vans and 9 buses with 573 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many Students can a bus carry?
Answers
Answer: A van can carry 12 students
A bus can carry 57 students
Explanation:
Let x represent the number of students that a van can carry
Let y represent the number of students that a bus can carry.
The senior class at High school A Rented and Filled 6 vans and 7 buses. This means that
the number of senior class students that the van carried is 6 * x = 6x
the number of senior class students that the bus carried is 7 * y = 7y
If both vehicles were filled with 471 students, it means that
6x + 7y = 471 equation 1
High School B rented and Filled 5 vans and 9 buses. This means that
the number of High School B students that the van carried is 5 * x = 5x
the number of High School B students that the bus carried is 9 * y = 9y
If both vehicles were filled with 573 students, it means that
5x + 9y = 573 equation 2
We would solve both equations by applying the method of elimination. To eliminate x, we would multiply equation 1 by 5 and equation 2 by 6. The new equations are
30x + 35y = 2355 equation 3
30x + 54y = 3438 equation 4
Subtracting equation 3 from equation 4, we have
30x - 30x + 54y - 35y = 3438 - 2355
19y = 1083
y = 1083/19
y = 57
Substituting y = 57 into x equation 1, we have
6x + 7 * 57 = 471
6x + 399 = 471
6x = 471 - 399 = 72
x = 72/6
x = 12
Thus,
A van can carry 12 students
A bus can carry 57 students
Find the value of x. Round your answer to the nearest tenth. The value of x is about .....
Answers
We are asked to find the length of one of the legs of the given right angle triangle by using the measure of the other leg, and the measure of the angle adjacent to the unknown leg "x"
Then, we use the trigonometric ratio which involves the tangent function:
tangent(angle) = opposite side/adjacent side
[tex]\tan (68)=\frac{24}{x}[/tex]We can solve for the unknown by first multiplying by "x" both sides, and then isolating the unknown as shown below:
[tex]\begin{gathered} \tan (68)=\frac{24}{x} \\ x\cdot\tan (68)=24 \\ x=\frac{24}{\tan (68)} \\ x\approx9.6966 \end{gathered}[/tex]Since the image is chopped, could you tell me what they say about the rounding they want? Round the answer to what?
If they want you to round the answer to one decimal (the nearest tenth) then we do:
x = 9.7
if they want us to round it to the nearest whole number, we give:
x = 10
p+3w=-79-5p+w=-5Solve the system using the elimination method if there is no solution put no solution if there is infinite solutions put infinite
Answers
p+3w=-79
-5p+w=-5
Multiply the second equation by 3 and then subtract the second equation:
p + 3w = -79
-
-15p + 3w = -15
_____________
16p = -64
p= -64/16
p= -4
Replace p on any equation and solve for w
-4 + 3w = -79
3w = -79 + 4
3w = -75
w= -75/3
w= -25
Solution:
p= -4
w= -25
Help me please, the one selected is the correct graph
Answers
SOLUTION
The table of values is shown below
So the missing values for y are 8 and then 6
The option for the graph is the 3rd graph, the one you selected
g(n)= -2n-4f(n)= 2n+1find (g-f) (2)
Answers
Now
[tex](g-f)(2)=g(2)-f(2)=-8-5\Rightarrow(g-f)(2)=-13[/tex]What is 3y + 5x = -15 written in slope-intercept form?O y- &x+5O y--gx-5o y- x-5O y--3x+5
Answers
The slope-intercept form of a linear equation is:
[tex]\begin{gathered} y\text{ = mx + c} \\ \text{where m is the slope} \\ \text{and c is the intercept} \end{gathered}[/tex]Given:
[tex]3y\text{ + 5x = -15}[/tex]Solution
By re-arranging the given expression, we have:
[tex]\begin{gathered} \text{Dividing through by the coefficient of y} \\ \frac{3y}{3}\text{ + }\frac{5x}{3}\text{ = }\frac{-15}{3} \\ y\text{ + }\frac{5}{3}x\text{ = -5} \\ y\text{ = -}\frac{5}{3}x\text{ - 5} \end{gathered}[/tex]Determine if the conclusion follows logically from the premises.Premise: If you have a maple tree, then you have to rake leaves in autumnPremise: Jon has to rake leaves in autumnConclusion: Jon has a maple treeValid argumentInvalid argument
Answers
The conclusion is an invalid argument.
Because if you have any tree you have to rake leaves in autumn. THen Jon could possibly have any tree.
Thus the argument is invalid
for the arithmetic sequence 42, 32, 22, 12... find the 18th term.
Answers
Answer:
The18th term of the given sequence is -128
Explanation:
To find the 18th term of the sequence:
42, 32, 22, 12, ..., we need to find the nth term of the sequence first.
The nth term of a sequence is given be the formula:
[tex]T_n=a+(n-1)d[/tex]Where a is the first term, and d is the common difference.
Here, a = 42, d = 32 - 42 = -10
[tex]\begin{gathered} T_n=42+(n-1)(-10) \\ =42-10n+10 \\ T_n=52-10n \end{gathered}[/tex]To find the 18th terem, substitute n = 18 into the nth term
[tex]\begin{gathered} T_{18}=52-10(18) \\ =52-180 \\ =-128 \end{gathered}[/tex]Write a ratio and a percent for the shaded area. A 3/10, 27% B. 1/2, 50% c. 1/3, 33.33% D. 3/10,30%
Answers
The total number of squares is 6x6 = 36
the number of squares of the shaded area is 3x4 = 12
RatioWe find the ratio by dividing those two quantities:
[tex]\frac{12}{36}=\frac{1}{3}[/tex]PercentageWe find the percentage by multiplying the result by 100%
[tex]\frac{1}{3}\times100=0.333\times100=33.33[/tex]Answer: C. 1/3 = 33.33%hueueueirt87ueueuueueuhe
Answers
let the number be represented by x
so, if 1 is added to the number
the result would be 5 more than (5 plus) 4 times the number
let's write out an equation for this
[tex]1+x=4x+5[/tex]the equation above is a mathematical translation of the statement
step one
collect like terms
[tex]\begin{gathered} 1+x=4x+5 \\ 1-5=4x-x \\ -4=3x \end{gathered}[/tex]step two
divide both sides by the coeffiecient of x
[tex]\begin{gathered} 3x=-4 \\ \frac{3x}{3}=-\frac{4}{3} \\ x=-\frac{4}{3} \end{gathered}[/tex]from the calculation above, the unknown number is -4/3
Write the equation of the horizontal line that goes through the point (9, 6).
Answers
Given the point:
(x, y) ==. (9, 6)
Let's write the equation of the horizontal line that goes through the given point.
On a horizonal line, every point on the line has the same value of y.
The slope of a horizontal line is 0.
Since every point on a horizontal line has the same value of y, to find the equation of a horizontal line, we are to use the y-coordinate of the point to find the equation of the horizontal line.
We have:
y-coordinate of the point = 6
Hence, the equation of the horizontal line that goes through the point is:
y = 6
ANSWER:
y = 6
i need the number that goes in the little boxes
Answers
Yes 6 is the solution of the equation because replacing x with 6 and simplifying on the left side results in - 2, which equals the right side.
What is the basic equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. An equation is an algebraic statement that demonstrates two mathematical expressions are equivalent in algebra, and this is how it is most usually used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." When two expressions are joined by an equal sign, a mathematical statement is called an equation.
The given equation is x - 9 = - 3.
The given solution to the equation is 6.
Put 6 in place of x in the equation
6 - 9 = - 3
- 3 = - 3
So, the left-hand side of the equation is equal to the right-hand side. So, 6 is the solution to the equation x - 9 = - 3..
To know more about the basic equations, visit:
brainly.com/question/15184412
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danielle read 5/6 hour each day for 5 days. Select all the expressions that tell how long Danielle read in all. Use drawings or number lines as needed.
Answers
Given data
Danielle read 5/6 hour each day.
For 5 days,
Danielle read = 5 x 5/6 First correct expression
Danielle read = 25/6 Second correct expression
[tex]\text{Danielle read = 4}\frac{1}{6}\text{ Third correct expression}[/tex][tex]\begin{gathered} F\text{ inal answer} \\ 5\text{ }\times\text{ }\frac{5}{6} \\ \frac{25}{6} \\ 4\frac{1}{6} \end{gathered}[/tex]