an airplane that is flying at an altitude of 30 000 ft is beginning to descend at a rate of 1000 feet per minute. a helicopter is beginning its trip, starting at an altitude of zero feet. the helicopter ascends more slowly than the airplane, going up at a rate of 500 feet per minute. after how many minutes will the airplane and the helicopter be at the same altitude

Answers

Answer 1

Using linear functions, it is found that the airplane and the helicopter will be at the same altitude after 20 minutes.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The functions that gives the height of the airplane and the helicopter, after t minutes, is given by:

A(t) = 30000 - 1000t.H(t) = 500t.

They will be equal when:

A(t) = H(t).

Hence:

30000 - 1000t = 500t

1500t = 30000

t = 30000/1500

t = 20 minutes.

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Related Questions

An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to
following claims must be true based on this information?
Note: More than one statement could be true. If none of the statements is true, mark the appropriate box.
Last year at least one of their clients made a profit of
exactly 10%.
Two years ago some of their clients made a profit of at least
10%.
Last year some of their clients made a profit of
0
10% or more.
O
O Last year all of their clients made a profit of more than 2%.
Last year, the number of their clients who made a profit of
10% or less was equal to the number of their clients who
made a profit of 10% or more.

Answers

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The statements that are true based on the information are:

1. Last year at least one of their clients made a profit of exactly 10%.

3. Last year some of their clients made a profit of 10% or more.

Options 1 and 3 are the correct answer.

We have,

1. Last year at least one of their clients made a profit of exactly 10%.

- True.

The investment company advertised that, on average, their clients made a profit of 10%.

This means there must be some clients who made exactly 10% profit.

2. Two years ago some of their clients made a profit of at least 10%.

Not enough information is given to determine the accuracy of this statement.

The information provided only refers to last year's profits, not profits from two years ago.

3. Last year some of their clients made a profit of 10% or more.

- True.

The average profit of the clients was 10%, indicating that some clients made a profit of 10% or more.

4. Last year all of their clients made a profit of more than 2%.

- Not necessarily true.

The average profit was 10%, but this does not guarantee that all clients made a profit greater than 2%.

Some clients might have made less than 2% or even incurred losses.

5. Last year, the number of their clients who made a profit of 10% or less was equal to the number of their clients who made a profit of 10% or more.

- Not enough information is given to determine the accuracy of this statement.

The average profit of 10% does not tell us about the distribution of profits among clients to make this comparison.

Thus,

The statements that are true based on the information are:

1. Last year at least one of their clients made a profit of exactly 10%.

3. Last year some of their clients made a profit of 10% or more.

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For the regions bounded by y = 6cosx and y = one fourth x squared minus 7.

Part A: Find the limits of integration. (10 points)

Part B: Write the expression representing the total area. (10 points)

Part C: Solve for the total area. (10 points)

Answers

For the regions bounded by y = 6cosx and y = one-fourth x squared minus 7, the limits of integration, the expression representing the total area, and the total area are mathematically given as

A=27.03squnit

What are the limits of integration, the expression representing the total area, and the total area.?

Generally, the equation for expression is mathematically given as

y = 6cosx

y=(1/4)x^2-7

therefore

[tex]A=\int^{b}_a (f(x)-g(x))dx[/tex]

The limits are

a=0 b=2\pi

Hence

[tex]A=\int ^{2\pi}_0 (6cosx -((1/4)x^2-7))dx\\\\solving\\\\A=\int^{2\pi}_0 (6cosx -((1/4)x^2-7))dx[/tex]

A=27.03squnit

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Round 7,485 to the nearest hundred.

Answers

You would round 485 up to 500 and then add the 7,000 back on to get 7,500

Answer:

7,500

Step-by-step explanation:

When you round you automatically round up unless told otherwise
so find the hundredth, which is 485 and you round that to 500
then put the 7 back → 7,500

he roots of the quadratic function describing the relationship between the number of products produced and overall profit margins are x= 0 and 150. the vertex is (75, 10000).

Answers

The question was incomplete. Below you will find the missing parts of the question.

The company actually loses money on their first few products as it costs them more to make them, but once they hit  ?   they break even again. The worst case scenerio is that they produce  ?   items, as they will have a profit of  ?   dollars. The first root tells us that the profit will be 0 when  ?   products are sold.

Answer: The company actually loses money on their first few products as it costs them more to make them, but once they hit  150   they break even again. The worst case scenerio is that they produce  75   items, as they will have a profit of  10000   dollars. The first root tells us that the profit will be 0 when  0   products are sold.

Because the roots are x = 0 and 150, the vertex is (75, 10000).

So, the function is y = [tex]-\frac{10000}{5625}(x-75)^{2} +10000[/tex]

When, y = 0,

[tex]0=-\frac{10000}{5625} (x-75)^{2} +10000[/tex]

⇒ [tex]\frac{10000}{5625} (x-75)^{2}=10000[/tex]

⇒ [tex](x-75)^{2} = 10000(\frac{5625}{10000})[/tex]

⇒ [tex](x-75)^{2} = 5625[/tex]

⇒ [tex]x-75=75[/tex]

⇒ x = 150

When y=0, then x =150, their income was in balance.

When x = 75, then y=10000, they will have a profit of 10000 dollars.

The first root tells us that the profit will be 0 when 0 products are sold.

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$10,000 is invested for 4 years at an annual simple interest rate of 16%.

Answers

Answer:

$16,400

Step-by-step Explanation:

Step 1: We multiply $10,000 by 16%, getting $1,600.

Step 2: We then multiply $1,600 by 4 (which is given). That gives us $6,400.

Step 3: Add that to $10,000. We get $16,400 as the answer!

Please mark me as brainliest! I really need it!!! Thanks!

Answer:

Simple interest = P  x  r  x  t

                         = 10,000  x  16/100  x   4

                         =  $6400

Final amount = P (1 +rt)

                       = 10,000 (1 + 16/100  x  4)

                       = $16400

(or you can just add the simple interest to the principle amount to get the final amount)

Enter the correct answer in the box.
Function g has the same a value as function f, but its vertex is 2 units below and 3 units to the left.
f(x) = x² - 4x - 32
Write the vertex form of the equation modeling function g.

Answers

The equation in the vertex form of g(x) is:

[tex]g(x) = (x + 1)^2 - 38[/tex]

How to get the equation of function g?

We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).

So first, let's rewrite f(x) to its vertex form:

[tex]f(x) = x^2 - 4x - 32[/tex]

The vertex is at:

[tex]x = -(-4)/2*1 = 2[/tex]

The y-value of the vertex is:

[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]

Then the vertex form of f(x) is:

[tex]f(x) = (x - 2)^2 - 36[/tex]

If we move this vertex 2 units below, and 3 units to the left, then we have:

[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]

That is the equation for g(x) in vertex form.

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How do you solve this question

Answers

[tex]a - 4 = ( \sqrt{a} - 2)( \sqrt{a} + 2)[/tex]

[tex] \frac{ \sqrt{a} - 2}{a - 4} = \frac{ \sqrt{a} - 2}{( \sqrt{a} - 2)( \sqrt{a} + 2) } = \frac{1}{ \sqrt{a} + 2 } [/tex]

Which expressions are equivalent to 9b?
Choose all answers that apply
A. b+2(b+2b)
B. 3b+b
C. 2(2b)​

Answers

Answer:

A. b+2(b+2b)

b + 2b + 4b = 7b

B. 3b + b = 4b

C. 2(2b) = 4b

None of them are equal to 9b

Answer:

[tex]\fbox {None}[/tex]

Step-by-step explanation:

A

b + 2(b + 2b)b + 2(b) + 2(2b)b + 2b + 4b7b

B

3b + b4b

C

2(2b)4b

Which of the following statements are true?
A. Both graphs have exactly one asymptote.
B. Both graphs have been shifted and flipped.
c. Both graphs are logarithmic functions.
D. Both graphs are exponential functions.

Answers

Both graphs are exponential functions

How do I solve for x?

Answers

Answer:

3

Step-by-step explanation:

1: Turn the mixed fraction into improper.

2: Multiply 3/5 to each side

3: The you get x = 3

You need to multiply the fraction instead of division because multiplying by the reciprocal is the same as dividing the normal fraction.

[tex]\huge\text{Hey there!}[/tex]


[tex]\mathsf{5 = 1\dfrac{2}{3}x}[/tex]

[tex]\mathsf{1\dfrac{2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{1\times3 + 2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]

[tex]\large\textbf{MULTIPLY }\rm{\bf \dfrac{3}{5}}\large\textbf{ to BOTH SIDES}[/tex]

[tex]\mathsf{{\dfrac{3}{5}\times\dfrac{5}{3}x= \dfrac{3}{5}\times 5}}[/tex]

[tex]\large\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]

[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]

[tex]\mathsf{x = \dfrac{15}{5}}[/tex]

[tex]\mathsf{x = 15\div5}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]

Please answer BOTH the questions tyyyyyysm

Answers

C and A

X = at least 45 and more

This means we need to have a full closed dot.

It's A because the question says more than 75 ft meaning only open dots.

transform each graph below.

(a) The graph of y=f(x) is shown. Draw the graph of y= f(2x).

(b) The graph of y=g (x) is shown. Draw the graph of y=1/2g(x).

Answers

Answer:

Step-by-step explanation:

A sample of size 400 was drawn and sample mean was found t
be 99. Test whether this sample could have come from a normal
population with mean 100 and variance 64 at 5%
significance.

Answers

Answer:

etrf4f3dvef3rf3rfr2wrgwrf2rg3rf3rgerferferfef I'm

Geometry question! Please help thanks!

Answers

The measure of the angles are Z = 90, X = 90, V = 90, Y = ∠20, W = ∠8 and W = ∠20

How to solve the angles?

The sum of angles on a straight line is 180 degrees.

This means that:

Z + 90 = 180

X + 90 = 180

V + 90 = 180

Solve for the variables

Z = 90;

X = 90

V = 90

Also, alternate angles are equal.

This means that:

Y = ∠20

W = ∠8

This is so because the above angles are alternate angles.

Lastly, corresponding angles are equal.

So, we have:

W = ∠20

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What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFraction EndRoot? Assume x ≠ 0.

StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction
StartFraction 6 Over 5 x squared EndFraction
Six-fifths x Superscript 10
Six-fifths x squared

Answers

The simplification form of the provided expression is 6/5x¹⁰ option first is correct.

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]\rm = \sqrt{\dfrac{72x^{16}}{50x^{36}}}[/tex]

[tex]\rm = \sqrt{\dfrac{72}{50}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]

[tex]\rm = \sqrt{\dfrac{36\times2}{25\times2}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]

[tex]\rm ={\dfrac{6x^{8}}{5x^{18}}}[/tex]

[tex]\rm ={\dfrac{6}{5x^{10}}}[/tex]

Thus, the simplification form of the provided expression is 6/5x¹⁰ option first is correct.

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Answer:

6x3

Step-by-step explanation:

Edge 2023

Which graph best represents the equation shown below? 3x + y = 2 A. B. C. D.

Answers

Answer:

The plots are (0,2) (1,-1)

Step-by-step explanation:

a slanted line starting from top left corner ending in the bottom right

A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?

Answers

The speed of the wind and the speed of the dragon in still air are respectively;  142.5 mph and 7.5 mph

How to calculate the speed?

The dragon flew 300 miles with the wind in two hours.

After flying against the wind for two hours, he had made 270 miles of the return trip.

Let s be the speed in still air

Let w be the speed of the wind

Thus;

(s - w) = effective speed against the wind

and

(s + w) = effective speed with the wind

We know that;

distance = time * effective speed

Thus;

2(s + w) = 300

2(s - w) = 270

This can be simplified to get;

s + w = 150   -----(1)

s - w = 135   -----(2)

Add both equations to get;

2s = 285

s = 285/2

s = 142.5 mph.

Then, plane speed in still air is;

142.5 + w = 150

w = 150 - 142.5

w = 7.5 mph is the speed of the wind

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The function f(x)= –StartRoot negative x EndRoot is shown on the graph.

Answers

The range of the required function f(x)  = -√-x is all real values less than or equal to 0.

The nature of the function is imaginary because of the negative sign present inside the root. Hence the range of the function exists only and only if the function gives real  values in each of its outcomes.

What are functions?

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

As per question
f(x) = -√-x
clearly, for each positive real number the function becomes imaginary.
So the domain of the given function lies  (-∞, 0).
and for every x in its domain function has its exists in range of all real values less than and equal to zero.

Thus, the range of the function f(x) ≤ 0.

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Find the formula for the area of the shaded region in the figure.
x² = 4py
ہے

Answers

The formula for the area of the shaded region in the figure.

x² = 4py is mathematically given as

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

What is the formula for the area of the shaded region in the figure?

Parameters

[tex]$x^{2}=4 p y$[/tex]

[tex]$y=h$[/tex]

[tex]\therefore x^{2}=4 p h \Rightarrow x=2 \sqrt{p h} \\[/tex]

Generally, the equation for the Area is mathematically given as

[tex]& A=2 \int_{0}^{2 \sqrt{p h}}\left(h-\frac{x^{2}}{4 p}\right) d x \\\\& A=2\left(h x-\frac{x^{3}}{12 p}\right]_{0}^{2 \sqrt{p h}} \\\\& A=2\left[\left[h 2 \sqrt{p h}-\frac{1}{12 p} \cdot(2 \sqrt{p h})^{3}-0\right]\right. \\[/tex]

[tex]&A=2\left[2 h^{3 / 2} \sqrt{p}-\frac{8(\sqrt{p})^{3}(\sqrt{h})^{3}}{12 p}-0\right] \\\\&A=2\left[2 h^{k / 2} \sqrt{p}-\frac{2}{3} \sqrt{p} \cdot h^{3 / 2}\right] \\\\&A=2 \times \frac{4 \sqrt{p} \cdot h^{3 / 2}}{3} \\\\&A=\frac{8}{3} \cdot \sqrt{p} \cdot \sqrt{h} \cdot h \\\\&A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

In conclusion,  the equation for the Area is

   

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

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Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect.

Answers

Using the binomial distribution, it is found that there is a 0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect, which means that it is a highly likely event.

What is the binomial distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

The values of the parameters are given as follows:

n = 20, p = 0.05.

The probability that 3 or fewer experienced insomnia as a side effect is given by:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

Then:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]

0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect.

Since this probability is greater than 95%, this is a highly likely event.

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Evaluate 3a-5b when a=-3 and b=-2

Answers

Answer: 1

Step-by-step explanation:

Substituting in the given values,

3a-5b=3(-3)-5(-2)=-9+10=

The following graph portrays the distribution of the number of spicy chicken sandwiches sold at a nearby Wendy's for the last 141 days.
The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67. (Round your answers to 2 decimal places.)

If we use the Empirical Rule, on 68 percent of the days sales will be between

95 percent of the days sales will be between

Answers

68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

What is the empirical rule?

If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.

We have:

The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.

As we know, from the empirical rule, 68% of the data will lie in one standard deviation of the mean, i.e., in the interval with the endpoints x±s

for samples and with endpoints u±б for the population.

x = 91.9

s = 4.67

x - s = 91.9 - 4.67 = 87.23

x + s = 91.9 + 4.67 = 96.57

68% of the day's sales will be between 87.23 and 96.57

95% of the data will lie within two standard deviations of the mean, which means in the interval with the endpoints  x±2s for samples and with endpoints  u±б population.

x - 2s = 82.56

x + 2s = 101.24

On 95% of the days, sales will be between 82.56 and 101.24

Thus, 68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

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Math: Surface Area word problem..10 pts for your help!

Answers

The formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]

How to determine the surface area?

We have:

[tex]S(r) = 4\pi r^2[/tex]

Also, we have:

[tex]P(t) = \frac 43t[/tex]

The above can be rewritten as:

[tex]r = \frac 43t[/tex]

Substitute [tex]r = \frac 43t[/tex] in S(r) to determine the function N(t)

[tex]S(r) = 4\pi (\frac 43t)^2[/tex]

Express as N(t)

[tex]N(t) = 4\pi (\frac 43t)^2[/tex]

Expand the exponent

[tex]N(t) = 4\pi *\frac {16}9t^2[/tex]

Evaluate the product

[tex]N(t) = \frac {64}9\pi t^2[/tex]

Hence, the formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]

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What is the greatest common factor of 20 and 36?
2
4
5
6

Answers

Answer:

GFC = 4

Step-by-step explanation:

Factors of 20     1   2   4   5   10  20

Factors of 36     1   2  3 4  6  9 12 18 36

Answer:4

Step-by-step explanation:nice and simple

Find x and Y pls help

Answers

Answer:

Step-by-step explanation:

Comment

The angle supplementary to x and 3x are equal.

Supplementary angles = 180

Solution

x + 3x = 180

4x = 180                  Divide by 4

4x/4 = 180/4

x = 45

The angle supplementary to x is 3x

3x = 3*45

3x = 135

This angle is vertically opposite y. Vertically opposite angles are equal. So  y = 135

Answer

x = 45

y = 135

Tan + Cos / 1 + Sin = Sec

Answers

[tex]\tan x+\frac{\cos x}{1+\sin x}\\\\ =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x}\\\\=\frac{\sin x(1+\sin x)+\cos^{2} x}{\cos x(1+\sin x)}\\\\=\frac{\sin^{2} x+\cos^{2} x+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1}{\cos x}\\\\=\sec x[/tex]

Which expression is equivalent to...​

Answers

5^50 is the answer ruejsnsvenksken heinekens. jen’s bash
Answer: C) 5^15

Detailed Answer:

Following the Laws of Exponents,
• a^n * a^m = a^(n + m)

Therefore,
= 5^10 * 5^5
= 5^(10 + 5)
=> 5^15

(08.01 MC)
Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.

A. 5 feet
B. 9 feet
C. 25 feet
D. 45 feet

Answers

Answer:

A. 5 feet

Step-by-step explanation:

A. 5 feet
Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Find the critical point for f(x)=x^2-2x+4 and determine their nature.
Select one:
O a. (3, 1) minimum point
O b. (1, 3) minimum point
O c. (1, 3) maximum point
O d. (3, 1) maximum point

Answers

b. (1, 3 minimum poing

The volume of a can of Pepsi is 0.33liter. There are 12 cans in 1 carton
What is the volume of 5 cartons of Pepsi?

Answers

Answer:

19 liters 800 milliliters

Step-by-step explanation:

0.33 * 12 * 5 = 19.8 liters

Other Questions
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