1. Let f(x)=8/1+3e^−0.7x. What is the value of f (−3)?
2. Let f(x)=20/1+9e^3x. What is the y-intercept of the graph of f(x)?
3. Let f(x)=24/1+3e^−1.3x. What are the asymptotes of the graph of f(x)?
4. Let f(x)=15/1+4e^−0.2x. What is the point of maximum growth rate for the logistic function f(x)?
5. Let f(x)=24/1+3e^−1.3x. Over what interval is the growth rate of the function decreasing?

Answers

Answer 1

Final answer:

This detailed answer covers evaluating functions at specified values, identifying the y-intercept of a function's graph, determining asymptotes, identifying points of maximum growth rate in logistic functions, and intervals where the function's growth rate is decreasing, all critical concepts in understanding mathematical functions in high school.

Explanation:

The questions provided are focused on evaluating specific values of functions, understanding the y-intercept of a graph, determining asymptotes, identifying points of maximum growth rate, and assessing intervals of decreasing growth rate for various exponential and logistic functions. Each of these concepts plays a crucial role in understanding the behaviors and characteristics of different types of mathematical functions, which are fundamental in high school mathematics.

To find f(-3) for the function f(x)=8/(1+3e^{-0.7x}), substitute x=-3 and evaluate.The y-intercept of a graph is found by evaluating the function at x=0.Asymptotes can be determined by evaluating the limits of the function as x approaches infinity or negative infinity.The point of maximum growth rate for a logistic function occurs at the point where the function's second derivative changes sign.The growth rate is decreasing over intervals where the second derivative of the function is negative.

Related Questions

Can anyone help me with these two true/false questions? :)

9. Determine whether the statement is always, sometimes, or never true.

A cubic function has an inverse.

a. always true
b. sometimes true
c. never true

10. Determine whether the statement is always, sometimes, or never true.

A linear function has an inverse relation.

a. always true
b. sometimes true
c. never true

___

Thanks!,

Answers

Answer:

9. b. sometimes true

10. a. always true

Explanation:

9. Any function will have an inverse relation. This question is not specific as to whether that inverse relation must be a function. We will assume that that is the intent.

The attached graph shows a cubic function with an inverse function (green), and another without (red).

A cubic function will have an inverse function sometimes.

____

10. As stated above, any function will have an inverse relation.

A linear function will have an inverse relation always.

The graph shows a linear function with an inverse function (green), and one that has an inverse relation, but not an inverse function (red).

A child walks due east on the deck of a ship at 4 miles per hour.
The ship is moving north at a speed of 12 miles per hour.

Find the speed and direction of the child relative to the surface of the water.

Speed = mph

The angle of the direction from the north = (radians)
i have the speed i couldn't find the direction !,

Answers

If you drew the two vectors for the velocity you find a triangle rectangle since the two directions East and North form an angle of 90°. I drew first the vector towards East and second the vector towards North.

Therefore, to get the speed relative to the surface you have to sum the two vectors, which means you can apply the Pythagorean theorem to find the hypotenuse, having the two legs.

h = √(4² + 12²) = √160 = 4√10 = 12.65mph

In order to find the direction, you need to use trigonometry:
- the sine of an angle is given by the ratio between the opposite side divided the hypotenuse;
- the cosine of an angle is given by the ratio between the adjacent side divided by the hypotenuse.

You can use either one, I will show you both:
sinα = O / H
inverting the formula: α = arcsin (O / H) = sin⁻¹ (O / H)
these two forms are equivalent.

Similarly:
cosβ = A / H
β = arccos (A / H) = cos⁻¹ (A / H).

Substituting your numbers:
α = sin⁻¹ (12 / 12.65) = sin⁻¹ (0.9486) = 1.25rad
β = cos⁻¹ (4 / 12.65) = cos⁻¹ (0.3162) = 1.25rad

As you can see, α = β so you can use either formula.

Your answer will then be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 1.25rad from East towards North.

ATTENTION!
If you drew first the vector towards North and then the one towards East, you get an equivalent triangle, which is rotated by 180° respect to the previous one. This way, what you earlier called Opposite is now Adjacent and vice-versa, but the formulas are still valid.
You will get:
α = sin⁻¹ (4 / 12.65) = sin⁻¹ (0.3162) = 0.32rad
β = cos⁻¹ (12 / 12.65) = cos⁻¹ (0.9486) = 0.32rad
And your answer will be: the child is moving relative to the surface of the water with a speed of 12.65mph at a direction of 0.32rad from North towards East.

A line has a slope of -1/2 and a y-intercept of –2. What is the x-intercept of the line? –4, –1, 1 ,4

Answers

to get the x-intercept, we simply set y = 0 and solve for "x".

now, we have the slope and the y-intercept, well, let's plug those two in the slope-intercept form, reason why is called that anyway,

[tex]\bf y=\stackrel{slope}{-\cfrac{1}{2}}x\stackrel{y-intercept}{-2}\implies 0=-\cfrac{x}{2}-2\implies \cfrac{x}{2}=-2\implies x=-4[/tex]

3/5, give the equivalent numerator if the denominator is 80
3
16
48

Answers

its 48. you see how much they multiplied the denominator (5) by, so you do 18 divided by 5 (which is 16). you then do the same to the numerator but instead multiply it by 16 so thats 48.

Vertical line that passes through the point (3,-8)

Answers

Hi there! The answer is x = 3.

All vertical lines have an undetermined slope (since the formula which represents the slope has a denominator of 0). Therefore the general formula of a vertical line is the following x = c, with c representing the x-coordinate of the point that is passed by the line. Therefore, in your situation we get the line x = 3. When we plot this line, we can see it is a vertical line with x-coordinate 3 and that all values of y are passed, also y = - 8.

Which of the following decimal numbers equals 4 thousand, 9 hundreds, 2 tens, and 6 ones?

Answers

we have
decimal numbers equals
4 thousand---------> 4000
9 hundreds--------> 900
2 tens-----------> 20
6 ones-------> 6
so
[4000+900+20+6]=4926

the answer is 4926

Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6 rolls of quarters containing 40 coins each. How much money does she have?

A. $106.20
B. $17.50
C. $8.00
D. $94.50

Answers

the total number of pennies she has - 3 x 50 = 150
value of penny - $ 0.01
value she has from pennies - $0.01 x 150 = $1.50

total number of nickels she has - 4 x40 = 160
value of nickel - $ 0.05
value she has from nickels - $0.05 x 160 = $8

total number of dimes she has - 5 x 50 = 250
value of dime - $ 0.10
value she has from dimes - $0.10 x 250 = $25

total number of quarters she has - 6 x 40 = 240
value of quarter - $ 0.25
value she has - $ 0.25 x 240 = $ 60

total amount of money she has = 1.50 + 8 + 25 + 60
money she has = $ 94.50
correct answer is D

Please help, I’m kinda confused

Answers

I'm not sure, but I think is 15 :/ Hope it helped

The function below can be used to calculate the cost of making a long distance call, f(m), which is based on a $2.50 initial charge and a fee of $.12 per minute, m, that the call lasts. If Natalie paid $6.82 for one call, how many minutes long was it?

Answers

f(m) = 2.5 + 0.12m

if Natalie paid $6.82

6.82 = 2.5 + 0.12m
0.12m = 6.82 - 2.5
0.12m = 4.32
m = 4.32 ÷ 0.12
m = 36

The call was 36 minutes long.

A hair salon charges a fixed rate of $25.00 for a haircut and an additional $15 for any other services. Write a function to model the cost of services at the salon and then evaluate the function to determine the cost for a haircut, shampoo, highlight, and blow dry.

Answers

25+15•3= 70 dollars she spent on the hair salon..... dang lotsa money

Answer:

Function : Cost =25 + 15x

Cost for a haircut, shampoo, highlight, and blow dry = $70

Step-by-step explanation:

Hi, to answer this we have to write an equation:

The cost of the services will be equal to the fixed cost for the haircut (25.00) plus the product of the number of additional services (x) and the price of each additional service (15).

Mathematically speaking:

Cost =25 + 15x

To determine the cost for a haircut, shampoo, highlight, and blow dry, we have to substitute x = 3 (because shampoo, highlight, and blow dry are additional services ) in the equation and solve.

Cost = 25+ 15 (3)

Cost = 25+45

Cost = $70

In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 7 in?
Enter your answer in the box.

Answers

14 inches. A 30-60-90 triangle has a set ratio for the sides which is x:x√3:2x for the sides opposite the corresponding angle. (30 = x, 60 = x√3, 90 =2x) the shortest side is the side opposite the 30-degree angle so x=7. The hypotenuse is the side opposite the 90-degree angle. they hypotenuse = 2x. Substitute x. 2(7)=14

The length of the hypotenuse is 14in

SOH CAH TOA identity

Given a 30-60-90 triangle where:

Length of the shorter leg = 5cm (adjacent)

The hypotenuse is what we need..

[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]

Substitute the given parameters

[tex]cos 60 = \frac{7}{h}\\ h =\frac{7}{cos 60}\\ h = \frac{7}{0.5}\\ h = 14in\\ [/tex]

Hence the length of the hypotenuse is 14in

Learn more on SOH CAH TOA here: https://brainly.com/question/20734777

Easy Algebra 2 Rational Expressions question

Answers

IF it is nonpermissible then we are checking the denominator to see where it equals 0 at

y - 3 = 0
y = 3 - this is where the fraction is undefined (or nonpermissible)

how is jimthompson so smart?

Also can you please help me with that question.
I got everything except for the Euler Diagram.

Answers

The statement is valid. To set up a Euler diagram, follow these steps

Step 1) Draw a large circle and label it circle A

Step 2) Inside this large circle, draw a smaller circle and label it circle B

Circle A will represent the set of all obtuse angles (any angles that are between 90 and 180 degrees). Circle B represents only one item: the angle value of 150 degrees. All of circle B is inside circle A because 150 degrees is between 90 and 180; therefore, 150 is obtuse. This is simply the definition of what "obtuse" means.

So if you threw a dart and it landed in circle B, then you know for sure it landed in circle A as well. This is effectively saying "if you get a 150 degree angle, then you know its obtuse"

This is a visual way to back up the conditional statements you used earlier and help add more evidence that the statement "A 150 degree angle is an obtuse angle" is a valid statement.

A wood frame costs $1.50. Use a property to write an equivalent expression for the cost of a wood frame.

Answers

Let the width of the frame = x
Let the cost of a linear foot of the frame = y
Let the inside dimension of the length of the frame = a
Let the inside dimension of the width of the frame = b.

The total length of the frame = 2*a + 4x
The total width of the frame = 2b

The total amount of the frame in feet is (2a + 4x + 2b)*y = Cost
If this is incorrect please leave a message on my home page.

How do I solve for h

Answers

All the triangles are similar, so the ratio of (long leg)/(short leg) is the same. The long leg of ΔADB is
.. AD = AC -DC = 20 -4
.. AD = 16

Then
.. (long leg)/(short leg) = AD/DB = BD/DC
.. 16/h = h/4
.. h^2 = 64
.. h = 8

Selection D is appropriate.

_____
You may see this again. The altitude (h) from the right angle in a right triangle is the geometric mean of segments AD and DC. That is,
.. h = √((AD)*(DC))

Which represents the explicit formula for the arithmetic sequence

Answers

[tex] a_{n} =7-3(n-1) \\ [/tex]
7-3(n-1) = 7 - 3n + 3 = -3n +10 [tex]f(n) = -3n+10[/tex]

So the answer is D.

F(x)=x+2/2 what is the value of f(-8)

A.-4
B.-3
C.-5
D.-6

Answers

Answer: Choice B) -3

------------------------------------------------------

Work Shown:

f(x) = (x+2)/2
f(-8) = (-8+2)/2 ... replace every x with -8; use PEMDAS
f(-8) = (-6)/2
f(-8) = -3

A set of 5 numbers has a mode of 12 a median of 11 a mean of 10 what could the numbers be?

Answers

The median is 11, so 11 is part of the data set. We have an odd number of values (5) which is why the median is part of the data set.

The mode is 12. The value 12 shows up the most times. Let's say it shows up twice. So far the data set is {11, 12, 12}

Let's introduce two more numbers x and y
The new data set is {x, y, 11, 12, 12}

Add up the five values and then divide by 5. We want this result to be equal to 10
(x+y+11+12+12)/5 = 10
(x+y+35)/5 = 10
x+y+35 = 10*5
x+y+35 = 50
x+y = 50-35
x+y = 15

So we don't know what x or y is, but we know that they must add to 15. So all you have to do is list two numbers that add to 15. One such pair is x = 6 and y = 9. Another pair is x = 7 and y = 8. There are infinitely many possibilities if you can use any real number.

So one possible set is {6, 9, 11, 12, 12}
Another possible set is {7, 8, 11, 12, 12}

A possible answer is 6, 9, 11, 12, and 12. Hope I helped (:

Translate three times the sum of a number and five

Answers

three times the sum of a number and five

number = n

the sum of a number and five: n + 5

3 times the sum of a number and five

3(n + 5) is your answer

hope this helps

Jana finished 1/4 of her homework at school and 2/3 of it before dinner. How much of her homework has she finished so far?

Answers

1/4+2/3
1/4×3/3+2/3×4/4
3/12+8/12
11/12

Final answer:

Jana has completed 11/12 or 11 out of 12 of her homework so far.

Explanation:

To find out how much of her homework Jana has finished so far, we need to add together the fractions of her homework completed at school and before dinner.

Jana finished 1/4 of her homework at school and 2/3 of it before dinner.

To add fractions, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12. So, we can convert both fractions to have a denominator of 12.

1/4 is equivalent to 3/12, and 2/3 is equivalent to 8/12.

Now, we can add the fractions: 3/12 + 8/12 = 11/12.

Therefore, Jana has completed 11/12 or 11 out of 12 of her homework so far.

find the perimeter of the quadrilateral. if x = 2 the perimeter is

Answers

the perimeter of any shape is equal to the sum of its sides.
then [tex]the perimeter=31+(4x^{2}+8x)+(7x+30)+(3x^{2}-5x+20)[/tex]
[tex] the perimeter= (4x^{2}+3x^{2})+(7x+8x-5x)+20+30+31=7x^{2}+10x+81[/tex]
for x=2
[tex] the perimeter= 7*(2)^{2}+10*2+81=7*4+20+81=28+101=129[/tex]

Note:
Please double check the substitution but the procedure is 100% right.

Answer:

Step-by-step explanation:

Since perimeter of any polygon is represented by sum of its all sides.

Therefore, perimeter of the given quadrilateral = (4x² + 8x) + (3x² - 5x + 20) + (7x + 30) + 31

A $6,300.00 principal earns 6% interest, compounded annually. After 3 years, what is the balance in the account?

Answers

7,503

Hope this helped!

Hello,

To find this answer, you have to start with 6,300 and multiply it by 1.06 three times. We are using 1.06 because we are adding 6% (0.06) onto the total 3 times.

6300 x 1.06 x 1.06 x 1.06 = $7,503.40
OR
6300(1.06)^3 = $7,503.40

The second equation is written as a compound interest equation. You just need to switch the 3 if you want to find the total for a different amount of years.

I hope this helps, Good luck!

Hey can somebody help me? I know it seems easy but I forgot the process on how to do this. Thanks in advance!
---------------------------------
1 1/2 - 1/2 = ???

Show your work please so I understand

Answers

Since we can break down 1 1/2 into 1 + 1/2, and we know that 1/2 - 1/2 = 0, we can just add one. So, the answer is 1.

Sorry if this was a bit unclear, I did my best to explain ;)

Hope this helps!

An artist drew a rectangle. the artist then modified the rectangle so thatthe length ofthe rectawngle increased by 30 percent and the width of the rectangle decreased by 40 percent. after the modification, what was the percent decrease in the area of the rectangle?

Answers

the dimensions of the original rectangle
length - L
width - W
area = L*W = LW
after the modification, new dimensions are
length increased by 30 %
Length = L * 1.3 = 1.3L
Width = W * 0.6 = 0.6W
new area = 1.3L * 0.6W
= 0.78LW
the percent decrease in area
decrease % = (difference in area)/original area * 100
= (LW - 0.78LW)/LW * 100
= 0.22LW/LW * 100
= 22%
percent decrease is 22%

Can anyone help me I don’t know how to do this

Answers

Start with the vertex form of the equation of a quadratic. Fill in the numbers you know and solve for the one you don't know.
y = a(x -h)² +k . . . . . . . . for some stretch factor "a" and vertex (h, k)

1. Vertex = (h, k) = (0, 0). Stretch factor can be found from the given point (x, y).
8 = a(-2 -0)² +0
8 = 4a . . . . . . . . simplify
2 = a . . . . . . . . . divide by the coefficient of "a"
Your equation is y = 2x².

Note the above method for solving these problems. It repeats.

2. As above, substitute what's given and solve for what's not.
3 = a(1 -2)² +0
3 = a
Your equation is y = 3(x -2)²

3. Repeat
-4 = a(-5 +3)² +0
-4 = 4a
-1 = a
Your equation is y = -(x +3)²

4. Are you seeing the pattern yet?
0 = a(-1 -0)² +1
0 = a +1
-1 = a
Your equation is y = -x² +1

5 & 6. You know that if you want a zero (x-intercept) to be located at x=a, then a factor of the quadratic will be (x -a). Multiply the factors together to get your quadratic function.

5. y = (x -0)*(x -2) = x² -2x

6. y = (x +5)*(x -5) = x² -25 . . . . . . . . . . you should recognize this "special form", the factoring of the difference of squares

Answer please anybody

Answers

Hi there.

f(x) = 2x + 1
g(x) = x^2 - 7
(f - g)(x);
(2x + 1) - (x^2 - 7);
-x^2 + 2x + 8.

Your correct answer is C.)

I hope this helps!

What is the value of x? Please Answer

Answers

The value of x would be 15 degrees.

This is a right angle and right angles are 90 degrees in total.

90-30= 60

We know that the missing part of the angle equals 60 degrees so we divide 60 by 4x.

60/4x=15.

I hope that was clear enough, sorry if it’s not. Have a great day and good luck!

If 3x + 8 = 5x - 6, then what is the value of 10x?

Answers

3x + 8 = 5x - 6
3x + 8 - 5x = 5x - 6 - 5x
-2x + 8 = -6
-2x + 8 - 8 = -6 - 8
-2x = -14
-2x/-2 = -14/-2
x = 7

10x
10 (7)
70
The value of 10x is 70. The value of x is 7.

Gina pumps 40 cubic inches of air per second into a balloon. The function below shows the total amount of air f(t) inside the balloon after t seconds. f(w) = 40t + 5 Which statement best describes the y-intercept of the graph of the function?

Answers

The y-intercept of the graph of the function is the initial amount of air inside the balloon (5 cubic inches)

For this case, the first thing you should know is that the intersection with the y-axis occurs when the time equals zero.
Mathematically we have:
For t = 0:
f (0) = 40 (0) + 5
f (0) = 0 + 5
f (0) = 5
Answer:
The intersection with the y-axis represents the total amount of initial air before starting to pump air.
The initial air quantity is:
5 in ^ 3

the statement 2n^2+5n-25=0 opens up because

Answers

The graph of 2n^2 +5n -25 opens up because the coefficient of n^2 is positive.

____
The statement 2n^2 +5n -25 = 0 defines two values of n.

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