The concept of exponential growth function is discussed below.
What is exponential function?An exponential function is of the form -
y = A(B)ˣ
Given is to explain exponential growth.
Exponential growth of a quantity happens if the rate of instantaneous change is directly proportional to the quantity itself. The general exponential function is -
y = A(B)ˣ
More specifically -
[tex]$f(x)=a(1+r)^{x}[/tex]
where -
f(x) = exponential growth function
{a} = initial amount
{r} = growth rate
{x} = number of time intervals
Therefore, the concept of exponential growth function is discussed above.
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{Question in english -
What is exponential growth?}
inverse function of f(x)= \frac{5}{x} +4
The inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
f ( x ) = ( 5/x ) + 4 be equation (1)
On simplifying the equation , we get
y = ( 5/x ) + 4
Now , replacing x with y , we get
x = ( 5/y ) + 4
On solving for y , we get
5/y = x - 4
y = ( 5 / x - 4 )
Now , the inverse of the function is f⁻¹ ( x ) = 5 / ( x - 4 )
Hence , the equation is f⁻¹ ( x ) = 5 / ( x - 4 )
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The lengths of the three sides of a triangle are x + 15 , 2x + 15 and x + 12 (where x cannot equal zero). What is the perimeter of the triangle? use the drop-down menu to complete the answer.
Answer:
4x + 42
Step-by-step explanation:
[tex]\text{Perimeter}=(x+15)+(2x+15)+(x+12)=4x+42[/tex]
_____
which two integers is between /-83
The two integers that are between -83 and +83 are -82 and +82.
What is integers ?
In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.
There are multiple pairs of integers that are between -83 and 83.
Here are two examples:
-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -50 0 50 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -75 0 75 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.
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I want the answer pleaseee
Answer:
8.6 m
Step-by-step explanation:
DE = 2 7/10 m
= 2 + 7/10
= 2 + 0.7
DE = 2.7 m
EF = 5 9/10 m
= 5 + 9/10
= 5 + 0.9
EF = 5.9 m
DF = DE + EF
= 2.7 + 5.9
= 8.6 m
On the following composite figure, the longer edge length is 14 millimeters. The shorter edge length is 8 millimeters. The width of the figure, at its longest point, is 11.3 millimeters. Find the area of the figure. Explain or show how you got your answer. Note: Lines that look parallel are parallel, and angles that look like right angles are right angles.
The area of the given composite figure with a side length of 14mm and an edge length of 8mm is 158.2 mm².
What is a composite figure?
A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. A variety of forms that we encounter every day are composite figures that can be created from two or more fundamental figures.
The figure is given below.
From the figure, we can see that the sides of a triangle at the top and bottom are the same.
So the triangle cut from the bottom is placed at the top of the figure.
When the cut triangle is placed back at the bottom, we get a rectangle of length 14 mm and breadth 11.3 mm, as given below.
So the area of the given composite figure is the same as the area of the rectangle.
The area of the rectangle = length * breadth = 14 * 11.3 = 158.2 mm²
Therefore the area of the given composite figure is 158.2 mm².
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A hole in a steel plate has a diameter of 1.166 cm
at 23.00 ∘C
At what temperature is the diameter of the hole equal to 1.164 cm
?
will give brainliest
So here we have a hole in a steel plate with a diameter of 1.166 cm. So we need to find the temperature at what temperature is the diameter of full equal to 1.165 cm. So you're given is D. I. That is equal to initial diameter. That is equal to 1.166 cm. and temporary Germany shirt temperature is equal to 23°C and DF is equal to 1.165 m. This is the final diameter. So you only need to find the value of P. F. So we know that whole diameter very nice linearly with And nature. So here we can say DFS equal to D. I multiplied by one plus alpha. They're dirty. Yeah, I'll find that coefficient of thermal expansion. So here we can say it this is for steel And the value of alpha is equal to 13, multiplied by 10, raised to -6. So D F. Is equal to B. I multiplied plus the I'm multiplied by alpha, multiplied by delta T. So here we can see it D F minus D. I. That is the initial final diameter minus initial diameter divided by D. I. Alpha. That is equal to delta P. So this will be where to tell 30. That is equal to -6.59717. multiplied by 10° to -5 divided by And there's do -6. So here the key Is equal to -65.9717 degree. So here P f minus T I is equal to minus 65.9717 degree. The T.F will be equal to 23 -65.9717. So therefore final temperature that this T.F is equal to -42.8717 degrees Celsius. So therefore this is the answer to the question. So here we can say hands, final temperature Is equal to -42.8717°C.
If the market price is below the equilibrium price, which of the following will occur?
Answer:
Shortage
Step-by-step explanation:
If the market price of a product is set below the equilibrium price, it will create a shortage of the product because the demand exceeds the supply.
What is the size, in degrees, of the missing angle?
45
65°
The three graphs represent the progress of three runners in a 500-meter race.
The red solid line represents runner A. The purple dotted line represents runner B.
The blue dashed line represents runner C.
Options: Runner A, Runner B, Runner C, 0, 20, 55, 90.
The answers include the following:
Runner B ran at a constant rate throughout the race.Runner C stopped running for a while and it occurred between 20 to 55.Runner A also sprinted at different speeds.Runner A won the race.What is Speed?This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.
From the graph, we can deduce that Runner A won the race because it attained a greater distance when compared to the time for all the other runners.
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Question 4 (10 points)
(03.06 MC)
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points
The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.
Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³
Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³
The volume of this cylinder is 1.5 times that of the cone
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content attribution
QUESTION 5. 1 POINT
1
A company offers one free book download to anyone that registers. The total number of people that register can be
modeled by the function f(x) = 8x³ +70x² +145x+182, where x is the number of months passed since starting the
company. The number of free books available to choose from can be modeled as 2x + 13. Write an expression that can be
used to determine the average number of people that download each of the free books.
Ous
Provide your answer below:
The expression for the average number of people (8x³ +70x² +145x+182)/(2x + 13)
How to determine the expression to determine the average number of peopleFrom the question, we have the following parameters that can be used in our computation:
The total number of people, f(x) = 8x³ +70x² +145x+182
Number of free books = 2x + 13
To determine the average number of people that download each of the free books,
We need to divide the total number of people that register by the number of free books available.
So, we have
Expression = (8x³ +70x² +145x+182)/(2x + 13)
Hence, the expression is (8x³ +70x² +145x+182)/(2x + 13)
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Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]
Please help me with this question
Answer:
= 7022cm
Step-by-step explanation:
The Perimeter of a rectangle =
[tex] = 2(l) + 2(w)[/tex]
From the question
L= 15.47m
w= 19.64m
therefore perimeter of a rectangle
=
[tex] = 2(15.47) + 2(19.64) \\ = 30.94 + 39.28 \\ = 70.22 m[/tex]
Also since rectangle are in centimetres
than if. 1 m = 100cm
than 70.22m = ?
therefore 70.22/1 = 100cm
=7022cm
therefore the Perimeter of a rectangle = 7022
the division or the multiplication property of equality to solve 1,145 = y
-——
224
Answer:
26.it is all about thinking
Which one of the following items is not necessary in preparing a statement of cash flows?
O Determine the cash provided by operations
O Determine cash from financing and investing activities
O Determine the cash in all bank accounts
Determine the change in cash
The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
What is meant by statement cash flows?In financial accounting, a cash flow statement, often called a statement of cash flows, is a financial statement that breaks down the analysis into operating, investing, and financing operations. It illustrates how changes in balance sheet accounts and income effect cash and cash equivalents.
A cash flow statement lists all of an organization's cash inflows from current operations and outside investment sources. The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
Functionally speaking, cash flows are categorized according to the nature of the underlying transaction. The statement's main goal is to give pertinent details about the agency's cash inflows and outflows during a given time period.
Therefore, the correct answer is option d) Determine the change in cash.
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Ten times the sum of a number and eight is -10. What is the number?
Answer:
Step-by-step explanation:
Answer:
The number is -10.4
Explanation:
Assume that the number we are looking for is x.
Now, we want to get 10 times te sum of half the number and 6 and equate this expression to 8. Then we can solve for x
Let's take this step by step:
half the number is 0.5x
the sum of half the number and 6 is 0.5x + 6
10 times the sum of half the number and 6 is 10(0.5x +6)
10 times the sum of half the number and 6 equals 8 is 10(0.5x+6) = 8
Now we can solve for x as follows:
10(0.5x + 6) = 8
5x + 60 = 8
5x = 8 - 60
5x = -52
x = -52/5
x = -10.4
Hope this helps :)
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.4 mmHg (millimeters of mercury) for a sample of size 686 and a sample standard deviation 5.5 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 90% confidence.
What is the 90% confidence interval to estimate the population mean? Round your answer to one decimal place.
Answer:
{30.1,30.7}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{90\%}=30.4\pm1.645\biggr(\frac{5.5}{\sqrt{686}}\biggr)\\\\CI_{90\%}\approx30.4\pm 0.3\\\\CI_{90\%}=\{30.1,30.7\}[/tex]
Thus, we are 90% confident that the true amount of mmHg that is lowered will be between 30.1 and 30.7 mmHg.
A boat heading out to sea starts out at Point A, at a horizontal distance of 1196 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 13°. At some later time, the crew measures the angle of elevation from point B to be 3 ° . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance from point A to point B measures is 1,269.9 feet.
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
Given;
The horizontal distance= 1196ft
Angle of elevation to the lighthouse’s=13°
Angle of elevation from point B =3 °
Now,
Distance from A to B = D;
D = Horizontal distance from B to LH - Horizontal distance from A to LH
Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet;
Therefore, by the trigonometric ratios the distance from point A to point B, D will be 1,269.9feet;
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How do I solve for side a and b and angle B when when side c equals 968m, angle a is 33 degrees abs 25 minutes and angle c is 90 degrees
Answer:
Step-by-step explanation:
Calculated based on 2 given angles and 1 given side.
∠B = 180° - A - C = 0.99484 rad = 57°
∠B = 57°
a = c·sin(A)/sin(C) = 527.21059
b = c·sin(B)/sin(C) = 811.83311
helpppp ASAP.
1. What is the height of the cone? Explain how you found the height. (4 points)
2. Now that you have the height of the cone, how can you solve for the slant height, s? (3 points)
3. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. (3 points)
1. The height of the cone is, 22.18 mm.
2. The slant height is, 28.14 mm.
3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
The volume of cone V = (1/3)πr²h
Given that,
The volume = 8792 mm³
1. by using the formula to solve for h,
we get h = (3V)/(πr²).
Plugging in the values given,
we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.
Therefore, the height of the cone is approximately 22.18 mm.
2. it is known that, from the Pythagoras theorem
s² = h² + r²,
where s is the slant height, h is the height, and r is the radius.
Plugging in the values we found in part 1,
we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².
Taking the square root of both sides, we get s ≈ 28.14 mm.
Therefore, the slant height is approximately 28.14 mm.
3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.
Using the value we found in part 2,
the length of the slant height is approximately 28.14 mm.
Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.
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someone help me please
The value of summation of ( x-2)² is 973
What is summation?A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.
if
x (x-2) ( x-2)²
15 13 169
13 11 121
13 11 121
4 2 4
19 17 289
12 10 100
6 4 16
5 3 9
14 12 144
Therefore the summation of (x-2)²
= 169+121+121+4+289+100+16+9+144 = 973
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Answer:answer
Step-by-step explanation:
The value of summation of ( x-2)² is 973
Solve the equation. 15 - 2x = -4(x + 1) + 9
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
x = -5
Step-by-step explanation:
15 - 2x = -4(x+1) + 9
-4(x+1) can be distributed and simplified to -4x - 4
15 - 2x = -4x - 4 + 9
15 - 2x = -4x +5
-2x + 4x = 5 - 15
2x = -10
x = -5
Answer:
[tex]x=-5[/tex]
Step-by-step explanation:
Given
[tex]15-2x=-4(x+1)+9[/tex]
Simplify the right side by applying the distributive property.
[tex]15-2x=(-4*x)+(-4*1)+9[/tex]
[tex]15-2x=-4x-4+9[/tex]
Add [tex]-4[/tex] and 9.
[tex]15-2x=-4x+5[/tex]
Add [tex]4x[/tex] to both sides of the equation.
[tex]15-2x+4x=5[/tex]
Add [tex]-2x[/tex] and [tex]4x[/tex].
[tex]15+2x=5[/tex]
Subtract [tex]15[/tex] from both sides of the equation.
[tex]2x=-10[/tex]
Divide both sides of the equation by [tex]2[/tex].
[tex]x=-5[/tex]
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Whats the correct answer answer asap for brainlist
A quotation isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2.
The option (a) is correct.
What is quote?Famous people who discuss their opinions on a given subject often employ quotation marks around their words. The brief nature of a quotation allows it to share individuality. The citation served as a means of sharing ideas and serving as a source of historical information.
The quotation, which is sometimes referred to as "quote vomit," was cut off from the remainder of the text.
The sentences are directed at their objective. Understanding how the universe functions and how we fit into it can be done through the metaphor of weaving.
As a result, the quote isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2. Therefore, option (a) is correct.
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A= (x| x es un mes del año ayúdeme a resolver no le entiendo
The elements of the set A are given as follows:
A = {January, February, March, April, May, June, July, August, September, October, November, December}.
How to obtain the elements of the set A?The set A in the context of this problem is defined as follows:
A = {x | x is a month of the year.}
Hence the set A is composed by 12 elements, which are all the months of an year, as follows:
A = {January, February, March, April, May, June, July, August, September, October, November, December}.
TranslationThe problem asks for all the elements of the set A, given as follows:
A = {x | x is a month of the year.}
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Complete the table for the given rule.
Rule:
�
=
�
+
0.6
y=x+0.6y, equals, x, plus, 0, point, 6
�
xx
�
yy
3
33
4.2
4.24, point, 2
2
22
y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given equation is y=x+0.6
Find the y value for x=3, 4.2, 2
When x=3
y=3+0.6=3.6
When x=4.2
y=4.2+0.6=4.8
When x=2
y=2+0.6=2.6
Therefore, y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.
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Solve the given initial-value problem.
y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) =
1
2
, y'(0) =
5
2
, y''(0) = −
11
2
the values for the first 3 derivatives derivatives of y are 1/2, 5/2, -11/2 respectively
The given differential equation:
y''' − 2y'' + y' = 2 − 24ex + 40e5x,
y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2
Therefore, the next solution is 13/2
Differential Equation:
In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.
Now,
Given differential equation is
y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ ------------ (1)
Auxiliary equation is m³ - 2m² +2m = 0
Now,
m(m² - 2m +2) = 0
⇒ m(m-1)² = 0
Therefore, m = 0,1,1
Therefore,
[tex]y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}[/tex]
Now, we have to find the particular solution by method of undetermined coefficient.
[tex]y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}[/tex]
⇒ [tex]y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}[/tex]
⇒ [tex]y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}[/tex]
⇒ [tex]y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}[/tex]
Putting these values in differential equation (1), we get:
y'''(0) = 13/2
Complete Question:
Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2
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Analyze the relationship in this table, and look for a pattern that relates x and f(x)
Part A
Identify the function type that could represent the data in the table. Explain your reasoning.
Type your response in the box.
A quadratic function could represent the data in the table, as the increase rate decreases as x increases, meaning that the function could be approaching it's vertex.
How to classify the function?Traditionally, functions are classified as either linear or exponential, as follows:
Linear: constant increase.Exponent: multiplicative increase.As there is not a constant neither a multiplicative rate of change for the table, the function is neither linear nor exponential.
Considering that from x = 1 to x = 4 the rate of change is of 4/3, while from x = 16 to x = 25 the rate of change is of 4/9, that is, the increase rate decreases as x increases, the function is classified as a quadratic function.
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What is the range of y= tan x?
OA. All real numbers
OB. z+TTT
c. -1≤ y ≤1
D. −1≤ x ≤ 1
Answer: The range of the tangent function is (-∞,∞). So the answer is A: All real numbers.
Step-by-step explanation:
Find the sum of the numbers. Express your answer in scientific notation.
(6.94 times 10 Superscript negative 7 Baseline) + (2.7 times 10 Superscript negative 8)
7.21 × 10⁻⁷
Step-by-step explanation:
(6.94 × 10⁻⁷) + (2.7 × 10⁻⁸) = 7.21 × 10⁻⁷
Help, Solve the system of linear equations by Elmination.
a. Yes, The answer is correct.
b. When we subtract the second equation from the first, the next step would be 3x = 9.
What is a system of linear equations?
The collection of two or more linear equations involving the same variables is known as a system of linear equations. In this case, linear equations are first-order equations, where the maximum power of the variable is 1.
Part a:
Given that, a customer purchases 8 bags of cat food and 2 bags of dog food, then the total weight of the purchase is 44 pounds.
Another customer purchases 5 bags of cat food and 2 bags of dog food, then the total weight of the purchase is 35 pounds.
let the weight of the cat food be 'x' and the dog food is 'y'.
For the first customer,
Total weight will be = 8x + 2y = 44 .....eq 1
For the second customer,
Total weight will be = 5x + 2y = 35 .....eq 2
Which are the two equations given above,
So, The equations are correct.
Part b:
Eliminate y terms from the equations.
Subtract eq 2 from eq 1:
8x + 2y = 44
-(5x + 2y = 35)
______
3x + 0 = 9
3x = 9, which contradicts the above-given step '13x = 79'
To learn more about the system of linear equations, refer to the link below:
https://brainly.com/question/2030026
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