Consider the following problem. A bicyclist is riding on a path modeled by the function f(x) = 0.03(8x − x^2), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 1. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Answers
The rate of change of elevation is 0.18
Explanation:Given the function:
[tex]f(x)=0.03(8x-x^2)[/tex]To find the rate of change, we take the derivative of f(x)
[tex]f^{\prime}(x)=0.03(8-2x)[/tex]At the point x = 1, we have:
[tex]\begin{gathered} f^{\prime}(1)=0.03(8-2) \\ =0.03(6)=0.18 \end{gathered}[/tex]The rate of change of elevation is 0.18
Related Questions
Find the value of x. Round lengths of segments to the nearest tenth andangle measures to the nearest degree.
Answers
Answer:
7.8
Explanation:
The length x, the side with length 6, and the angle of 40 degrees are related by the trigonometric function cosine, so
[tex]\cos 40=\frac{6}{x}[/tex]Because x is the hypotenuse and 6 is the adjacent side.
Solving for x, we get
[tex]\begin{gathered} x\cos 40=x\cdot\frac{6}{x} \\ x\cos 40=6 \\ \frac{xcos40}{\cos40}=\frac{6}{\cos 40} \\ x=\frac{6}{\cos 40}=\frac{6}{0.766}=7.8 \end{gathered}[/tex]Therefore, the value of x is 7.8
The distance from Earth to the sun is about 9.3 × 107 miles. The distance from Jupiter to the sun is about 4.84 × 108 miles. How much closer is the Earth to the sun than Jupiter to the sun?
Answers
The earth is 3.91×10^8 miles closer to the sun than jupiter
What is distance?Distance is the space or gap between two points or bodies. It is a scalar quantity and measured in cm, m, km, miles e.t.c
The distance between the earth and the is 9.3×10^7 miles and the distance of Jupiter from the sun is 4.84×10^8 . This shows that the earth is closer to sun than Jupiter.
The dimension of how closer the earth is to the sun than Jupiter is therefore
( 4.84×10^8)-(9.3×10^7)= 3.91×10^8 miles
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18) Find the greatest common factor (GCF) for list of terms: 10x3y5, -15x4y8, 20x5y6
Answers
10x3y5,
-15x4y8,
20x5y6
[tex]undefined[/tex]greatest common factor of 10, 15, and 20 is 5
greatest common factor of x^3, x^4 and x^5 is x^3
greatest common factor of y^5, y^8 and y^6 is y^5
Therefore the greatest common factor of all is:
5x^3y^5
[tex]5x^3y^5^{}[/tex]The price of a local newspaper increases from 80p to £1.
Find the percentage increase
Answers
Answer:
25%Step-by-step explanation:
The price of a local newspaper increases from 80p to £1.
Find the percentage increase
increase = Increase ÷ Original Number × 100
increase = 1 : 0.8 x 100
increase = 125
so the percentage increase is
125 - 100 =
25%
Find the values of x and y
Answers
Check the picture below.
[tex]13y=20x+3y\implies 10y=20x\implies y=\cfrac{20x}{10}\implies y=2x \\\\[-0.35em] ~\dotfill\\\\ 13y+(8x+y)=180\implies 14y+8x=180\implies \stackrel{\textit{substituting}}{14(\underset{y}{2x})+8x=180} \\\\\\ 28x+8x=180\implies 36x=180\implies x=\cfrac{180}{36}\implies \boxed{x=5}~\hfill \boxed{\stackrel{y = 2(5)}{y = 10}}[/tex]
Instructions: Identify the type of sequence and write the explicit rule.
Answers
SOLUTION:
Case: Sequences
Method:
3, 12, 48, 192,...
Step1:
The sequence is increasing exponentially
Type: Geometric/Exponential Sequence
Step 2:
The Explicit rule is gotten from the formula:
[tex]a_n=ar^{n-1}[/tex]a= 3,
r= (12/3)
r= 4.
The rule, therefore:
[tex]a_n=3(4)^{n-1}[/tex]Final answer:
Type: Geometric sequence
Explicit rule
[tex]a_n=3(4)^{n-1}[/tex]N N Which of the following is an equation of line k in the xy-plane above? (A) y=-x-4 (B) y = x+2 (C) 2y - 3x = -8 (D) 2y - 3x = -4
Answers
Answer:
[tex]2y-3x=-8[/tex]Explanation:
Given the graph in the attached image;
The intercept of the line on the y-axis is at;
[tex]\begin{gathered} y=-4 \\ At\text{ point;} \\ (0,-4) \\ \text{ intercept b is;} \\ b=-4 \end{gathered}[/tex]At the x=2, the value of y is;
[tex]\begin{gathered} y=-1 \\ at\text{ point;} \\ (2,-1) \\ \end{gathered}[/tex]The slope of the line can be calculated using the two points on the graph;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-(-4)}{2-0}=\frac{-1+4}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]The slope intercept equation of a straight line is of the form;
[tex]y=mx+b[/tex]substituting the slope m and intercept b we have;
[tex]y=\frac{3}{2}x-4[/tex]As this is not among the given options, let us solve further;
multiply through by 2 and move the x term to the left side;
[tex]\begin{gathered} y(2)=\frac{3}{2}x(2)-4(2) \\ 2y=3x-8 \\ 2y-3x=-8 \end{gathered}[/tex]Therefore, from the given options the correct equation for the line is C;
[tex]2y-3x=-8[/tex]Write an equation (-5,-2) and (-4,-3)
Answers
The equation from (-5, -2) and (-4, -3) is y = -1x - 7
What is Equation of line?
A straight line's equation is a mathematical formula that describes the relationship between the coordinate locations along the line. It can be expressed in a variety of ways and provides the line's slope, x-intercept, and y-intercept.
Given:
P1: (-5, -2)
P2: (-4, -3)
Find:
The equation for the line that passes thru P1 & P2
Solution:
y = mx + b
Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept
m = ( y2 - y1 ) / ( x2 - x1 )
= ( -3 + 2 ) / ( -4 + 5 ) )
= -1 / 1
∴ m = -1
Using either P1 or P2, plug in one of their respective x- and y-values into:
y = -1 x + b
For (-5, -2)
-2 = -1 ( -5 ) + b
-2 = 5 + b
-7 = b
∴ b = -7
∴ y = -1x - 7 is the equation of the line that passes thru both points (-5, -2) and (-4, -3)
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Salim sells fax machines that come in Standard and Enhanced models. The Standard model sells for $325 and the Enhanced model sells for $385. If Salim sold a total of 45 units and took in $15,525, how many of the Enhanced model did he sell?
Answers
On the first day a man did 3/8 of a job on the next day he completed another 2/5of the job what fraction the job was left undone?
Answers
Step-by-step explanation:
3/8+2/5
L.C.M=40
15+16/40=31/40
1/1-31/40
40-31/40
9/40
The value of y is directly proportional to the value of x.If y=12 when x=9, what is the value of x when y=80
Answers
Step 1:
Write the formula connecting y and x.
[tex]\begin{gathered} y\text{ }\propto\text{ x} \\ y\text{ = kx} \\ k\text{ = }\frac{y}{x} \end{gathered}[/tex]Step 2:
Find the value of k when y = 12 and x = 9
[tex]\begin{gathered} k\text{ = }\frac{y}{x}\text{ = }\frac{12}{9}\text{ = }\frac{4}{3} \\ \text{Therefore} \\ y\text{ = }\frac{4}{3}x \end{gathered}[/tex]Step 3
You can find x when y = 80.
[tex]\begin{gathered} \text{Frpm y = }\frac{4}{3} \\ \text{When y = 80} \\ 80\text{ = }\frac{4x}{3} \\ \text{Cross multiply} \\ 4x\text{ = 80}\times3 \\ 4x\text{ = 240 Divide both sides of the equation by 4} \\ x\text{ = }\frac{240}{4} \\ x\text{ = 60} \end{gathered}[/tex]Final answer
x = 60
Find the value of x in the triangle shown below.227ASCAssChoose 1 answer:MY= 45Col= 9MY= 5ProProD2 = 53Tea
Answers
The given triangle is a right triangle as shown by the square symbol inside. With this, we can solve the length "x" of this triangle using the Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]where c = length of the hypotenuse and "a" and "b" are any of the remaining sides.
In our triangle, we have 7 as our hypotenuse and 2 as the length of the one side. Let's apply these values in the formula above.
[tex]\begin{gathered} 7^2=2^2+b^2 \\ 49=4+b^2 \\ 49-4=4+b^2-4 \\ 45=b^2 \\ \sqrt[]{45}=\sqrt[]{b^2} \\ \sqrt[]{45}=b \\ 3\sqrt[]{5}=b \end{gathered}[/tex]Therefore, the value of x is √45.
(2x^3+13x^2+16x+5)÷(x^2+9x+5)
Answers
The answer will be (x-1). (2x-1). The polynomial equation P(x) = 0 has roots, or solutions, that may be found by setting each factor to 0 and figuring out what x is. Factor the polynomial equation to find the solution. Set each variable to 0. x - 6 = 0 or x + 1 = 0 or 2x4 = 0
Finding polynomial roots (zeroes) is the focus of this solution.
What is quadratic equations?Due to the fact that the variable is squared, the word "quadratic," which means "square," was coined (like x2).
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a). See examples of how to solve different equations using the formula.
f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
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In this example, the rapper wants to divide a recipe in half to make a cake for 5 people instead of 10. Explain why he multiplies the first ingredient, ⅔ of a cup sugar, by ½.
Answers
Answer:1 889 - 1927 = 1889 - 1927 =9
Step-by-step explanation:
Could I get help with this problem I have in algebra?
Answers
Answer
Explanation
Cost of a lower deck ticket = 42 dollars
Cost of an upper deck ticket = 75%
The table shows the cost of shampoo at a discount store Cost $ 2.95 $4.50 $6.05 Number of bottles 1 2 3is the cost of the shampoo bottles proportional to the amount of bottles ?
Answers
Answer:
Not proportional
Explanation:
First, we determine the unit rate for each of the pairs of points.
[tex]\begin{gathered} UnitRate=\frac{\text{Cost}}{\text{Number of bottles}} \\ \frac{2.95}{1}=\$2.95\text{ per bottle} \\ \frac{4.50}{2}=\$2.25\text{ per bottle} \\ \frac{6.05}{3}=\$2.02\text{ per bottle} \end{gathered}[/tex]We see that the unit rates are not the same.
Therefore, the cost of the shampoo bottles IS NOT proportional to the number of bottles
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Students in Mrs. McGee's third grade class are working on times tables, and they demonstrate mastery by passing tests. Rebecca has passed 12 tests so far. Her classmate, Marie, has passed 3 tests of them. From now on, Rebecca plans to take and pass 2 tests per week. Meanwhile, Marie plans to do 5 per week. At some point, Rebecca will catch up to Marie. How long will it take? How many tests will each child have passed? In weeks, the children will each have passed tests.
Answers
Solution
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Represent the unknown terms
Let x represents the number of weeks
Let y represents the total number of test passed
STEP 2: Interpret the statements
For Rebecca
[tex]y=2x+12[/tex]For Marie
[tex]y=5x+3[/tex]STEP 2: Find the number of weeks they will pass the same amount of test.
This means that y will be equal to y
[tex]\begin{gathered} y=y \\ 2x+12=5x+3 \\ 2x-5x=3-12 \\ -3x=-9 \\ x=\frac{-9}{-3}=3\text{ weeks} \end{gathered}[/tex]Hence, they will both pass the same number of tests in 3 weeks
STEP 3: Find the amount of tests passed
For Rebecca
[tex]\begin{gathered} 2x+12 \\ x=3 \\ y=2(3)+12=6+12=18 \end{gathered}[/tex]For Marie
[tex]\begin{gathered} y=5x+3 \\ x=3 \\ y=5(3)+3=15+3=18 \end{gathered}[/tex]Both will pass 18 tests in 3 weeks
ANSWER:
In 3 weeks, the children will each have passed 18 tests.
Is the following relation a function? Justify your answer.
y
X
6
-1.
4
2
-1
3
O No, because there is an input value with more than one output value
O No, because there is an output value with more than one input value
Yes, because each input value has only one output value
Yes, because each output value has only one input value
Answers
No, because there is an input values with more than one output value is the following relation a function.
Based on the given function is,
x y
6 2
-1 -1
4 3
What is the Function :A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
So,
We can write,
One input value has more than output values.
In this function we have,
-1 is mapped to both -2 and -1
In this case,
-1 input value is mapped to both output values of -2 and -1.
Therefore,
No, because there is an input values with more than one output value is the following relation a function.
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Shen runs each lap in 4 minutes. He will run at least 48 minutes today. What are the possible numbers of laps he will run today?Use n for the number of laps he will run today.Write your answer as an inequality solved for n.
Answers
From the statement, we know that:
0. Shen runs each lap in 4 minutes,
,1. he will run ,at least, 48 minutes today ⇒ t ≥ 48 min.
(1) From point 1, we know that Shen's speed is:
[tex]s=\frac{1\text{ lap}}{4\text{ min}}=\frac{1}{4}\cdot\frac{\text{lap}}{\text{min}}.[/tex](2) The speed (s) times the time (t), we get the # of laps (n):
[tex]n=s\cdot t\ge\frac{1}{4}\cdot\frac{\text{laps}}{\text{min}}\cdot48\text{ min}=\frac{48}{4}\text{ laps}=12\text{ laps}\Rightarrow n\ge12\text{ laps.}[/tex]Answern ≥ 12
The ratio of 8 books to 20 books isA) 2:5B) 5:2C) 4:5D) 5:4
Answers
the ratio of 8 books to 20 books is:
[tex]8\colon20[/tex]now we can divide by the same number so:
[tex]\begin{gathered} \frac{8}{2}\colon\frac{20}{2} \\ \frac{4}{2}\colon\frac{10}{2} \\ 2\colon5 \end{gathered}[/tex]SO is option A)
can you help me to answer 2736×2
Answers
Answer
[tex]\begin{gathered} 2\text{ 7 3 6} \\ \times\text{ 2} \\ =5\text{ 4 7 2} \end{gathered}[/tex]2 7 3 6
x 2
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5
what is the midpoint of the segment that would be created between points L and N on the graph
Answers
Given:
The figure KLMN on graph.
Required:
what is the midpoint of the segment that would be created between points L and N .
Explanation:
We know the mid point formula
[tex]LN=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]We have L(-2, 3) and N(6, 3)
and
[tex]\begin{gathered} LN=(\frac{-2+6}{2},\frac{3+3}{2}) \\ =(\frac{4}{2},\frac{6}{2}) \\ =(2,3) \end{gathered}[/tex]Answer:
Midpoint is (2,3).
fractions and geometry studying for a win test workeys
Answers
Given that the pharmacist can fill 250 prescriptions in 40 hours.
Consider the following,
[tex]\begin{gathered} 1\text{ hour}=60\text{ minutes} \\ 40\text{ hour}=40\times60=2400\text{ minutes} \end{gathered}[/tex]So it can be understood that the pharmacist can fill 250 prescriptions in 2400 minutes.
Then the time taken to fill 1 prescription is calculated as,
[tex]\begin{gathered} 250\text{ prescriptions}\equiv2400\text{ minutes} \\ \Rightarrow1\text{ prescription}\equiv\frac{2400}{250}=9.6\text{ minutes} \end{gathered}[/tex]Thus, it will take 9.6 minutes to fill 1 prescription.
Therefore, option (E) is the correct choice.
Определите количество сторон правильного многоуголь
ника, если угол, смежный с углом многоугольника, составляет 2/3 угла многоугольника
Answers
Answer:
n=6
Step-by-step explanation:
Угол многоугольника 2х, смежного угла х.
2х+х=180.
3х=180.
х=60° .
Углы многоугольника 120°.
Формула углов правильного многоугольника.
аₙ=(n-2)/n * 180.
120=(n-2)/n *180. после преобразования
3(n-2)=2n.
n=6.
Answer: n=6.
Step-by-step explanation:
Sort the sequences into categories. Determine which sequences are arithmetic and which are geometric. Drag each label to the correct location on the table. Each label can be used more than once. Arithmetic Sequence Geometric Sequence (90, 87, 84, 81, 78, ...) (4, 12, 36, 108, 324, ...) (8,1,1/8,1/64,1/512,...) (3, 10, 17, 24, 31,...) (1,1.4,1.8, 2.2, 2.6, ...) (3,1.5, 0.75, 0.375,...)
Answers
Given the sequences we are asked to identify whether they are geometric or arithmeti. This can be seen below.
Explanation
For an arithmetic sequence
[tex]T_2-T_1=T_3-T_2^[/tex]For a geometric sequence
[tex]\frac{T_2}{T_1}=\frac{T_3}{T_2}[/tex]Therefore;
Answer:
[tex]\begin{gathered} Arithmetic\text{ sequence}\Rightarrow90,87,84,81,78,.. \\ Geometric\text{ sequence}\Rightarrow4,12,36,108,324,... \\ Geometric\text{ sequence}\Rightarrow8,1,1/8,1/64,1/512,... \\ Arithmetic\text{ sequence}\Rightarrow3,10,17,24,31..... \\ Arithmetic\text{ sequence}\Rightarrow1,1.4,1.8,2.2,2.6.... \\ Geometric\text{ sequence}\Rightarrow3,1.5,0.75,0.375,... \end{gathered}[/tex]in the rhombus shown below AC and BD are 6 and 4in respectively determine the area of the figure in square inches
Answers
The area of a rhombus is computed as follows:
A = p*q*1/2
where p and q are the diagonals of the rhombus.
In this case:
A = AC*BD*1/2
A = 6*4*1/2
A = 12 square inches
Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive integer value. x^2=4(x-9)
Answers
Given the following equation:
[tex]x^2=4(x-9)[/tex]First of all, we note that the quadratic equation is written in the general form shown below;
[tex]ax^2+bx+c=0[/tex]We shall now attempt to re-write the equation given in the form shown above. This is shown as follows;
[tex]\begin{gathered} x^2=4(x-9)_{} \\ We\text{ shall now expand the parenthesis;} \\ x^2=4x-36 \\ We\text{ shall now collect all like terms;} \\ \text{Subtract 4x and add 36 to both sides to both sides} \end{gathered}[/tex][tex]\begin{gathered} x^2-4x+36=4x-4x-36+36 \\ x^2-4x+36=0 \end{gathered}[/tex]We now have our quadratic equation as shown above.
Comparing this with the general form of a quadratic equation, we can now identify a, b and c as follows;
[tex]\begin{gathered} a=1 \\ b=-4 \\ c=36 \end{gathered}[/tex]ANSWER:
a = 1
b = -4 and
c = 36
Find the area of this circle. Use3.14 for i.7 AtThe area of the circle is aboutfta.(Round to the nearest hundredth as needed.)
Answers
153.86 ft²
Explanation:[tex]\text{Area of a circle = }\pi r^{2}[/tex][tex]\begin{gathered} r\text{ = radius = 7 ft} \\ \pi\text{ = 3.14} \\ In\text{serting into the formula:} \\ \text{Area of the circle = 3.14 }\times7^2 \end{gathered}[/tex][tex]\text{Area of the circle = 153.86 ft}^2[/tex]To the nearest hundredth, Area of the circle = 153.86 ft²
In the year 2003, a person bought a new car for $12500. For each consecutive year after that, the value of the car depreciated by 7%. How much would the car be worth in the year 2005, to the nearest hundred dollars?
Answers
Answer + Explanation:
13500x0.07 = 945
945 x 2 = 1890
13500 - 1890 = 11610
To the nearest hundred dollars: 11,600
ANSWER: 11,600
I need help on this one! Please and thank you!
Answers
Given:
[tex]\cos \theta\text{ =- }\frac{1}{8}[/tex]Solving for the angle measure:
[tex]\begin{gathered} \theta\text{ = }\cos ^{-1}(-\frac{1}{8}) \\ =\text{ }97.181 \end{gathered}[/tex]Hence, we can find the exact value of sin theta:
[tex]\begin{gathered} But\text{ }\theta\text{ is in the third quadrant.} \\ \sin (97.181\text{ -180) = sin(-82.8190}) \\ =\text{ -0.992} \end{gathered}[/tex]Hence, the exact value of sin theta is -0.992
