The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours.
Estimate the value of T′(8). Give units in your answer.
What is the meaning of T′(8)?
t 0 2 4 6 8 10 12 14
T 73 73 70 68 73 80 86 89
Answers
We need to estimate the value of T'(8) and then we need to give the meaning of this value. Since we have a table and not an expression of a function our goal is to find the Average Rate of Change between two points.
For a nonlinear graph whose slope changes at each point, the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is the slope of the line through the two points. So:
[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} =\frac{Change \ in \ y}{Change \ in \ x}=m_{sec}[/tex]
1. Estimated value of T′(8).
T'(8) means the derivative of the function T(t) when t = 8 hours. So, we can estimate this value using the average rate of change:
[tex]ARC=\frac{T(8)-T(6)}{8-6} =\frac{73-68}{8-6}=\frac{5}{2} \ degrees \ per \ hours[/tex]
2. The meaning of T′(8)
This means the average temperature after midnight in Phoenix on March 15, from t = 6 to t = 8 hours, that is, for each hour the temperature rises 5/2 degrees on the Fahrenheit scale. The points have been plotted in the Figure bellow.
The rate of change of the temperature is 3 degrees Celsius per hour. This response means that temperature has an instantaneous increase rate of 3 degrees Celsius per hour at [tex]t = 8\,h[/tex].
We can estimate the rate of change of the temperature, in degrees Celsius per hour, by calculating the average of two consecutive secant lines, whose expression is presented below:
[tex]T'(t) \approx \frac{1}{2}\cdot \left[\frac{T(t+\Delta t)-T(t)}{\Delta t} + \frac{T(t)-T(t-\Delta t)}{\Delta t} \right][/tex] (1)
If we know that [tex]\Delta t = 2[/tex], [tex]T(6) = 68[/tex], [tex]T(8) = 73[/tex] and [tex]T(10) = 80[/tex], then the estimated value of the rate of change of the temperature is:
[tex]T'(8) = \frac{1}{2}\cdot \left[\frac{80-73}{2}+\frac{73-68}{2} \right][/tex]
[tex]T'(8) \approx 3\,\frac{^{\circ}C}{h}[/tex]
The rate of change of the temperature is 3 degrees Celsius per hour. This response means that temperature has an instantaneous increase rate of 3 degrees Celsius per hour at [tex]t = 8\,h[/tex].
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Related Questions
For f(x) = 2x + 1 and g(x) = x2 – 7, find (f – g)(x).
A. –x2 + 2x – 6
B. 2x2 – 15
C. x2 – 2x – 8
D. –x2 + 2x + 8
HELP!! give me the correct answer
Answers
(f-g)(x)=2x+1-x^2+7
(f-g)(x)= -x^2+2x+8
For the function, f(x) = 2x + 1 and g(x) = x² – 7, (f – g)(x) will be D. –x² + 2x + 8
How to calculate the functionTo find (f - g)(x), we need to subtract the function g(x) from the function f(x).
f(x) = 2x + 1
g(x) = x² - 7
(f - g)(x) = f(x) - g(x)
Substituting the given functions:
(f - g)(x) = (2x + 1) - (x² - 7)
Now let's simplify:
(f - g)(x) = 2x + 1 - x² + 7
Combining like terms, we have:
(f - g)(x) = -x² + 2x + 8
Therefore, the answer is D. -x² + 2x + 8.
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A father and his daughter together weigh seven times the daughter's weight x. The father weighs 180 lbs. Which equation can be used to find the daughter's weight?
A. 180-7x = x
B. x -180 = 7x
C. 180 -x = 7x
D. 180 + x = 7x
...?
Answers
x-7x=-180
-6x=-180
x=180/6
x=30 pounds
180+30=210
I really need help solving this whole problem.
Answers
No, you do not have enough information to determine the price of both gasoline and oil from the prices that "you" and "your friend" paid at the station. If you look closely, you'll notice that "your friend" bought half the amount of gas and oil that you did and paid half the price-- you won't get a satisfactory answer from just this information.
b.
Yes, with this you can use elimination to solve the systems, as you bought 2 quarts of oil and 10 gallons of gas for $45.50 and the receipt owner bought 2 quarts of oil and 8 gallons of gas for $38.40.
c.
Alright, so here is elimination, that is, eliminating a variable if you add two equations together. (This is a confusing answer so I would suggest you ask someone else for a better one).
So, first we make an equation out of the word problem in the beginning.
I'll treat 1 gallon of gas as "g", and one quart of oil as "o".
45.50 = 10g + 2o
+ 38.40 = 8g + 2o
You'll note that there are 2 "o"s in each equation. So, we'll multiply the bottom equation by -1 so the "o" cancels out and we can get the value of "g".
45.50 = 10g + 2o
+ (38.40 = 8g + 2o) * -1
This becomes:
45.50 = 10g + 2o
+ -38.40 = -8g - 2o
Subtract, and this becomes
7.1 = 2g
/2
g = 3.55
Alright, so now we know the value of a gallon of gas. Let's substitute this back into the original equation to find the price for the oil.
45.50 = 10(3.55) + 2o
45.50 = 35.5 + 2o
-35.5 -35.5
10 = 2o
/2
o = 5
So we know that 1 gallon of gas is $3.55 and one quart of oil is $5.00.
What is the greatest common factor of 34n and 8n^2?
Answers
_________________________________
The greatest common factor (GCF) of 34n and 8n² is: 2n .
__________________________________________
Explanation:
_______________
First, break down EACH term into prime factors:
__________________________________________
Start with the first term given: "34n" :
__________________________________________
34n = 17 * 2 * n
__________________________________________
Now, do so with the second term given: "8n² " :
__________________________________________
8n² = 2 * 2 * 2 * n * n
_______________________________________________
Now, look for factors that exist in EACH of the two terms:
_______________________________________________
In the term: "34n"; there is a "17", and a "2" and a "n" — and that's it!
_______________________________________________
In the term: "8n² " that is a "2" and an "n".
_______________________________________________
So: 2 * n = 2n ; which is our answer:
_______________________________________________
The greatest common factor (GCF) of 34n and 8n² is: 2n .
_________________________________________________________
The greatest common factor of 34n and 8n² is 2n, as both expressions share the variable n and the highest common numerical coefficient is 2.
The greatest common factor (GCF) of two algebraic expressions can be found by identifying the highest powers of common factors in the terms. For the expressions 34n and 8n², both terms have n as a common factor. Since we want the greatest common factor, we take the highest power of n that appears in both terms, which is n (not n² because n is the highest power in the least degree term, 34n). Next, we find the GCF of the numerical coefficients 34 and 8, which is 2. Therefore, the greatest common factor of 34n and 8n² is 2n.
Is 8.92 greater or less than 8.9
Answers
8.92 > 8.9
Evaluate BC for A = 5, B = -4, and C = 2
Answers
B=-4
C=2
B times C=-4 times 2=-8
-4•2= -8
What is the simplified form of the following expression? (x10)(x2)
Answers
I'm pretty sure the answer would be x^12
Can someone smart help me here?
Solve the mathematical puzzle.
S is a three digit number.
Determine the digits of S from the clues.
All the digits are odd.
The last two digits add to make ten.
The first and last digits add to make eight.
The first two digits add to make twelve.
S is
Answers
S is the three digit number.
h - a number of hundreds
t - a number of tens
o - a number of ones
S = 100h + 10t + o
The last two digits add to make ten: t + o = 10
The first and last digits add to make eight: h + o = 8
The first two digits add to make twelve: h + t = 12
t + o = 10 ⇒ o = 10 - t
h + o = 8 ⇒ o = 8 - h
_______
10 - t = 8 - h
h + t = 12 ⇒ h = 12 - t
_______
10 - t = 8 - (12 - t)
10 - t = 8 - 12 + t
10 - t = -4 + t
10 + 4 = t + t
2t = 14
t = 14/2 = 7
______
h = 12 - t = 12 - 7 = 5
______
o = 8 - h = 8 - 5 = 3
S = 100h + 10t + o
h = 5
t = 7
o = 3
S = 100*5 + 10*7 + 3
= 500 + 70 + 3
= 573
What is the lcm of 21, 84, 126?
Answers
So, your final answer is 252
Hope this helps!
Which statement is modeled by the expression?
150/k
The Henderson family drove 150 miles each day of their vacation. If their vacation lasted for k days, then 150/k is the total number of miles they traveled on their vacation.
The cafeteria has a capacity of 150 seats. If k is the number of people in the cafeteria at lunch time, then 150/k is number of seats that were not used at lunch time.
A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.
Cory had 150 dollars in his savings account. He withdrew k dollars to buy a catcher's mitt. He then had 150/k dollars left in his savings account.
Answers
Example : lets say there are 10 shelves.....so k = 10
150/10 = 15 books on each shelf.
Hey
I hope you are having a great day
The answer would be A librarian had 150 books to be placed on shelves with an equal number of books on each shelf. If k is the number of shelves to be used, then 150/k is the number of books on each shelf.
Explanation: Lets see Option 1 is obviously out Option 2 does not make
sense When it comes to option 3 that makes the most sense Option 4 could be right but option 3 is the best and correct answer
So that's your answer
Hope This Helps :)
-Sprinkles
What is 0.021 in fraction form?
Answers
= 21/1000
Fill in the missing number to complete the factorization:
x 3 + x 2 - 21x - 45 = (x + 3)(x - 5)(x +
Answers
Missing number to complete the factorization is 3.
What is factorization?Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.
Given expression
[tex]x^{3}+x^{2} -21x-45=(x+3) (x-5) (x+a)[/tex]
Let a be the missing number
(x + 3) (x - 5) (x + a)
= [tex](x^{2} -5x+3x-15)(x+a)[/tex]
= [tex](x^{2} -2x-15)(x+a)[/tex]
[tex]x^{3}+x^{2} -21x-45=x^{3} +x^{2} a-2x^{2} -2xa-15x-15a[/tex]
By comparing the expressions
-2xa - 15x = -21x
⇒ -2xa = -6x
⇒ a = 3
[tex]x^{2} (a-2) = 1x^{2}[/tex]
⇒ a - 2 = 1
⇒ a = 3
-15a = -45
⇒ a = 3
Hence, missing number to complete the factorization is 3.
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15. TRIANGLES Find the dimensions of a triangle if the base is 2/3 the measure of the height and the area is 12 square centimeters. (Lesson 4-3)
Answers
The height is unknown.
Let h = height.
The base is also unknown, but it is known in terms of the height.
The base is 2/3 the measure of the height.
Since the height is h, the base is 2/3 of h, or (2/3)h.
Now we have an expression for the height, h, and an expression for the base, (2/3)h. We can use the formula for the area of a triangle.
A = bh/2
12 = (2/3)h * h / 2
Now you have an equation in only one variable, h, so you can solve for h.
Once you know h, find the base.
The dimensions of the triangle with a base that is 2/3 of its height and an area of 12 square centimeters are a base of 4 centimeters and the height of 6 centimeters.
Explanation:The question asks for the dimensions of a triangle. We are given that the base is 2/3 of the height and the area is 12 square centimeters. The formula for the area of a triangle is 1/2 * base * height. Since we know that the base is 2/3 of the height, we can denote the height as 'h' and the base as (2/3)h. From here, we can set up the equation 12 = 1/2 * (2/3)h * h, which simplifies to 12 = 1/3 * h². Solving for 'h', we find the height is √36 or 6 centimeters. Given the base is 2/3 of the height, the base, therefore, is 4 centimeters.
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what is the answer to 8y - 1 = 31
Answers
8y-1=31
8y=31+1
8y=32
Y=32/8
Y=4
What is another name for 34/8 as a mixed number??
Answers
4 2/8 = 4 1/4
So another name for 34/8 as a mixed number is 4 1/4. I hope this helps!
Determine the x values that cause the function to be (a) Zero, (b) Positive and (c) Negative, then d) sketch a graph of the function.
Answers
find roots
determine intervals between roots for which function is positive or negative
sketch
or use calculus either way
Determine whether the dilation from A (blue figure) to B (green figure) is an enlargement or reduction, then find the scale factor of the dilation.
a. reduction; scale factor of 2/5
b. enlargement; scale factor of 5/2
c. reduction; scale factor of 2/3
d. enlargement; scale factor of 3/2
Answers
Answer:
Option B
Step-by-step explanation:
In the figure attached we have to find the scale factor of dilation of figure A to figure B.
Since figure A is smaller than figure B, it concludes figure A has been enlarged to form figure B.
Now we have to find the scale factor of enlargement.
Scale factor = [tex]\frac{\text{one side of the larger figure}}{\text{one side of the smaller figure}}[/tex]
= [tex]\frac{5}{2}[/tex]
Therefore option B is the correct answer.
How do u simplify 2/5 x 6/7? and what the answer?
Answers
2/5 x 6/7 would be 5/2 x 7/6
5 x 7 = 35
2 x 6 = 12
35/12
divide by a common number to get the smallest answer possible.
im not going to do it completely.
Jimmy was 12 years old in 2014 and now in 2016 he is 15 how did he grow 3 years in 2 years?
A. HE WAS BORN ON MAY 1ST
B. HE WAS BORN ON DECEMBER 23RD
C. HE WAS BORN ON NOVEMBER 15TH
D. HE WAS BORN ON JANUARY 20TH
Answers
If he was born on January 20th, he would be the oldest in his school classes. Right when the new year starts, his birthday comes up.
1)A discriminant of 0 indicates what type of roots?
A)Two Complex
B)One Rational Double
C)Two Rational
D)Two Irrational
2)The quadratic 2x2 + 6x + 3 has what type of roots?
A)Two Irrational
B)Two Complex
C)One Rational Double
D)Two Rational
3)The quadratic x2 + 20x + 100 has what type of roots?
Answer
A)Two Irrational
B)Two Rational
C)One Rational Double
D)Two Complex
4)What is the possible discriminant of the graph?(graph in the link)
A)0
B)–11
C)73
D)25
5)What is the possible discriminant of the graph?(Graph in the link)
A)0
B)17
C)25
D)–15
...?
Answers
1. A discriminant of 0 indicates a rational double, which will be -b/2a for a quadratic of the form ax^2 + bx + c. The answer would be C.
2. The quadratic 2x2 + 6x + 3 has two irrational roots. The answer would be option A.
3. The quadratic x2 + 20x + 100 has One Rational Double root. The answer would be C.
4. The possible discriminant of the graph given would be -11. The answer is option B.
5. The possible discriminant of the graph given would be 0. The answer is A.
Hope these answers help.
Which of the following are quadratic functions?
Check all that apply.
a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1 Which of the following are quadratic functions?
Check all that apply.
a. y=2(x-3x^2+1)
b. y=5+2x
c. y=1/2x^2-13x+4
d. y= x/x-1
Answers
Final answer:
The quadratic functions are: y = 2(x - 3x² + 1), y = 1/2x² - 13x + 4, and y = 1.
Explanation:
A quadratic function is a polynomial function of degree 2, which means its highest power of x is 2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.
Out of the given options, the quadratic functions are:
a. y = 2(x - 3x² + 1)
c. y = 1/2x² - 13x + 4
d. y = x/x - 1 (this can be simplified to y = 1)
The options b. (y = 5 + 2x) is not a quadratic function because it only has a linear term (power of x is 1).
What is the inverse of the function f(x) = 2x – 10? h(x) = 2x – 5 h(x) = 2x + 5 h(x) = x – 5 h(x) = x + 5
Answers
y = 2x -10
Switch y and x,
x = 2y -10
solve for y,
x + 10 = 2y
x/2 + 10/2 = y
x/2 + 5 = y
y = x/2 + 5 or h(x) = x/2 + 5
Hence, the inverse of the function f(x) = 2x-10 is h(x) = x/2 + 5
The inverse of a function is gotten by swapping the x and y coordinates.
The inverse of function f(x) is[tex]h(x) = \frac x2 + 5[/tex]
Given
[tex]f(x) = 2x - 10[/tex]
Rewrite as:
[tex]y = 2x - 10[/tex]
Swap x and y
[tex]x = 2y - 10[/tex]
Solve for y
[tex]2y = x + 10[/tex]
Divide by 2
[tex]y = \frac x2 + 5[/tex]
So, we have:
[tex]h(x) = \frac x2 + 5[/tex]
Hence, the inverse function is[tex]h(x) = \frac x2 + 5[/tex]
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URGENT MATH HELP!
Which shows the conversion of 0.21 millimeters to inches?
There is 0.03937 inch in 1 millimeter.
A.
0.21 mm × 0.03937 in./mm = 0.0083 inches
B.
0.21 mm + 0.03937 in./mm = 0.24937 inches
C.
0.21 mm ÷ 0.03937 in./mm = 5.34 inches
D.
0.21 mm × 0.03937 in./mm = 8.3 × 10^-2 inches
Answers
________________________________
0.21 mm × 0.03937 in./mm = 0.0083 inches
_________________________________
What happened to the little boy who swallowed a silver dollar?
Answers
Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000, what is the closing cost amount?
Answers
Answer:
Proportion states that two fractions or ratios are equal.
Let x be the closing cost amount.
As per the statement:
Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000.
Purchased Price = $275,000
then, by definition of proportion :
[tex]\frac{4}{100}=\frac{x}{275000}[/tex]
By cross multiply we have;
1,100,000 = 100x
Divide both sides by 100 we have;
11,000 = x
or
x = $ 11,000
Therefore, the closing cost amount is, 11,000
What step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment?
Answers
To copy a line segment and ensure it has the same length as the original, use a compass to measure and create a duplicate line segment.
Explanation:To copy a line segment and ensure that the new line segment has the same length as the original, we can use a compass. Here are the steps:
Place the compass needle on one endpoint of the original line segment.Open the compass to the length of the original line segment.Without changing the compass width, place the compass needle on the other endpoint of the original line segment and draw an arc.Use the compass to measure the same length on the arc and draw a line segment connecting the two marks.By using this method, we can create a duplicate line segment with the same length as the original.
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A trail mix has 4 cups of raisins, 3 cups of chocolate, 6 cups of peanuts, and 2 cups of cashews. Which ingredients are in the same ratio as cashews to raisins?
Answers
Chocolate: peanut 3:6 or 1:2
So it is chocolate to peanuts
What is 0.666 in a fraction?
Answers
The school’s guidance department compares the grade-point averages and standardized state test scores for 10 students in each grade. The table below shows the correlation coefficient for each data set.
Grade Level and Correlation Coefficient
9th grade 0.3
10th grade –0.1
11th grade 0.2
12th grade –0.8
For which data set(s) is a linear regression model reasonable?
~ 9th grade and 11th grade data sets
~ 10th grade data set
~ 10th grade and 12th grade data sets
~ 12th grade data set
Answers
This is because both have a negative correlation coefficient, meaning they are showing regression, or decrease.
Answer:
12th grade data set
Step-by-step explanation:
How many solutions x 2x 7 = 3x - 7?