An equation of a function y(t) is shown.
y(t)=−t²+14t−40
Which of the following statements are true about the graph of y(t) for
6≤t≤8 and WHY?
a. The value of y(t) increases over the interval 6≤t≤7
b. The value of y(t) increases over the interval 7≤t≤8
c. The average rate of change over the interval 6≤t≤8 is 0
d. The value of y(t) is constant over the interval 6≤t≤8
e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8
Answers
y(t)=-t^2+14t-40
thus the graph will be as shown in the figure:
From the graph we deduce that the correct statement is:
y'(t)=-2t+14=0
thus
t=7
thus
y(7)=0
thus the correct statement is:
c. The average rate of change over the interval 6≤t≤8 is 0
The graph of y(t) increases over the interval 6≤t≤7 because the derivative is positive. The average rate of change over the interval 6≤t≤8 is 0 due to symmetry about the vertex of the parabola at t=7. The rate of change over the intervals 6≤t≤7 and 7≤t≤8 are equal in magnitude but opposite in direction.
Given the quadratic function y(t)=-t²+14t-40, we need to analyze its behavior over the interval 6≤t≤8. The first derivative y'(t) of the function, which represents the slope of the tangent line to the graph at any point t, is -2t + 14. To determine the intervals of increase and decrease, we can set the first derivative to zero to find the vertex of the parabola, yielding t=7, which means the function increases on the interval 6≤t≤7 and decreases on 7≤t≤8.
The average rate of change over an interval is calculated by taking the difference in the function values at the endpoints of the interval over the difference in t. For the interval 6≤t≤8, since this is a symmetrical interval around the vertex, the average rate of change is 0. Furthermore, it follows from symmetry that the average rate of change over the intervals 6≤t≤7 and 7≤t≤8 should be equal in magnitude but opposite in sign.
Considering the stated properties and analyzing the equation, we can conclude that:
The value of y(t) increases over the interval 6≤t≤7.The value of y(t) decreases over the interval 7≤t≤8, so statement b is false.The average rate of change over the interval 6≤t≤8 is 0, making statement c true.The value of y(t) is not constant over the interval 6≤t≤8.The average rates of change over both intervals 6≤t≤7 and 7≤t≤8 are not equal in value; they are opposite, making e false.Related Questions
The population of a major U.S. city is 8,550,405. The land area of the city is 1213.4 square kilometers. What is the best approximate population density of the city? 7047 peoplekm2 7124 peoplekm2 7167 peoplekm2 7500 peoplekm2
Answers
people
7047 ---------
km^2
The population of a major U.S. city = 8,550,405
Area of the city = 1213.4 sq.km
Density = [tex] \frac{Population}{area} [/tex]
Density = [tex] \frac{8,550,405}{1213.4} [/tex]
Density = 7046.6499 [tex] \frac{People}{km^{2}} [/tex]
As the density here will not be in decimal so after rounding the density in whole number,
Density = 7047 [tex] \frac{People}{km^{2}} [/tex]
Option A is the answer
What is the equation of the line whose y-intercept is 3 and slope is 1?
y=x-3
y=x+3
y=3x+1
Answers
Hope this helps! :)
Solve the equation. 20 = –d + 16
A. 4
B. –10
C. –6
D. –4
Answers
The correct answer to this question would be D: negative 4
This is because the negatives from negative 4 and negative d would cancel each other out, to make it a positive 4, resulting in the equation being: 20 = 4 + 16 , which is true
I hope this helped ^^
If sinA/sinB=p,cosA/cosB=q,find tanA and tanB
Answers
cosA/cosB=q
tanA/tanB=p+q
Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
The calculated area of the shape is 50.24 square units
Finding the area of the shape.
From the question, we have the following parameters that can be used in our computation:
The shape
The area of the shape is calculated as
Area = 1/4πr²
Where
Radius, r = 8
Substitute the known values into the equation
Area = 1/4π * 8²
Evaluate
Area = 16π
So, we have
Area = 16 * 3.14
Evaluate
Area = 50.24
Hence, the area of the shape is 50.24 square units
Question
Find the area of the shape.
Use 3.14 for pi. Round your answer to the nearest hundredth.
PLEASE HELP !! URGENT!! ILL MARK THE BRAINLIEST FOR THE CORRECT ANSWER
add or subtract
\frac{x}{x^2-36} -\frac{6}{x^2-36}
Answers
[tex]\frac{x}{x^{2-}36} +\frac{6}{x^{2}-36} = \frac{x+6}{(x-6)(x+6)} = \frac{1}{x-6} , when x \neq 6, and\\x \neq -6.[/tex]
Answer:
x + 6; where x ≠ -6, +6
Step-by-step explanation:
Last week christi spent 2 3/4 hours playing piano this week she spent 3 2/4 hours playing the piano how much more time did she play the piano this week
Answers
3 2/4-2 3/4
Converting the above into proper fraction we get:
14/4-11/4
=(14-11)/4
=3/4
Thus she spent and extra 3/4 hours=45 minutes this week
It’s 3/4 hours which is 40 mins how I did this was I did that then I finished BOOM DONE KID
The english alphabet contains 21 consonants and five vowels. how many strings of six letters, each of which is drawn from the english alphabet, contain (a) exactly one vowel?
Answers
Answer: 20 420 505
2/5x = -3/15 + 1/x
x=0
x=15
x=5
x=3
Answers
Answer:
x = 3
Step-by-step explanation:
[tex]\dfrac{2}{5x}=-\dfrac{3}{15}+\dfrac{1}{x}\\\\\dfrac{1}{5}=\dfrac{5-2}{5x}\qquad\text{add $\frac{3}{15}-\frac{2}{5x}$}\\\\x=3\qquad\text{multiply by 5x}[/tex]
Three different bags of pretzels are sold at the store. which bag of pretzels is the best buy? bag a:10 ounces for $1.10 bag b:12 ounces for $1.38 bag
c.6 ounces for $0.84
Answers
Bag a:
----------------------
10 ounces = $1.10
1 ounce = $1.10 ÷ 10 = $0.11
----------------------
Bag b:
----------------------
12 ounces = $1.38
1 ounce = $1.38 ÷ 12 = $0.115
----------------------
Bag c:
----------------------
6 ounces = $0.84
1 ounce = $0.84 ÷ 6 = $0.14
--------------------------------------------------
Answer: Bag A is the best buy.
--------------------------------------------------
8.Find the value of c that makes the expression be a perfect square trinomial p^2-30p+c
9.Use quadratic formula to solve. 4x^2+7x-15=0
10.Find the number of real number solutions using the discrimination. x^2+4x-32=0
Please help these are my final questions and I need help with them
Answers
Problem 8
p^2 - 30p + c
Step One
Take 1/2 of - 30
1/2 * -30 = - 15
Step 2
Square -15
(-15)^2 = 225
c = 225
Problem Nine
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]
a = 1
b = 4
c = -15
[tex]\text{x = }\dfrac{ -4 \pm \sqrt{4^{2} - 4*1*(-15) } }{2*1} [/tex]
[tex]\text{x = }\dfrac{ -4 \pm \sqrt{\text{16} + \text{60} } }{2} [/tex]
x = [-4 +/- sqrt(76)] / 2
x = [-4 +/- 2*sqrt19]/2
x = [-4/2 +/- 2/2 sqrt[19]
x = - 2 +/- sqrt(19)
x1 = - 2 + sqrt(19)
x2 = -2 - sqrt(19)
These two can be broken down more by finding the square root. I will leave them the way they are. It's just a calculator question if you want it to go into decimal form.
Problem Ten
a = 1
b = 4
c = -32
The discriminate is sqrt(b^2 - 4ac)
D = sqrt(b^2 - 4ac)
D = sqrt(4^2 - 4(1)(-32)
D = sqrt(16 - - 128)
D = sqrt(16 + 128)
D = sqrt(144)
D = +/- 12
Since D can equal + or minus 12 there must be 2 possible (and different) roots. As a matter of fact, this quadratic can be factored.
(x + 8)(x - 4) = y
But that' s not what you were asked for.
The discriminate is > 0 so the roots are going to be real.
Answer; The discriminate is > 0 so there will be 2 real different roots.
please help asap 45 pts
Answers
hope that help
Expenses that are bi-weekly are paid twice a week twice a month every two weeks every two months
Answers
Answer:
Expenses that are bi-weekly are paid every two weeks.
Step-by-step explanation:
Expenses that are bi-weekly are paid every two weeks.
A bi-weekly pay schedule is the most commonly used pay period by employers. It is also called every other week pay period.
This payment method results in 26 paychecks in a year.
How to find the third side of a triangle if two sides are known?
Answers
Final answer:
To find the third side of a triangle when two sides are known, you can use the Triangle Inequality Theorem or the Law of Cosines.
Explanation:
To find the third side of a triangle when two sides are known, you can use the Triangle Inequality Theorem or the Law of Cosines.
Triangle Inequality Theorem:
Take the two known sides of the triangle.
Add the lengths of the two sides together.
Subtract the sum from the total perimeter of the triangle.
Law of Cosines:
Label the two known sides as 'a' and 'b', and the angle between them as 'C'.
Use the formula c² = a² + b² - 2abcos(C) to find the square of the third side.
Take the square root of the result to find the length of the third side.
I need help please help me!!
Answers
2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft^3
(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.
(b) Would the density of the water change if the aquarium was only half full? Explain. Answer:
Answers
As the table can only support 200 lbs the aquarium should not be put on the table.
(b) No the deisity of the water is a constant
(a)
3*3*3=27
27*62=1674
Your answer: 1674
(b)
No, no matter how much water there is, the density will never change.
Using the sample results, estimate the proportion of the entire population that would like to take a cruise to Bermuda.
Answers
That proportion is 5/150, matching ...
A) 0.03
Suppose y varies directly with x and y=-25 when x=5. find y when x=3
Answers
Final answer:
To solve for y when x = 3, we first determined the constant of proportionality (k) using the given values (y = -25 when x = 5). With k found to be -5, we then calculated y for x = 3 to find that y = -15.
Explanation:
The question asks us to find the value of y when x = 3 given that y varies directly with x and that y = -25 when x = 5. Because y is directly proportional to x, we can write the relationship as y = kx, where k is the constant of proportionality.
First, we solve for k:
Set up the equation based on the given information: y = kx
Substitute the known values: -25 = k(5)
Solve for k: k = -25 / 5 = -5.
Now that we have found k, we can use it to find y when x = 3:
Use the determined value of k: y = -5(3)
Multiply to find y: y = -15.
Therefore, when x = 3, y is -15.
What is the following quotient?
3^√60
------------
3^√20
Answers
Answer:
its 3√3 bud
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A counterexample for the expression sin(x)+cos(x)=1 is 45°
True or False?
Answers
sin (x) + cos (x) = 1
Substituting x = 45 degrees we have:
sin (45) + cos (45) = 1
(root (2) / 2) + (root (2) / 2) = 1
Rewriting:
(root (2) + root (2)) / 2 = 1
(2 * root (2)) / 2 = 1
root (2) = 1
We observe that the equation is not fulfilled.
Answer:
Yes, A counterexample for the expression sin (x) + cos (x) = 1 is 45 °.
TRUE
Answer:
true
Step-by-step explanation:
14) Jillian has $50 that she plans on investing in an account that will double her money every week. This can be represented by the equation M = 50(2)x where M represents the amount of money she has and x represents the number of weeks that have passed. Her uncle Charlie gives her a gift of $400 so she decides to start her investement with that money plus the $50 she already had. What should be changed in the equation M = 50(2)x to represent the new situation?
Answers
Jenny has a rope that is 7 1/2 She wants to cut it into pieces that are 3/4of a foot long.
How many pieces of rope will Jenny get?
5 5/8
8
10
1/10
Answers
Hope this helps:)
Jenny will get 5 pieces of rope.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
To find out how many pieces of rope Jenny will get, we need to divide the total length of the rope by the length of each piece:
Total length of the rope = 7 1/2 = 15/2
Length of each piece = 3/4
Number of pieces = (15/2) ÷ (3/4)
We can simplify this expression by dividing the numerator and denominator of the left-hand side by 2:
Number of pieces = (15/2) × (4/3)
Number of pieces = 30/6
Number of pieces = 5
Therefore, Jenny will get 5 pieces of rope.
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NEED HELP PLEASE I BEG!!!!!!
The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations.
What is the survey’s margin of error?
Enter your answer in the box. ± ___ %
The answer goes on the underscores
Answers
[tex]C.I.=\hat{p}\pm M.E.[/tex]
where: [tex]\hat{p}[/tex] is the sample proportion, which is midway between the two intervals and M.E. is the margin of error which is the difference between each of the intervals and the sample proportion.
i.e.
[tex]\hat{p}= \frac{76+84}{2} \% \\ \\ = \frac{160}{2} \%=80\%[/tex]
Therefore, the margin of error is 4%.
Final answer:
The margin of error for the survey, given a range between 76% and 84% satisfaction for seat locations, is calculated to be ±4%.
Explanation:
The margin of error in a survey indicates how much the survey results might differ from the actual opinions of the total population.
In this case, the survey indicates a satisfaction range between 76% and 84% for seat locations among season ticket holders.
The margin of error is half of the width of the range, which is the difference between the upper and lower percentage bounds of the confidence interval divided by two.
To calculate the margin of error, subtract the lower percentage (76%) from the upper percentage (84%) and then divide by 2. That is, (84 - 76) / 2 = 8 / 2 = 4.
Thus, the margin of error for the survey is ±4%.
If you divided 26 objects into sets of 6, how many sets of 6 could you make, and how many are left over?
Answers
hope this helps
I NEED ANSWER ASAP!!! TEST DUE IN 30 MINUTES!!
What is the volume of the composite figure?
1,024 cm^3
896 cm^3
832 cm^3
64 cm^3
Answers
Answer:
896 cm^3
Step-by-step explanation:
formula for the triangle prism is
V= 1/3 Bh
V = 1/3 (8 x 3) (8) The base is 8 seen the base of the rectangel prism is 8 to its consider as base to.
V= 1/3 (24 x 8)
V= 1/3 (192)
V = 64
Now we need to find the volume so the rectangle formula is
V= lwh
V= (13x 8) (8)
V= 832cm
Add your two answers and u get
832 + 64 = 896 cm^3
The solution is : 896 cm^3 is the volume of the composite figure.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Here, we have,
Volume formula for the triangle prism is
V= 1/3 Bh
V = 1/3 (8 x 3) (8)
The base is 8 seen the base of the rectangle prism is 8 to its consider as base to.
V= 1/3 (24 x 8)
V= 1/3 (192)
V = 64
Now we need to find the volume so the rectangle formula is
V= lwh
V= (13x 8) (8)
V= 832cm
Add your two answers and u get
832 + 64 = 896 cm^3
Hence, The solution is : 896 cm^3 is the volume of the composite figure.
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The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form.
(Please see attached picture)
8 square units
20 square units
24 square units
28 square units
Answers
We have then:
Rectangle 1:
[tex]A1 = (2) * (1) A1 = 2[/tex]
Rectangle 2:
[tex]A2 = (2) * (4) A2 = 8[/tex]
Rectangle 3:
[tex]A3 = (4) * (1) A3 = 4[/tex]
Then, the prism area is given by:
[tex]A = 2A1 + 2A2 + 2A3 [/tex]
Substituting values:
[tex]A = 2 (2) + 2 (8) + 2 (4) A = 4 + 16 + 8 A = 28[/tex]
Answer:
the surface area of the prism is:
28 square units
An old adage states that "You can't fit a square peg in a round hole." Actually, you can, it just won't fill the hole. If a hole is 4 inches in diameter, what is the approximate width of the largest square peg that fits in the round hole?
Answers
It will be a right triangle with two sides of 2 and 2 because the diameter is 4.
c=√(2²+2²)
c=2√2
so the width of the largest peg is 2√2 or 2.83 inch
In a circle, a 225 degrees sector has area 490pi in2. What is the radius of the circle?
Answers
area of a sector=(∅*pi/360°)*r²--------> when ∅ is in degree
r=√[360°*(area of a sector)/(∅*pi)]
area of a sector=(∅/2)*r²--------> when ∅ is in radians
r=√[2*(area of a sector)/∅]
let's calculate the radius of the two ways
1) r=√[360°*(area of a sector)/(∅*pi)]
area of a sector=490*pi in²
∅=225°
r=√[360°*(490*pi)/(225°*pi)]-------> r=√784-----> r=28 in
2) r=√[2*(area of a sector)/∅]
area of a sector=490*pi in²
∅=225°-----> convert to radians-----> ∅=225°*pi/180-----> ∅=1.25*pi
r=√[2*(490*pi)/(1.25*pi)]----> r=√[980/1.25]---> r=√784----> r=28 in
the answer is
the radius is 28 in
HELPP ILL GIVE MAD POINTS!!
Which series has a sum of 5?
Answers
Answer:
C
Step-by-step explanation:
The formula is S=a1/1-r
The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a series shown in the picture.
The geometric sequence is shown in the options.
As we know, in the geometric sequence there is a first term and common difference
In the first sequence:
First term a = 2
Common difference = 2(0.1)/2
Common difference d = 0.1
The sum of the infinite series is:
S = a/(1 - r)
S = 2/(1 - 0.1)
S = 2.22
In the second sequence:
First term a = 15
Common difference = 15(0.3)/15
Common difference d = 0.3
The sum of the infinite series is:
S = a/(1 - r)
S = 15/(1 - 0.3)
S = 21.42
In the third sequence:
First term a = 4
Common difference = 4(0.2)/4
Common difference d = 0.2
The sum of the infinite series is:
S = a/(1 - r)
S = 4/(1 - 0.2)
S = 5
Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.
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If A(-1,3), B(4,4), C(8,1) , then classify ABC as scalene, isosceles, or equilateral.
Answers
We have then:
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
For AB:
AB = root ((4 - (- 1)) ^ 2 + (4-3) ^ 2)
AB = 5.099019514
For AC:
AC = root ((8 - (- 1)) ^ 2 + (1-3) ^ 2)
AC = 9.219544457
For BC:
BC = root ((8-4) ^ 2 + (1-4) ^ 2)
BC = 5
We observe that it has three sides with different dimensions, therefore, the triangle is scalene.
Answer:
Scalene