Options:
A. [1,10] B. [10,20] C. [15,25] D. [1,30]
Answer:
A. [1,10]
Step-by-step explanation:
Given
[tex]N(t) = 100e^{-0.023t}[/tex]
Required
Interval with the fastest rate of decay
The rate of change over [a,b] is calculated as:
[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]
So, we have:
A. [1,10]
[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]
[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]
Calculate N(10) and N(1)
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]
B. [10,20]
[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]
[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]
Calculate N(20) and N(10)
[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
So:
[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]
C. [15,25]
[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]
[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]
Calculate N(25) and N(15)
[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]
[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]
So:
[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]
D. [1,30]
[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]
[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]
Calculate N(30) and N(1)
[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]
By comparing the values of the calculated rates,
-2.03 is the smallest, in other words; the fastest rate
Hence, the interval [1,10] has the fastest rate of decay
The required average rate of change is the fastest on [tex][1,10][/tex].
The average rate of change :The formula for the average rate of change on the interval [tex][a,b][/tex] is,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]
Now, applying the given function into the above function is,
Now, [tex]a=1,b=10[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]
Now, [tex]a=10,b=20[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]
Now, [tex]a=15,b=25[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]
Now, [tex]a=1,b=30[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]
So the average rate of change is fastest on [tex][1,10][/tex]
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a) Work out the value of angle x.
X
X=
b) Give reasons for your answer.
Answer:
x = 60° (Alternate angles)
Step-by-step explanation:
a) x = 60°
b) Reason: Alternate angles
Answer:x=60
Step-by-step explanation: all angles in a triangle add up to 180 degrees, x is the same as the angle next to it, therefore x=60 degrees
Find the value of x.
Please help me
if (1x2y6z) is a number divisible by 9 , then what os the least value of x+ y+z ?
Given:
Number 1X2Y6Z is divisible by 9.
To find:
The least value of X+Y+Z = ?
Solution:
First of all, let us learn the divisibility rule of 9.
A given number will be divisible by 9 if and only if the sum of digits of the given number is also divisible by 9.
For example:
Let us consider a number 923463.
The sum of digits = 9 + 2 + 3 + 4 + 6 + 3 = 27
27 is divisible by 9 so the number 923463 will also be divisible by 9.
Let us consider another example 8972.
Sum of digits = 26
26 is not divisible by 9 so the number 8972 will also be not divisible by 9.
Now, we are given the number 1X2Y6Z.
Sum of digits = 1 + X + 2 + Y + 6 + Z = 9 + X+Y+Z
The number 1X2Y6Z will be divisible by if 9+X+Y+Z is divisible by 9.
The least value of X+Y+Z can be zero, so the sum of digits = 9 + 0 = 9
which will make the number 1X2Y6Z divisible by 9.
So, the answer is:
Least value of X+Y+Z = 0 so that the number 1X2Y6Z is divisible by 9.
9514 1404 393
Answer:
0
Step-by-step explanation:
For a number to be divisible by 9, the sum of the digits must be divisible by 9. The given digits total 9, so x+y+z must be a multiple of 9. The least possible multiple of 9 is 0.
The least value of x+y+z is 0.
_____
102060/9 = 11340
What are the values of x and y if you answer is not a whole number write it as a decimal and round if neccasasry
a) 3x + 5y = 26
b) 2x + 2y = 12
First, we need to find a way to equate either the x terms or the y terms in each equation. a) 6x + 10y = 52
b) 6x + 6y = 36
Then take equation b) from the equation a) to eliminate the x component.
a) 6x + 10y = 52
- b) 6x + 6y = 36
0x + 4y = 16
y = 4 ?
Then substitute the value of y into either equation to find the value of x.
b) 2x + 2y = 12
2x + (2x4) =12
2x + 8 = 12
2x = 4
x = 2
I hope this new information i read helps you maybe understand it and as an example!
Marie runs a dog-walking business. She charges a $10.75 base fee for each dog she walks, plus an additional $7.10 per hour that she walks the dog. Each day she spends $5.50 on dog treats. How much money Marie would earn in one day if she worked for 4 12 hours? A. $26.45 B. $31.95 C. $37.20 2. $42.70
Answer:
I believe 31 dollars and 95 cents
Step-by-step explanation:
Marie would earn $37.2 in 4 1/2 hour.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Marie charges a $10.75 base fee for each dog she walks,
and, additional $7.10 per hour that she walks the dog.
Each day she spends $5.50 on dog treats.
So, if Marie works for 4 1/2 hour then she can earn
= 10.75 + 4 1/2 x 7.1 - 5.5
= 10.75 + 4.5 x 7.1 - 5.5
= $37.2.
Hence, Marie would earn $37.2.
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A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 15 cm long and 4 cm wide. The diameter of each circle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for pi
Answer:
The area of the rectangle is Length x width. So 12x4 would =48 sq cm. The area of the circle is ( 3.14 ) x r2.
The area of the circle would be = (3.14)x2^2)=12.56 cm sq.
So the total area is= Area of rectangle +Area of circle
TA=48+12.56
TA=60.56 sq cm
:)
Smart people of Brainly who know math
Plot function G on the graph
(Picture provided)
Answer:
Down below
Step-by-step explanation:
The graph is attached to the answer.
What is function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Given is a function,
g(x) = -3, -8≤x-2
1, -2≤x≤4
5, 4≤x≤10
The function g(x) is a discrete function. It is continuous between -8 to -2, -2 to 4, and 4 to 10.
And the open circle at -8, -2, 4, and 10.
More about the function; click,
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Put in smallest to biggest 0.56, 0.50, 0.4, 0.4
Find the surface area of the cone. Use 3.14 for π.
Answer:
S.A. = 138.16
Step-by-step explanation:
S.A. = πrl+πr²
3.14 x 4 = 12.56
12.56 x 7 =87.92
3.14 x 4 = 12.56
12.56 x 4 = 50.24
87.92 + 50.24 = 138.16
Let me know if this helps!
what is 5^2 simplified
Answer:
25
Step-by-step explanation:
guyss help plss i need serious answer I'm buriéd with work plss beg :(
Answer:
solution given:
B.
CE=2×2=4[base side is double to the line of mid point]
AB=15/2=7.5[b is a mid point]
m<AEC=75°[ corresponding angle]
5.
given:
BD=x+1
CE=x+10
we have
2BD=CE
2(x+1)=x+10
2x+2=x+10
2x-x=10-2
x=8
write an expression for the number of days in y hours.
Answer:
The number of days in y hours is y/24
Step-by-step explanation:
Here, we want to write an expression
Mathematically;
1 day = 24 hours
? days = y hours
? days = (y * 1)/24
? days = y/24
What is the side of a right triangle across from the right angle called?
Answer:
Hypotenuse
Step-by-step explanation:
Answer:
it's called the hypothenuse
Write an equation of the line with the given slope and y-intercept
slope: 1.4, y-intercept: 5.6
O y = 1.4x + 5.6
Oy=-*x+5.6
O y = 1.4x -5.6
O y=-1.4x + 5.6
Someone help?
Answer:
y = 1.4x + 5.6
Step-by-step explanation:
plug the slope and y-intercept into the formula: y = ax + b (a is the slope and b is the y-intercept)
thus, y = 1.4x + 5.6
There are 25 questions in a quiz.
Every correct answer scores 3 points.
Each incorrect answer loses 2 points.
A question not answered scores 0 points.
It is possible to finish the quiz with a negative score.
a) What is the maximum score you could get on the quiz?
b) What is the minimum score you could get on the quiz?
c) A student answers 15 questions.
10 are correct. How many points does he score?
d) Another student answers 21 questions.
6 are correct. How many points does she score?
Answers of the quiz are as follows
A. 75
B. -50
C. 20
D. -12
We have been given that -
Number of questions= 25
Correct answers= x and score= 3
Incorrect answers= y and score= -2
Not answered= z and score= 0
We can calculate the score as:
A) What is the maximum score you could get on the quiz?
Maximum score one can get on the quiz if he / she correct all i.e. -
25 × 3 = 75.
B) What is the minimum score you could get on the quiz?
Minimum score one can get on the quiz if he / she correct all i.e. -
25 ×-2 = -50.
C) A student answers 15 questions.10 are correct. How many points does he score?
Scored points = (10 × 3) + (5 × -2)
= 30 -10
=20 points
D) Another student answers 21 questions. 6 are correct. How many points does she score?
= 6 × 3 + (15 × -2)
= 18-30
= - 12 points
Hence, the answer are a- 75 , b- -50 , c - 20, d- -12.
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Find the volume of a cylinder with a diameter of 14mm and a height of 3.4mm Round to the nearest tenth.
Answer:
V≈5.23×10-7m³
Step-by-step explanation:
V=π(d
2)2h=π·(0.014
2)2·3.4×10-3≈5.23389×10-7m³
Answer: 523.1 mm^2
You first want to find the radius for the volume of cylinder formula. You first do 14 divided by 2 to get the radius. You should get 7. Then after you find the radius you then put it into the formula which is v=3.14 x radius^2 x height. The equation with all the numbers from the problem is 3.14 x 7^2 x 3.4. After you put the equation into your calculator you should get 523.1 mm^2.
[tex]4(3-5x)=15-(8x-25)[/tex]
The line of which equation passes through points (0,6) and (4,-1)
Answer:
y=-7/4x+6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-6)/(4-0)
m=-7/4
y-y1=m(x-x1)
y-6=-7/4(x-0)
y-6=-7/4(x)
y-6=-7/4x
y=-7/4x+6
A new iPhone cost $829 and is on sale at a 25% discount. What is the sale price.
Answer:
621.75
Step-by-step explanation:
Hope this helps!!!
Using the net below, find the surface area
of the pyramid.
4cm
2 cm
12 cm
Surface Area
=
[?] cm2
Enter
Answer:
everything is in the picture
Triangle STU is rotated 270 clockwise about the origin to create triangle S'T'U'. If point U of triangle STU is a (a,b), which algebraic representation best describes point U' of triangle S'T'U'?
Answer:
(b, -a)
Step-by-step explanation:
First note that the rule for a rotation by 270° about the origin is (x,y)→(y,−x)
Note that the coordinates were swapped and the x coordinates negated. Similarly;
Given the coordinate of the point U as (a, b), if the triangle is rotated 270degrees clockwise, the resulting coordinate will be (b, -a)
Q1 - What is the area of a circle with a diameter of 6.2 inches?
Q2 - A round table has a radius of 15in a round tablecloth hangs 2in over the edge of the entire table.what is the area of the tablecloth
Answer:
Q1; 124.72
Sorry I don’t understand the second one
Step-by-step explanation:
does this function equal 4 on the interval [4, 5]?
[tex] \frac{10 \cos(xπ) }{x-2} [/tex]
=- No way
Step-by-step explanation:
The two legs of a right triangle measure 7 inches and 5 inches. Find the measure of the acute angle that is included between the longer leg and the hypotenuse. WILL GIVE BRAINIEST TO FIRST RIGHT ANSWER
Answer:
44.4 degrees
Step-by-step explanation:
Given the following
Hypotenuse = 7
Longer leg = 5 (adjacent])
Let the acute angle angle between both sides be x
According to SOH CAH TOA
Cos theta = adj/hyp
Cos x = 5/7
x= arccos (5/7)
x = arccos (0.7143)
x = 44.4degrees
Hence he measure of the acute angle that is included between the longer leg and the hypotenuse is 44.4 degrees
Which exponential expression is equivalent to the one below? (6x3)^5
25 POINTS!!!!!!
Answer:
D) 6^5 · 3^5
Step-by-step explanation:
(6 · 3)^5 = 1889568
A) WRONG
(5 · (6 · 3)) = 90
B) WRONG
9^5 = 59049
C) WRONG
6 · 3^5 = 1458
D) CORRECT
6^5 · 3^5 = 1889568
Put in order from least to greatest
5.670
56.72
56.27
Answer:
5.670, 56.27,5.72.
Step-by-step explanation:
All you do is pay attention to that decimal and remember that the places where the numbers are present; they are invisible zero so,
56.72 is the same as 56.720000.
It's pretty clear for this question since the numbers are clear so all you do is look at the decimals.
5 Find the area of the polygon.
$ cm
9 cm
2 em
A 45 cm
B. 90 cm
C. 94.5 cm
D. 72 cm
HELP PLEASE
I just wanna make sure i’m doing this right
Answer:
175%
Step-by-step explanation:
The first one is a whole=1
the second one is cut in four but only 3 are shaded so 1/4=0.25 0.25*3=0.75
3/4/0.75 is shaded
so 1+0.75=1.75
1.75=175%
The area of a rectangle is x^2-6x-16. If the width is x+2, what is the length?
Answer:
8
Step-by-step explanation:
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x = -10 + y
-16x – 2y = -2