Answer:
(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.
(b) [tex]c =0.51995[/tex]
Step-by-step explanation:
Given
[tex]f(x) = e^{-4x};\ [0,2][/tex]
Solving (a); Does the function satisfy M.V.T on the given interval
We have:
[tex]f(x) = e^{-4x};\ [0,2][/tex]
The above function is an exponential function, and it is differentiable and continuous everywhere
Solving (b): The value of c
To do this, we use:
[tex]f'(c) = \frac{f(b) - f(a)}{b - a}[/tex]
In this case:
[tex][a,b] = [0,2][/tex]
So, we have:
[tex]f'(c) = \frac{f(2) - f(0)}{2 - 0}[/tex]
[tex]f'(c) = \frac{f(2) - f(0)}{2}[/tex]
Calculate f(2) and f(0)
[tex]f(x) = e^{-4x}[/tex]
So:
[tex]f(2) = e^{-4*2} = e^{-8} = 0.00033546262[/tex]
[tex]f(0) = e^{-4*0} = e^{0} = 1[/tex]
This gives:
[tex]f'(c) = \frac{0.00033546262 - 1}{2}[/tex]
[tex]f'(c) = \frac{-0.99966453738}{2}[/tex]
[tex]f'(c) = -0.4998[/tex]
Note that:
[tex]f'(x) = (e^{-4x})'[/tex]
[tex]f'(x) = -4e^{-4x}[/tex]
This implies that:
[tex]f'(c) = -4e^{-4c}[/tex]
So, we have:
[tex]f'(c) = -0.4998[/tex]
[tex]-4e^{-4c} =-0.4998[/tex]
Divide both sides by -4
[tex]e^{-4c} =\frac{-0.4998}{-4}[/tex]
[tex]e^{-4c} =0.12495[/tex]
Take natural logarithm of both sides
[tex]\ln(e^{-4c}) =\ln(0.12495)[/tex]
[tex]\ln(e^{-4c}) =-2.0798[/tex]
Apply law of natural logarithm
[tex]\ln(e^{ax}) =ax[/tex]
So:
[tex]-4c =-2.0798[/tex]
Solve for c
[tex]c =\frac{-2.0798}{-4}[/tex]
[tex]c =0.51995[/tex]
y = 4x-9
y = x-3
Which method and why? Solve, shoving all work
Answer:
(2,-1)
Step-by-step explanation:
The ys in both questions are isolated on one side of the equation in both. The numerical coefficient of both is 1. Therefore you should equate the the left side of each equation to the other left side. The solution is the easiest one to solve because there is only 1 unknown on both sides.
4x - 9 = x - 3 Subtract x from both sides.
4x-x - 9 = -3 Combine
3x -9 = - 3 Add 9 to both sides
3x - 9+9 = - 3+9
3x = 6 Divide by 3
3x/3 = 6/3
x = 2
===============
Now use the second equation to solve for y
y = x - 3
y = 2 - 3
y = -1
==============
The solution is (2,-1)
sharon bought a $2,100 high definition television set on a six month rent to own plan. the down payment was 10%. what was the dollar value of the down payment? her monthly payments were $75 per month. if she decides not to buy the HDTV after the six months, what was her cost to rent it?
Answer:
Total Sharon spent $660 for the tv
The down payment was $210
The amount that she paid for rent after 6 months is $450
Step-by-step explanation:
To find out how much her down payment was you would need to find out how much 10% of $2,100 is which is $210, so you know her down payment was $210.
Then you would find out the total cost of rent is after 6 months so you would do 6 times $75 which is $450. So if she decides to not buy it then after 6 months she would have spent $450 to rent it.
And total she would have spent $660 which you can find out by doing $450 + $210 = $660.
I need help SHOW YOUR WORK
Answer:
S=100x^8y²z^6 is your answer
Step-by-step explanation:
we have
S=4πr²
when
r=5x⁴yz³
new S
will be
S=4π(5x⁴yz³)²=4×5²×x^(4×2)×y²×z^(3×2)
=100x^8y²z^6
Brainliest for correct answer asap
Answer:
1st one
Step-by-step explanation:
Step-by-step explanation:
answerss
the Last one or the 1st one but go w it the last
caculate the VAT inclusive amount for R42,42
Answer: R47.66
Step-by-step explanation:
Assuming this amount of R42.42 is Indian Rupees, then the relevant VAT rate to use is 12.36% which is the VAT rate in India.
The VAT inclusive amount is therefore:
= 42.42 * ( 1 + tax rate)
= 42.42 * ( 1 + 12.36%)
= R47.66
00
A group of 150 middle school students were asked whether they prefer playing video games or watching TV in their spare time. The genders of the students and
their responses are reported in the following table.
Playing video
games
Watching TV
Girls
23
64
Boys
43
20
E
(a) What percentage of the students are girls?
(b) What percentage of the students prefer watching TV?
х
$
2
Answer:
58%56%Step-by-step explanation:
a) Number of girls:
23 + 64 = 87Percentage:
87/150*100% = 58%b) Number of students prefer watching TV:
64 + 20 = 84Percentage:
84/150*100% = 56%Answer:
no of percentage of girls=no of girls/total ×100%
=87/150×100%=58%
percentage of the students prefer watching TV
=total no the students prefer watching TV/total std.×100%
=84/150×100%=56%
Study island on 5a area
Answer:
d'Italia dies does did
Step-by-step explanation:
sun will use this rod hero oath his ryu
Which expression is equivalent to (xy)z?
Answer:
[tex](xy)z = xyz[/tex]
Step-by-step explanation:
Given
[tex](xy)z[/tex]
Required
Equivalent expression
No option is given. So, I will solve generally.
To solve this question, we simply open the bracket.
So:
[tex](xy)z = xyz[/tex]
The results of an independent-samples t test were t(19) = 4.02, p < 0.05. In this example,
the sample size is:
The results of an independent-samples t test were t(19) = 4.02, p < 0.05. The sample size is 19.
What is independent t-test?The independent t-test is a defined as an statistical test in order to determine if we have statistically significant difference between the means of two unrelated groups.
Effect size is defined as a "quantitative measure of the magnitude of the experimenter effect" So, If we have a high value for the effect size then we can conclude that we have a stronger relationship between two variables.
T test is used to compare group means is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
We perform one sample z-test;
One sample z-test is performed if the sample size is large enough (n > 30) and we want to know if the sample comes from the specific population.
The results of an independent-samples t test were t(19) = 4.02, p < 0.05. In this example,
The sample size is 19.
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Hello, who would you do me the favor of helping me with this question?
He says:
Show, using the property of the number of diagonals of a polygon, that the triangles have no diagonals.
I hope they help me
Step-by-step explanation:
diagonal of a polygon formular =sum of diagonal =5-3-5/2. A triangle do not have diagonal
a circular table top has a radius of 3 feet. a decorative trim is placed along the outside edge if the table. how long is the trim
Answer:
about 18.85
Step-by-step explanation:
i didn’t mean to pick that but can some one please give me the answer :(
Answer:
you were right
Step-by-step explanation:
180-104 is 76 76-10=66 66/2 is 33
Answer: x = 33
Step-by-step explanation:
Well since that line is basically equal to 180 all you have to do is plug in those numbers for x. Since 33 + 10 = 43 Alll you gotta do is add that up. So we have 104 + 33 + 43 = 180. I’m not the best at explaining things but I hope this helped :)
Sarah has two pizzas each pizza is cut into 10 equal slices she and her friends 14
slices what part of the pizza did they eat and how much is left right your answer as a decimal
what's the answer? (Zearn)
Answer:
Step-by-step explanation:
Write the equation of the line that passes through the point (-1,-5) and has a slope of -2?
Answer: Answer is B hope this helps
Step-by-step explanation:
Answer:
the correct answer is D. Hope it helps
9482 ÷ 497 answer pls
Answer:
19.0784708249
Step-by-step explanation:
What is the domain of the function y=xVx?
- 0
0
0
O 15x<0
Answer:
Option A will be your answer
Step-by-step explanation:
hope it helps...
have a great day!!
The cube root function , has no domain restrictions. The domain of the cube root function is all real numbers, or ℝ .
What is domain ?The domain of a function is the complete set of possible values of the independent variable.
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
When finding the domain, remember:
The denominator (bottom) of a fraction cannot be zero.
The number under a square root sign must be positive in this section.
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Domain: (- ∞ , ∞) , {x | x ∈ [tex]\mathbb{R}[/tex]}
Hence, The domain of the cube root function is all real numbers, or ℝ .
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I WILL GIVE YOU BRAINLIEST!
What is the measure of n?
12
4
n
m
n =
V[?]
Enter
After answering the question provided, we can predict that the result will be as in the triangle by Pythagorean theorem = [tex]\sqrt{12^2 - 4^2}[/tex] => N = [tex]\sqrt{144 - 16}[/tex] => n = [tex]\sqrt{132}[/tex]
What precisely is a triangle?A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.
by Pythagorean theorem
n = [tex]\sqrt{12^2 - 4^2}[/tex]
N = [tex]\sqrt{144 - 16}[/tex]
n = [tex]\sqrt{132}[/tex]
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A parallelogram has a base of 10 feet and a height of 12 feet.
Use the figure to complete the statements.
The area of the parallelogram is __________ft2.
First choice: 120
Second choice: 100
Third choice: 144
Fourth choice: 22
Step-by-step explanation:
♨ [tex] \underline{ \underline{ \large{ \tt{G \: I \: V \: E \: N}}}} : [/tex]
Base ( b ) = 10 ftHeight ( h ) = 12 ft♨ [tex] \underline{ \underline{ \large{ \tt{ T\: O \: \: F \: I \: N \: D}}} }: [/tex]
Area of the parallelogram☪ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T\: I \: O \: N}}}} : [/tex]
[tex] \boxed{ \large{ \sf{Area \: of \: a \: parallelogram ( \: A \: )= base \: (b) \times height \: (h)}}}[/tex]
⟼ [tex] \large{ \sf{10 \: ft \times 12 \: ft}}[/tex]
⟼ [tex] \boxed{ \large \sf{120 \: {ft}^{2} }}[/tex]
☃ [tex] \boxed{ \boxed{ \large{ \sf{OUR \: FINAL \: ANSWER : \boxed{ \underline{ \bold{120 \: {ft}^{2} }}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
Let me know if you have any questions regarding my answer! ☄
☞ [tex] \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ✎
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Answer:
First choice: 120 ft² is a required answer.
Step-by-step explanation:
The area of the parallelogram is __________ft2.
=base ×height=10×12=120ft²
Find the area of a regular 15-gon with radius 64 mm
Answer:
To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.
Step-by-step explanation:
URGENT GIVING BRAINLY and pts
Answer:
I think it's C.
please help me:(***********
Answer:
A:
Square
Rectangle
Parallelogram
Quadrilateral
Rhombus
Step-by-step explanation:
All sides and angles are equal so it is a square
All angles are 90 degrees so it is a rectangle (eliminate C)
Opposing angles and side lengths are congruent so it is a parallelogram (eliminate D)
It has 4 sides so it is a quadrilateral (eliminate B)
Since all of the other answers are eliminated you don't necessarily need to prove that is is a rhombus, but it is good practice.
Opposing sides are congruent so it is a rhombus.
Find an angle between 0 and 2 pi that is coterminal with -17 pi/ 10
Answer:
3pi/ 10
Step-by-step explanation:
Enter a problem...
Trigonometry Examples
Popular Problems
Trigonometry
Find the Reference Angle (17pi)/10
17π1017π10
Since the angle 17π/ 10 is in the fourth quadrant, subtract 17π/10 from2π.
2π−17π/10
The angle between 0 to [tex]2\pi[/tex] that is coterminal with [tex]-\frac{17\pi }{10}[/tex] is [tex]\frac{3\pi }{10}[/tex].
What is coterminal angle?Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.
Angles are considered to be in standard position if the initial side is on the positive x-axis and the vertex at the (0,0) point of the Cartesian plane. All angles generated that share the same terminal side are coterminal angles. These are angles that have differences of multiples of 360n or n2pi where n is an integer.
A coterminal angle is found by simply adding or subtracting 360 and its multiples.
The coterminal angles of 20 degrees for example are 20 + 360 = 380 or 20 - 360 = -340. This may continue by adding or subtracting 360 each time.
To get coterminal angles, you simply have to add or subtract 2[tex]\pi[/tex].
According to this problem,
We are looking for a coterminal angle that is between 0 to 2[tex]\pi[/tex], so we will add [tex]2\pi \ to \ \frac{-17\pi }{10}[/tex].
= [tex]\frac{-17\pi }{10} +\frac{20\pi }{10}[/tex]
= [tex]\frac{-17\pi +20\pi }{10}[/tex]
= [tex]\frac{3\pi }{10}[/tex]
Hence,
The angle between 0 to [tex]2\pi[/tex] that is coterminal with [tex]-\frac{17\pi }{10}[/tex] is [tex]\frac{3\pi }{10}[/tex].
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Find the quadratic root of 3x2-4x+2=0
Answer:
Step-by-step explanation:
What is the measure of n?
n
20
m
5
N= [?]
Please help I’ll give brainliest
Answer:
n = 10
Step-by-step explanation:
n is the altitude of the right triangle.
Apply the right triangle altitude theorem/geometric mean theorem to find n.
Which is:
h = √(xy)
Where,
h = n =?
x = 5
y = 20
Plug in the value into the equation
n = √(20*5)
n = √100
n = 10
Answer:
Step-by-step explanation:
Find five numbers so that the mean, median, mode and range are all 4.
Answer:
The set of five numbers would be {2,4,4,4,6}
Answer:
The example set could be:
S
=
{
2
,
4
,
4
,
4
,
6
}
See explanation.
Explanation:
First you can notice that if the set was:
S
1
=
{
4
,
4
,
4
,
4
,
4
}
then it would fulfill 2 conditions: mean and median, but
the set does not have the mode because all numbers are the same,
the range is zero (again all numbers are the same)
To have the mode the set would have to have at least one element different from
4
, but if we changed only one element the mean would change, so at least two numbers need to be changed to keep mean equal to
4
..
Now to get the range the difference between the changed numbers should be
4
. That leads us to adding two to one number and subtracting two from the other.
Finally we can get the set from the answer.
Tickets to a play cost $8.00 each.
Write an expression to find the
total cost of "b" boys &
"g" girls.
Answer:
Step-by-step explanation:
b + g = 8x
9 tens =
Ones how many ones are in 9 10 tens ?
Answer:
90
Step-by-step explanation:
There are 10 ones in 1 ten.
So if you have 9 tens then...
10 x 9 = 90
Convert the following polar-form vectors of the form ⟨r,θ⟩ into component-form vectors of the form ⟨x,y⟩. Your answers should be in the form "< #, # >". ⟨13,50∘⟩= ⟨1.77,250∘⟩= ⟨5.8,150∘⟩=
9514 1404 393
Answer:
a) <8.356, 9.959>
b) <-0.605, -1.663>
c) <-5.023, 2.9>
Step-by-step explanation:
Many calculators can perform polar ⇔ rectangular conversion. Attached is the result from one of them. Of course, you can also program a spreadsheet to do it. (The ATAN2( ) function is useful for finding the correct angle.)
If you want to do these calculations by hand, the conversion is ...
<r, θ> ⇒ <r·cos(θ), r·sin(θ)>
In the attached, the rectangular coordinates are shown as complex numbers. The imaginary component is the y-component of the vector.
PLS HELP ME ASAP! Dont answer for points & no links for other sites or i will report you. I'm running out of points plss