Solution :
It is given that :
[tex]$f'(t) = (350 \ln t)'$[/tex]
[tex]$=350(\ln t)'$[/tex]
[tex]$=\frac{350}{t}$[/tex]
So, [tex]f(5)=350 \ln (5) \approx 563[/tex]
[tex]$f'(5) = \frac{350}{5}$[/tex]
[tex]=70[/tex]
The relative change is then,
[tex]$\frac{f'(5)}{f(5)}=\frac{70}{350\ \ln(5)}$[/tex]
[tex]$=\frac{1}{5\ \ln(5)}$[/tex]
[tex]$\approx 0.12$[/tex]
[tex]=12\%[/tex]
This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.
The Natural History Museum has a 1:60 scale model of a tyrannosaurus rex dinosaur. The length of the model is 20 centimeters. Find the
actual length (in meters) of a tyrannosaurus rex.
Answer:
12 meters
20cm*60 = 1200cm = 12 meters
100cm = 1m btw
solve solve solve solve
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: \: 1 \frac{1}{15} \:(or) \: 1.0667}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{4}{5} \div \frac{3}{4} [/tex]
= [tex] \: \frac{4}{5} \times \frac{4}{3} [/tex]
= [tex] \: \frac{4 \times 4}{5 \times 3} [/tex]
= [tex] \: \frac{16}{15} [/tex]
= [tex] \: 1 \frac{1}{15} [/tex]
( OR )
= [tex] \: 1.0667[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35\:♨}}}}⋆[/tex]
Step-by-step explanation:
[tex] \frac{4}{5} \div \frac{3}{4} \\ = \frac{4}{5} \times \frac{4}{3} \\ = \frac{16}{15} \\ thank \: you[/tex]
what is the next numbers in the sequence 0, 5, 20, -, -,-
Answer:
51, 104, and the next number of series is 185
Step-by-step explanation:
I hope this will help u
Answer:
the next number in the sequence should be 45
A metal can in the shape of a right circular cylinder needs to hold a volume of V cm3 . Throughout this problem V > 0 is a parameter that needs to be left as V . Suppose that the metal for the sides costs 5 cents per square cen- timeter to manufacture, whereas the top and bottom cost 10 cents per square centimeter to manufacture. Find the shape of the least expen- sive can. What is the cost of the least expensive can
Answer:
C(min) = 0.5*V + √V/1.256 $
Step-by-step explanation:
The volume of a circular cylinder is: V(c) = π*r²*h where r is the radius of the circumference of the base and h is the height
The cost of the can is = the cost of (base and top) + lateral cost
Base surface = top surface = π*r²
Then cost of ( base + top ) is = (2* π*r² )*0,1
Lateral surface is = 2*π*r*h
Then cost of lateral surface is: (2*π*r*h)*0,5
Total cost C(t) = (2* π*r² )*0,1 + (2*π*r*h)*0,5
V = π*r²*h
Total cost as a function of (V >0 a parameter) and r then
h = V / π*r²
C(V,r) = (2* π*r² )*0,1 + π*r*(V / π*r²)
C(V,r) = 0.2*π*r² + V*/r
Taking derivatives on both sides of the equation we get:
C´(V,r) = 2*0.2*π*r - V/r²
C´(V,r) = 0 0.4*π*r - V/r = 0
Solving for r
0.4*π*r² - V = 0 ⇒ 1.256*r² = V r = √ V/ 1.256 cm
and h = V /π * (√ V/ 1.256)²
h = 1/ 1.256*π
h = 0.254 cm
C(V,r) = 0.2*π*r² + V*/r
C(min) = 0.2*π* (√ V/ 1.256)² + V/ √ V/ 1.256
C(min) = 0.2*π*V/1.256 + V/ √ V/ 1.256
C(min) = 0.5*V + √V/1.256 $
Express the function H in the form f ∘ g. (Enter your answers as a comma-separated list. Use non-identity functions forf(x) and g(x).)H(x) = |1 − x3|
Answer:
We know that:
H(x) = |1 - x^3|
and:
We want to write H(x) as f( g(x) ) , such that for two functions:
So we want to find two functions f(x) and g(x) such that:
f( g(x) ) = |1 - x^3|
Where neither of these functions can be an identity function.
Let's define g(x) as:
g(x) = x^3 + 2
And f(x) as:
f(x) = | A - x|
Where A can be a real number, we need to find the value of A.
Then:
f(g(x)) = |A - g(x)|
and remember that g(x) = x^3 + 2
then:
f(g(x)) = |A - g(x)| = |A - x^3 - 2|
And this must be equal to:
|A - x^3 - 2| = |1 - x^3|
Then:
A = 3
The functions are then:
f(x) = | 3 - x|
g(x) = x^3 + 2
And H(x) = f( g(x) )
Which absolute value equation represents the graph
Answer:
the first one
Step-by-step explanation:
Hope this helps!
This table shows values that represent a quadratic function.
х
y
0
-1
1
SON
| N|مي | |
-10
4
-17
-26
6
-37
What is the average rate of change for this quadratic function for the interval
from x= 4 to x= 6?
A. 10
B. -10
C. 20
D. -20
Answer:
[tex]Rate = -10[/tex]
Step-by-step explanation:
Given
The table
Required
The average rate if change over (4,6)
This is calculated as:
[tex]Rate = \frac{f(6) - f(4)}{6-4}[/tex]
[tex]Rate = \frac{f(6) - f(4)}{2}[/tex]
From the table:
[tex]f(6) = -37[/tex]
[tex]f(4) = -17[/tex]
So:
[tex]Rate = \frac{-37 --17}{2}[/tex]
[tex]Rate = \frac{-37 +17}{2}[/tex]
[tex]Rate = \frac{-20}{2}[/tex]
[tex]Rate = -10[/tex]
Instructions: Find the area of the sector. Round your answer to the nearest tenth.
I’ll mark brainliest please help me
Answer:
[tex]area \: = \frac{165}{360} \times \pi {8}^{2} \\ = 92.1533845053 \\ = 92 \: in^{2} [/tex]
F(x) = x3 + x2 -8x - 6
According to the Fundamental Theorem of Algebra, how many solutions/roots will there be?
According to Descartes' Rule of Signs, what are the possible combinations of positive, negative, and/or complex roots will there be?
Using the Rational Root Theorem, list all the possible rational roots.
Use a combination of Synthetic Division, Factoring, and/or the Quadratic Formula to find all the roots. PLEASE SHOW ALL WORK!
This is my 4th time posting this and no ones helping. Please someone who is smart help me out lol
Answer:
Given function:
f(x) = x³ + x² - 8x - 6This is the third degree polynomial, so it has total 3 roots.
Lets factor it and find the roots:
x³ + x² - 8x - 6 = x³ + 3x² - 2x² - 6x - 2x - 6 = x²(x + 3) - 2x(x + 3) - 2(x + 3) = (x + 3)(x² - 2x - 2) = (x + 3)(x² - 2x + 1 - 3) = (x + 3)((x - 1)² - 3) = (x + 3)(x - 1 + √3)(x - 1 - √3)The roots are:
x = -3x = 1 - √3x = 1 + √3It has highest degree 3 so 3 roots
1 positive and 2 negative rootsLets find
x³+x²-8x-6=0x²(x+3)-2x(x+3)-2(x+3)=0(x+3)(x²-2x-2)=0(x+3)(x-2.732)(x+0.732)=0Roots are
-3,2.732,-0.732the end of day values of a stock market index for the week of December 9-13 are graphed to the right
Answer: 33.4
Step-by-step explanation:
Given Tan A= 2/3 and that angle A is in quadrant 1, find the exact value of sec A in simplest radical form using a rational denominator.
Answer:
[tex]\sec A =\frac{\sqrt{13}}{3}[/tex]
Step-by-step explanation:
Given
[tex]\tan A = 2/3[/tex]
Required
[tex]\sec\ A[/tex]
First, we have:
[tex]\tan A = \frac{x}{y}[/tex]
Where
[tex]x \to oppo site\\[/tex]
[tex]y \to adja cent[/tex]
[tex]z \to hypotenuse[/tex]
So:
[tex]\tan A = \frac{x}{y} =\frac{2}{3}[/tex]
By comparison:
[tex]x = 2; y =3[/tex]
Using Pythagoras, we have:
[tex]z^2 = x^2 +y^2[/tex]
[tex]z^2 = 2^2 +3^2[/tex]
[tex]z^2 = 13[/tex]
[tex]z = \sqrt{13[/tex]
[tex]\sec A =\frac{z}{y}[/tex]
[tex]\sec A =\frac{\sqrt{13}}{3}[/tex]
Which of the following is the simplified form of? Jx/
xVx?
ox
x21
O 21 /
Points eamed on this question: 0
Use the following property below:
[tex] \large \boxed{ \sqrt[n]{a} \times \sqrt[n]{a} \times \sqrt[n]{a} = { (\sqrt[n]{a}) }^{3} }[/tex]
Therefore,
[tex] \large{ \sqrt[7]{x} \times \sqrt[7]{x} \times \sqrt[7]{x} = { (\sqrt[7]{x}) }^{3} }[/tex]
Then we use next property.
[tex] \large{ \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } }[/tex]
Hence,
[tex] \large{ \sqrt[7]{ {x}^{3} } = {x}^{ \frac{3}{7} } }[/tex]
Answer
x^(3/7)What is the slope of the line below?
(-2,4) (5,4)
A. Positive
B. Zero
C. Undefined
D. Negative
Answer:
B
Step-by-step explanation:
the slope is 0
the y intercept is ( 0,4 )
Help and explain please and thankyouuu’!!!!!
here,
f(x)=x-4
then, f(-3.2)=(-3.2)-4
[ replace the value of x in the equation by -3.2]
therefore,f(-3.2)=-7.2 answer....
HOPE THIS HELPS YOU.HAVE A NICE DAY/NIGHT.....
9514 1404 393
Answer:
(a) f(-3.2) = -7
Step-by-step explanation:
The ceiling function returns the smallest integer greater than or equal to its argument value. For an argument of -3.2, the next larger integer is -3.
[tex]f(-3.2)=\lceil -3.2\rceil-4=-3-4=\boxed{-7}[/tex]
slove the system of linear equations by graphing.
-x+y=3
x+y= -3
Answer: it is a linear line
Step-by-step explanation:
They both together make 0
Inequality of y<-4+3 on graph
Answer:
[tex]y < - 1[/tex]
Step-by-step explanation:
[tex]y < - 4 + 3[/tex]
[tex]y < - 1[/tex]
Hope it is helpful...[tex] \sf \: y < - 4 + 3 \\ \sf \: y < - 1[/tex]
[tex] \sf \: Just \: add \: - 4 \: and \: 3 \: and \: you \: \\ \sf will \: get \: the \: inequality \: in \: the \: simplest \: form.[/tex]
two angles of traingle is 40° and 60° . find the measurement of the third angle
Answer:
80 degrees
Step-by-step explanation:
the angles in a triangle all add up to 180 degrees
Answer:
Let the third angle be [tex]{x°}[/tex]
Since the sum of all three angles of a triangle is 180°,
We have
40°+60°+[tex]{x}[/tex] = 180°
→ 100+[tex]{x}[/tex] = 180°
[tex]{x}[/tex] = 180-100 = 80°
The measure of the third angle is 80°
Solve for x. Leave your answer in simplest radical form.
Answer:
7√2
Step-by-step explanation:
Leg of the right triangle = greater base - smallest base = 10- 3 = 7
Leg 2 = height = 7
x = [tex]\sqrt{7^2 + 7^2} = \sqrt{49 * 2} = 7\sqrt{2}[/tex]
what is the answer to tjis question? 7 more than h
Answer:
7>h
Step-by-step explanation:
A jogger travelled 52km in 4 days.what is the rate he travelled per day?
Answer:
13km per day
Step-by-step explanation:
If this does not involve complex rules then we can calculate the rate just by dividing 52 with 4 which results 13km per day
Goodluck
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
Answer:
B
Step-by-step explanation:
LA = radius x 2 x pi x height = 6 x 2 x pi x 13 = 489.8 ft^2
In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.
8, 16, 14, 8, 16
(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to four decimal places.)
(b) Add 8 to each data value to get the new data set 16, 24, 22, 16, 24. Compute s. (Enter your answer to four decimal places.)
(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?
Adding the same constant c to each data value results in the standard deviation remaining the same.
Adding the same constant c to each data value results in the standard deviation increasing by c units.
Adding the same constant c to each data value results in the standard deviation decreasing by c units.
There is no distinct pattern when the same constant is added to each data value in a set.
Answer:
3.6661
3.6661
A, Adding a constant does nothing to the standard deviation
Step-by-step explanation:
I'm gonna assume s=standard deviation
The standard deviation is just the square root of the second moment minus the first moment squared
Because we were not told otherwise I think it's pretty safe to assume that all events are equally likely
Let's start by calculating the first moment (AKA The mean)
1/5(8+16+14+8+16)= 12.4
Let's then find the second moment
1/5(8²+16²+14²+8²+16²)= 167.2
√(167.2-12.4²)=3.6661
b.
While I could just tell you that adding something to the standard deviation (and the variane as well) doesn't do anything let's calculate it for fun
same process
.2(16+24+22+16+24)= 20.4
.2(16²+24²+22²+16²+24²)=429.6
√(429.6-20.4²)= 3.6661
Can y’all help me on question 16?!
Answer:
C
Step-by-step explanation:
173.6 • 9= 1562.4
please answer and help me on this question!
=====================================================
Explanation:
The double tickmarks show that segments DE and EB are the same length.
The diagram shows that DB = 16 cm long
We'll use these facts to find DE
DE+EB = DB
DE+DE = DB
2*DE = DB
DE = DB/2
DE = 16/2
DE = 8
-------------
Now let's focus on triangle DEC. We just found the horizontal leg is 8 units long. The vertical leg is EC which is unknown for now. We'll call it x. The hypotenuse is CD = 9
Use the pythagorean theorem to find x
a^2+b^2 = c^2
8^2+x^2 = 9^2
64+x^2 = 81
x^2 = 81 - 64
x^2 = 17
x = sqrt(17)
That makes EC to be exactly sqrt(17) units long.
If you follow those same steps for triangle ADE, then you'll find the missing length is AE = 6
---------------
So,
AC = AE+EC
AC = 6 + sqrt(17)
AC = 10.1231056256177
AC = 10.1 cm approximately
The perimeter of triangle ABC is 56 cmThe length of AB is С 4x - 4 degrees; 2x + 6 degrees; 70 degrees B A A 16 B of these 18 cm D 5 E 20 cm
Answer:
Step-by-step explanation:
A farmer has a rectangular field with length 1 mile and width 0.5 miles. How much fencing would it take to enclose his field?
Answer:
3 mi of fencing would be required to enclose this field.
Step-by-step explanation:
Here we are finding the perimeter of a field with given length and width. We apply the perimeter formula P = 2L + 2W. Substituting the given dimensions, we get:
P = 2(1 mi) + 2(0.5 mi), or
P = 2 mi + 1 mi = 3 mi
3 mi of fencing would be required to enclose this field.
Answer:
15840 feet of fencing = Perimeter = 15840ft
However, if fencing is 6ft or 10ft we need to divide by the length of each fence for panels.
See bold.
Step-by-step explanation:
6ft fencing = 5280/6 = 880 fences one length
880 x 2 = 1760 6ft fences 2 sides
0.5 x 1760 = 880
1760+ 880 = 2640 fences each 6ft
Total feet of fence = 2640 x 6 =15840 feet of fencing
(0.020(5/4) + 3 ((1/5) – (1/4)))
Answer:
- 0.125
Step-by-step explanation:
Given the equation :
(0.020(5/4) + 3 ((1/5) – (1/4)))
0.020(5/4) = 0.025
3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15
0.025 + - 0.15 = 0.025 - 0.15 = - 0.125
Compute using long division: 9,876 divided by 123
Answer:
C 80 R36
Step-by-step explanation:
See attached image for explanation.
Determine the value of "k" when the lines y=k3x+2 and y=14x+2 are perpendicular. Show your work. (3 marks/PS)
Answer:
[tex]k=-\frac{1}{42}[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2)Given the equation [tex]y=14x+2[/tex], we can identify the slope (m) to be 14. This means that the slope of a perpendicular line would have to be [tex]-\frac{1}{14}[/tex] since that is its negative reciprocal.
In the equation [tex]y=k*3x+2[/tex], the slope would be 3k. 3k would be equal to [tex]-\frac{1}{14}[/tex]:
[tex]3k=-\frac{1}{14}[/tex]
Divide both sides by 3 to solve for k
[tex]k=-\frac{1}{42}[/tex]
I hope this helps!
what is the prime factorization of 225 in exponent form
Answer:
prime factorization of 225 = 32•52.
Step-by-step explanation:
The number 225 is a composite number so, it is possible to factorize it. 225 can be divided by 1, by itself and at least by 3 and 5.
A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In other words, a composite number is any integer greater than one that is not a prime number.