Answer:
[tex]\sqrt[4]{e};\frac1{4e}[/tex]
Step-by-step explanation:
The first derivative of [tex]f(x)[/tex] will give, for each x, the slope of the tangent at that specific x. Let's calculate the derivative, applying the quotient rule.
[tex]D(\frac AB) = \frac{A'B-AB'}{B^2}\\f'(x)= \frac1{x^8}[(\frac1x)x^4-(lnx)(4x^3)]=\frac1{x^8}[x^3(1-4lnx)]=\frac{1-4lnx}{x^5}[/tex]
Now, to find the point with an horizontal tangent (called "stationary points"), we set the first derivative equal to 0. Considering that we're working with [tex]x > 0[/tex] we deal only with the numerator.
[tex]1-4lnx = 0 \rightarrow lnx= \frac14\\x=e^\frac14 =\sqrt[4]{e}[/tex]
At this point we Replace the value we found in the equation to find it's y coordinate
[tex]f(\sqrt[4]e) = \frac{ln\sqrt[4]e}{\sqrt[4]e^4}= \frac{\frac14}{e} = \frac1{4e}[/tex]
PLEASE HELP ASAP!!
A population of zombies in Happy Town, USA doubles every week. The number of zombies in Happy Town is currently 75. How many more zombies will there be after an additional 4 weeks? (no commas just numbers)
Answer:
1200
Step-by-step explanation:
since the first week has 75 doubling it is 150 doubling that is 300 doubling that is 600 doubling that for the final week is 1200.
1200 more zombies will there be after an additional 4 weeks.
What is Sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members (also known as elements or phrases), just like a set. The length of the series is the number of elements (potentially infinite).
At initial the zombies are= 75
Now, the zombies doubles at every week.
So, After 1 st week the population of zombies are
= 75 x 2
= 150
Then, After 2 nd week the population of zombies are
= 150 x 2
= 300
Then, After 3 rd week the population of zombies are
= 300 x 2
= 600
Then, After 4th week the population of zombies are
= 300 x 2
= 1200
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Which ordered pair is a solution of...
x-y = -3
2x+y = 0
a. (-3,0)
b. (-1,2)
c. (0,0)
d. (1,4)
Answer:
the answer to your question is B
3. What is the area of the triangle below?
6.0 ft^2
8.6 ft^2
15.0 ft^2
17.2 ft^2
Answer:
6.0 ft^2
Step-by-step explanation:
hope this helps
Identify C on the following diagram
Answer: X-axis
Step-by-step explanation: The arrow is pointing to the horizontal line on the on the graph. That horizontal line is the x-axis.
The parabola y=x^2 is scaled vertically by a factor of 8
Answer:
2x8=16 so there for y=x^18
Step-by-step explanation:
There are 30 students in Mrs. Jones class. 20% of the students received an A on the last math test. How many students received an A?
Answer:
20% of 30
= 20/100 * 30
= 6
hence 6 students recieved A grade
find the value of (0.81÷0.09)+(0.81÷9)
Answer:
9.09
Step-by-step explanation:
[tex]\frac{0.81}{0.09} + \frac{0.81}{9}[/tex]
= 9 + [tex]\frac{0.81}{9}[/tex]
= 9+ 0.09
= 9.09
I hope this helped!! If so please rate and mark brainliest <3!!
Write a formula that shows the dependence of: the length of the side (a) of a cube on the surface area (S) of the cube
Write the formula for the parabola that has x-intercepts (-3-√2,0) and (-3+√2,0), and y-intercept (0,-5)
Answer:
Let a = side length of a cube
Let S = surface area of a cube
Area of a square = a²
Since a cube has 6 square sides: S = 6a²
To make a the subject:
S = 6a²
Divide both sides by 6:
[tex]\sf \implies \dfrac{S}{6}=a^2[/tex]
Square root both sides:
[tex]\sf \implies a=\sqrt{\dfrac{S}{6}}[/tex]
(positive square root only as distance is positive)
-----------------------------------------------------------------------------------------------
[tex]\sf x=-3-\sqrt{2} \implies (x+[3+\sqrt{2}])=0[/tex]
[tex]\sf x=-3+\sqrt{2} \implies (x+[3-\sqrt{2}])=0[/tex]
Therefore,
[tex]\sf y=a(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex] for some constant a
Given the y-intercept is at (0, -5)
[tex]\sf \implies a(0+3+\sqrt{2}) (0+3-\sqrt{2})=-5[/tex]
[tex]\sf \implies a(3+\sqrt{2}) (3-\sqrt{2})=-5[/tex]
[tex]\sf \implies a(9-2)=-5[/tex]
[tex]\sf \implies 7a=-5[/tex]
[tex]\sf \implies a=-\dfrac57[/tex]
Substituting found value of a into the equation and simplifying:
[tex]\sf y=-\dfrac57(x+[3+\sqrt{2}]) (x+[3-\sqrt{2}])[/tex]
[tex]\sf \implies y=-\dfrac57(x^2+6x+7)[/tex]
[tex]\sf \implies y=-\dfrac57x^2-\dfrac{30}{7}x-5[/tex]
Solve using area model. 53x95
53x95 = 5035!
hopes this helps! ^^
Answer:
5605
Step-by-step explanation:
If VZ=p–7 and WY=p–21, what is the value of p?
Using the midline property;
[tex]2wy = vz[/tex]
[tex]2(p - 21) = p - 7[/tex]
[tex]2p - 42 = p - 7[/tex]
[tex]2p - p = - 7 + 42[/tex]
[tex]p = 35[/tex]
Two of which shape can make a circle
Answer:
2 semi circles put together
Step-by-step explanation:
just cut the circle in half
Please help I will give brainliest.
Answer:
t = 0, and t = 4/5
Step-by-step explanation:
1. Write the equation in standard form:
-75t^2+60t=0
2. Solve with the Quadratic formula:
[tex]t_{1,2} = \frac{-60 +- \sqrt{60^2 - 4(-75)}0}{2(-75)} \\\\t_{1,2} = \frac{-60+-60}{2(-75)} \\\\3. Separate the fractions:\\t_{1} = \frac{-60+60}{2(-75)} , t_{2} = \frac{-60-60}{2(-75)} \\\\4. Solve for each:\\t_{1} = \frac{0}{-150} = 0\\t_{2} = \frac{-120}{-150} = 4/5[/tex]
hope this helps!
cereal set roster notation
Answer:
Step-by-step explanation:
Notation for Cereal Set Roster
The roster form is one of the simplest ways to represent the set. The elements of a set are represented in a row and separated by a comma in roster form. For example, the first five positive even numbers are denoted as A = 2, 4, 6, 8, 10.
A = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 is an example of roster notation: A = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.
Hope that helps you understand :)
Terrence measured an Italian restaurant and made a scale drawing. The scale of the drawing was 7 centimeters = 2 meters. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Answer:
200/7
Step-by-step explanation:
(2 meters)/(7 centimeters) or (2m/7cm)
1 meter = 100 cm
(2m/7cm)*(100cm/1m) = 200/7 (or 28.57) scale factor.
Find two integers having a product of positive 27 and a sum of negative 12.
I know you're looking for an answer but i'm doing a challenge where i have to answer 10 questions by the end of today, I'm sorry! :(
Solve 7x -4 = 5x + 15 for x.
19/12
11/2
19/2
Answer:
Third option
Step-by-step explanation:
Given the following question:
[tex]7x-4=5x+15[/tex]
To find the answer we need to use inverse of operations to simplify the equation in till we isolate the variable and find the value of x.
[tex]7x-4=5x+15[/tex]
[tex]-4+4=0[/tex]
[tex]15+4=19[/tex]
[tex]7x=5x+19[/tex]
[tex]5x-5x=0[/tex]
[tex]7x-5x=2x[/tex]
[tex]2x=19[/tex]
[tex]2x\div2=x[/tex]
[tex]19\div2=\frac{19}{2}[/tex]
[tex]=\frac{19}{2}[/tex]
Your answer is the third option or "19/2."
Hope this helps.
Question
Find the perimeter of the figure to the nearest hundredth.
Answer:
50.29in
Step-by-step instructions:
First find the semi-circular part:- 1/2×2πr
=1/2×2×22/7×9
=28.29
Find whole perimeter:- 28.29+5+5+12 = 50.29 in
i need help with problem 1
Can someone help me please
first add the ratio numbers which is 12
[tex] \frac{2}{12} \times 6000 = 1000[/tex]
then divide 1000 with 175
=5.71
5.71×2.25
=12.85 ruro
What transformation did Tory perform?
Answer:
She translated each vertex of Figure 1 seven units to the right.
Step-by-step explanation:
PLS HELP ME I WILL MARK THE BRAINLIEST
#1
First the rectangle
L=18mB=7mArea
18(7)126m^2.For semicircle
d=7m=>r=3.5mArea
=πr^2/2=12.25π/2Total area
126+2(12.25π/2)126+12.25πm^2#2
r=15fttheta=332°=332×π/180=0.92πArea:-
r^2\theta15^2(0.92)207ft^2The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain? ; 13.5 mg ; 34.6 mg ; 0.2 mg ; 4.6 mg
The required equation f(10) = 13.52 mg remains.
We have given that ,
m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60
What is the fromula for he amount of a radioactive substance remaining after t years?The amount of a radioactive substance remaining after t years is given by the function
[tex]f(t)=m(0.5)^{t/h}[/tex]............ (1),
where m = initial mass and h= half-life in years.
Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,
then from equation (1) we get,
[tex]f(10)=50(0.5)^{10/5.3}[/tex]
Therefore the required equation f(10) = 13.52 mg .
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Answer:
The required equation f(10) = 13.52 mg remains.
We have given that ,
m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60
What is the fromula for he amount of a radioactive substance remaining after t years?
The amount of a radioactive substance remaining after t years is given by the function
............ (1),
where m = initial mass and h= half-life in years.
Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,
then from equation (1) we get,
Therefore the required equation f(10) = 13.52 mg .
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In a school there are 1970 pupils. If there are 799 boys, how many more girls are there than boys?
As per linear equation, there are 372 more girls in school than boys.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant."
Given, there are 1970 pupils.
There are 799 boys in the school.
Therefore, the number of girls in the school is
[tex]= (1970-799)\\= 1171[/tex]
Therefore, the number of girls more than boys in the school is
[tex]= (1171-799)\\= 372[/tex]
In that school , there are 372 more girls than total number of the boys.
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PLEASE HELP! DUE TODAY! TY!
Use the diagram to find measure of Arc HJ.
Work:
(HJ) =
Answer: 44 degrees
Step-by-step explanation:
Number 3. (Look at the Image) Using the formula ū = ||T||(cos o 7 + sin 0 j) Il, find the magnitude and direction of ū= (3,-V3).
Magnitude should be written in simplified radical form.
ů= 11 ull (cosoit sin 63
ů
find magnitude and direction of
ů - <333)
Answer:
its 54
Step-by-step explanation:
1+2=3 3x5=15 15x2=30 30+16=46 46+8=54
50 POINTS NEED HELP
If u = 3 inches, v = 4 inches, w = 7 inches, x = 7 inches, y = 8 inches, and z = 4 inches, what is the area of the object?
A.
52 square inches
B.
53 square inches
C.
56 square inches
D.
54 square inches
Hey so I have a question do u need to explain?
The number of goldfish in a tank is 12, and the volume of the tank is 45 cubic feet. What is the density of the tank?
Answer: 0.27
Population density of the species in water:
Population density of a species in the water is given by the expression,
Density =Given in the question,
Number of goldfish in the tank = 12
Volume of the tank = 45 cubic feet
Substitute these values in the expression,
Density =
= 0.267
≈ 0.27 goldfish per cubic feet
Therefore, density of the tank will be 0.27 goldfish per cubic feet.
A robot vacuum cleans a dirty floor using multiple passes. During each pass, 24% of the dirt is removed. If the floor initially has 550 ml of dirt, write a function to find out how much dirt will remail after 10 passes?
please include function and value.
The function is given by y = 550(0.76)ˣ, after 10 passes, the number of dirts is about 35.36 ml
How to solve an exponential function?
Let y represent the amount of dirt on the floor after x passes.
The floor initially has 550 ml of dirt, hence a = 550.
During each pass, 24% of the dirt is removed. Hence b = 100% - 24% = 76% = 0.76
The equation is given by:
y = 550(0.76)ˣ
After 10 passes:
y = 550(0.76)¹⁰ = 35.36 ml
The function is given by y = 550(0.76)ˣ, after 10 passes, the number of dirts is about 35.36 ml
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Suppose that 18 inches of wire costs 72 cents.
At the same rate, how many inches of wire can be bought for 44 cents
3. How many 3 digit all even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
Step-by-step explanation:
Only 3 numbers are possible at units place (2, 4 & 6) as we need even number.
But at tens & hundreds place all 6 are possible
Number of 3 digit even numbers
= 3x6x6 = 108
36
Step-by-step explanation:[tex]Solution:[/tex]
[tex]6\times6=36[/tex]
[tex]such\ as:[/tex]
[tex]11\ \ \ 22\ \ \ 33\ \ \ 44\ \ \ 55\ \ \ 66\\ 12\ \ \ 21\ \ \ 31\ \ \ 41\ \ \ 51\ \ \ 61\\ 13\ \ \ 23\ \ \ 32\ \ \ 42\ \ \ 52\ \ \ 62\\ 14\ \ \ 24\ \ \ 34\ \ \ 43\ \ \ 53\ \ \ 63\\ 15\ \ \ 25\ \ \ 35\ \ \ 45\ \ \ 54\ \ \ 64\\ 16+263646+56\\ 6+6+6+6+6+6\\ =36.[/tex]
I hope this helps you
:)