Answer: [tex]y=Ce^(^3^t^{^9}^)[/tex]
Step-by-step explanation:
Beginning with the first differential equation:
[tex]\frac{dy}{dt} =27t^8y[/tex]
This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:
[tex]\frac{1}{y} \frac{dy}{dt} =27t^8[/tex]
Multiply both sides by 'dt' to get:
[tex]\frac{1}{y}dy =27t^8dt[/tex]
Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:
[tex]\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt[/tex]
[tex]ln(y)=27(\frac{1}{9} t^9)+C[/tex]
[tex]ln(y)=3t^9+C[/tex]
We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:
[tex]e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)[/tex]
[tex]y=e^(^3^t^{^9} ^+^C^)[/tex]
We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:
[tex]y=e^(^3^t^{^9}^)e^C[/tex]
The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:
[tex]y=Ce^(^3^t^{^9}^)[/tex]
To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:
[tex]\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))[/tex]
[tex]\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)[/tex]
[tex]\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8[/tex]
Now check if the derivative equals the right side of the original differential equation:
[tex](Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)[/tex]
[tex]Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)[/tex]
QED
I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.
Form a polynomial whose zeros and degree are given. Zeros: 2, multiplicity 1; 4, multiplicity 2; degree 3
Answer:
If the polynomial is degree 3, then it is of the form y = Ax3 + Bx2 +Cx + D
And if the zeros are -2 with multiplicity of 1, then the factor is (x+2)1 = x+2
The other zero is -4 with multiplicity of 2, so it's factor is (x+4)2 = x2 +8x+16
So in general, if we let A = 1, then the polynomial is y = (x+2)(x+4)2 which multiplies out to
(x+2)(x2+8x+16) = x3 + 8x2 + 16x + 2x2 + 16x + 32
Combining like terms gives the polynomial:
y = x3 +10x2 + 32x + 32
If A is not 1, then y = A(x3 +10x2 + 32
You have a bag of marbles. In the bag, there is a red, blue,
white, yellow, orange and black marble. Find the probability
that you choose the red, then the blue marble (you don't
replace the first marble you draw). Express your answer as a
simplified fraction.
Answer:
1/6 probability that you choose red
1/6 probability that you choose blue
Step-by-step explanation:
There are 6 marbles and only one is red, same with blue, so out of six times you pick a marble you will get the blue once and red once.
What is the area
of a sector
when 0=pi/2 radians and
8/
3?
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =\stackrel{radias}{angle}\\[-0.5em] \hrulefill\\ r=\frac{8}{3}\\ \theta =\frac{\pi }{2} \end{cases}\implies A=\cfrac{~~ \left( \frac{\pi }{2} \right)\left( \frac{8}{3} \right)^2~~}{2}\implies A=\cfrac{~~ \left( \frac{\pi }{2} \right)\left( \frac{64}{9} \right)~~}{2} \\\\\\ A=\cfrac{~~\frac{32\pi }{9} ~~}{\frac{2}{1}}\implies A=\cfrac{32\pi }{9}\cdot \cfrac{1}{2}\implies A=\cfrac{16\pi }{9}[/tex]
Julie has 30 pounds of chocolate that she is selling for a fundraiser. She is putting the chocolate into boxes that each hold 2/3 pound of chocolate. How many boxes can she fill?
Answer:
45 boxes.
Step-by-step explanation:
30 / 2/3
= 30 * 3/2
= 90/2= 45
The height of a triangular truss is 5 ft less than the base. The amount of drywall needed to cover the triangular area is 84 ft2. Find the base and height of the triangle to the nearest tenth of a foot.
Answer:
Base: 15.1 ft
Height: 11.1 ft
Step-by-step explanation:
(15.1 x 11.1)/2 = 84.07
84.07 ≈ 84
This is the closest answer.
a woman 1.65. tall stood 50m away from the foot of a tower,and observe that the angle of elevation of the top of the tower to be 50⁰ what is the height of the tower
[tex]\sf\huge\underline{\star Solution:-}[/tex]
[tex]\rightarrow[/tex]Let the women's height be AE and distance between the women and tower be AC.
Also let the height of tower be BC.
[tex]\rightarrow[/tex]Now, clearly it is forming a triangle.
So, in triangle ABC,
[tex]\rightarrow[/tex][tex]\sf{Tan50° \:= \: \frac{BC}{AC}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{1.19 \:= \: \frac{BC}{50}}[/tex]
[tex]\rightarrow[/tex][tex]\sf{1.19 ×50\:= \: BC}[/tex]
[tex]\rightarrow[/tex][tex]\sf{59.5m\:= \: BC}[/tex]
[tex]\rightarrow[/tex]Hence, BC = 59.5m
So, BD(total height of the tower)[tex]\sf{ = \:BC+CD}[/tex]
[tex]\sf{= \:59.5+1.65}[/tex]
[tex]\sf{=\: 61.15m}[/tex]
Therefore, total height of the tower =[tex]\sf\purple{ 61.15m.}[/tex]
________________________________
Hope it helps you:)
Answer:
61.24 m to the nearest hundredth.
Step-by-step explanation:
tan 50 = H / 50
H = 50 tan 50
Height of the tower = H + height of the woman
= 50 tan 50 + 1.65
= 61.2377 m
help please!
x+2/2x-2 = 7/x+3
Answer:
im sorry I don't know I didn't do this in school
What is the value of x in this equation? 5x= 15
Answer:
x=3
Step-by-step explanation:
15 divided by 5= 3
5(3)=15
so x=3
(7y to the fourth power) to the second power
Answer:
7y^(8)
Step-by-step explanation:
(7y^4)^2
=7y^(4×2)
=7y^(8)
Find the slope of the line graphed below.
Answer:
—7/3
Step-by-step explanation:
1) Choose two points on it.
like (1,3) and (4,—4)
2) slope is
[tex]slope = \frac{y2 - y1}{x2 - x1} = \frac{3 + 4}{1 - 4} = \frac{7}{ - 3} = - \frac{7}{3} [/tex]
Answer:
-7/3
Step-by-step explanation:
Slope formula:
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
The two points on the graph are (1,3) and (4,-4).
Substitute into the formula:
[tex]\frac{-4 - 3}{4 - 1}[/tex]
Simplify:
[tex]\frac{-4 - 3}{4 - 1} = \frac{-7}{3}[/tex]
help me please with this problem
Answer:
20.4
Step-by-step explanation:
First you do 8947.95/30.25 and you will get 295.8 the you divide that by 14.5 and you will get 20.4 and that will be your answer
A triangle has angle measurements of 36°, 83°, and 61°. What kind of triangle is it?
Answer:
It is an acute truangle.
Step-by-step explanation:
It is an acute triangle since all of the side are less than 90 degrees.
Which decimal is equivalent to 0.75?
Answer:
Fracción
3/4
Fracciones equivalentes
6/8
Decimal
0,75
Answer:
3/4.
Step-by-step explanation:
0.75 = 75/100
= 3/4
John works at Klein’s Dry Cleaning. He earns $8.45 per hour. If John worked 39 hours this week, what is his pay? *
Answer: 329.55
Step-by-step explanation: multiple 8.45 by 39 which is 329.55
8.45 * 39 = 329.55
Each model represents one whole. In which model does the shaded section represent the
product of 5/8and 3/8 ?
You would show the answer choices for this one. 5/8 x 3/8 is 15/64 or about 0.234375.
cos ∅ = 5/13 and sin ∅ < 0. Identify the quadrant of ∅ and find sin ∅.
Answer:
Step-by-step explanation:
A square pyramid is shown sitting on its base.
Answer:
312
Step-by-step explanation:
First we find the measure of the basea and that is 144 becuase 12x12
To find one side we do b*h over 2 and that is 7x12/2 which is 42 then we know that there are 4 more of those sides and we get 42*4 168
When we add 144+168 we will get 312
The perimeter of a deck is 48 ft. If the length is 16 ft., what is the width?
Answer:
8
Hope This Helps1 :) Please give Brainliest if this does!
Refer to attachment below;
If nitrogen is warmer than -320 degrees Fahrenheit, it will be a gas.
Write an inequality that is true only for temperatures at which nitrogen is a gas.
Answer:
Step-by-step explanation:
If nitrogen is warmer than -320 degrees farenheit it will be gas .write an inequality that is true only for temperatures (t) at which nitrogen is a gas.
✓ t>-320=gas if I'm thinking about it correctly
Write an inequality for the given graph.
Answer:
y ≤ -3/4x + 3Step-by-step explanation:
Calculating slope
m = Rise/Runm = -3/4Y-intercept : (0, 3)
Equation of line
y = mx + cy = -3/4x + 3Inequality
y ≤ -3/4x + 3A cup of brewed tea has 54 milligrams less caffeine than a cup of brewed coffee. If a cup of tea has 66 milligrams of caffeine, how much caffeine is in a cup of coffee?
Answer:
120 milligrams
Step-by-step explanation:
x=coffee
x-54=tea
x-54=66
x=66+54=120
MAX POINTS
WILL GIVE BRANLIEST PLEASE HELP
h(x)=3/x-h +k
Oh no! He seems to be missing some parts though. He was "robbed" of his
asymptotes.
Luckily, he can remember what they were:
1. This functions vertical asymptote was x=-5.
2. This functions horizontal asymptote was y = 12.
Please recreate this function with those identifying features! Please make sure it
looks like the function in the picture
Let's do
[tex]\\ \rm\dashrightarrow y=\dfrac{3}{x-h}+k[/tex]
Release k for some while
If
we take h=0So
y=3/xSo vertical asymptote is at origin now
It mentioned that it's at x=-5 so we need to change x
put -5 in place of h[tex]\\ \rm\dashrightarrow y=\dfrac{3}{x-(-5)}[/tex]
[tex]\\ \rm\dashrightarrow y=\dfrac{3}{x+5}[/tex]
Vertical asymptote at x=-5Now
for k=0 horizontal asymptote at originBut it's given
y is at 12Same put y=12 in place of k
[tex]\\ \rm\dashrightarrow y=\dfrac{3}{x+5}+12[/tex]
h=-5k=12Graph attached for verification
Answer:
h(x)=3/x+5 +12
Step-by-step explanation:
What is the slope-intercept equation for this line?
Answer:
the slope intersection is xy
y=-3x+4
Solution:We are given 2 points: (1,1) and (0,4)We can use these points to find the slope of the line:[tex]m=\displaystyle\frac{y2-y1}{x2-x1}[/tex][tex]\displaystyle\frac{4-1}{0-1}[/tex][tex]\displaystyle\frac{3}{-1}[/tex][tex]-3[/tex]Now, let's identify the y-intercept.The y-intercept is the point where the graph touches the y-axis.Since the graph touches the y-axis at (0,4) the y-intercept is equivalent to (0, 4) or 4.Hope it helps.
Do comment if you have any query.
HELP PLS GIVING 20 POINTS!!!! LOOK AT PICTURE FOR QUESTION!!!
Answer:
75; 76; 77
Step-by-step explanation:
four times the sum of 3 consecutive numbers
first number is X
second is X+1
third is X+2
4 × (x + x+1 + x+2) = 912
4(3x + 3) = 912
12x = 912 - 12
x = 900/12
x = 75
the three numbers are : 75 , 76 , 77
what is fhe solution of the system of these equations? (i’m giving brainliest)
Answer:
Top-left system: (3,5)
Bottom-right
system: (-1,0)
Step-by-step explanation:
One way to solve a system of equations is to graph them. The solution is the point of intersection (where the lines cross). If you need to give the x-value and y-values separately, the first number in the pair is the x and the second number is the y.
Help help help help help help math math
Evaluate the piecewise function by matching the domain values with the range values.
The subfuctions of the piecewise function f(x) are linear functions
The matching values of the domain values with the range values are
x f(x)
-4 -7
-2 -8
0 -2
2 4
4 -4
8 -12
How to evaluate the piece-wise function?The function is given as:
[tex]f(x) = \left[\begin{array}{cc}x-3&x\le-4\\3x-2&-4 < x\le 2\\-2x+4&x > 2\end{array}\right][/tex]
The above definition means that:
All x values less than or equal to -4 would be evaluated using f(x) = x - 3All x values greater than -4 but less than or equal to 2 would be evaluated using f(x) = 3x - 2All x values greater than 2 would be evaluated using f(x) = -2x + 4Using the above highligts, we have:
f(-4) = -4 - 3 = -7
f(-2) = 3(-2) - 2 = -8
f(0) = 3(0) - 2 = -2
f(2) = 3(2) - 2 = 4
f(4) = -2 * 4 + 4 = -4
f(8) = -2 * 8 + 4 = -12
So, the matching values are
x f(x)
-4 -7
-2 -8
0 -2
2 4
4 -4
8 -12
Read more about piecewise functions at:
https://brainly.com/question/10733545
Suppose a sample of 313 tankers is drawn. Of these ships, 235 did not have spills. Using the data, estimate the proportion of oil tankers that had spills.
Answer:
78
Step-by-step explanation:
313 - 235 = 78
Volume of a box If a box has a volume of 42 cubic feet, is it possible for you to
fit inside the box? Explain your answer
Answer:
yes ,because the average human hight
cannot exceed 7squared feets
Without knowing the dimensions of the box or the size of the person, we cannot determine whether the person can fit inside the box or not.
What is a box?In mathematics, a box is a three-dimensional shape that has six rectangular faces.
It is also called a rectangular prism.
The faces on opposite sides of a box are congruent and parallel. A box has a height, width, and length, which are usually labeled as h, w, and l.
The volume of a box can be found by multiplying its length, width, and height: V = l × w × h.
We have,
The volume of a box is a measure of the amount of space inside the box, typically measured in cubic units such as cubic feet or cubic meters.
If a box has a volume of 42 cubic feet, it is simply telling us the amount of space inside the box.
Whether a person can fit inside the box or not depends on the size of the box and the size of the person.
Without knowing the dimensions of the box or the size of the person, we cannot determine whether the person can fit inside the box or not.
So,
We need more information to answer this question.
Thus,
Without knowing the dimensions of the box or the size of the person, we cannot determine whether the person can fit inside the box or not.
Learn more about box here:
https://brainly.com/question/16183371
#SPJ2
What is the hydronium ion concentration in a solution with a pH of 4.25?
Answer:
5.6 × 10⁻⁵ mol/L
Step-by-step explanation: