Answer:
C. [tex]\displaystyle y = 5e^{tan(x)}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
FunctionsFunction Notation|Absolute Values|Anything to the 0th power is 1Algebra II
Logarithms and Natural logsEuler's number eCalculus
Derivatives
Derivative Notation
Trig Derivatives
Differential Equations
Separation of variablesGeneral and particular solutionsAntiderivatives - Integration
Integration Constant C
Trig Integration
Logarithmic Integration
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{dy}{dx} = ysec^2(x)[/tex]
x = 0, y = 5
Step 2: Rewrite Differential
Separation of variables
[Division Property of Equality] Isolate y terms together: [tex]\displaystyle \frac{1}{y}\frac{dy}{dx} = sec^2(x)[/tex][Multiplication Property of Equality] Isolate x terms together: [tex]\displaystyle \frac{1}{y}dy = sec^2(x)dx[/tex]Step 3: Find General Solution
[Equality Property] Integrate both sides: [tex]\displaystyle \int {\frac{1}{y}} \, dy = \int {sec^2(x)} \, dx[/tex][1st Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \int {sec^2(x)} \, dx[/tex][2nd Integral] Integrate [Trig Integration]: [tex]\displaystyle ln|y| = tan(x) + C[/tex][Equality Property] e both sides: [tex]\displaystyle e^{ln|y|} = e^{tan(x) + C}[/tex]Simplify: [tex]\displaystyle |y| = Ce^{tan(x)}[/tex]Rewrite: [tex]\displaystyle y = \pm Ce^{tan(x)}[/tex]Step 4: Find Particular Solution
Substitute in variables [Function]: [tex]\displaystyle |5| = Ce^{tan(0)}[/tex]Evaluate absolute value: [tex]\displaystyle 5 = Ce^{tan(0)}[/tex]Evaluate trig: [tex]\displaystyle 5 = Ce^0[/tex]Evaluate exponent: [tex]\displaystyle 5 = C(1)[/tex]Multiply: [tex]\displaystyle 5 = C[/tex]Rewrite: [tex]\displaystyle C =5[/tex]Substitute in C [General Solution]: [tex]\displaystyle y = 5e^{tan(x)}[/tex]∴ Our answer is C.
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differential Equations
Book: College Calculus 10e
Please help me with this!!!!!!!!!!!!!!! MATHHHHHH
A silo has a cylindrical part and a roof that is a hemisphere.
The radius of the cylinder is 3m and its height is 12m.
Find the volume of the silo.
Answer:
339.29
Step-by-step explanation:
Use formula for cylinder: [tex]V=\pi r^2h[/tex].
Note: I rounded to the nearest hundreth.
please help in this........
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hi pls, help me with this, I am giving 15 points 10 for answering the question and 5 for telling me what is Q1 meaning and Q2 meaning ty!
The table below shows 10 data values:
125, 138, 132, 140, 136, 136, 126, 122, 135, 121
What values of minimum, Q1, median, Q3, and maximum should be used to make a box plot for this data?
A.) Minimum = 121, Q1 = 125, median = 133.5, Q3 = 136, maximum = 140
B.) Minimum = 121, Q1 =136, median = 133.5, Q3 = 125, maximum = 140
C.) Minimum = 125, Q1 = 130.25, median = 132.5, Q3 = 134.5, maximum = 138
D.) Minimum = 125, Q1 =134.5, median = 132.5, Q3 = 130.25, maximum = 138
Answer:
we have to put the numbers in order..
(121,122,125, 126,132),M,(135,136,136,138,140)
Step-by-step explanation:
minimum : (smallest number) = 121
Q1 : 125
Q2 (median) : (132 + 135) / 2 = 267/2 = 133.5
Q3 : 136
maximum : (largest number) = 140
I did this a long time ago so im not so sure
Answer:
Step-by-step explanation:
121 122 125 126 132 135 136 136 138 140
140 -121 =19 range
Min=121 max =140
Mean = 131.1
Median = 132+135=267/2=133.5
ASAP PLEASE ‼️‼️❗️‼️‼️❗️
A group of 25 people are going to run a race. The top 12 finishes advance to the finals. find the of possibilities.
Answer:
I dont know what thats asking
Step-by-step explanation:
0.4567304 x 2.5678093 = ?
Answer:
1.17279656871
Step-by-step explanation:
Answer:
1.72796569
Step-by-step explanation:
0.4567304 x 2.5678093 = 1.72796569
Please Help!!!! Write an exponential function. In your own words, describe the rate of change of this function and what the graph looks like.
Answer:
A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change=change in y change in x. Rates of change can be positive or negative.
Step-by-step explanation:
Answer:
A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change=change in y change in x. Rates of change can be positive or negative.
Step-by-step explanation:
what is linear graph
Answer:
A linear graph is nothing but a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.
Answer: is a diagram which shows a connection or relation between two or more quantity.
Step-by-step explanation:
Which of the following is equivalent to 3x - 4y = 6?
y=7
1 x
v==
y
V = 3*+2
v
y= *-2
Answer:
the answer is option D
y =(3/4)x - (3/2)
What is the volume of this rectangular prism?
2
cm
2
cm
5
cm
5
Answer:
The volume is 8
Step-by-step explanation:
Volume=abc
V=(2/5)(2/5)(2/5)
V=8
What is the horizontal asymptote of j (x) = StartFraction 14 x cubed + 45 Over 2 x cubed + x + 9 EndFraction
Answer:
C. y=7
Step-by-step explanation:
guy above me was right
The horizontal asymptote of the given function [tex]f(x) = \dfrac{14x^{3} +45}{2x^{3}+x+9}[/tex] would be y = 7.
When do we get horizontal asymptote for a function?The line y = a is a horizontal asymptote if the function f(x) tends to 'a' from the upside of that line y = a, or from downside of that line.
The given function is
[tex]f(x) = \dfrac{14x^{3} +45}{2x^{3}+x+9}[/tex]
We need to determine the horizontal asymptote.
Horizontal asymptote;
From the given function, it is obvious that the denominator's degree is smaller than the numerator's degree.
Then, the horizontal asymptote is the y-axis.
Thus, the horizontal asymptote is y = 7.
Learn more about horizontal asymptotes here:
https://brainly.com/question/2513623
#SPJ2
plz plz help me for math
Answer:
Oasis idiot and a good time in the day before
If angle a has the terminal ray that falls in the fourth quadrant and cosine a equals 5/9 then determine the value of sin a in simplest radical form
Answer: [tex]-\dfrac{2\sqrt{14}}{9}[/tex]
Step-by-step explanation:
Given
[tex]\cos a=\dfrac{5}{9}[/tex]
[tex]a[/tex] lies in the fourth quadrant
So, sine must be negative in the fourth quadrant
Using identity [tex]\sin ^2 x+\cos^2 x=1[/tex] to find sine value
[tex]\Rightarrow \sin^2 a=1-\dfrac{5^2}{9^2}[/tex]
[tex]\\\\\Rightarrow \sin^2 a=1-\dfrac{25}{81}\\\\\\\Rightarrow \sin^2 a=\dfrac{56}{81}\\\\\\\Rightarrow \sin a=-\sqrt{\dfrac{56}{81}}\\\\\\\Rightarrow \sin a=-\dfrac{2\sqrt{14}}{9}[/tex]
Please don’t report I need help. I’m going to be a high school sophomore next fall and I’m selecting my courses should I take Geometry I or Algebra II?????
Answer:
I would say geometry. its easier
If the principal is $4,500 and the rate of interest is 8%, what is the amount of interest after one year? Formula is I =PRT
Step-by-step explanation:
I=?
P= $4500
R=8%=0.08
T=1 year
8%*0.01= 0.08
I=(4500)(0.08)(1)
(4500)(0.08)=360
360*1=360
The interest after one year is $360
If a box has 5 red, 3 green, and 4 blue jelly beans, then what is the probability of choosing
at random a red jelly bean?
7/12, 5/12, 1/12, 2/7
Answer:
2/7
Step-by-step explanation:
Answer:
5/12
Step-by-step explanation:
All the beans are equally likely to be chosen, so the bottom (denominator) of the fraction is 12 (there are 12 beans in the box).
The numerator is 5 because that's the number of red beans in the box.
Will mark brainliest
Answer:
I think the answer should be Mat A cause it has more space.
There were 24 students running in a race. How many different arrangements of first,
second, and third place are possible?
pls help me on this !!!!!!!!!!!
Answer:
11.8 m
Step-by-step explanation:
2/3πr^3=1100π
r^3=1650
r=11.8
A rectangle has an area of 96 in2. The rectangle's base is 4 in. What is the height of the rectangle?
A. 384in
b. 24in
c. 92in
d. 100in
Answer:
B. 24
Step-by-step explanation:
Formula for area of a rectangle: base × height/ length × width
To find the height, divide the area by the base.
[tex]96/4=24in[/tex]
[tex]formula=base *height/length*width[/tex]
[tex]4*24=96in^2[/tex]
which number line shows the soulution
Answer:
The answer is C.
Solve: 8 (5 + 3)
1. What number are you distributing?
2. Show your work
3. Answer is?
Answer:
64
you are distrbuting both the 8 which =64
Step-by-step explanation:
See the steps below:)
Answer:
Step-by-step explanation:
8(5+3)
You distribute what's in the Parentheses
8 x 5 = 40 and 8 x 3 = 24
40+24 = 64
Plssss help me cuhhh
Answer:
i believe your answer is C. Rectangle
Step-by-step explanation:
I hope this helps! :D
maybe consider brainliest?
Which is the inverse of the difference of 1/3-1/4?
A.0/1
B.1/12
C.7/12
D.12/1
Answer:o/1
Step-by-step explanation:
Hellpppppppppp pleaseee
Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the northbound car has traveled 4 kilometers, and the eastbound car has traveled 3 kilometers. Measured in a straight line, how far apart are the two cars?
Answer:
The distance between them is 5km
Step-by-step explanation:
Given
[tex]Car\ A =4km[/tex]
[tex]Car\ B =3km[/tex]
Required
Distance between them
The scenario can be represented with the attached image
The distance between them is then calculated using Pythagoras theorem
[tex]d^2 = 4^2 +3^2[/tex]
[tex]d^2 = 16 +9[/tex]
[tex]d^2 = 25[/tex]
Take square roots of both sides
[tex]d = \sqrt{25[/tex]
[tex]d = 5[/tex]
12. You are measuring the height of a Sitka spruce tree in Alaska. You stand 45 feet from the base of
the tree. You measure the angle of elevation from a point on the ground to the top of the tree
to be 59º. Estimate the height of the tree.
Answer:
tangent 59° = Tree height / 45 feet
Tree Height = 1.6643 * 45
Tree Height = 74.8935 Feet
Step-by-step explanation:
Find the volume of the figure. Use 3.14 for Pi
Answer:
The answer would be 17
Step-by-step explanation:
The answer would be 17 because if you add 12 plus 5 That would be your answer
Multiplying by which number is equivalent to finding 15%?
Answer:
The answer is still 15. Because
The number is × which is 0.so it is still 15%use the information given to find the value of n in each of the following sets of number
Answer:
No picture try uploading it again and I can see if I can help you