To find y(7) given dy/dt = 4y and y(2) = 400, we can solve the differential equation, find the constant of integration, and substitute the value of t to find y(7).
Explanation:To solve the differential equation dy/dt = 4y, we can separate the variables and integrate them. Starting with dy/y = 4dt, we get ln|y| = 4t + C, where C is the constant of integration.
Using the initial condition y(2) = 400, we can solve for C: ln|400| = 4(2) + C, C = ln|400| - 8. Now we can find y(7): ln|y(7)| = 4(7) + ln|400| - 8. Exponentiating both sides, we get |y(7)| = e^(28 + ln|400| - 8), and since y(7) is positive, y(7) = e^(28 + ln|400| - 8).
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Does the following system have 1 solution, no solutions, or infinite solutions? y=2x+6 and y=8x+6
1 solution
No Solution
Infinite Solution
Reg sells cars. he makes a base salary of $25,000, plus $1500 per car he sells. the function that models this situation is s = 1500x 25000. after working at the car dealership for 2 years, he gets a raise. he now makes $1700 per car he sells. what is the new function that models this situation?
the inverse sine of sin(2pi/3) = 120degrees, correct? ...?
The following set of coordinates represents which figure?
(3, -5), (5, -2), (10, -4), (8, -7)
A. parallelogram
B. rectangle
C. trapezoid
D. square
...?
Answer:
Option A is correct.
Step-by-step explanation:
Given:
Coordinates of the figure are ( 3 , -5 ) , ( 5 , -2 ) , ( 10 , 4 ) and ( 8 , -7 )
To find: Shape of the figure.
First we plot the given coordinates of the point on the graph then see which shape we obtained.
Graphing these points we get attached graph.
Clearly from graph it is a parallelogram because opposite sides are equal and parallel.
It is not a rectangle as clearly from graph angles at vertex are not right angle.
Therefore, Option A is correct.
To identify the geometric figure that the coordinates represent, plot the points, determine the slopes and lengths of the sides, and verify the properties of the geometric figures such as parallel sides and right angles.
Explanation:The student has provided the coordinates of a figure and asks which geometric figure they represent. To determine the figure, we need to consider the characteristics of the points given.
The coordinates provided are (3, -5), (5, -2), (10, -4), and (8, -7). By plotting these points on a Cartesian plane and connecting them in order, we could identify the figure based on the slopes of the sides and the lengths of the segments, which indicate parallel and perpendicular lines.
We need to calculate the distances between consecutive points and the slopes of the lines to confirm whether opposite sides are equal and parallel (a characteristic of a parallelogram) and whether all angles are right angles (a characteristic of a rectangle). These calculations can confirm the identity of the figure.
4 (x+5)=3 (x-2)-2 (x+2)
Three dentists wanted to compare the ages of their patients. They each calculated their patients’ mean age and the mean absolute deviation of their ages. They displayed the results in a table.
Which statements are true?
Choose exactly two answers that are correct.
DentistMean patient ageMAD
Appiah439.7
Cantwell2913.9
Singh4114.1
A. Dr. Appiah’s patients’ ages vary more than do Dr. Cantwell’s patients’ ages.
B. Dr. Appiah’s patients’ ages vary less than do Dr. Singh’s patients’ ages.
C. Dr. Cantwell’s patients’ ages and Dr. Singh’s patients’ ages vary about the same amount.
A woman at a point A on the shore of a circular lake with radius r=4 wants to arrive at the point C diametrically opposite A on the other side of the lake in the shortest possible time. She can walk at the rate of 10mph and row a boat at 5mph. What is the shortest amount of time it would take her to reach point C?
I'm not sure where to start... :(
The shortest possible time for the woman to reach the point diametrically opposite on the other side of the lake is 0.8 hours, regardless if she chooses to walk around the lake or row across it.
Explanation:The subject of this problem is about distance and speed, and involves optimizing the total travel time. The woman has two main options: to walk around the lake or to row across it. The diameter of the lake is 2r=8, if she walked, it would take her 8/10=0.8 hours to reach point C.
However, if she rows straight across the lake, the distance is the radius of the lake, which is 4 miles. The time taken to row across the lake is therefore 4/5=0.8 hours.
So, both options take the exact same time of 0.8 hours. Therefore, the shortest amount of time it would take for her to reach point C is 0.8 hours whether she chooses to walk around the lake or row across it.
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The shortest amount of time it would take for the woman to reach point C is [tex]2[/tex] hours.
1. Walking from A to B:
- Distance [tex]\( AB = 4 \)[/tex] miles
- Walking speed = 10 mph
- Time [tex]\( \text{Time}_{\text{walk}} = \frac{4}{10} = 0.4 \) hours[/tex]
2. Rowing from B to C:
- Distance [tex]\( BC = 8 \)[/tex] miles (since [tex]\( AC = 8 \)[/tex] miles and [tex]\( AC = 8 \)[/tex] miles)
- Rowing speed = 5 mph
- Time [tex]\( \text{Time}_{\text{row}} = \frac{8}{5} = 1.6 \) hours[/tex]
3. Total time:
[tex]\( \text{Total time} = \text{Time}_{\text{walk}} + \text{Time}_{\text{row}} = 0.4 + 1.6 = 2 hours[/tex]
Therefore, the shortest amount of time it would take for the woman to reach point C is [tex]2[/tex] hours.
i need more likes plz
You are dividing two square roots, and the radicand in the denominator does not divide into the radicand in the numerator. Explain what you need to do.
Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, how long will it take them to mow the lawn?
Answer:
The answer is A, 30
Step-by-step explanation:
what is the standard form of this number
1.46e-6
Answer:
0.00000146
Step-by-step explanation:
Your welcome, and you better call saul
The standard form of 1.46e - 6 is 0.00000146.
To convert the number 1.46e-6 to standard form, we need to move the decimal point to the left as many times as indicated by the exponent of the scientific notation, which is -6 in this case.
This means moving the decimal point six places to the left.
Start with the number in scientific notation:
1.46e - 6.
Move the decimal point six places to the left (because of the negative exponent):
0.00000146.
What is the area of the triangle in the diagram?
Answer:
The answer is the option A
[tex]\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
we know that
The area of the triangle is equal to
[tex]A=\frac{1}{2}bh[/tex]
where
b is the base
h is the height
In this problem
[tex]b=AB, h=AC[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
[tex]A(0,0), B(x2,y2)[/tex]
substitute
[tex]dAB=\sqrt{(y2-0)^{2}+(x2-0)^{2}}[/tex]
[tex]dAB=\sqrt{(y2)^{2}+(x2)^{2}}[/tex]
Find the distance AC
[tex]A(0,0), C(x1,y1)[/tex]
substitute
[tex]dAC=\sqrt{(y1-0)^{2}+(x1-0)^{2}}[/tex]
[tex]dAC=\sqrt{(y1)^{2}+(x1)^{2}}[/tex]
Find the area of the triangle
we have
[tex]b=\sqrt{(y2)^{2}+(x2)^{2}}, h=\sqrt{(y1)^{2}+(x1)^{2}}[/tex]
substitute
[tex]A=\frac{1}{2}(\sqrt{(y2)^{2}+(x2)^{2}})(\sqrt{(y1)^{2}+(x1)^{2}})[/tex]
[tex]A=\frac{1}{2}(\sqrt{[(y2)^{2}+(x2)^{2}]*[(y1)^{2}+(x1)^{2}]})[/tex]
Answer:
A for plato users
Step-by-step explanation:
Marta walked at 3.9 miles per hour for 0.72 hours. How far did she walk?
How do i describe the shape of the graph of each cubic function by determining the end behavior and number of turning points?
for ex. y=3x^3-x-3 ...?
Quick Search Inc. has hired you to work on a new search algorithm for their data base. Your annual salary is $52,680 and you are paid biweekly. If you are planning your monthly budget based on a two week pay period, how much do you get paid every two weeks? Round your answer to the nearest cent. a. $2,026.15 c. $2,680.10 b. $2,506.32 d. $2,751.14
$2,026.15 is the payment for every two weeks
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that annual salary is $52,680 and you are paid biweekly.
In a year we have 52 weeks
If you are planning your monthly budget based on a two week pay period
So there are 52/2 = 26 periods where you get paid
For every two weeks we get paid of 52680/26 = 2,026.153846
Hence, $2,026.15 is the payment for every two weeks
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What is 1/2 divided by 4?
On average, sloths spend 16.5 hours per day sleeping. what percent of the day do sloths spend sleeping? round your answer to the nearest percent.
How many feet is 132 inches??
The table shows the result of a restaurant survey.
Meals Service Good Service poor Total
Lunch 49 39 88
Dinner 19 15 34
Total 68 54 122
Find the probability the service was poor, given that the meal was dinner.
Which term describes the dotted line in the quadrilateral?
A. vertex
B. side
C. diagonal
D. angle ...?
Find the possible value or values of z in the quadratic equation z2 – 4z + 4 = 0. A. z = 2√ 2 + 2, z = −√ 2 + 2 B. z = 2 C. z =√ 2 + 2, z = −√ 2 + 2 D. z = 10, z = 6
Answer:
z=2
Step-by-step explanation:
im not going to explain it because the other person explained it but i will just show you a trick, might not always work but for the equation z^2 -4z+4=0 if you try putting 2 in for z it will be true 0=0... (2)^2 -4(2) +4= 0
Elise pays $21.75 for 5 student tickets to the fair.what is the cost of each student ticket
Answer:
Cost of each student ticket is, $4.35
Step-by-step explanation:
Given the statement: Elise pays $21.75 for 5 student tickets to the fair.
Unit rate defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.
[tex]unit rate = \frac{Total ticket Cost}{No of students}[/tex]
Given total cost paid by Elise = $21.75
Number of students = 5
then;
Unite rate per student = [tex]\frac{21.75}{5} = \$4.35[/tex]
Therefore, the cost of each student ticket is, $4.35
4.2(3.9r – 5.9s) 7.9s – 9.53r
Answer:
D
Step-by-step explanation:
i just did the quiz
The product of 8 and the sum of 4 and a number is 112. What is the number?
Which equation could be used to solve for the number?
What is the equation of this line in slope-intercept form?
y=−3x+2y=−3x+2
y=−1/3x+2y=−1/3x+2
y=3x−2y=3x−2
y = 3x + 2
Answer:
y=3x+2 is in slope intercept form. If you have a graph to go with this problem, if this equation is correct there should be points on (0,2) and (1,3)
Step-by-step explanation:
Rotating a triangle by 50 degrees will change the measures of the exterior angles by _________.
A. -50 degrees
B. 50 degrees
C. 0 degrees
find the factorization of the polynomial below. Enter each factor as a polynomial in descending order.
x^2 + 5x + 6 ...?
which of the following is a factor of 7x^2 -12x-4?
a) x+2
b)none of the above
c)7x-2
d)x-4 ...?
Answer:
The factors of the 7x² - 12x - 4 = 0 are (7x + 2)(x -2) .
Option (b) is correct i.e none of the above .
Step-by-step explanation:
As the expression given in the question.
7x² - 12x - 4 = 0
7x² - 14x + 2x - 4 = 0
7x (x - 2) + 2(x - 2) = 0
(7x + 2)(x -2) = 0
Thus the factors of the 7x² - 12x - 4 = 0 are (7x + 2)(x -2) .
Option (b) is correct i.e none of the above .
For the function below, find the vertex, axis of symmetry, maximum or minimum value, and the graph of the function.
f(x)=(x^2/2) + 2x +1 ...?
Answer and Explanation :
Given : Function [tex]f(x)=\frac{x^2}{2}+2x+1[/tex]
To find : The vertex, axis of symmetry, maximum or minimum value, and the graph of the function.
Solution :
The quadratic function is in the form, [tex]y=ax^2+bx+c[/tex]
On comparing, [tex]a=\frac{1}{2}[/tex] , b=2 and c=1
The vertex of the graph is denote by (h,k) and the formula to find the vertex is
For h, The x-coordinate of the vertex is given by,
[tex]h=-\frac{b}{2a}[/tex]
[tex]h=-\frac{2}{2(\frac{1}{2})}[/tex]
[tex]h=-\frac{2}{1}[/tex]
[tex]h=-2[/tex]
For k, The y-coordinate of the vertex is given by,
[tex]k=f(h)[/tex]
[tex]k=\frac{h^2}{2}+2h+1[/tex]
[tex]k=\frac{(-2)^2}{2}+2(-2)+1[/tex]
[tex]k=2-4+1[/tex]
[tex]k=-1[/tex]
The vertex of the function is (h,k)=(-2,-1)
The x-coordinate of the vertex i.e. [tex]x=-\frac{b}{2a}[/tex] is the axis of symmetry,
So, [tex]x=-\frac{b}{2a}=-2[/tex] (solved above)
So, The axis of symmetry is x=-2.
The maximum or minimum point is determine by,
If a > 0 (positive), then the parabola opens upward and the graph has a minimum at its vertex.
[tex]a=\frac{1}{2} >0[/tex] so, the parabola opens upward and the graph has a minimum at its vertex.
The Minimum value is given at (-2,-1)
Now, We plot the graph of the function
At different points,
x y
-4 1
-2 -1
0 1
Refer the attached figure below.
Critical Thinking: Buses on your route run every 9 minutes from 6:00 AM to 10:00 AM. You get to the bus stop at 7:16 AM,…
a. What is the maximum amount of time you should have to wait for the bus?
b. How many minutes after the buses begin running at 6:00 AM, do you arrive at the bus stop?
c. What time does the first bus of the day arrive at the bus stop?
...?