[tex]\bf y=\cfrac{1}{x+1}+x\qquad \qquad \begin{cases} u=x+1\\ \frac{du}{dx}=1\\[-0.5em] \hrulefill\\ u-1=x \end{cases}\qquad \qquad y=\cfrac{1}{u}+(u-1) \\\\\\ y=u^{-1}+u-1\implies \cfrac{dy}{du}=\stackrel{\textit{chain-rule}}{-u^{-2}\cdot \cfrac{du}{dx}}+\stackrel{\textit{chain-rule}}{1\cdot \cfrac{du}{dx}}+0 \\\\\\ \cfrac{dy}{dx}=-\cfrac{1}{u^2}\cdot 1+1\cdot 1\implies \cfrac{dy}{dx}=-\cfrac{1}{u^2}+1\implies \cfrac{dy}{dx}=-\cfrac{1}{(x+1)^2}+1[/tex]
if dy/dt=-10e^-t/2 and y(0)=20 what is the value of y(6)
ANSWER
[tex]y (6)= \frac{20}{ {e}^{3} } [/tex]
EXPLANATION
The given equation is:
[tex] \frac{dy}{dt} = - 10 {e}^{ - \frac{t}{2} } [/tex]
We integrate with respect to t to get,
[tex]y = 20 {e}^{ - \frac{t}{2} } + k[/tex]
The initial condition is y(0)=20
We apply the initial condition to get,
[tex]20= 20 {e}^{ - \frac{0}{2} } + k[/tex]
[tex]k = 0[/tex]
This implies that;
[tex]y = 20 {e}^{ - \frac{t}{2} } [/tex]
[tex]y (6)= 20 {e}^{ - \frac{6}{2} } [/tex]
[tex]y (6)= 20 {e}^{-3} [/tex]
Or
[tex]y (6)= \frac{20}{ {e}^{3} } [/tex]
The required solution is [tex]y(6) = 20e^{-3}[/tex]
IntegrationGiven the following differential equation [tex]dy/dt=-10e^{-t/2}[/tex]
To get the value of y, we will integrate the equation to have:
[tex]y=-20e^{-t/2} + k[/tex]
Given that y(0) = 20, hence;
[tex]20=-20e^{-0/2} + k\\ 20 = 20 + k\\ k = 0[/tex]
Hence the solution to the given integral is [tex]y=-20e^{-t/2} [/tex]
Next is to get y(6)
[tex]y(6)=-20e^{-6/2} \\ y(6) =20e^{-3}}[/tex]
Hence the required solution is [tex]y(6) = 20e^{-3}[/tex]
Learn more on differentiation here: https://brainly.com/question/25081524
a large pizza has a diameter of 14 inches and is cut into 6 equal pieces. Find the area of 2 pieces, round to the nearest hundredth
Answer:
The area of two pieces is [tex]51.28\ in^{2}[/tex]
Step-by-step explanation:
step 1
Find the area of the circle (large pizza)
The area is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ in[/tex] ----> the radius is half the diameter
assume
[tex]\pi =3.14[/tex]
substitute
[tex]A=(3.14)(7)^{2}[/tex]
[tex]A=153.86\ in^{2}[/tex]
step 2
Divide the area into 6 pieces
[tex]153.86/6=25.64\ in^{2}[/tex]
step 3
Find the area of two pieces
[tex]25.64*2=51.28\ in^{2}[/tex]
6 cm x 5cm x 4cm what is the volume of the prism in cubic centimeters
Answer:
120 [tex]cm^{3}[/tex]
Step-by-step explanation:
6 x 5 x 4 =120
Answer:
120 cm^3
Step-by-step explanation:
volume = length * width * height
volume = 6 cm * 5 cm * 4 cm
volume = 120 cm^3
what type of checking account requires a certain amount of money to be kept in it at all times in order to avoid fees
Answer:
Minimum balance account requires an amount of money to left in it all times in order to avoid fees.
Step-by-step explanation:
We have "many types of account" available in the banking sectors. As per the convenience of the customer, they opt from them. The minimum balance account is the type of account in which the customer has to maintain a standard amount prescribed by the bank in his account, failing to maintain it will lead to the gathering of fine or fee.
Answer:
Minimum Balance account.
Step-by-step explanation:
A minimum balance account is an account type that requires a minimum balance as set by the bank, at all times, in order to waive maintenance fees.
Failing this, certain amount is charged when money is deposited in that account. It can range from few dollars to 500 dollars in some banks.
which equation shows the quadratic function used to solve 7x^2=9+x for x?
Answer:
Step-by-step explanation:
For this case we have the following equation of the second degree:
[tex]7x ^ 2 = 9 + x[/tex]
Rewriting:
[tex]7x ^ 2-x-9 = 0[/tex]
The solutions will be given by the following equation:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 7\\b = -1\\c = -9[/tex]
Substituting the values:
[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (7) (- 9)}} {2 (7)}\\x = \frac {1 \pm \sqrt {(- 1) ^ 2 + 4 (7) (9)}} {2 (7)}[/tex]
Answer:
Option D
Find the height of the cylinder below whose volume is approximately 1000 cubic inches use 3.14 for pi rounder you're answer to the nearest hundredth show your work pls help this is. Big test I got 3 more questions to ask
Answer:
[tex]h=15.73\ in[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]V=1,000\ in^{3}[/tex]
[tex]r=9/2=4.5\ in[/tex] ----> the radius is half the diameter
substitute and solve for h
[tex]1,000=(3.14)(4.5)^{2} h[/tex]
[tex]h=1,000/[(3.14)(4.5)^{2}][/tex]
[tex]h=15.73\ in[/tex]
Answer:
r = 11 in V =968 pi in3
Step-by-step explanation:
got it right on edge
suppose that one student is randomly selected during lunch time. what is the experimental probability if students the brought lunch from house is 55 and students that order school lunch is 45
Answer:
p(A) = 0.55
p(b) = 0.45
Step-by-step explanation:
Experimental probability = [tex]\frac{Number of favorable outcomes}{Total number of outcomes}[/tex]
total students = 55 + 45 ⇒ 100
let A be the probability that students brought lunch from house = [tex]\frac{55}{100}[/tex] ⇒ 0.55
let B be the probability that students order school lunch = [tex]\frac{45}{100}[/tex] ⇒ 0.45
Help!!!!!!
complete the problem involving the linear equation.
Answer:
8. slope = 29. y-intercept = -310. in the attachmentStep-by-step explanation:
The slope-intercept form y = mx + b
m - slope
b - y-intercept → (0, b)
We have the equation
y - 2x = -3 add 2x to both sides
y = 2x - 3
slope m = 2
y-intercept b = -3
We need two points to draw a graph of this linear function.
One is y-intercept (0, -3). The second one is calculated by choosing any value of x and put it to the equation:
for x = 2 → y = 2(2) - 3 = 4 - 3 = 1 → (2, 1).
If Johnny has twice more bottles of dish soap than Carolyn, and Carolyn has 20 more bottles of dish soap than Mr. White, how many bottles of dish soap does Johnny have if Mr. White has 35 bottles of dish soap?
Answer:
110
Step-by-step explanation:
Answer:
Jesus
Step-by-step explanation:
Why all this dish soap. Sounds like that vine.
Use the information given in the table on the right to complete each of the following statements.
Brenda is 50 inches tall. Her z-score is
.
Answer:
0.5
Step-by-step explanation:
Given that height of 7 year old children are normally distributed with mean =49 inches and std deviation = 2inches
Brenda is 50 inches tall
This means her X score is 50
To convert this X score to Z score we use the formula given below
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Here we know all the values of x, mu and sigma
Just substitute
Z score
=[tex]\frac{50-49}{2} =\frac{1}{2} \\=0.5[/tex]
Thus Z score of Brenda is 0.5
Answer:
0.5
Step-by-step explanation:
What is the area of this figure?
Select from the drop-down menu to correctly complete the statement.
Answer:
146cm^2
Step-by-step explanation:
Area of trapezoid:
(4+14)/2*10=90
Area of triangle:
(14*8)/2=56
90+56=146
For this case we have a figure composed of a trapezoid and a triangle.
By definition we have that the area of a trapezoid is given by:
[tex]A = \frac {(B + b) * h} {2}[/tex]
Where:
B: It's the biggest side
b: It is the minor side
h: It's the height.
So:
[tex]A = \frac {(14 + 4) * 10} {2}\\A = 90 \ cm ^ 2[/tex]
For its part, the area of a triangle is:
[tex]A = \frac {b * h} {2}[/tex]
Where:
b: It's the base
h: It's the height
[tex]A = \frac {14 * (18-10)} {2}\\A = \frac {14 * 8} {2}\\A = \frac {14 * 8} {2}\\A = 56 \ cm ^ 2[/tex]
Thus, the total area is the sum of the two areas:
[tex]146 \ cm ^ 2[/tex]
ANswer:
[tex]146 \ cm ^ 2[/tex]
Which expression is equivalent to 7^3 • 7-^5
I need help !
Anwer:
1/7^2
explantion:
The expression equivalent to 7^3 • 7-^5 is 1 / 7^2.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
7^3 • 7-^5
Now using the exponential property,
n^a . n^b = n^(a+b)
Therefore, we can write as,
7^3 • 7-^5 = 7^(3-5)
Solving we get,
7^3 • 7-^5 = 7^-2
Since, n^-a = 1/n^a
⇒7^-2 = 1 / 7^2
Therefore, we can write
7^3 • 7-^5 = 1 / 7²
this is the required equivalent expression.
Thus, the expression equivalent to 7^3 • 7-^5 is 1 / 7^2.
To learn more about equivalent expression :
brainly.com/question/10188283
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When you use the distance Formula you are building a right triangle whose ____ connects two given points....
It’s C) , I believe..
Answer:
option C
Step-by-step explanation:
When we use the distance formula for two points ( x, y ) and ( x', y¹ )
Then formula is (distance)² = (x - x¹)² + (y - y¹)²
This is quite similar to the formula used in a right angle triangle to determine hypotenuse
(Hypotenuse)² = (base)²+(height)²
Therefore, option C is the answer.
write the slope intercept equation. the graph of f passes through (-6,4) and is perpendicular to the line that has an x-intercept of 2 and a y intercept of -6
Answer:
y = [tex]-\frac{1}{3} x[/tex] + 2
Step-by-step explanation:
The slope of the line that has an x intercept of (2,0) and y-intercept of (0,-6) is:
Slope(s) = Change in y ÷ change in x
s = [tex]\frac{0 - -6}{2 - 0}[/tex] = 3
The slope of the perpendicular line to this line with slope of 3 has to have a slope of -1 ÷ 3 = [tex]-\frac{1}{3}[/tex]
Reason: The product of slopes of lines perpendicular to each other have to be -1
So the slope of the perpendicular line that passes through (-6,4) is [tex]-\frac{1}{3}[/tex]
As mentioned earlier, we derive a slope of a line by dividing the change in y by the change in x
Taking another point (x,y) on the line,
[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x - -6}[/tex]
[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x + 6}[/tex]
y - 4 = [tex]-\frac{1}{3}[/tex]x - 2
y = [tex]-\frac{1}{3}[/tex]x + 2
To find the slope-intercept equation of a line that passes through a given point and is perpendicular to another line, we can determine the slope of the given line and use it to find the equation.
To find the slope-intercept equation of a line, we need to know the slope and the y-intercept. Since the line that this problem is referring to is perpendicular to a line with an x-intercept of 2 and a y-intercept of -6, we can determine the slope of the line we are looking for by taking the negative reciprocal of the slope of the given line.
The slope of the given line is found using the formula: slope = (y2 - y1) / (x2 - x1)
Once we have the slope, we can use the point-slope form of a linear equation to find the equation of the line that passes through (-6,4) and has the determined slope. Finally, we can rearrange the equation to obtain the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Learn more about Slope-intercept equation here:https://brainly.com/question/13048634
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What is the volume of the cone pictured? (Use 3.14 for π.)
785 ft 3
104.67 ft 3
261.67 ft 3
314 ft 3
Answer:
261.67 [tex]ft^{3}[/tex]
Step-by-step explanation:
The formula is 1/3 [tex]\pi r^{2}h[/tex]
Answer:
261.67 ft^3
Step-by-step explanation:
mark me brainy plz!
20 points EZ question plz help urgent
What should be the height of the bar for 11-15 text messages?
A) 1
B) 2
C) 4
D) 5
Answer:
Its C
hope this helps!!
The correct answer is A .)1
State the x-intercept and the y-intercept of the line
[tex]x=-10, y=5\Longrightarrow\boxed{-10, 5}[/tex]
Which function is a linear function?
Answer:
y = f(x) = a + bx
Step-by-step explanation:
independent variable = x
dependent variable =y
Answer:A linear function is a straight line which is just a linear function with the equation y=mx+b
Step-by-step explanation:
Which of the following would not round to 1.2 when rounded to the nearest tenth?
A.1.149
B.1.209
C.1.22
D.1.18
Answer:
Step-by-step explanation:
A is correct answer
Jim earns 3% commission every month on his total sales. This month, his total sales were $620,000. How much commission did Jim earn? Plz show work:)
A. $18,600
B.$20,600
C. $186,000
D. $206,000
The answer is A. $18,600 because $620,000 × 3% = $18,600
Centennial park is evaluating
Answer:
270,000
Step-by-step explanation:
So, you have a number of people (15) that can stand comfortably within a certain area (5x8 ft = 40 sq feet). And you need to find out how many people can fit in the whole park area.
First step is to find out how big the park is, in square feet, so we can then evaluate the number of people that we can fit in.
You had the right number for calculating the area of the park:
A = 400 yards x 200 yards = 1,200 feet x 600 feet = 720,000 sq feet
Now, how many people can we fit in there? Let's use a simple cross-multiplication (x being the number of people fitting in the whole park, what we are looking for):
[tex]\frac{x}{720 000} = \frac{15}{40}[/tex]
By isolating x, we have x = (720,000 * 15) / 40 = 10,800,000 / 40 = 270,000
So, the park could accommodate 270,000 people.
That is of course if there are no trees, no benches, no kids playground or any other infrastructure in the park.
The distance between points (3,7) and (x1,y1) is the square root of (x1 - 3)2 + (y1 - 7)2
True or False?
Answer : True
Explanation : It is according to distance formula.
The answer is True -Apex
plz help 5 star reating and a thanks if someone help
Answer:
B - +4.
Step-by-step explanation:
The person does not get 4.5 yards.
1/4, -1/4, and -4 do not work as well because negative numbers express loss, and not gain, and the person does not get any fractions.
Answer:
I believe the answer is B. +4
Step-by-step explanation:
A distance of 30 miles on a map is represented by a 2-inch line. If the map is enlarged to 3 times its size, what will be the scale of the enlarged map?
PLEASE HELP!
Answer:
[tex]\frac{1}{5}\frac{in}{miles}[/tex]
Step-by-step explanation:
we know that
The original scale of the map is
[tex]\frac{2}{30}\frac{in}{miles}=\frac{1}{15}\frac{in}{miles}[/tex]
If the map is enlarged to 3 times its size
then
the new scale will be
[tex]\frac{2*3}{30}\frac{in}{miles}=\frac{6}{30}=\frac{1}{5}\frac{in}{miles}[/tex]
The scale of the original map is 2 inches to 30 miles. After enlarging the map 3 times, the new scale will be 1 inch to 15 miles, as 6 inches on the enlarged map would represent 90 miles.
Explanation:The question is asking to determine the scale of a map after it has been enlarged. The original map scale is such that 2 inches represent 30 miles. If the map is enlarged 3 times its original size, each inch on the original map would now be represented by 3 inches on the enlarged map. Therefore, the 2 inches that originally represented 30 miles would now be stretched out to 6 inches on the enlarged map.
We can determine the new scale setting up a proportion:
We know the distances must remain consistent, so we set up the proportion:
By cross-multiplication, we find that:
The scale of the enlarged map will therefore be 1 inch representing 15 miles, as we can conclude from 6 inches representing 90 miles.
ASAP!! The coordinates g(7,3), h(9,0), I(5,-1) form what type of polygon
Answer:
Triangle (scalene)
Step-by-step explanation:
Polygon is a closed figure.
The names of polygons depends on the number of sides. Some common polygons are:
3 sides - triangle
4 sides - quadrilateral
5 sides - pentagon
6 sides - hexagon
Triangle and Quadrilaterals have their own types as well.
The points G, H , and I are shown in the attached image. As you can see, it creates a 3-sided figure, which is a triangle.
Note: Since all 3 sides have different length, we call it a "scalene triangle"
Find the area given figure. A) 44 B)60 C) 84 D) 72
Answer:
D) 72
Step-by-step explanation:
The way to find the area of this figure easily is to break it down in regular shapes we know. You can then see it as two horizontal rectangles on top and bottom, measuring 6 x 4 each, then a vertical rectangle in the middle measuring 4 x 6.
So, overall, we have 3 similar rectangles measuring 4x6 or 6x4... which are equivalent.
The area of each of those 3 rectangles is 24 units (6x4).
Since we have 3 of those: 3 * 24 = 72.
Anaba is stacking cereal boxes in a pyramid-shaped display. The bottom layer has 10 boxes. There are two fewer boxes in each layer than the layer below. How many boxes are in display.
Answer:
30 boxes
Step-by-step explanation:
~ You begin with the bottom row, which has 10 boxes.
~ You do 10 - 2 to get the number of boxes in the next layer, which is 8.
~ You then take 8 - 2, which is 6 for the next layer up.
~ Take 6 - 2, which is 4 for the next layer up.
~ Take away another two: 4 - 2 is 2.
~ When you take 2 away from 2, you get 0, so you have no more boxes.
~ Then, you add all the different amounts of boxes for each layer:
-> 10 + 8 + 6 + 4 + 2
-> Group smaller numbers together to get two bigger ones:
-> 18 + 12
= 30
Help me guys ....
1.What is the probability that a passenger is traveling for business ?
2.Given a passenger did not check their bag,what is the probability that the passenger is traveling for business ?
Answer:
1. .21
2. .79
Step-by-step explanation:
1. 103/490
2. 387/490
Jane entered her artworks in a state competition. Her art scores from 7 judges are listed. 9,9,8,7,9,6,8 what is Jane’s mean score? A.6 B.7 C. 8 D.9
Answer:
C!
Step-by-step explanation:
To find the the mean add all the numbers and divde by the number of numbers. The sum of all the numbers is 56. There are 7 numbers.
56/7 is 8.
B
Because I like the letter b so ha
what is the next step in the construction of an angle bisector of angle ABC?
Answer:
A. Use straightedge to connect vertex B to right-most vertex of the equilateral triangle.
Step-by-step explanation:
The process is to create a bisector of angle ABC... so it means cutting angle at vertex/summit B in half.
Drawing a line from the vertex B to the right-most vertex of the equilateral triangle will deliver you the bisector.
The only answer choice that includes vertex B is the answer A, all other answers are dealing with vertex A and C... which will not help you to draw the bisector or angle ABC.
Answer:
Option A is right
Step-by-step explanation:
Given in the picture is an angle B formed by line segments AB and BC
To construct bisector of angle B
First with centre at B a circle is drawn which meets AB and BC at D and E respectively. With same radius equal to DE and centres of D and E two circles are drawn which intersect at the right most point.
The next step is join B to the rightmost vertex of equilateral triangles
This will be the angle bisector of angle ABC
Hence option A is right