Find the derivative of the function.
g(x)=∫5x4xu2−1u2+1 du.
Answer:
[tex]g'(x) = \dfrac{5 *(25x^2-1)}{(25x^2+1)}- \dfrac{4 * (16x^2-1)}{(16x^2+1)}[/tex]
Step-by-step explanation:
Given that:
[tex]g(x) = \int^{5x}_{4x} \dfrac{u^2-1}{u^2+1} \ \ du[/tex]
Then: the derivative of the function is as follows:
[tex]g'(x) = \dfrac{(5x)^2-1}{(5x)^2+1} \ \ \dfrac{d}{dx}(5x) -\dfrac{(4x)^2-1}{(4x)^2+1} \ \ \dfrac{d}{dx}(4x)[/tex]
[tex]g'(x) = \dfrac{5 *(25x^2-1)}{(25x^2+1)}- \dfrac{4 * (16x^2-1)}{(16x^2+1)}[/tex]
A 250-gal tank is initially filled with brine (salt-water mixture) containing 100 lb of salt. Brine containing 3 lb of salt per gallon enters the tank at the rate of 7 gal/s, and the well-mixed brine in the tank flows out at the rate of 9 gal/s. Find the amount x(t) of salt in the tank after 1 minute.
Answer:
x(t) = 581.66 lb
Step-by-step explanation:
From the given information:
Consider the salt quantity in the tank at time t be x(t) lb.
∴ the rate of change of salt content in the tank is [tex]\dfrac{dx}{dt}= Rate \ of \ \ inflow - rate \ of \ \ outflow[/tex]
where:
the rate of inflow = salt conc. × flow rate = 3 lb/gallon × 7 gallons
=21 lb/s
rate of outflow = salt conc. in the tank × flow rate
= x/250 × 9
= 9x/250 lb/s
∴
[tex]\dfrac{dx}{dt} = 21 - \dfrac{9x}{250}[/tex]
[tex]\dfrac{dx}{dt} + \dfrac{9x}{250}= 21[/tex]
This is a 1st order linear differentiation,
The integrating factor if [tex]e^{^{ \int \dfrac{9}{250}\ dt}} = e^{^{ \dfrac{9t}{250} }}[/tex]
∴
[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = \int 21 e^{\dfrac{9t}{250}} \ dt + C[/tex]
[tex]e^{^{ \dfrac{9t }{250}}} \ \ x(t) = 21 \times \dfrac{250}{9}e^{\dfrac{9t}{250}} + C[/tex]
[tex]x(t) = \dfrac{1750}{3}+Ce^{^{\dfrac{-9t}{250}}}[/tex] at t = (0) and x(0) = 100 lb
Hence;
[tex]100 = \dfrac{1750}{3}+C[/tex]
[tex]C = \dfrac{1750}{3} -100[/tex]
[tex]C = - \dfrac{1450}{3}[/tex]
∴[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9t}{250}}}[/tex]
after time t = 1 minute i.e 60 s
[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-9 \times 60}{250}}}[/tex]
[tex]x(t) = \dfrac{1750}{3}-\dfrac{1450}{100}e^{^{\dfrac{-540}{250}}}[/tex]
x(t) = 581.66 lb
A helicopter is flying from Hong Kong to Jakarta. The latitude of Jakarta is -6.20°, and its longitude is 106.80°. The latitude of Hong Kong is 22.27°, and its longitude is 114.15°. What is the helicopter’s net change in latitude and longitude as it travels from Hong Kong to Jakarta?
A. -28.47° latitude and 7.35° longitude
B. -28.47° latitude and -7.35° longitude
C. 28.47° latitude and -7.35° longitude
D. 38.34° latitude and 220.95° longitude
E. -38.34° latitude and 220.95° longitude
Answer:
I think the answer is A
Step-by-step explanation:
Because you add both latitude (22.27+ -6.20) = -28.47 because a negative plus a positive equals a a negative then you add the longitude (114.15 -106.80) = 7.35 so the answer would be
-28.47 latitude and 7.35 longitude.
the answer would be C.)28.47 lat -7.35 long
give me the answer now
Answer:
what is the Question
Step-by-step explanation:
There are 12 red pens, 20 blue pens and 5 black pens in a bag. What is the probability that you will pick a black pen? Round
Answer:
The probability of getting a black pen from the bag is 13.5%.
Step-by-step explanation:
To determine the percentage probability that a black pen will be obtained from the bag, the following calculation must be performed:
12 + 20 + 5 = 37
37 = 100%
5 = X
(5 x 100) / 37 = X
500/37 = X
13.5 = X
Thus, it is determined that the totality of pens is 100%, and through a cross multiplication the percentage of the 5 black pens with respect to the total of pens is obtained.
Therefore, the probability of getting a black pen from the bag is 13.5%.
6/31. There are 6 black pens left and the red pen was removed, so the original sample size of 32 is reduced to 31.
Jessica walks 7 times as far to school as Taylor does . Jessica walks 5 miles. How many miles does Taylor walk?
Answer:
Step-by-step explanation:
Jessica: 5 miles
Taylor: 5/7 = .7143 miles
At 6 am, the temperature was 73 degrees Fahrenheit. By noon, then temperature had rose 8 degrees. At 4 pm, the temperature was 5 degrees warmer than it was at noon. By 9 pm, the temperature had dropped 16 degrees. What was the temperature at 9 pm?
Answer:
70 degrees Fahrenheit
Answer:
70
Step-by-step explanation:
We started at 73 degrees and the temperature rose by 8 degrees so 73 + 8 = 81. At 4 pm, the temperature rose again by 5 degrees so 81 + 5 = 86. By 9 pm, the temperature dropped 16 degrees so 86 - 16 = 70, Therefore, the temperature at 9 pm was 70 degrees.
Study the dot patterns in parts (a) and (b) below. Assume that each pattern continues to increase by the same number of dots and in the same locations for each figure.
For each pattern, sketch the 4th and 5th figures. Then predict how many dots will be in the 100th figure.
Answer:
east-56 a=+b 2squared
Step-by-step explanation:
Find the dimensions of a rectangle whose width is 8 miles less than its length and whose area is 105 square miles
Area of a rectangle = w*l
w = width
l = length
In our problem,
Area = 105mi^2
l = x
w = x - 8
Let's plug our values into the formula above.
105mi^2 = x(x - 8)
Distribute the x
105mi^2 = x^2 - 8x
Subtract 105mi^2 from both sides.
0 = x^2 - 8x - 105
Let's factor the right side.
0 = (x - 15)(x + 7)
Set both terms equal to 0
x - 15 = 0
Add 15 to both sides.
x = 15
x + 7 = 0
Subtract 7 from both sides.
x = -7
Since the length cant be a negative number, 15 is the correct answer.
Length = x = 15 mi
Width = x - 8 = 15 - 8 = 7 mi
The length of the rectangle is 15 miles while the width is 7 miles.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
The perimeter of rectangle = 2( length + width).
Suppose the length is L while the width is W.
Area of rectangle = length × width.
L x W = 105
W = L - 8
By substitution,
L x (L - 8) = 105
L² - 8L - 105 = 0
L² - 15L + 7L - 105 = 0
L(L - 15) + 7(L - 15) = 0
(L + 7)(L - 15) = 0
L = -7, L = 15
Since length will not be negative thus L = 15 miles.
W = 15 - 8 = 7 miles
Hence "The length of the rectangle is 15 miles while the width is 7 miles."
For more about rectangles,
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Write the expression as a square of a monomial. 4/9b^6
Answer:
Step-by-step explanation:
It just so happens that all the numbers and variables in that expression are perfect squares. 4 has a square root of 2; 9 has a square root of 3; and b^6 has a square root of b^3. Putting that altogether into one simplified expression that we can square is:
[tex](\frac{2}{3}b^3)^2[/tex]
The expression as a square of a monomial (4/9b⁶) is (2²/3²b³)²
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
A monomial is a polynomial that has only one term.
Given, a monomial (4/9b⁶).
To write this monomial in terms of as a square of a monomial we'll factor out the power of 2 from each f the constants and variables contained in the monomial which is,
= (2²/3²b³)²
learn more about polynomials here :
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William and his puppy Rover are out for a morning jog at a comfortable pace of 10 minutes per mile. If they keep up this pace for 2 hours, how many miles will they jog?
Answer:
12 miles
Step-by-step explanation:
60 min in 1 hr and 10 min = 1 mile..... so 6, 10 min intervals..... and so 6 time 2 is 12
help!
what is the answer to this problem?
Answer:
D
Step-by-step explanation:
Because 12 is greater than -5 and when you divide a postive and a negative you get a negative number. And negative numbers are less than 0 .
Which angles could you add to 1 to make a supplementary angle. Please helppp
Help please, will mark you as brainliest!!
Need help on both..
Answer:
the answer is c for the second one and the first one is A
solve for x 7x½+2=0
Answer:
here's your answer
hope this helped you
please mark as the brainliest (ㆁωㆁ)
Answer: 7/2x + 2
Step-by-step explanation:
Solve the inequality and graph the solution set for 2(3r − 10) ≤ 3r − 5
Answer:
r≤5
Step-by-step explanation:
Steps are in the photo. Hope this helps.
100 POINTS!! ASAP - Pls Show all WORK
Answer:
x ≈ 28.7 ft
Step-by-step explanation:
Step 1: Define variables
Height (vertical leg of triangle) = 2 ft
∅ = 4°
We are trying to find the length of the hypotenuse x
Step 2: Use trig
sin∅ = opposite over hypotenuse
sin4° = 2/x
Step 3: Solve for x
xsin4° = 2
x = 2/sin4°
x = 28.6712
x ≈ 28.7 ft
Answer:
the Length of ramp is 28.7 feet.
Step-by-step explanation:
see attached image for clarity
give:
height (h) of clinic = 2 feet
angle of ramp = 4°
find:
Length (L) of ramp
using the formula : sin(Ф) = height (h)
Length of ramp (hypothenuse)
plugin values into the formula:
sin (4) = 2
L
L = 2
sin(4)
L = 28.7 feet
therefore,
the Length of ramp is 28.7 feet.
The opposite of -4 is
A) 4
B) -4
C) -(-(-4))
D) -|4|
Answer:
the answer is A
Step-by-step explanation:
60 point question!...........
Answer:
dhsfhb
Step-by-step explanation:
top secret
Answer:
Have a good day, dont see a picture?
Step-by-step explanation:
Ms. D bought 18 bagels for $1.35 each and 2 containers of cream cheese for $3.45 each. Write and evaluate ONE expression to find the total cost of the food.
Answer:
(18+2)x($1.35+$3.45)= $96
Could I please have BRAINLIEST.
Katie deposited $1,000 in the bank for 6 years. She earned a simple interest rate of 1.5%. How much interest did she earn?
Answer:
Idl but I believe its 2340
Step-by-step explanation:
but I could be wrong
4|m−n| if m=−7 and n=2 i really need to know what this is asap please
Answer:
36
Step-by-step explanation:
Plug in -7 as m and 2 as n into the expression:
4 | m - n |
4 | -7 -2 |
Solve:
4 | -9 |
4(9)
= 36
solve for p in the literal equation 8p+5r=q
How do we Round with any numbers, (on a number line) ?
Answer:
round it to the nearest 10th?
Step-by-step explanation:
that's what I do at least.
Answer: Round up or down.
Step-by-step explanation: When you round up, look at the number to the right of the number you wanna round. If it’s less than 5, you round down, if it’s more than 5, you round up. On a number line, for ex. Let’s say you wanna round 550 to hundreds, 600 or 500, 600 would be the answer because 550 is more closer to 600 by default.
Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of the longest side is unknown. What is the smallest possible whole-number length of the unknown side?
Answer:
17 inches.
Step-by-step explanation:
Answer:
answer is 17 inches
Step-by-step explanation:
Mr. Josey is tasked with cutting the grass this weekend. He can cut 1/4 of the yard in 20 minutes. How long will it take to cut the entire yard?
Plz help asap In 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be. Find their ages now.
Answer:
Harry is 2, Jim is 6
Step-by-step explanation:
The first statement tells us they are 4 years part. Then you need to find two numbers that are 4 apart and that has one that is half the other, like 4 and 8. Finally, subtract two because this will happen in two years and you need their ages now.
Sorry if this was confusing.
PLEASEEE HELP
1. Andrea ran and biked for a total of 32 mi in 4 hours. Her average running speed was 5 mph and her average biking speed was 13 mph.
Let x = total hours Andrea ran.
Let y = total hours Andrea biked.
Use substitution to solve for x and y. Show your work. Check your solution.
(a) How many hours did Andrea run?
(b) How many hours did she bike?
Answer:
Ran: 2.5hr
Biked: 1.5hr
Step-by-step explanation:
x = total hrs ran
y = total hrs biked
4 = total hours ran + biked
soo.....
x + y = 4hr
then you can convert that for solving y or x
Ex. x = 4-y or y = 4-x
Then just plug in either x or y
EQUATION: 5x + 13y = 32
Dont plug in both x or y at the same time. Pick one and solve
The length of chen’s office is 15.5 feet and the width is 7.8 feet find of the office
Answer:
The area of Chen's office (if that's what you're looking for) is 120.9 feet
Step-by-step explanation:
All I did was a = lw, the formula for finding the area of something using length and width
a = lw
a = 15.5 × 7.8
a = 120.9
Hope this helped.
the sum of 12 and the quantity 8 times a number k is equal to 48
Answer:
12 + (8k) = 48
k= 9/2
Step-by-step explanation: