Let y = √x, so that y ² = x and 2y dy = dx. Then the integral becomes
[tex]\displaystyle \int_{25}^{81} \frac{\sqrt x}{x-1}\,\mathrm dx = \int_{\sqrt{25}}^{\sqrt{81}} \frac y{y^2-1}(2y\,\mathrm dy) = 2 \int_5^9 \frac{y^2}{y^2-1}\,\mathrm dy[/tex]
Now,
y ² / (y ² - 1) = 1 + 1 / (y ² - 1) = 1 + 1/2 (1/(y - 1) - 1/(y + 1))
so integrating gives us
[tex]\displaystyle 2\int_5^9\frac{y^2}{y^2-1}\,\mathrm dy= \int_5^9\left(2+\frac1{y-1}-\frac1{y+1}\right)\,\mathrm dy \\\\= (2y+\ln|y-1|-\ln|y+1|)\bigg|_5^9 \\\\= \boxed{8+\ln\left(\dfrac65\right)}[/tex]
11 Emilio makes metal fences.
He is making a fence using this design.
1.44 m
DO NOT WRITE IN THIS AREA
1.8 m
.
The fence will need
3 horizontal metal pieces of length 1.8m
2 tall metal pieces of length 1.44 m
5 medium metal pieces
6 short metal pieces as shown on the diagram.
The heights of the tall, medium and short metal pieces are in the ratio 9:8:7
.
How many metres of metal in total does Emilio need to make the fence?
Answer:
Step-by-step explanation: 7 3 13 31
3 × 1.8 long pieces Calculate the ratios
2 × 1.44 9 tall vertical piece 1.44 / 9 = x / 9 x = 1.44
5 × ___ 8 medium vertical pieces 1.44 / 9 = x / 8 x = 1.28
6 × ___ 7 short vertical pieces 1.44 / 9 = x / 7 x = 1.12
3 × 1.8 long pieces
2 × 1.44 9 tall vertical piece 1.44 / 9 = x / 9 x = 1.44
5 × 1.28 8 medium vertical pieces 1.44 / 9 = x / 8 x = 1.28
6 × 1.12 7 short vertical pieces 1.44 / 9 = x / 7 x = 1.12
3 × 1.8 long pieces = 5.4 m
2 × 1.44 9 tall vertical piece = 2.88 m
5 × 1.28 8 medium vertical pieces = 6.4 m
6 × 1.12 7 short vertical pieces = 6.72 m
Total = 21.4 m
Please ignore the writing in blue as I tried to work it out but couldn’t
Answer:
[tex]k=35[/tex]°
Step-by-step explanation:
The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.
[tex]130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95[/tex]
The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;
[tex](unknown_1)+(unknown_2)+(k)=180[/tex]
Substitute,
[tex]50+95+k=180[/tex]
Simplify,
[tex]50+95+k=180\\\\145+k=180\\\\k=35[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND :}}}[/tex]
The measure of angle [tex]k[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ [tex]x[/tex] + 85° = 180°
➪ [tex]x[/tex] = 180° - 85°
➪ [tex]x[/tex] = 95°
Also,
Exterior angle of a triangle is equal to sum of two opposite interior angles.
And so we have,
➪ 130° = [tex]k[/tex] + [tex]x[/tex]
➪ [tex]k[/tex] + 95° = 130°
➪ [tex]k[/tex] = 130°- 95°
➪ [tex]k[/tex] = 35°
Therefore, the value of [tex]k[/tex] is 35°.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ 50° + 35° + 95° = 180°
( where 50° = 180° - 130°)
➪ 180° = 180°
➪ L. H. S. = R. H. S.
Hence verified.
(Note: Kindly refer to the attached file.)
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
A motel in New Orleans charges $90 per day for double occupancy and $80 per day for single occupancy during off-season. If 80 rooms are occupied for a total of $6,930, how many rooms of each kind are occupied?
double occupancy room=x
single occupancy room=y
x + y = 80,
90x + 80y = 6930
x=53
y=27
what number when multiplied by 5 is one third of the sum of 64 and 56?
Answer:
8
Step-by-step explanation:
Create an expression to model the situation. One can do this by simply rewriting the written expression in terms of numbers and variables. Use the variable (x) to represent the unknown value.
[tex]5(x)=\frac{1}{3}(64+56)[/tex]
Simplify this expression,
[tex]5(x)=\frac{1}{3}(64+56)\\5x=\frac{1}{3}(120)\\5x=40\\[/tex]
Use inverse operations to solve for (x),
[tex]5x=40\\x=8[/tex]
This is the graph of y=x^2+2x-2 what is the range of this function
One hundred sixty people were surveyed and asked if believed in ufos, ghosts, and bigfoot. 42 believed in ufos 45 believed in ghosts 21 believed in bigfoot 11 believed in ufos and ghosts 6 believed in ghosts and bigfoot 4 believed in ufos and bigfoot 2 believed in all three how many people surveyed believed in at least one of these ?
Answer:
[tex]P(A\cup B \cup C)=89[/tex]
Step-by-step explanation:
From the question we are told that:
Believed in UFO's [tex]A=42[/tex]
Believed in Ghosts [tex]B=45[/tex]
Believed in Bigfoot [tex]C=21[/tex]
Believed in UFO's & Ghosts [tex]A&B=11[/tex]
Believed in Ghosts & Bigfoot [tex]B&C=6[/tex]
Believed in UFO's & Bigfoot [tex]A&B=4[/tex]
Believed in ALL [tex]A&B&C=2[/tex]
Generally with a well detailed Set diagram of the Number of People that that believed in at least one of them is mathematically given by
[tex]P(A\cup B \cup C)=n(A\cap C)-n(B\cap C) +n(A\cap B \cap C)[/tex]
[tex]P(A\cup B \cup C)=42+45+21-11-6-4+2[/tex]
[tex]P(A\cup B \cup C)=89[/tex]
Please help! Rewrite the function
Answer:
The answer is below
Step-by-step explanation:
A function is used to show the relationship between two or more variables. This variables are known as the input variables and output variables.
The input variables are variables which do not depend on other variables while the output variables are variables that depends on other variables.
Given that g(x) = 12x / (x-5); rewriting in the form g(x) = [a/(x-h)] + k, gives:
[tex]g(x)=\frac{60}{x-5}+12[/tex]
The graph of g(x) was plotted using online geogebra graphing calculator. The graph is attached.
A ball is thrown upward with an initial velocity (v) of 15 meters per second. Suppose that the initial height (h) above the ground is 7
meters. At what time will the ball hit the ground? The ball is on the ground when S = 0. Use the equation S = -52 + vt + h.
The ball will hit the ground in how many
seconds?
Answer:
Step-by-step explanation:
Your equation is weird. The position equation for this situation is
[tex]s(t)=-4.9t^2+15t+7[/tex] and set it equal to 0 to solve for the time it takes to hit the ground. Those times come out to be
t = 3.47 sec and t = -.411 sec. But since time can never be negative, our time is 3.47 seconds
(What is that -52?)
The Sureset Concrete Company produces concrete. Two ingredients in concrete are sand (costs $6 per ton) and gravel (costs $8 per ton). Sand and gravel together must make up exactly 75% of the weight of the concrete. Also, no more than 40% of the concrete can be sand and at least 30% of the concrete be gravel. Each day 2000 tons of concrete are produced. To minimize costs, how many tons of gravel and sand should be purchased each day
Answer:
The Sureset Concrete Company
The tons of gravel and sand that should be purchased each day are:
Sand = 800 tons
Gravel = 700 tons
Step-by-step explanation:
Two ingredients for producing concrete = sand and gravel
Cost of sand per ton = $6
Cost of gravel per ton = $8
Sand and gravel = 75% of the concrete
Therefore 25% (100 - 75%) will be made up of cement and water
Tons of concrete produced each day = 2,000
Sand and gravel = 1,500 (2,000 * 75%)
Sand <= 40% of 2,000 = 800 tons
Gravel => 30% of 2,000 = 700 (1,500 - 800) tons
To minimize costs, 800 tons of gravel and 700 tons of sand should be purchased each day.
Total cost incurred daily for both sand and gravel = $10,400 (800 * $6 + 700 * $8)
Why is the number of operators per shift multiplied by approximately 4.5 to obtain the total number of operators required to run the plant
I believe you meant "why is the number of shifts multiplied by approximately 4.5 to obtain the total number of operators required to run the plant"
Answer and Explanation:
There are 3 shifts per day, 49 weeks per year and 5 shifts per operator per week
To get total number of operators required to run the plant, we multiply number of shifts in a year by number if operators per shift.
49 weeks×5 shifts= 245 shifts per operator per year
365×3 shifts= 1095 shifts per year
1095/245=4.5 operators per shift
total number of operators required to run the plant(per day) = 4.5×3= 13.5 approximately 14
total number of operators required to run the plant(per year) =4.5×1095=4927.5 approximately 4928
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected (without replacement).
Answer:
The probability of getting two good coils is 77.33%.
Step-by-step explanation:
Since a batch consists of 12 defective coils and 88 good ones, to determine the probability of getting two good coils when two coils are randomly selected (without replacement), the following calculation must be performed:
88/100 x 87/99 = X
0.88 x 0.878787 = X
0.77333 = X
Therefore, the probability of getting two good coils is 77.33%.
HELP PLSSSSS
Solve each system with substitution
Answer:
x = -1 and y = -3
Step-by-step explanation:
1.
y = x-2 ....(1)
y = 4x+1 ....(2)
Put the values of y from equation (1) to (2).
x-2 = 4x+1
-2-1 = 4x - x
-3 = 3x
x = -1
Now put the value of x in equation (1).
y = -1-2
y = -3
So, the values of x and y are -1 and -3 respectively.
During a party, Eli loses a bet and is forced to drink a bottle of lemon juice. Not long thereafter, he begins complaining of having difficulty breathing, and his friends take him to the local emergency room. His blood pH is 7.28. What does this mean
Answer:
It means acidosis.
Step-by-step explanation:
When the pH level of the human blood is less than 7.35, the condition is known as acidosis.
When the pH level of the human blood is more than 7.45, the condition is known as alkalosis.
The organs which help to regulate the pH of human body is lungs.
Lungs remove the carbon di oxide through breathing or respiration.
what is the perimeter of a triangle?
Answer:
P = side a + side b + side c
Step-by-step explanation:
The perimeter of any polygon is all sides added together.
Answer:
3 X sides please mark me brainlist
Log(4) 5 + log (4) ? =log(4) 35
Answer:
7
Log(4) 5 + log (4) 7 =log(4) 35
Step-by-step explanation:
In this triangle, D is the midpoint of AB and E is the midpoint of BCIf AC = 36 what is the length of DE?
Answer:
A. 18
Step-by-step explanation:
Recall: the Mid-segment Theorem states that the length of the mid-segment theorem of a triangle is half the length of its third side.
DE = ½(AC) (Triangle Mid-segment Theorem)
AC = 36 (given)
Plug in the value
DE = ½(36)
DE = 18
in an examination 30% of the candidates failed in English and 35% failed in general studies and 27% failed in both subjects.if310 candidates passed in both how many candidates appeared in the examination
Answer:
500
Step-by-step explanation:
help me with this please pleaseee!
Answer:
2
Step-by-step explanation:
Since the two rectangles are similar, the ratio of their similar sides will be a constant k
Hence;
18/9 = 12/6 = k
Since they are all the same, then;
k = 18/9
k = 2
Hence the scale factor is 2
Answer:
D. 1/2Step-by-step explanation:
The scale factor is the ratio of corresponding sides:
k = 9/18 = 1/2or
k = 6/12 = 1/2Correct choice is D
15 greater than y is at least 150 interval notation
Step-by-step explanation:
I think this is the ans and I have got this ans from brainly.
kxndjdkdkdkkdkskskdkdjdjdjskskskdjdjddjd
Answer:
Not a functionFunctionFunctionNot a functionNot a functionHope this helps!
What is the sum of 4th squared number and the 2nd cube number
Answer:
mark me as brinalist if answers are correct
what is the value of -2(7-15)/4
When 50% of a number is added to the number, the results is 165
Answer:
this would look like
0.5x+x=165
1.5x=165
x=110
Hope This Helps!!!
help please!!!!!!!!!!!!!!!!!!!!!:):)
Answer:
1-g
2-b
3-a
4-i
5-f
6-e
7-d
8-c
identify an equation in slope-intercept form for the line parallel to y=-3x+7 that passes through (2,-4)
Answer:
y = -3x + 2
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope.
The first line is y = -3x + 7. Its slope is -3. A line parallel to this one will also have a slope of -3.
Plug this value (-3) into your standard point-slope equation of y = mx + b.
y = -3x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (2, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -3(2) + b
To find b, multiply the slope and the input of x (2)
-4 = -6 + b
Now, add 6 to both sides to isolate b.
2 = b
Plug this into your standard equation.
y = -3x + 2
This equation is parallel/perpendicular to your given equation (y = -3x + 7) and contains point (2, -4)
Hope this helps!
A six sided number cube rolled once. what is the probability of landing on a multiple of 2. write the probability as a fraction, percent and decimal.
Answer:
12 is the correct answer
Find the indicated side of the
right triangle.
45
у
9
45
х
x = [?]
Enter
Answer:
9
Step-by-step explanation:
Find a power series representation for the function. (Give your power series representation centered at x = 0.)
f(x) = x2 x 4 + 81
f(x) = [infinity] n = 0.
Answer:
attached below
Step-by-step explanation:
The Function; F(x) = x^2 / (x^4 + 81 )
power series representation
F(x) = x^2 / ( 81 + x^4 )
= ( x^2/81 ) / 1 - ( -x^4/81 )
attached below is the remaining part of solution
simplify 2x²y²÷m³×m²÷2xy
rotation 90° clockwise about the origin
Answer:
Take the picture you uploaded.
Click the rotate 'button' once.
Change the x to y and y to x on the graph. (axis labels)
Done
J (0, -1)
K(-4,-3)
I ( -4,-1)