Apply l'Hopital's rule:
[tex]\displaystyle\lim_{x\to\pi}\frac{\displaystyle\int_\pi^x (1+\tan(t))\,\mathrm dt}{\pi\sin(x)}=\lim_{x\to\pi}\frac{1+\tan(x)}{\pi\cos(x)}=\frac{1+\tan(\pi)}{\pi\cos(\pi)}=\boxed{-\frac1\pi}[/tex]
where
[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\left[\int_\pi^x(1+\tan(t))\,\mathrm dt\right]=1+\tan(x)[/tex]
follows from the fundamental theorem of calculus.
When Max got home from school yesterday, he went into the kitchen to get a snack. There was 3/4 pan of brownies on the counter. Max ate 1/4 of what was left. What part of the pan of brownies did Mark eat?
Answer:
1/2
Step-by-step explanation:
3/4-1/4=1/2
Subtract. Simplify (or reduce) your answer, if necessary.
2 1/5 - 5/6 =
Answer:
2 1/5 - 5/6 = 41/30
Step-by-step explanation:
Turn the denominator to be the same because if the denominator is not the same so you can't subtract neither can you add.
Next find the least common multiple of both denominator (5, and 6) and ask yourself what time the denominator would give you the least common multiply you got.
1/5 x 6/6 = 6/30 and 5/6 x 5/5 = 25/30
Your expression now would be 2 6/30 - 25/30
You can't subtract 6 from 25 so you have to turn the proper fraction into a improper fraction
2 6/30 = 2 x 30 + 6 = 66/30. 25/30 = 0 x 0 + 25 = 25/30.
Your new expression would be:
66/30 - 25/30
Now you can subtract 66 - 25 and you get 41
Therefore the correct answer is 41/30 you can not simplify the answer because the numerator is a odd number and the denominator is a even number.
This function can be used to determine the number of bacteria in a culture h hours after the culture was started.
f(x) = - 10(3)^h
Which statement best describes the meaning of the equation f(2) = 90 ?
Answer:
The statement means that after 2 hours, there are 90 bacteria in the culture.
Step-by-step explanation:
The number of bacteria after x hours is given by the function states in the exercise. We have that f(x) will be the number of bacteria after x hours.
Which statement best describes the meaning of the equation f(2) = 90 ?
The statement means that after 2 hours, there are 90 bacteria in the culture.
Four sisters are all 2 years apart in age. The
total of their ages is equal to 36 years. How
old is the youngest sister
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The four sisters are all 2 years apart in age. The total of their ages is equal to 36 years.
Let x be the age of the youngest sister. Then the age of other sister will be x + 2, x + 4, and x + 6. Then the equation is given as,
x + x + 2 + x + 4 + x + 6 = 36
4x + 12 = 36
4x = 36 - 12
4x = 24
x = 24 / 4
x = 6
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
More about the Algebra link is given below.
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7 - 6a = -5 -8a solve please
a=-5/2
Step-by-step explanation:
-6a=-5-8a
-6a+8a=-5-8a+8a
2a=-5
a=-5/2
Answer:
a = -6
7 -6a = -5 -8a
- 6a = - 5 - 8a - 7
- 6a + 8a = - 5 - 7
2a = - 12
2a/2 = - 12/2
a = -6
Help me out to get this math problem solve
Answer:
1. 1900 children.
2. 600 adults.
Step-by-step explanation:
Let c represent the number children.
Let a represent the number of adult.
From the question given above, we were told that 2500 people entered the fair. This can be obtained as follow:
2500 = c + a ..... (1)
From the question given above, we were told that:
Cost per child = $ 2
Cost per adult = $ 4
Total amount collected = $ 6200
Thus, we can write the above as:
6200 = 2c + 4a .....(2)
Summary:
2500 = c + a ..... (1)
6200 = 2c + 4a .....(2)
1. Determination of the number of children that attended the fair.
From equation 1
2500 = c + a
Make a the subject by rearranging
a = 2500 – c ....... (3)
Substitute the value of 'a' in equation 3 into equation 2
6200 = 2c + 4a
a = 2500 – c
6200 = 2c + 4(2500 – c)
Clear bracket
6200 = 2c + 10000 – 4c
Collect like terms
6200 – 10000 = 2c – 4c
–3800 = –2c
Divide both side by –2
c = –3800 / –2
c = 1900
Thus, 1900 children attended the fair
2. Determination of the number of adults that attended the fair.
Substitute the value of c into equation 3.
a = 2500 – c
c = 1900
a = 2500 – 1900
a = 600
Thus, 600 adults attended the fair.
The manager of a theater wants to know whether the majority of its patrons were adults or children. one day 5100 tickets were sold in the receipts totaled $22,210. The adult admission is $5.50, and the children’s admission is $3.50. How many adult patrons were there?
Answer:
x= 2,180
x= number of adult tickets sold
Step-by-step explanation:
First, we need to establish the system of equations:
x= number of adult tickets sold
y= number of children tickets sold
5.5x + 3.5y = 22,210
x + y = 5,100
Now, we isolate one variable in a formula and substitute its value in the other:
x= 5,100 - y
5.5*(5,100 - y) + 3.5y= 22,210
28,050 - 5.5y +3.5y = 22,210
2y= 5,840
y= 2,920
x= 5,100 - 2,920
x= 2,180
There are 160 adults and 275 children at a zoo. The zoo makes a total of $5,470 from the entrance fees, and the cost of an adult and a child to attend is $27, how much does it cost each for a parent and a child? Let a represent an adult. Letc represent a child. Enter a system of equations to represent the situation then solve the system. The system of equations is and The adult tickets cost $ and the child tickets cost $
they will have 200$ each
PLEASE HELP! The avenues in a particular city run north to south and are numbered consecutively with 1st Avenue at the western border of the city. The streets in the city run east to west and are numbered consecutively with 1st Street at the southern border of the city. For a festival, the city is not allowing cars to park in a rectangular region bordered by 6th Avenue to the west, 10th Avenue to the east, 11th Street to the south, and 13th Street to the north. If x is the
avenue number and yis the street number, which of the following systems describes the region in which cars are not allowed to park?
Answer: D
Step-by-step explanation:
Just did it
You have 60 teaspoons of peppercorns. You need 0.25 teaspoons to make one serving of beef brisket. How many servings can you make?
Answer:
One Serving - 1/4 teaspoon
240 Serving - 60 teaspoon
plz mark as brainliest
If a room has a length of 15 feet, then what is the length in yards? Hint: 3 feet= 1 yard
Answer:
5 yards
Step-by-step explanation:
Given;
1 yard = 3 feet
The length of a room is 15 feet
Find;
The length of the room in yards
Set up a proportion;
[tex]\frac{1yard}{3feet}=\frac{x-yards}{15feet}[/tex]
Solve;
x = 5 yards
what is 3 6/7 times 4 2/28
Answer:
15.7040816327
Step-by-step explanation:
Answer:
it is 15 69\98 hope this helps!!
Step-by-step explanation:
Urgent!!!! Solve 3∣∣x+2∣∣<12.
Graph the solutions on the number line.
Step-by-step explanation:
First, you have to solve the inequality of x :
| x + 2 | < 12
x + 2 < 12
x < 10
AND
- x - 2 < 12
- x < 14
x > - 14
Therefore, the values of x is -14 < x < 10 so you have to draw it on the number line.
It's for middle SCHOOL PLZzzz HELPPP!!!
You have a coupon for an additional 25% off the price of any sale item at a store. The store has put a robotics kit on sale for 15% off the original price of $40. What is the price of the robotics kit after both discounts?
Answer:
$25.50
Step-by-step explanation:
Answer:
(40)(15/100)=6
(40)(25/100)=10
10+6=16
orginal price at 40
After discounts 16
40-16=24
so you can buy it in 24$
Hope it helped you
If an angle has a measure of x radians, what is the measure of the angle in degrees?
 degrees
Write a function ff that determines the degree measure of an angle in terms of the radian measure of the angle, x.
f(x)=
Answer:
Step-by-step explanation:
2π radians = 360°
x radians · 360°/(2π radians) = (180x/π)°
f(x) = 180x/π
The measure of the angle in degrees would be (180x/π)° and the function would be f(x) = 180x/π which determines the degree measure of an angle in terms of the radian measure of the angle x.
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
Given that an angle has a measure of x radians,
So the measure of the angle in degrees
Since 2π radians = 360°
Therefore x radians · 360°/(2π radians)
= (180x/π)°
A function f represents the degree measure of an angle in terms of the radian measure of the angle, x.
⇒ f(x) = 180x/π
Hence, the measure of the angle in degrees would be (180x/π)° and the function would be f(x) = 180x/π which determines the degree measure of an angle in terms of the radian measure of the angle x.
Learn more about the function here:
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y = 2x + 4
and
y = 2x - 8
Solve the systems by substitution
Answer:
-x - y - z = -8 ........ (1a)
-4x + 4y +5z = 7 ..... (2a)
2x + 2x = 4 .......... (3a)
since (3a) a is an equation solely in x make x the subject of the equation
2 ( x + x) = 4
divide both sides by 2
(x + x) = 2
2x = 2
x = 1 ....... (3b)
substitute x in (3b) for x in (1a)
-(1) - y - z = -8
make y the subject of the equation
-y - z = -8 + 1
-y = -7 + z
y = 7 - z ..... (1b)
substitute y in (1b) for y in (2a) as well as the value of x ( x= 1)
-4(1)+ 4( 7 - z ) +5z = 7
- 4 + 28 - 4z + 5z = 7
-24 + z = 7
z = 7 + 24
z = 31
By using (1a) solve for y
-(1) - y - (31)= -8
-1 - y - 31 = -8
y = -1 - 31 + 8
y = -24
∴ the solutions of the system are x = 1 ; y = -24 ; z = 31
Hope this helps!!!!!!!
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write an equivalent expression for the following using distributive property A(9b+13)
apply distributive property AKA (A • 9b)+(A • 13)
9Ab + 13A
I hope this helps :)
x + 6 >10 or 3x + 11 ≤ −7
Answer:
x>4 or x≤-6
Step-by-step explanation:
x+6>10 or 3x+11≤-7
x>4 or 3x≤-18
x>4 or x≤-6
What property represents (-3)+3=0?
Commutative or Additive Inverse
Answer:
additive inverse
Step-by-step explanation:
C= 3x2 + 10x - 32.7
Answer: True
Step-by-step explanation:
3 x 2 = 6
12.6 = 6x
6x = 5y
5y = 32
+
Answer:
C is -321 I hope this helps ^^
Help plz:)))I’ll mark u Brainliest
Answer:
11, 21, 31
Step-by-step explanation:
In a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex], any two sides must have a sum larger than the third.
Using this rule, the possible side lengths out of these choices that could form a triangle are:
21,
11,
31
A dog eats 2/5
of a bag of dog food in ten days. How many bags of
food will the dog eat in 12 weeks? Express your answer as a decimal.
Point A is in Quadrant III. The ordinate in this point is _______.
A. both – and +
B. negative (-)
C. positive (+)
D. zero
Answer:
if im right its negative
Negative I’m pretty sure sorry if I’m wrong
Please help thank you
Answer:
B
Step-by-step explanation:
Increasing trials promotes the chance of reaching theoretical.
(help me it is not much)
Which form of a linear equation should we use when given the y-intercept and the slope of
the line?
Point-Slope form
Slope-intercept form
Standard form?
Answer:
Slope Intercept Form
Step-by-step explanation:
its the basics
Susan reads a book at a rate of 1 page every 3 minutes. If her reading rate remains the same, which method could be used to determine the number of minutes for her to read 18 page? *
Answer:
54 minutes
Step-by-step explanation:
Hope I helped!
I can almost guarantee this answer is correct.
Have a nice day!
Answer:
54 minutes
Step-by-step explanation:
Every 3 minutes she reads 1
18x3=54
Hope it helps
Which equation is graphed in the picture.
PLEASE HELP!!!!!
Answer:
2x + 3y = 6
Step-by-step explanation:
Write an equation to determine the total length in kilometers (h)(h)left parenthesis, h, right parenthesis of Josh's hike.
Answer:
Step-by-step explanation:
H
the formula C = 6p + 200 gives C , the total cost in dollars of hosting a birthday party for p guests at a local ice cream parlor .
A : solve the formula for p .
B : isabella can spend $350 for her birthday party . how many people can she invite ?
Find the value of x
12
36
18
24
27
36
0 11
9
0 10
012
Answer:
11
Step-by-step explanation:
I think if I am wrong I am sorry