Answer:
Step-by-step explanation:
Find derivative of the function:
y' = -2·sin(2·x)
-2·sin(2·x) = 0
x1 = 0
x2 = 3.142
f(0) = 1
f(3.142) = 1
Answer
fmin = 1, fmax = 1
Let $n$ be a positive integer. (a) Prove that \[n^3 = n + 3n(n - 1) + 6 \binom{n}{3}\]by counting the number of ordered triples $(a,b,c)$ of positive integers, where $1 \le a,$ $b,$ $c \le n,$ in two different ways. (b) Prove that \[\binom{n + 2}{3} = (1)(n) + (2)(n - 1) + (3)(n - 2) + \dots + (k)(n - k + 1) + \dots + (n)(1),\]by counting the number of subsets of $\{1, 2, 3, \dots, n + 2\}$ containing three different numbers in two different ways.
Answer:
Description of the given points can be defined as follows:
Step-by-step explanation:
In points A, If b is less than a and c. so, it calls the smiley face (a, b , c), so we'll have a smiling smile whenever we create a chart! And if b is bigger then a and c, then it should be an angry face, although when we switch the head inside out, they get a grumpy face.
In point b, the smirks, which including a greater than b and c, then it is the neutral faces like a is equal to and b equal to c , it can also be seen in certain forms of faces. When the facial is positive, therefore b and b is similar to c. because when we pick a, b and c, but there's a choice of n are neutral.
Its quantity of scowls has been counted. There are many n options to choose a or n-1 forms of picking b. Each value that we can choose for the could also have been the price of b or c. There is also multiplication by 3. Thus 3n(n-1) scowls were present.
A number of happy face faces we note now. There will be n options for such a then n – 1 options for b, but n – 2 options for c. There were the happy faces of n(n-1)(n-2) = 3C(n,3). There are many grumpy face faces of the configuration of 3C(n,3).
Thus, n^3 = n + 3n(n – 1)+ 6C(n,3) was its total amount of faces.
(b) We can select two groups of 2 categories one at two numbers to choose three numbers and the other with one group. Its total number of n+2 can be divided into two groups.
First, there are many two numbers with one group, then n number in another one. This makes up n + 2 number of all. C(2,2) = 1 represents selecting two digits from the two sets. There are many C(n,1) = n forms to select a single organization amount. Which offers us a first 1*n term.
21. Which of the following is an identity? a) sin (a) cos (a) = (1/2) sin(2 a) b) sin a + cos a = 1 c) sin(-a) = sin a d) tan a = cos a / sin a
Answer:
A
Step-by-step explanation:
[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) [/tex]
[tex] \sin( \alpha ) \cos( \alpha) = \frac{1}{2} \sin( 2\alpha ) [/tex]
write down a fraction that is more than 41% less than 42%
brainiest awarded!
Answer:
83/200
Step-by-step explanation:
41%=41/100=0.410
42%=21/50=0.420
41.5%=83/200=0.415
HELP ME PLS ASAP !!!!!!!!!!!!!
Answer:
_
-58
Step-by-step explanation:
Im pretty sure hope it helps
If a polygon has an area of 10 cm² and is dilated by a factor of 2, what will be the area of the dilated polygon?
Area depends on the product of sides,
so if the sides are shortened by a factor of 2, area will reduce by a factor of 4. (2×2)
new area = 10/4=2.5 cm²
represent 1/3 and 5/2 on the same number line
Answer:
Picture below
Step-by-step explanation:
● 5/2 is 2.5 so just divide the space between 3 by 2
● for 1/3 divide the space between 0 and by 3
Ms. Mitchell brings in 700 sour worms to distribute to the students at ... /1
her school. She gives 2/7 of the worms to the Kindergartners. Of the
remaining worms, she gives 7/25 to the 1st graders. Of the remaining
worms, she gives 4/9 to the 2nd graders. Of the remaining worms, she
gives 37/50 to the 3rd graders. Ms. Mitchell then distributes the
remaining worms evenly between the 4th graders. If there are 13 4th
graders, how many worms does each 4th grader get?
================================================
Explanation:
We'll step through the grade levels in increasing order
The teacher starts with 700 sour worms total. Then 2/7 of that is given to the Kindergartners
2/7 of 700 = (2/7)*700 = 200
So Ms. Mitchell handed out 200 worms to the Kindergartners.
This means she has 700-200 = 500 left over.
-----------------
Now onto the 1st graders.
The teacher hands out 7/25 of the remaining total (500) to the first graders
7/25 of 500 = (7/25)*500 = 140
She hands out 140 worms to the first graders and has 500-140 = 360 worms left.
-------------------
Now the 2nd graders
"Of the remaining worms, she gives 4/9 to the 2nd graders" tells us that
4/9 of 360 = (4/9)*360 = 160 worms are given to the second graders
This leaves 360-160 = 200 worms left
-------------------
Now the 3rd graders
37/50 of 200 = (37/50)*200 = 148
The teacher hands out 148 worms to the 3rd graders
There are 200 - 148 = 52 worms left.
--------------------
Finally, we're at the 4th graders
Each 4th grader gets the same number of worms (aka the amount is distributed equally). Since there are 52 worms left, and 13 fourth graders, this means each fourth grader gets 52/13 = 4 worms. It's a slightly interesting coincidence that the number '4' matches up with the grade level. It's possible your teacher adjusted the numbers to make this an intentional goal.
--------------------
To recap everything, we found these worm counts for each grade level
Kindergarten = 200 wormsFirst graders = 140 wormsSecond graders = 160 wormsThird Graders = 148 wormsFourth graders = 52 wormsNote how those values add back up to 700, ie 200+140+160+148+52 = 700. This helps confirm the answer.
Then once we see that 52 worms are left, each fourth grader gets 52/13 = 4 worms a piece.
So this is why the final answer is 4.
if the first step of the equation -8 - 7x = -5x - 10 is " add 10" then what should be done next?
Answer:
Add 7x to each side
Step-by-step explanation:
-8 - 7x = -5x - 10
Add 10 to each side
-8 - 7x+10 = -5x - 10+10
2 -7x = -5x
Add 7x to each side
2-7x+7x = -5x+7x
2 = 2x
Answer: See below
Step-by-step explanation:
[tex]-8 - 7x = -5x - 10[/tex]
I believe it is adding 8 on both sides
The next step after adding 8 on both sides is adding 5x on both sides
[tex]-7x=-5x-2[/tex]
[tex]-7x+5x=-5x-2+5x[/tex]
[tex]-2x=-2[/tex]
x=1
If 1 pound of grass seed costs 25x cents, represent in terms of x the cost of 7 pounds of seed? In polynomial simplest form
Answer:
175 cents
Step-by-step explanation:
25x=
25 • 7
25 • 7 = 175
Therefore the cost of 7 pounds of seed is 175 cents.
The lines on a 2-cup liquid measuring cup divide each cup into eighths. If you measure 1 3/4 cups of water, between which two quantities can you be certain that your exact measurement will be?
Answer:
1 3/4 cups is between the 13th and 15th lines from the bottom.
Step-by-step explanation:
The bottom of the cup has no line and corresponds to 0 eights.
1st line up: 1/8 cup
2nd line up: 2/8 cup this is also called 1/4 cup
3rd line up: 3/8 cup
4th line up: 4/8 cup this is also called 1/2 cup
5th line up: 5/8 cup
6th line up: 6/8 cup this is also called 3/4 cup
7th line up: 7/8 cup
8th line up: 8/8 cup this is also called 1 cup
9th line up: 9/8 cup
10th line up: 10/8 cup this is also called 1 1/4 cup
11th line up: 1 3/8 cup
12th line up: 1 4/8 cup this is also called 1 1/2 cup
13th line up: 1 5/8 cup
14th line up: 1 6/8 cup this is also called 1 3/4 cup
15th line up: 1 7/8 cup
16th line up: 1 8/8 cup this is also called 2 cups
1 3/4 cups is between the 13th and 15th lines from the bottom.
What is the value of the expression below when y = 4?
3y2 + y + 8
Answer:
3y²+y+8
=3(4)²+4+8
=3(16)+4+8
=48+4+8
=60
SOMEBODY PLS HALP ;( According to the number line, which statement MUST be true? A) A > 1 B) B > 4 C) C < 4 D) D < 0
Answer:
B
Step-by-step explanation:
B sqrtb is right in front of 2, so 2 squared is 4, so a little bit more than 2 squared will be a little more than four.
Answer:
C) C < 4
Step-by-step explanation:
because c is on the right side of four on the number line
Help me on Domain and Range
Answer:
Domain: 0 ≤ x < 9
Range: 0 < y ≤ 3
Step-by-step explanation:
The domain is the set of all values used for x-coordinates of all points on the curve.
The range is the set of all values used for y-coordinates of all points on the curve.
Look at the graph. The leftmost point is (0, 3). That point is included in the graph since there is no open circle there.
So far we know this:
Domain goes from 0 to ...
Range goes from 3 to ...
Now we look at the rightmost point. It is (9, 0), but there is an open circle on it, so that point itself is not included in the domain or range.
Now we know this:
Domain goes from 0 to just less than 9.
Range goes from 3 to to just more than 0.
Domain: 0 ≤ x < 9
Range: 0 < y ≤ 3
According to Hooke's Law, the force needed to stretch a spring varies directly to the amount the spring is stretched. If 50 pounds of force stretches a spring five inches, how much will the spring be stretched by a force of 180 pounds? inches
The length a spring stretches when subjected to the given load is required.
The spring is stretched by 18 inches.
Hooke's lawF = Force
k = Spring constant
x = Stretched length
[tex]F=50\ \text{lbf}[/tex]
[tex]x=5\ \text{inch}[/tex]
Hooke's law is given by
[tex]F=kx\\\Rightarrow 50=k5\\\Rightarrow k=\dfrac{50}{5}\\\Rightarrow k=10\ \text{lbf/inch}[/tex]
[tex]F=180\ \text{lbf}[/tex]
For the required spring
[tex]F=kx\\\Rightarrow x=\dfrac{F}{k}\\\Rightarrow x=\dfrac{180}{10}\\\Rightarrow x=18\ \text{inches}[/tex]
Learn more about Hooke's law:
https://brainly.com/question/2648431
Priya, Han, and Mai each measured one of the circular objects from earlier. Priya says that the bike wheel is 24 inches. Han says that the yo-yo trick is 24 inches. Mai says that the glow necklace is 24 inches. 1. Do you think that all these circles are the same size? 2. What part of the circle did each person measure? Explain your reasoning.
Answer:
Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).
Each person measures the circumference of the circle.
Step-by-step explanation:
Given that :
Priya, Han, and Mai each measured one of the circular objects from earlier.
Priya says that the bike wheel is 24 inches.
Han says that the yo-yo trick is 24 inches.
Mai says that the glow necklace is 24 inches.
Do you think that all these circles are the same size?
Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).
What part of the circle did each person measure?
Each person measures the circumference of the circle.
The circumference also known as the perimeter of the circle is denoted by :
C = 2π r
The circumference of a circle is the distance round the edges of the circle.
Given that C = 24
24 = 2π r
r = 24/(2π)
r = 3.8 inches
This confirms the claim that all the circle are of the same size since they possess the same radius.
Answer:
The person who answered first is WRONG
Step-by-step explanation:
I did this and these are the answers the teacher gave me:
the circles are NOT the same size
and they are measuring by diameter, radius, and circumfrence
Find the value of x in the figure below.
A. 25
B. 35
C. 45
D. 65
Answer:x=45
Step-by-step explanation:
can u help me. where do u plot it. what is x and what is y
Answer:
Step-by-step explanation:
for the first equation x= -2 and y=-7
the second equation x=3 and y is 3 now just plot x and y from the same equation on the same line
Answer:
[tex]\huge\boxed{x = -4; y = 7}[/tex]
Step-by-step explanation:
By plotting the points, we see that both of the lines intersect at (-4, 7)
Which means (X,y) = (-4,7)
So,
x = -4
y = 7
See the attached file so that you can know how would it be graphed.
HELP ME PLZZzzzzzzzz
Answer:
5 cm
Step-by-step explanation:
The volume (V) of milk in the container is calculated as
V = 8 × 15 × 12 = 480 cm³
After change of position with depth d then
8 × 15 × d = 480
120d = 480 ( divide both sides by 120 )
d = 4 cm
(-2 + 1)² + 5(12 : 3) - 9.
Answer:
5(12 : 3) -8
Step-by-step explanation
when you solve the first half of the equation you get 1.
so 9-1 is 8.
if a car covers 82.5 km in 5.5L of gas, how much distance will it cover in 13.2L of gas?
Answer:
198 KM
Step-by-step explanation:
82.5KM/5.5L= 15KM per liter
13.2 x 15 = 198 KM
Convert 40.78° to degrees, minutes, and seconds.
Answer:
Degrees- 40°
Minutes- 46'
Seconds- 48.00"
Step-by-step explanation:
40° + 46'/ 60 + 48.00"/ 3600= 40.78°
Answer:
Step-by-step explanation:
40.78°=40°+0.78°=40°+(78/100)×60=40°+46.8'=40°+46'+0.8'=40°46'+(8/10)×60=40°46'48''
It is an equation
What is -
x+3x=25
2x+36x=2
Answer:
Answer 1 : 25/4
Answer 2 : 1/19
Step-by-step explanation:
Question 1:
x + 3x = 25
4x = 25
x = 25/4
Question 2:
2x+36x=2
38x = 2
x = 2/38
x = 1/19
Bryce is making a model building. He raises the walls of the building by 2centimeters five times. By how many centimeters does Bryce raise the walls all together?
Answer:
C. 10cm
Step-by-step explanation:
Bryce is making a model building.
He raises the walls of the building
by 2 centimeters five times. By how
many centimeters does Bryce raise
the walls all together?
(A) 2 cm
(C) 10 cm
(B) 5 cm
(D) 20 cm
Bryce raises the walls of the building 2centimeters five times
This means, he raises the walls 2centimeters five different times
By how many centimeters does Bryce raise the walls all together?
We can solve this by finding the product of 2centimeters five times
The total centimeters Bryce raises the walls altogether= 2 centimeters × 5 times
=2cm × 5
=10cm
find x,y in the following pictures
Answer:
not detectable
Step-by-step explanation:
Firstly the question is not clear and the second thing is that the given information don't seem to be enough for calculation
How would you write Five times the difference of a number and 7
Answer:
5(x-7)
Step-by-step explanation:
5(x-7) or 5x-35
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Answer: 5*(x-7)
Step-by-step explanation:
no work needed
difference of a number means x
Who can do 20 assignments in math for me rn needs to b finish in 5 hours?
u need to finish 4 assignments in 1 hour
x + x(x + y) + y; use x = 4, and y = 1
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{x + x(x + y) + y}[/tex]
[tex]\huge\text{= 4 + 4(4 + 1) + 1}[/tex]
[tex]\huge\text{= 4 + 4(5) + 1}[/tex]
[tex]\huge\text{= 4 + 20 + 1}[/tex]
[tex]\huge\text{= 24 + 1}[/tex]
[tex]\huge\text{= 25}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: 25}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
Hi,
we need to substitute 4 and 1 in the equation, so for every y, we replace it with a 1 and every X with 4 as X= 4, Y = 1
equation: X + X (X + Y) + Y
equation after substituting the numbers: 1 + 1 (1 + 4) + 1
Bidmas rules apply.
expand the bracket first. 1 (1 + 4)=
1 X 1= 1
1 X 4= 4
1 + 4 = 5
then the equation becomes: 1 + 5 + 1= 7
your answer is 7 if you want to evaluate it.
your answer is 1 + 1 (1 + 4) + 1 if you need the equation.
, hope that helps :)
the distance travelled by light in 1year is called light year. the valued of 1 light year is about 9460000000000km.express it in scientific notation.
Answer:
9.46×10¹²
Step-by-step explanation:
To express that number in scientific notation you have to move the invisible decimal point from the end to the left in between the first and second number to the left
9460000000000
9.46×10¹²
i hope this helps and if you have any more questions please feel free to ask.
When dividing polynomials using factorization, canceling identical factors in the denominator and the numerator will give the _______.
Answer:
quotient
Step-by-step explanation:
Answer:
quotient
Step-by-step explanation:
Cancelling identical factors in the numerator and the denominator will give the quotient. For example,x2+5x+6x+3=(x+2)(x+3)x+3 = x + 3
Suppose average pizza delivery times are normally distributed with an unknown population mean and a population standard deviation of six minutes. A random sample of 28 pizza delivery restaurants is taken and has a sample mean delivery time of 36 minutes. Find a 90% confidence interval estimate for the population mean delivery time.
Answer:
90% confidence interval = (34.069,37.931)
Step-by-step explanation:
90% 1.645
Xbar / Point Est. 36
µ 0
σ 6
n 28
Confidence Interval
(34.069,37.931)