Water is not a liquid if its temperature is above 100 °C or below 0 °C.
0
40
80
120
160
Write a compound inequality to show the levels that are within the range described
above.
Answer:
[tex]0 \leq x \leq 100[/tex]
0, 40, and 80 are the values that work for this compound inequality.
Step-by-step explanation:
To create a compound inequality, we have to examine the conditions for [tex]x[/tex] to work.
Since [tex]x[/tex] can not be below 0° C, that means that [tex]x[/tex] must be greater than or equal to 0.
Which is represented as [tex]x\geq 0[/tex], or [tex]0\leq x[/tex].
Since [tex]x[/tex] can not be above 100° C, that means [tex]x[/tex] must be less than 100.
Which is represented as [tex]x \leq 100[/tex].
We can combine both inequalities into one, where [tex]x[/tex] is shared between the two. This creates [tex]0\leq x \leq 100[/tex].
Let's test each value of [tex]x[/tex] .
0 is equal to 0 and less than 100, so it works.
40 is greater than 0 and less than 100, so it works.
80 is greater than 0 and less than 100, so it works.
120 is greater than 0 and greater than 100, so it doesn't work.
160 is greater than 0 and greater than 100, so it doesn't work.
Hope this helped!
Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx 3 , 0 ≤ x ≤ 3
Answer:
[tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]
Step-by-step explanation:
Given that
curve [tex]y = \dfrac{\pi x}{3}, 0 \leq x \leq 3[/tex]
The objective is to find the area of the surface obtained by rotating the above curve about the x-axis.
Suppose f is positive and posses a continuous derivative,
the surface is gotten by the rotating the curve about the x-axis is:
[tex]S = \int ^b_a 2 \pi f (x) \sqrt {1 + (f' (x))^2 } \ dx[/tex]
The derivative of the function [tex]y' = \dfrac{\pi}{3} cos \dfrac{\pi x}{3}[/tex]
As such, the surface area is:
[tex]S = \int ^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt {1 +(\dfrac{\pi}{3}cos \dfrac{\pi x}{3})^2 } \ dx[/tex]
Suppose ;
[tex]u = \dfrac{\pi}{3}cos \dfrac{\pi x}{3}[/tex]
[tex]du = -( \dfrac{\pi}{3})^2 sin \dfrac{\pi x}{3} \ dx[/tex]
If x = 0 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (0)}{3} = \dfrac{\pi}{3}[/tex]
If x = 3 , then [tex]u = \dfrac{\pi}{3}cos \dfrac{\pi (3)}{3}[/tex]
[tex]u = \dfrac{\pi}{3}(-1)[/tex]
[tex]u = -\dfrac{\pi}{3}[/tex]
The equation for S can now be rewritten as:
[tex]S = \int^3_0 2 \pi sin \dfrac{\pi x}{3} \sqrt{1+(\dfrac{\pi}{3} cos \dfrac{\pi x}{3})^2 }\ dx[/tex]
[tex]S = 2 \pi \int ^{-\frac{\pi}{3} }_{\frac{\pi}{3}}(-\dfrac{9 \ du }{\pi^2} ) \sqrt{1+u^2}[/tex]
[tex]S = 18 \pi * \dfrac{1}{\pi ^2 } \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]
[tex]S = \dfrac{18} {\pi} \int ^{-\frac{\pi}{3}}_{\frac{\pi}{3}} \sqrt{1+u^2} \ du[/tex]
[tex]S = \dfrac{18} {\pi} (2 \int ^{-\frac{\pi}{3}}_{0} \sqrt{1+u^2} \ du)[/tex]
since [tex](\int ^a_{-a} fdx = 2\int^a_0 fdx , f= \sqrt{1+u^2} \ is \ even )[/tex]
Applying the formula:
[tex]\int {\sqrt{1+x^2}} \ d x= \dfrac{x}{2} \sqrt{1+x^2}+ \dfrac{1}{2} In ( x + \sqrt{1+x^2})[/tex]
[tex]S = \dfrac{36}{x}[ \dfrac{u}{2} \sqrt{1+u^2}+ \dfrac{1}{2} \ In (u+ \sqrt{1+u^2}) ] ^{\frac{\pi}{3}}_{0}[/tex]
[tex]S = \dfrac{36}{x}[ \dfrac{\dfrac{\pi}{3}}{2} \sqrt{1+\dfrac{\pi^2}{9}}+ \dfrac{1}{2} \ In (\dfrac{\pi}{3}+ \sqrt{1+\dfrac{\pi^2}{9}})-0 ][/tex]
[tex]S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})[/tex]
Therefore, the exact area of the surface is [tex]\mathbf{S =6 \sqrt{1 + \dfrac{\pi^2}{9} }+ \dfrac{18}{\pi} In (\dfrac{\pi}{3}+ \sqrt{1+ \dfrac{\pi^2}{9}})}[/tex]
The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex].
Given that,
The exact area of the surface obtained by rotating the curve about the x-axis. y = sin πx\3 , 0 ≤ x ≤ 3.
We have to determine,
Area of the surface obtained by rotating the curve.
According to the question,
Suppose f is positive and posses a continuous derivative,
The surface is gotten by the rotating the curve about the x-axis is:
Area of the surface is given by,
[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+ (f'(x))} } \, dx[/tex]
The given curve is x-axis,
[tex]y = \dfrac{sin\pi x}{3}[/tex]
The derivative of the function is,
[tex]\dfrac{dy}{dx} =\dfrac{\pi }{3} \dfrac{ cos\pi x}{3}[/tex]
The surface area is,
[tex]S = \int\limits^b_a {2\pi f(x) .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]
Substitute the value of f(x),
[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx[/tex]
Suppose;
[tex]u = \dfrac{\pi }{3}cos\dfrac{\pi x}{3}dx\\\\\du =( \dfrac{-\pi }{3})^2 sin\dfrac{\pi x}{3}dx\\\\if \ x = 0, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (0)}{3} = \dfrac{\pi }{3}\\\\if \ x = 3, \ then \ u = \dfrac{\pi }{3}cos\dfrac{\pi (3)}{3} = \dfrac{\pi }{3}(-1)= \dfrac{-\pi }{3}[/tex]
Then,
[tex]S = \int\limits^3_0{2\pi\dfrac{sin\pi x}{3} .\sqrt{1+(\dfrac{\pi }{3} \dfrac{ cos\pi x}{3})^2} }}} \, dx\\\\S = 2\pi \int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} (\dfrac{-9du}{\pi ^2})\sqrt{1+u^2} \ du\\\\S = 18\pi \times \dfrac{1}{\pi ^2}\int\limits^{\frac{-\pi}{3}}_ \frac{\pi }{3} \sqrt{1+u^2} \ du\\\\S = \dfrac{18}{\pi}\int\limits^{\frac{-\pi}{3}}_ {0} 2\sqrt{1+u^2} \ du\\\\\\[/tex]
Since,
[tex](\int\limits^a_{-a}{f} \, dx = 2\int\limits^a_0 {f} \, dx , \ f = \sqrt{1+u^2}\ is \ even)[/tex]
By applying the formula to solve the given integration,
[tex]\int {\sqrt{1+x^2} } \, dx = \dfrac{x}{2}\sqrt{1+x^2} + \dfrac{1}{2} \ ln(x+\sqrt{1+x^2})\\\\S = \dfrac{36}{2} [ \dfrac{u}{2} \sqrt{1+u^2} + \dfrac{1}{2} \ ln(u+\sqrt{1+u^2})}]^{\frac{\pi }{3}}_0\\\\[/tex]
[tex]S = \dfrac{36}{2} [ \dfrac{\dfrac{\pi }{3}}{2} \sqrt{1+\dfrac{\pi^2 }{9}} + \dfrac{1}{2} \ ln(\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}}-0)]\\\\S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]
Hence, The area of the surface is,[tex]S = 6\sqrt{1+\dfrac{\pi ^2}{3}} + \dfrac{18}{3}\ ln (\dfrac{\pi }{3}+\sqrt{1+\dfrac{\pi ^2} {9}})[/tex]
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One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 10 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer:
Step-by-step explanation:
x + x + 10 + 3x = 180
5x + 10 = 170
5x = 170
x = 36°
3(36)= 108° the largest angle
Evaluate 12(20 - 17) - 3•6
A.18
B.205
C.1320
D.198
Answer:
A. 18
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out expression
12(20 - 18) - 3(6)
Step 2: Multiply parenthesis
12(20 - 18) - 18
Step 3: Parenthesis
12(3) - 18
Step 4: Multiply
36 - 18
Step 5: Subtract
18
What’s 11 + 9/35 make sure answer is a mixed number
Answer: 11 9/35
Step-by-step explanation: just add the whole number to the fraction.
Answer & Step-by-step explanation:
[tex]11+\frac{9}{35}[/tex]
Add the whole number to the fraction:
[tex]11 \frac{9}{35}[/tex]
:Done
The diameter of a strand of rope is 1.2 × 10^ -3 inch. The diameter of a strand of floss is 2.0 × 10^ -4 inch. How much longer is the diameter of the strand of rope than the diameter of the strand of floss? A. 2.0 × 10^ -7 inch B. 1.0 × 10^ -7 inch C. 2.0 × 10^ -3 inch D. 1.0 × 10^ -3 inch
Answer:
D
Step-by-step explanation:
I answer this already. XD
Answer:
D
Step-by-step explanation:
sorry i needed these points XD
Which pair of numbers have a greatest common factor of 7? Select each correct answer. 21 and 3 7 and 14 28 and 7 7 and 1
Answer:
Hey there!
There are actually multiple answers.
7 and 14 have a GCF (greatest common factor) of 7, and so do 7 and 7.
Let me know if this helps :)
Answer:
answers are:
7 and 14
The factors of 7 is: 1, 7
The factors of 14 is: 1, 2, 7, 14
28 and 7
Factors of 28: 1, 2, 4, 7, 14, 28
Facotrs of 7: 1, 7
Step-by-step explanation:
others:
21, 3 is GCF is 3
The factors of 3 are: 1, 3
The factors of 21 are: 1, 3, 7, 21
7, 1 is GCF is 1
The factors of 1 are: 1
The factors of 7 are: 1, 7
Solving Expressions with Fractions
Match each arithmetic expression with its simplified equivalent.
3/5 + 1/3
5/6 - 314
000
6/1 x 2/3
Answer:
6/1 x 2/3
Step-by-step explanation:
Answer: Same numbers different set for Edg
6/1 - 2/3------------------ 4
5/6 x 3/4------------- 1/12
3/5 divide 1/3---------------------9/5
Step-by-step explanation:
Solve each of the following equations. a. 24 = -3 + 3n b. 11 + 4x = x - 10 c. -216 = 1 + 7(1 + 8m) d. 3p - 3(2 - 2p) = 34 + 4p You must show all of your work to receive credit.
Answer:
a. 24 + 3 =3n
27=3n
27/3 =3n/3
9=n
b.4x-x = -10 -11
3x = -21
3x/3 = -21 / 3
x = -7
c. -216 = 1 + 7 + 56m
-216 - 1 - 7 = 56m
- 224 = 56m
- 224 / 56 = 56m / 56
- 4 = m
d. 3p - 6 + 6p = 34 + 4p
3p + 6p - 4p = 34 + 6
5p = 40
5p / 5 = 40 / 5
p = 8
Suppose there are n independent trials of an experiment with k3 mutually exclusive outcomes, where pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this situation?
Complete question :
Suppose there are n independent trials of an experiment with k > 3 mutually exclusive outcomes, where Pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this situation?
Answer: Ei = nPi
Step-by-step explanation:
Since Pi represents the probability of observing the ith outcome
The number of independent trials n = k>3 :
Expected outcome of each count will be the product of probability of the ith outcome and the number of the corresponding trial.
Hence, Expected count (Ei) = probability of ith count * n
Ei = nPi
The formula of an expected count is given by .
[tex]E_i=np_i[/tex]
Suppose there are n independent trials of an experiment with k > 3 mutually exclusive outcomes,
where pi represents the probability of observing the ith outcome.
The expected counts for each possible outcome are given by .
[tex]E_i=np_i[/tex]
Where, [tex]p_i[/tex] is the probability of observing the ith outcome
[tex]E_i[/tex] is the expected count of the ith outcome.
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Find the area of the triangle below. Be sure to include the correct unit in your answer.
When given the base of and height of a triangle, you can use this formula:
[tex]area = \frac{1}{2} bh[/tex]
Plug in the known values:
[tex]area = \frac{1}{2} (18)(6)[/tex]
Solve:
[tex]area = \frac{1}{2} \times 108[/tex]
[tex]area = 54[/tex]
Add units:
[tex]area = 54cm^{2} [/tex]
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 29 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x = 45°, y = 53°, z = 82°
Step-by-step explanation:
x is the first angle, y is the second, and z is the third.
The sum of the second and third, which is denoted by y + z, is 3 times the measure of the first, which is just x. So, we have:
y + z = 3 * x
Additionally, the third angle, z, is 29 more than the second, y, so:
z = 29 + y
We also know that the sum of the three is 180, so:
x + y + z = 180
Let's substitute y + z in the last equation with 3 * x:
x + y + z = 180
x + 3x = 180
4x = 180
x = 45
Now, we know that y + z = 3 * 45 = 135. We also know that z = 29 + y, so substitute 29 + y in for z in y + z = 135:
y + z = 135
y + (29 + y) = 135
2y + 29 = 135
2y = 106
y = 53
Finally, use this value of y to solve for z:
z = 29 + y
z = 29 + 53 = 82
Thus, the angles are x = 45°, y = 53°, and z = 82°.
~ an aesthetics lover
How long would three 4 foot long pieces of rope be if they were laid end to end?
-24 = -3(x + 4)
Help :)
Answer:
x= 4 i think
Step-by-step explanation: -24 divided by 3 equals 8 subtract for and there is your answer
WILL GIVE BRAINLIEST IF YOU ANSWER CORRECTLY AND ASAP
What is the leading coefficient in the polynomial 5x - 6 + 3x2 ?
(HINT: The polynomial must be written in standard form)
6
5
3
-6
which of the following expression has more than one term? t-t, 18, dz, or 4q
Answer:
t-t
Step-by-step explanation:
A computer outlet store receives a shipment of 2000 computer chips. The owner decides to randomly choose 36 chips and test them. (a) What is the population (actually the group of elementary units) in this study? (b) What is the sample? (c) If the 36 chips are all chosen from the top layer of the box of 2000 chips, is this a random sample? why or why not?
Answer:
a
The population is 2000
b
The sample is 36
c
No this is not a random sample
Step-by-step explanation:
From this question we are told that
A computer outlet store receives a shipment of 2000 computer chips
The number of unites chosen by the owner is n= 36
Generally the population for this statistical test is N = 2000
This is because the 2000 is the entire pool from which a statistical sample is drawn
Generally 36 is the sample because this is the number that will be statistically tested and its result will be generalized for every other element of the population
Now if the 36 chips are all selected from the top then the sample is not a random sample because in a sample each element of the sample have an equal likelihood of been selected from the population but in the case of the question each element are selected base it accessibility
describe an infinite list of decimals. all of which are greater than 3.514, but get closer and closer to 3.514
3/5=x/11 solve for x give your answer as an improper fraction in its simplest form
Answer:
3/5=x/11.
If you cross multiply it will be 11×3=5×x...which is 33=5x which is x=33/5...... since it can't be cut into its simplest form then this is the answer....
A.$454.75
B.$502.75
C.$327.75
D.$327.25
E.None of These
Answer:
D. 327.25
Step-by-step explanation:
You start out with a gross pay of $415.00. When you have a deduction from your gross pay, it means it gets subtracted. So subtract the deductions of 48, 31.25, and 8.50 from 415 and it leaves you with 327.25.
415 48-31.25-8.50 = 327.25
Please I need help! ❤️
Answer:
8,0
8,-9
2,1
Step-by-step explanation:
It is always going to be the opposite.
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , thus
L(- 8, 0 ) → L'(8, 0 )
M(- 8, 9 ) → M'(8, 9 )
N(- 2, - 1 ) → N'(2, - 1 )
The problem is attached.
Answer:
Cosec θ = – 25/24
Step-by-step explanation:
From the question given, we obtained the following information:
Tan θ = – 24/7
Cosec θ =?
Tan θ is negative in the forth quadrant.
Please see attached photo.
Tan θ = Opposite /Adjacent
Opposite = – 24
Adjacent = 7
Hypothenus = x
Thus, we can obtain the value of x by using the pythagoras theory as illustrated below:
x² = (–24)² + 7²
x² = 576 + 49
x² = 625
Take the square root of both side
x = √625
x = 25
Next, we shall determine Sine θ. This can be obtained as follow:
Opposite = – 24
Hypothenus = 25
Sine θ = ?
Sine θ = Opposite /Hypothenus
Sine θ = –24/25
Finally, we shall determine the Cosec θ. This can be obtained as follow:
Cosec θ = 1 /Sine θ
Sine θ = –24/25
Cosec θ = 1 ÷ –24/25
Cosec θ = 1 × – 25/24
Cosec θ = – 25/24
James ate 4/5 of his banana and Eric ate 7/9 of his banana. Who ate more of their banana?
Answer:
James
Step-by-step explanation:
4/5 = 80% of banana
7/9 = 77.77% of banana
4/5 is greater than 7/9, so James ate more of his banana.
Please mark Brainliest if it helped you.
Answer:
James
Step-by-step explanation:
Because when reduce 4/5= 0.8
And 7/9= 0.77778
Simplify 8 + 10a - 3 + 5a when a=3
Answer:
50
Step-by-step explanation:
8 + 10a - 3 + 5a when a=3
8+10(3)-3+5(3)=
8+30-3+15=
38+15-3=50
How many milliliters are equal to 4 liters?
Answer: 4000000 cubic millimeters
Step-by-step explanation:
The answer of your question is 4000ml
Provide two examples that show that all square roots are not irrational numbers ?
Answer:
[tex]\sqrt{4}, \ \sqrt{9} \text{ are rational numbers.}[/tex]
Step-by-step explanation:
Hello,
[tex]\sqrt{n^2}=n \ for \ n\geq 0\\\\\text{For instance}\\\\\sqrt{2^2}=2=\sqrt{4}\\\\\sqrt{3^2}=3=\sqrt{9}[/tex]
Which number is one hundredth more than 14.31?
Answer:
14.32
hope this helps
consider the ratio of 153 per 108. write this ratio in different forms. a ratio written as a reduced fraction and as a decimal rounded to the hundredths.
Answer:
153:108
1.42
1 [tex]\frac{5}{12}[/tex]
1.42 is the approximate value of the ratio [tex]\frac{153}{108}[/tex].
What is the ratio?The ratio is the number of times one value contains or is contained within the other in a quantitative relationship between two numbers.
What is the required answer?The ratio of 153:108 is given.
Other forms of the ratio are
[tex]\frac{153}{108}=\frac{17}{12}[/tex]
[tex]=1.41666...\approx 1.42[/tex] (rounded to the hundredth place.
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4/5 = 5/4 =
Your answer
Answer:
not equal
Step-by-step explanation:
Answer:
4/5 is not equal to 5/4.
4/5 x 4 = 16/20
5/4 x 5 = 25/20
25/20 > 16/20
Write an algebraic expression for the phrase.
the product of d and 4
An expression is a combination of numbers, variables, and functions such as addition, subtraction, multiplication or division, etc.
The expression for the product of d and 4 is d x 4.
What is an expression?An expression is a combination of numbers, variables, and functions such as addition, subtraction, multiplication or division, etc.
Example:
3 added to 2 will be 3 + 2.
4 times 3 is 4 x 3.
4 less than 6 is 6 - 4.
We have,
The product of d and 4.
This can be written as:
= d x 4
Thus the expression for the product of d and 4 is d x 4.
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