Answer:
2 1/2 cups = 1.25 or 1 and 1 quarter liquid pint (U.S)
Step-by-step explanation:
I am confused on how to solve this. NOTE: the lower limit for the second function is (-6) NOT 6. Wouldn't let me type it in correctly.[tex]\int\limits^6_3 {|x-4|} \, dx + \int\limits^0_6 {\sqrt{36-x^2} } \, dx[/tex]
I think how you approach this depends on your knowledge of calculus.
If you don't know how to compute definite integrals yet, but you do know that they represent signed areas under curves, then you can plot both curves |x - 4| and √(36 - x ²), then recognize that the areas represented by these integrals are areas of geometric shapes. (See attached images)
First integral: if you plot |x - 4| on the interval [3, 6], you'll see that the integral corresponds to the area of two triangles. One of them has base = height = 1, and the other has base = height = 2. Then
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac12\times1\times1+\frac12\times2\times2=\frac52[/tex]
Second integral: if [tex]y=\sqrt{36-x^2}[/tex], then [tex]x^2+y^2=6^2[/tex], meaning this curve is the upper half of a circle with radius 6. On the interval [-6, 0], the area amounts to 1/4 of the total area of such a circle, so that
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\frac{\pi\times6^2}4=9\pi[/tex]
* * *
If you already know a few things about calculus and integration, you can compute these areas directly.
First integral:
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\int_3^4(4-x)\,\mathrm dx+\int_4^6(x-4)\,\mathrm dx[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(4x-\frac{x^2}2\right)\bigg|_{x=3}^{x=4}+\left(\frac{x^2}2-4x\right)\bigg|_{x=4}^{x=6}[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\left(\left(4\times4-\frac{4^2}2\right)-\left(4\times3-\frac{3^2}2\right)\right)+\left(\left(\frac{6^2}2-4\times6\right)-\left(\frac{4^2}2-4\times4\right)\right)[/tex]
[tex]\displaystyle\int_3^6|x-4|\,\mathrm dx=\frac52[/tex]
Second integral:
Substitute x = 6 sin(t ) and dx = 6 cos(t ) dt, then
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=\int_{-\frac\pi2}^0\sqrt{6^2-(6\sin(t))^2} (6\cos(t))\,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{1-\sin^2(t)} \,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) \sqrt{\cos^2(t)} \,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos (t) |\cos(t)| \,\mathrm dt[/tex]
For t ∈ [-π/2, 0], cos(t ) > 0, so |cos(t )| = cos(t ) :
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=36\int_{-\frac\pi2}^0\cos^2(t)\,\mathrm dt[/tex]
Recall the half-angle identity,
cos²(t ) = (1 + cos(2t )) / 2
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\int_{-\frac\pi2}^0(1+\cos(2t))\,\mathrm dt[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(t+\frac{\sin(2t)}2\right)\bigg|_{t=-\frac\pi2}^{t=0}[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=18\left(\left(0+\frac{\sin(2\times0)}2\right)-\left(-\frac\pi2+\frac{\sin\left(2\times\left(-\frac\pi2\right)\right)}2\right)\right)[/tex]
[tex]\displaystyle\int_{-6}^0\sqrt{36-x^2}\,\mathrm dx=9\pi[/tex]
Please help when Kevin bought a new office phone, he borrowed $1,200 at a rate of 18% for 9 years
Answer:
where is the rest of the questions
4. Aaliyah swims at an average speed of 8 meters per second, how long will it
take her to complete the race of 200 meters' length? *
3/5x2/3 thanks for the help
3 x 2 6
-- -- = --
5 3 15
6/15 can be simplified to 2/5.
---
hope it helps
A chemist wishes to mix a solution that is 12% acid. She has on hand 6 liters of a 4% acid solution and wishes to add some 16% acid solution to obtain the desired
12% acid solution. How much 16% acid solution should she add?
Complete the table.
Liters of
Solution
Percent Acid Liters of
(as a decimal) Pure Acid
0.04
6
Х
0.16
0.12
Answer:
25 liters of the 16% solution should be added.
Step-by-step explanation:
pure acid amount + pure acid amount = total pure acid amount
0.02*10 + 0.16*x = 0.12*(10+x) <<<---=== it is your balance equation; x is the amount (in liters) of the 16% solution.
0.02*10 + 0.16x = 0.12*10 + 0.12*x
0.16*x - 0.12*x = 0.12*10 - 0.02*10
(0.16 - 0.12)*x = 0.12*10 - 0.02*10
x = %280.12%2A10-0.02%2A10%29%2F%280.16-0.12%29 = 25.
Answer. 25 liters of the 16% solution should be added.
Check. %280.02%2A10+%2B+0.16%2A25%29%2F%2810+%2B+25%29 = 0.12 = 12% of concentration of the final mixture. ! Correct !
How to do 264 in Expanded form
Answer:
200+60+4
Step-by-step explanation:
200+60+4=264
state whether the number is a solution to the given inequality
7/12 > 9/16
Answer:where the numbers ? like a.3,b.5 somethin like that
Step-by-step explanation:
but its True
7/12>9/167
0.583333>0.053892
true
A square has vertices at the points A(-4,-4), B(-5,-4), C(-5,-3), and D(-4,-3). What is the area of this square? A. 1 square unit B. 4 square units C. 9 square units D. 2 square units
Answer:
Step-by-step explanation:
The length of AB = 1 unit.
area of square = 1² unit² = 1 square unit.
Answer:it is 1
Step-by-step explanation:
Need help asap!!!
Convert to exponential form
Answer:
B
Step-by-step explanation:
Please help!
Given the figure is a square, find x, y and z
Answer:
Step-by-step explanation:
Did u find it? Because I can’t figure it out euther
15 * 3/5
14. Will the product be greater than 15?
Answer:
NoStep-by-step explanation:
When you divide by a fraction or a decimal you are essentially multiplying that by something lesser than one and so the Calculator, if you are using a Calculator to solve this will, see multiplying something by a decimal or a fraction as a division and vice versa.
need help with thiss guys!!!
Write an expression for the sequence of operations described below.
10 plus the quotient of 8 and u
Do not simplify any part of the expression.
Answer:
[tex]10 + \frac{8}{u}[/tex]
Step-by-step explanation:
Given
10 [tex]plus[/tex] the [tex]quotient[/tex]of 8 and u
Required
Represent as a mathematical expression
Square out the operators
10 [[tex]plus[/tex]] the [[tex]quotient[/tex]] of 8 and u
[tex]plus => +[/tex]
[tex]quotient => /[/tex]
Replace the operators with their signs
[tex]10 + \frac{8}{u}[/tex]
200 students attend Ridgewood Junior High School. 25% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
sorry est un site Web Internet spécialement conçue 4
ill mark brainlist plss help
Answer:
it's the3rd one
Step-by-step explanation:
it's is 182 feet
What is -3/4x + 1/2y - 9/4x - 11/2y in simplest form?
Answer: -3x-5y
Step-by-step explanation:
Combine like terms
x + 10x-30= -8
Answer: x=2
Isolate the variable by dividing each side by the factors that don't contain variables.
Please explain in words.
Answer:
Negative
Step-by-step explanation:
The following expression will be negative. This is because, the fraction in x is a negative fraction. The fraction in y is a positive fraction. The expression is x * y, so if you were to multiply the two it would be negative. This is because a negative multiplied by a positive will be equal to a negative.
Hope this helps!!
-Ketifa
(Can I get brainliest?)
A triangular pyramid has a base area of 74 square inches and a height of 9 inches. Which is closest to the volume of the pyramid?
a 351 cubic inches
b 702 cubic inches
c 224 cubic inches
d 234 cubic inches
Answer:
702
Step-by-step explanation:
because 74 x 9 = 666 and 702 is close
Round 117.22666 to the nearest tenths
Answer:
117.2
Step-by-step explanation:
Rounding a number to the nearest tenth:
A number rounded to the nearest tenth will have one decimal place.
To do this, we look at the second decimal digit.
If it is less than 5, the first decimal digit is kept.
Otherwise, one is added to the first decimal digit.
In this question:
117.22666
The second decimal digit is 2, which means that we keep the first decimal digit which is also 2.
So, the number rounded to the nearest tenth is 117.2.
Lia cut a long piece of into 2 pieces. One pieces of the string is 24 inches long, and the other piece of the string is 12 inches long. How many feet long was the piece of string before lia cut it?
Answer:
24+12=36you find the total length
Answer:
3 feet
Step-by-step explanation:
Sam plans to use two flags on his float for the parade. Each flag is a right triangle and the triangles are similar.What is the width, x, of the larger flag in feet? halp please!!! 100 POINTS
Answer:
6.25 ft
Step-by-step explanation:
The smaller flag width is 5. And the larger flag is not that big in size. So the close answer is 6.25
Answer:
6.25ft
Step-by-step explanation:
What is the conjugate of (x2-6)?
Answer:
2(x - 3)
Step-by-step explanation:
Determine the equivalent system for the given system of equations.
4x − 5y = 2
10x − 21y = 10
A. 4x − 5y = 2
3x − y = 4
B. 4x − 5y = 2
24x − 47y = 22
C. 4x − 5y = 2
10x + 3y = 15
D. 4x − 5y = 2
14x + 26y = 12
Answer:
B) 4x − 5y = 2
24x − 47y = 22
Jane has 6 more than half the number of pairs of shoes that Mercedes has. Jane has j pairs of shoes, and Mercedes has m pairs of shoes. Write an equation that shows the relationship between j and m.
Select the true statement about triangle ABC.
A. sin A = sin C
B. sin A = cos B
C. sin A = cos C
D. sin A = tan c
how many 8ths are in a pound
Answer:There are 129 eighths in one pound of
Step-by-step explanation:
A bookstore had 60 copies of a magazine. Yesterday, it sold 1/4 of them. Today, it sold 2/3 of what remained. How many copies does the bookstore have left?
Answer:
15
Step-by-step explanation:
60×1÷4=15(1/4)
60-15=45
45×2÷3=30(2/3)
45-30=15
In 2008, there were 1570 bears in a wildlife refuge. In 2010, the population had
increased to approximately 1884 bears. If this trend continues and the bear population is
increasing exponentially, find the number of bears in 2015?
Answer:
it would be about 4500 bears
Step-by-step explanation:
Please help me math inequality grade 8
Answer: x > 2/3
Step-by-step explanation:
-1 - x/2 < x
Simplify:
-1/2x + 1 < x
Subtract x from both sides:
-1/2x + 1 - x < x - x
-3/2x + 1 < 0
Subtract 1 from both sides:
-3/2x + 1 - 1 < 0 - 1
-3/2x < -1
Multiply both sides by 2/(-3):
2/(-3) (-3/2) < 2/(-3) (-1)
x > 2/3