Find the area bounded by the curves x = 2y2 and x = 1 - y. Your work must include an integral in one variable.
Please help!!
Answer:
Hello,
in order to simplify, i have taken the inverses functions
Step-by-step explanation:
[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]
find the values of x and y for the following matrix equations
Answer:
Step-by-step explanation:
What is 3 times 10^9
Answer:
3 times 10 ^ 9
Step-by-step explanation:
3 × 10 ^ 9 = 3000000000
The length AB of a rectangle ABCD is 8cm and its diagonal BD and measures 10 cm Find its breadth BC
Find the length of DM
Answer:
67
Step-by-step explanation:
DM=JM-JD=84-17=67
Answer:
Step-by-step explanation:
A company produces 2 types of computers; desktops and laptops
Answer:
?
Step-by-step explanation:
Sets L and M are defined as follows.
L={-1,1,4,5,7,8)
M={1,2,7)
Answer each part below. Write your answer in roster form or as Ø.
(a) Find the union of L and M.
(b) Find the intersection of L and M
Answer:
the union of l and m is minus 1,1,2,4,5,7,8.....and the intersection of l and m is 1.......
Solve for x
X-8 = -10
A) X = 2
B) X = -2
C) X = 18
D) X = -18
Answer:
x=–2
Step-by-step explanation:
x-8=-10
x=-10-8
x=–2
Answer:
-8= -10
, = -10+8
, = -2
Tìm vi phân toàn phần của các hàm số sau:
ln(x+√(x^2+y^2 ) ) ln(sin(y/x))
Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).
Then the total differential is
[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]
[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]
work out the value of y when x = 4 30 points
Answer:
y = 54/25 when x = 4.
Step-by-step explanation:
y is given by the equation:
[tex]\displaystyle y = p\times q^{x-1}[/tex]
Where p and q are numbers.
We are also given that when x = 1, y = 10 and when x = 6, y = 0.7776.
And we want to determine the value of y when x = 4.
Since y = 10 when x = 1:
[tex]\displaystyle (10) = p\times q^{(1)-1}[/tex]
Simplify:
[tex]10 = p \times q^0[/tex]
Any number (except for zero) to the zeroth power is one. Hence:
[tex]p=10[/tex]
Thus, our equation is now:
[tex]y = 10\times q^{x-1}[/tex]
When x = 6, y = 0.7776. Thus:
[tex](0.7776) = 10\times q^{(6)-1}[/tex]
Simplify and divide both sides by ten:
[tex]\displaystyle 0.07776 = q^5[/tex]
Take the fifth root of both sides:
[tex]\displaystyle q = \sqrt[5]{0.07776}[/tex]
Use a calculator. Hence:
[tex]\displaystyle q = \frac{3}{5} = 0.6[/tex]
Our completed equation is:
[tex]\displaystyle y = 10\times \left(\frac{3}{5}\right)^{x-1}[/tex]
Then when x = 4, y equals:
[tex]\displaystyle \begin{aligned} y &= 10\times \left(\frac{3}{5}\right)^{(4)-1} \\ \\ &= 10\times \left(\frac{3}{5}\right)^3 \\ \\ &= 10\times \left(\frac{27}{125}\right) \\ \\ &= \frac{54}{25}\end{aligned}[/tex]
A lab technician needs 35 ml of 15% base solution for a certain experiment,
but she has only 10% solution and 20% solution. How many milliliters of
the 10% and the 20% solutions should she mix to get what she needs?
Answer:
17.5ml- of 10 percent solution, 17.5ml- of 20 percent solution
Step-by-step explanation:
35:100*15=5.25- ml of alkali in the base solution
Suppose we need x ml of 10 percents solution and 35-x - of 20 percents.
Then The quantity of alkali in the first one (10 percents) is x/100*10=0.1x
when in the second one we have (35-x)/100*20= 7-0.2x of alkali
0.1x+7-0.2x=5.25
7-0.1x= 5.25
0.1x=1.75
x=17.5- 0f 10 percents
35-17.5=17.5 - of 20 percents
Which best describes the process of selecting a cluster sample?
Clusters that each represent the population are sampled from such that no two members of the same cluster are included in the sample.
Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample.
Members of a population are ordered by some characteristic, and then a cluster sample is formed by selecting every kth member.
Members of a population are separated into clusters based on a characteristic important to the study and a random sample is selected from each cluster.
Answer:
"Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample"
Step-by-step explanation:
In cluster random sampling, "the population is divided, usually geographically, into groups that generally have the same size. A certain number of groups are randomly chosen, and every individual in the chosen groups are chosen for the sample."
In accord with this logic, the second choice, "Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample" seems to be correct.
NOTE: This may not be the correct answer. I am simply basing my answer on the definition I have learnt.
Answer:
B
Step-by-step explanation:
find the value of z, angles related to a circle
Use the differential to approximate the expression. Then use a calculator to approximate the quantity, and give the absolute value of the difference in the two results to four decimal places.
√
53
9514 1404 393
Answer:
0.0056
Step-by-step explanation:
f(x) = √(49 +x)
f'(x) = 1/(2√(49 +x))
A linear approximation of f(x) expanded about x=0 is ...
f(x) ≈ f(0) + f'(0)x = 7 +x/(2·7)
Then for √53, we have x=4
f(4) ≈ 7 +4/14 = 7 2/7 . . . . . approximate √53 using differentials
__
The calculator value of √53 is about 7.280110, so the difference in results is ...
approx - actual ≈ 7.285714 -7.280110 = 0.005604 ≈ 0.0056
urgent !!!!!! plz image below
Answer:
[tex]216\ km^2[/tex]
Step-by-step explanation:
1. Approach
The surface area of a three-dimensional figure is the two-dimensional distance around the figure. The easiest way to find the surface area of a figure is to find the area of each of its facets, then add up the area to get the total surface area. The given pyramid is composed of four congruent triangles and a square. Find the area of one of the triangles, and then the area of the rectangle. Multiply the area of the triangle by four to account for the fact that there are four congruent triangles. Then add the area of the base to the result, the result attained is the surface area of the prism.
2. Find the area of the triangles
The formula to find the area of a triangle is the following:
[tex]A_t=\frac{b*h}{2}[/tex]
Where (b) represents the base and (h) represents the height of the triangle. Substitute the given values into the formula and solve for the answer.
[tex]A_t=\frac{b*h}{2}[/tex]
[tex]A_t=\frac{9*7.5}{2}[/tex]
[tex]A_t=\frac{67.5}{2}[/tex]
[tex]A_t=33.75[/tex]
3. Find the area of the rectangle
The formula to find the area of a rectangle is the following,
[tex]A_r=b*h[/tex]
Substitute the given values in and solve,
[tex]A_r=b*h[/tex]
[tex]A_r=9*9[/tex]
[tex]A_r=81[/tex]
4. Find the total surface area
Multiply the area of the triangle by four to account for the fact that there are four triangles. Then add its area to the area of the rectangle.
[tex]A_t+A_t+A_t+A_t+A_r=A[/tex]
[tex]4(A_t)+(A_r)=A[/tex]
[tex]4*33.75+81=A[/tex]
[tex]135+81=A[/tex]
[tex]216=A[/tex]
help me now where are you all helppppp
A fraction means division.
To find the decimal equivalent of a fraction, divide the top number by the bottom number.
If an angle of a right angle triangle is 81 find the remaining angle in grades
Answer:
9
Step-by-step explanation:
90+81+mising angle=180, missing angle is 9
A truck is said to get 18 miles per gallon on a highway, but this value can fluctuate, at most, by 4 miles per gallon. Which of the following absolute value inequalities matches this scenario? Question 23 options: |x + 18| ≤ 4 |x – 18| ≤ 4 |x – 4| > 18 |x + 18| > 4
Answer:
the correct answer is |x – 18| ≤ 4
just took the test
Step-by-step explanation:
If f(x)=logx, show that f(x+h)-f(x)/h=log[1+h/x]^1/h, h=/=0 (Picture attached, thank you!)
Answer:
Step by step proof shown below.
Step-by-step explanation:
To prove the equation, you need to apply the Logarithm quotient rule and the Logarithm power rule. Here's how the quotient rule looks like.
[tex]log_b(x/y) = log_b(x) - log_b(y)[/tex]
And here's how the power rule looks like
[tex]log_a(x)^n = nlog_a(x)[/tex]
First let's apply the quotient rule.
[tex]\frac{f(x+h)-f(x)}{h} = \frac{log_a(x+h)-log_a(x) }{h} = \frac{log_a(\frac{x+h}{x} )}{h}[/tex]
Now we can do some quick simplification, and apply the power rule.
[tex]\frac{1}{h} log_a(1 + \frac{h}{x} ) = log_a(1+\frac{h}{x} )^\frac{1}{h}[/tex]
16: The temperature yesterday at noon was 68.5 degrees. Today at noon
it was 59.9 degrees. What was the difference in temperature?
O A. 8.4 degrees
OB. 8.5 degrees
C. 8.6 degrees
O D. 8.7 degrees
Answer:
C
Step-by-step explanation:
It is 8.6 because we are finding the difference and using subtraction.
So I did 68.8-59.9 and I got 8.6
Decompose -6x/(x+2)(x+8) into partial fractions.
The partial fraction expansion takes the form
-6x/((x + 2) (x + 8)) = a/(x + 2) + b/(x + 8)
Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.
Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:
-6x = a (x + 8) + b (x + 2)
Expand the right side and collect terms by powers of x :
-6x = (a + b) x + (8a + 2b)
It follows that
a + b = -6 and 8a + 2b = 0
==> a = -2 and b = 8
So we end up with
-6x/((x + 2) (x + 8)) = -2/(x + 2) + 8/(x + 8)
Help please and thank you!!!!!
9514 1404 393
Answer:
a) 2 and 4; b) 1&2, 2&3, 3&4x = 16Step-by-step explanation:
1a. Vertical angles share a vertex and are composed of opposite rays. Here, angles 2 and 4 are vertical angles.
1b. Consecutively numbered angles are adjacent, as are angles 1 and 5. The pairs of interest can be chosen from ...
1&2, 2&3, 3&4, 4&5, 5&1
__
2. Angles 1 and 3 have the same measure, because they are vertical angles. Then we have ...
78° = (5x -2)°
80 = 5x . . . . . . . divide by °, add 2
16 = x . . . . . . . divide by 5
find the surface area of the prism
Answer:
114 cm²
Step-by-step explanation:
Surface area of the rectangular prism,
2×(wl+hl+hw)
=2×(3×8+3×8+3×3)
= 2×(24+24+9)
= 2×(57)
=114 cm²
25(0.3x-4)-5(1.5x-6)+100(13/4) simplify the following expression and evaluate for x=0.345
Answer:
255
Step-by-step explanation:
Given :
Simplify the expression :
25(0.3x-4)-5(1.5x-6)+100(13/4)
Open each Bracket:
7.5x - 100 - 7.5x + 30 + 325
7.5x - 7.5x - 100 + 30 + 325
= 255
The simplified equation = 255
X/6 - y/3 = 1
please explain in detail!
Answer:
x=12,y=3
Step-by-step explanation:
x/6-y/3=1
x can equal 12 because 12/6 is equal to 2.
y can equal 3 because 3/3 equals 1
2-1=1
sold 72 books, if ratio of books to bookmarks sols was 9:2, how many bookmarks sold?
16 book marks has been sold
Answer:
16 bookmarks
Step-by-step explanation:
9/72 = 2/x
72/9 = 8
2 x 8 = 16
hope this helps
√10 Multiple √15 is equal to
(a) 5√6
(b) 6√5
(c) √30
(d) √25
step by step for BRAINLIST
Solve :-
Answer:
a). 5√6
[tex] \sqrt{10} \times \sqrt{15} \\ = ( \sqrt{5} \times \sqrt{2} ) \times ( \sqrt{5} \times \sqrt{3} ) \\ = {( \sqrt{5}) }^{2} \times ( \sqrt{2} \times \sqrt{3} ) \\ = 5 \times ( \sqrt{6} ) \\ = 5 \sqrt{6} [/tex]
Find the measure of the missing angles.
Answer:
Step-by-step explanation:
e = 61°, f = 119°, and d = 90°
We know that vertically opposite angles are equal.
So, e = 61° [Vertically opposite angles]
We know that linear pair of angles are supplementary (180°).
So, f + 61° = 180° [Linear pair of angles]
=> f = 180° - 61°
=> f = 119°
and d + 90° = 180° [Linear pair of angles]
=> d = 180° - 90°
=> d = 90°
a shopkeeper marked price a article a certain price above the cost price and he allowed 16% discount to make 5% profit if a customer paid 9492 with 13% vat to buy it by what percent is the mp above cp
Answer:
if I had known this
Step-by-step explanation:
then I won't be using this app right now..
The ratio of the volumes of two similar solid polyhedra is equal to the square root of the ratio between their edges. True or False? HELP QUICK PLSSSSS
Answer:
FALSE.The ratio of the volumes of two similar solid polyhedra is equal to the square of the ratio between their edges. This statement is false. A polyhedron is a shape that has no gaps between their edges or vertices.
Answer:
it's false
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