The value of the double integral for the function f(x, y) and the given region R is -60.
We can use the double integral to translate our understanding of volumes under surfaces in a three-dimensional coordinate system from areas under curves in a two-dimensional coordinate system. Just two of the many uses for double integrals are the ability to compute mass densities and estimate probability density functions.
We may get the volume under the area enclosed by the region using the double integral. By evaluating integrals with respect to only one variable while holding the other variable constant, we can compute double integrals.
Given function is: f(x, y) = 8xy³; R is the rectangle defined by -2 ≤ x ≤ 0 and -1 ≤ y ≤ 2.
Firstly integrate w.r.t y and apply the limits, similarly integrate w.r.t x and apply the corresponding limits.
The value of this double integral is calculated to be -60.
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what is the period for tangent functions? (Answer in radians)
Answer: 2 radians
Step-by-step explanation: You welcome
Ellen read a book a day for 10 weeks. How many books did
she read in all?
1 week = 7 days
10 weeks = 10×7 days
= 70 days
if Ellen reads 1 book in a day
Therefore,
1 day = 1 book
70 days = 70×1
= 70 books.
Thus Ellen reads 70 books in 10 weeks.
Hope helps
Answer:
70 books
Step-by-step explanation:
Ellen reads one book per day for 10 weeks.
All we need to do to know the number of books Ellen read overall is to multiply 1 (number of books he read each day) and 10 weeks (total number of days).
Each week is 7 days, so 10 weeks is equal to 70 days.
The equation will be: 1 x 70
We can conclude that Ellen read 70 books overall within 10 weeks.
There are 2,900 students at our school. If 51% of them are female, how many female students are there at our school?
Answer:
Step-by-step explanation:
1479
Please help quick what is the answer thank you
Answer:
y= -3x+4
Step-by-step explanation:
y=mx+c
m= y2-y1 ÷ x2-x1
m= -3
y=-3x+c
7=-3(-1)+c
c=4
y=-3+4
how many liters of 70% alcohol solution and 20% alcohol solution must be mixed to obtain 20 liters of 60% alcohol solution?
Answer:
16 liters of 70% alcohol
4 liters of 20% alcohol
Step-by-step explanation:
Let x = volume of 70% alcohol and y = volume of 20% alcohol. Since we need total of 20 liters, the first equation is x + y = 20. Next, calculate the amount of alcohol in the 20 liters of 60% alcohol. 60% is equivalent to 0.6, so there is 20*0.6 = 12 liters of alcohol in the 20 liter solution. Therefore the second equation is 0.7x + 0.2y = 12.
x + y = 20
0.7x + 0.2y = 12
2x + 2y = 40
7x + 2y = 120
-5x = -80
x = 16
16 + y = 20
y = 4
Evaluate the expression if a=2,b=-3,C=-1, and D=4
-2(b^2-5c)
Answer:
Your answer is - 28
Step-by-step explanation:
Given,
a = 2
b = - 3
c = - 1
d = 4
Now,
- 2 ( b² - 5 c )
= - 2 ( -3² - 5 ( - 1 ) )
= - 2 ( 9 + 5 )
= - 2 × 14
= - 28 ans….
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a) An adult who visited a therapist during the past year is randomly selected. What is the probability this adult used non-prescription antidepressants? Round your answer to decimal places.
(b) What is the probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants? Round your answer to decimal places.
The probability that this adult used non-prescription antidepressants is 0.78.
How to calculate the probability?Based on the information given, the following can be deduced:
Let A = event where adults visit therapist.
Let B = event where adults used non prescription antidepressants.
P(A) = 0.27
P(B) = 0.46
P(A n B) = 0.21
The probability that a randomly selected adult who visited the therapist used non-prescription antidepressants will be:
= 0.21/0.27
= 0.78
The probability that an adult visited a therapist during the past year, given that he or she used non-prescription antidepressants will be:
= 0.21/0.46
= 0.46
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Someone please help me with this question asap!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Correct choice = B[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Take HJ = a, GH = b and GJ = c
a = b + 2 c = a + b - 17 a + b + c = 73put the value of a from equation 1 in equation 2
[tex]\qquad❖ \: \sf \:c = (b + 2) + b - 17[/tex]
[tex]\qquad❖ \: \sf \:c = 2b - 15[/tex]
now, put the value of a and c in equation 3
[tex]\qquad❖ \: \sf \:b + 2 + b + 2b - 15 = 73[/tex]
[tex]\qquad❖ \: \sf \:4b - 13 = 73[/tex]
[tex]\qquad❖ \: \sf \:4b = 86[/tex]
[tex]\qquad❖ \: \sf \:b = 21.5 \: \: in[/tex]
Now, we need to find HJ (a)
[tex]\qquad❖ \: \sf \:a = b + 2[/tex]
[tex]\qquad❖ \: \sf \:a = 21.5 + 2[/tex]
[tex]\qquad❖ \: \sf \:23.5 \: \: in[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option B is correctAnswer:
23.5 in
Step-by-step explanation:
To find the length of HJ in triangle GHJ, create three equations using the given information, then solve simultaneously.
Equation 1
HJ is two inches longer than GH:
⇒ HJ = GH + 2
Equation 2
GJ is 17 inches shorter than the sum of HJ and GH:
⇒ GJ + 17 = HJ + GH
Equation 3
The perimeter of ΔGHJ is 73 inches:
⇒ HJ + GH + GJ = 73
Substitute Equation 1 into Equation 2 and isolate GJ:
⇒ GJ + 17 = GH + 2 + GH
⇒ GJ + 17 = 2GH + 2
⇒ GJ = 2GH - 15
Substitute Equation 1 into Equation 3 and isolate GJ:
⇒ GH + 2 + GH + GJ = 73
⇒ 2GH + GJ = 71
⇒ GJ = 71 - 2GH
Equate the two equations where GJ is the subject and solve for GH:
⇒ 2GH - 15 = 71 - 2GH
⇒ 4GH = 86
⇒ GH = 21.5
Substitute the found value of GH into Equation 1 and solve for HJ:
⇒ HJ = 21.5 + 2
⇒ HJ = 23.5
Given u = 3i − 8j and v = −4i + 8j, what is u • v? 73 8 −76 −56
Explanation:
We're applying the dot product.
u dot v = 3*(-4) + (-8)*8
u dot v = -12 - 64
u dot v = -76
The idea is that we multiply the x coordinates together, and the y coordinates together separately. Afterward you add the products. The result of any dot product is a scalar value, aka a single number.
The dot product is useful in many applications. One of which is to determine if two vectors are orthogonal.
An envelope contains $1.20 in dimes and nickels. if the dimes were quarters and the nickels were dimes, there would be $1.35 more in the envelope. How many nickels are in the envelope?
The nickels in the envelope is $0. 12
How to determine the number
From the information given, we have that;
Dimes + nickels = $1. 20
1/4 dimes + dimes = $ 1. 35
Let dimes = d
Nickels = n
d + n = 1. 20 equation a
d/4 + d = 1. 35 equation b
Make 'd' subject from equation a
d = 1. 20 - n
Substitute into equation b
1. 20 - n/ 4 + 1. 20 - n = 1. 35
0. 3 - 0. 25n + 1. 20 - n = 1. 35
collect like terms
- 1. 25n = 1. 35 - 1. 5
- 1. 25 = - 0. 15
n = -0. 15/ -1. 25
n = 0. 12
Thus, the number of nickels in the envelope is $0. 12
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Multiply each of the following(X+7)and(y-7)
Answer:
xy-49
Step-by-step explanation:
x x y is xy and -7x7 is 49 so the answer is xy- 49
need heeeelp please
Answer:
Initial population: 222 fish
After 7 years: 871 fish
Step-by-step explanation:
Initial population size:
Let t=0
∴P(0)=[tex]\frac{2000}{1+8e^0}[/tex]
=[tex]\frac{2000}{1+8}[/tex]
=[tex]\frac{2000}{9}[/tex]
=222 fish
After 7 years:
Let t=7
∴P(7)=871 fish
What is the range for the possible sizes of x?
(Fill in the boxes)
Answer:
1.6 and 9.6
Step-by-step explanation:
pls help
heather had some candy to give to her five children. she first took eight pieces for herself and then evenly divided the rest amount her children. each child received four pieces. with how many pieces did she start?
Answer: She started with 28 pieces of candy.
Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.
Answer:
She started with 28 candies.
Explanation:
Let the total amount of candies be c
Build equation:
heather took out 8 candies for herself→ remaining: c - 8
then divided the remaining candies to her five children→ each gets: (c - 8)/5
Here given each gets 4 candies
So,
(c - 8)/5 = 4
c - 8 = 5(4)
c - 8 = 20
c = 20 + 8
c = 28
If s(x) = x - 7 and f(x) = 4x²-x + 3, which expression is equivalent to (t*s) (x)?
Answer: [tex]4x^3 -29x^2 +10x-21[/tex]
Step-by-step explanation:
[tex](4x^2 -x+3)(x-7)\\\\=4x^3 -28x^2 -x^2 +7x+3x-21\\\\=4x^3 -29x^2 +10x-21[/tex]
Find the measure of a.
The measure of angle a is 70 degrees
How to determine the measure of a?The angle in a semicircle is a right angle.
This means that:
a + d = 90
Where O is the center of the circle
From the figure, we have:
Angle d and the angle with a measure of 20 degrees are corresponding angles
This means that
d = 20
Substitute d = 20 in a + d = 90
a + 20 = 90
Subtract 20 from both sides of the equation
a = 70
Hence, the measure of angle a is 70 degrees
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4/7=×/6 what does × =
Answer:
3.42857143
Step-by-step explanation:
You multiply 4/7 by 6 to isolate the variable
Answer:
3 3/7 or 24/7
As a decimal: 3.42857143
Step-by-step explanation:
Rewrite the proportion:
4/7 = x/6
Multiply both sides by 6 to isolate x:
(4/7) * 6 = x
Multiply 4 and 6, 7 is multiplied by 1 since 6 = 6/1:
x = 24/7
Rewrite as mixed number:
7 * 3 = 21
24 - 21 = 3
x = 3 3/7
Brainliest, please :) (Hoping to become a genius)
a chord subtend an angle of 72⁰ at the center of a circle with radius 24.5m. calculate the perimeter of the minor segment
The perimeter of the minor segment is 77. 4m
How to determine the perimeter
The formula for determining the perimeter of the minor segment is given as;
Perimeter = θ/360 × 2πr + 2r sin θ/2
where;
radius = 24. 5mθ = 72Substitute into the formula;
Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)
Perimeter = 30. 79 + 46. 60
Perimeter = 77. 4 m
Thus, the perimeter of the minor segment is 77. 4m
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giving brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The given focal points and the lengths of the minor and major axis of 16 and 20 gives the equation of the ellipse as the option;
[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
Which method can be used to obtain the ellipse?The equation of an ellipse is presented as follows;
[tex] \mathbf{ \frac{(x - h)^{2}}{ {a}^{2} } + \frac{(y - k)^{2}}{ {b}^{2} } } = 1 [/tex]
Where;
(x, y) = Coordinates of the center of the ellipse
a = Semi major axis
b = Semi minor axis
Length of minor axis = 16 units
Length of major axis = 20 units
By observation of the coordinates of the focal point, we have;
y-value of the center of the ellipse, k = 2
x-value of the center, h = (-9 + (3 - (-9))/2 = -3
The equation of the ellipse is therefore;
[tex] \frac{(x - ( - 3))^{2}}{ {10}^{2} } + \frac{(y - 2)^{2}}{ {8}^{2} } = 1 [/tex]
[tex] \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
The equation that represents the ellipse is the option;
[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]
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If the measure of angle ABC is 68°, what is the measure of arc AB?
Answer:
136
Step-by-step explanation:
While there is no picture for this question, I was able to find this question online, so that should be the correct answer.
value of element a23
Answer:
2
Step-by-step explanation:
a23
2 is column and 3 is row
(g) Every student of class IV donated as much money as their number to make a fund for landslide, If there are 68 students in class IV how much money did they collect?
Answer:$2346
Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.
Please help. The one answer for this question isn't right so I'll repost it. PLEASE!
Factor 30-6v-18w30−6v−18w30, minus, 6, v, minus, 18, w to identify the equivalent expressions.
Choose 2 answers:
THX ANSWER ASAP
The factor of given expression is 6(5-v-3w) and 2(15-3v-9w). correct option is c and d.
Given that factor 30-6v-18w.
Equivalent expressions are expressions that work the same way, even if they look different. If two algebraic expressions are equivalent, the two expressions have the same value if we enter the same values for the variables.
For option A
Factor the expression:
2(15-2v)≠6(5-v-3w)
get the result: False
Answer: False
For option B
Factor the expression:
3(10-3v+6w)≠6(5-v-3w)
get the result: False
For option C
Factor the expression:
6(5-v-3w)=6(5-v-3w)
get the result: True
For option D
Factor the expression:
6(5-v-3w)=2(15-3v-9w)
get the result: True
Hence, the equivalent expression of the factor 30-6v-18w is 6(5-v-3w) and 2(15-3v-9w).
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Please separate your final answer.
One second later, the distance between the two stones will change in a speed of 6.86 m/s
What is distance ?Distance can be defined as the length of change of position. When an object change from one position to another, the length between the points or position is known as distance.
If a dropped stone has a distance d = 4.9t²
Let us assumed that the time taken = 3 seconds
The distance d = 4.9 × 3² = 44.1 m
If another stone is dropped one second later, then the time t = 4 s
The distance = 4.9 × 4² = 78.4 m
One second later, the time = 5 seconds
The speed of change in distance = ( 78.4 - 44.1 )/ 5
The speed of change in distance = 34.3 / 5
The speed of change in distance = 6.86 m/s
Therefore, one second later, the distance between the two stones will change in 6.86 m/s
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Which best describes the composition of tranformations that maps ∆LMN to ∆L'M'N'. 0,0 is the center of the dilation in each choice.
A. a reflection over the line y=3 followed by a dilation of scale factor 2
B. a dilation of scale factor 2 followed by a dilation of scale factor 12
C. a dilation of scale factor 12 followed by a translation left 1 down 3
D. a dilation of scale factor 2 followed by a translation right 1 up 3
Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'
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What is the distance from (-5,2) and (0,4)?
Answer:
d = [tex]\sqrt{29}[/tex]
Step-by-step explanation:
The distance between two points is given by
d = [tex]\sqrt{ ( x2 - x1) ^2 - ( y2-y1)^2}[/tex] where ( x1,y1) and ( x2,y2) are the two points
d = [tex]\sqrt{( 0 - -5) ^2 + (4 - 2) ^2}[/tex]
d = [tex]\sqrt{5^2 + 2^2}[/tex]
d = [tex]\sqrt{25 +4}[/tex]
d = [tex]\sqrt{29}[/tex]
Answer: [tex]\Large\boxed{Distance=\sqrt{29} }[/tex]
Step-by-step explanation:
Given information
[tex](x_1,~y_1)=(-5,~2)[/tex]
[tex](x_2,~y_2)=(0,~4)[/tex]
Given the distance formula
[tex]Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute values into the formula
[tex]Distance =\sqrt{((0)-(-5))^2+((4)-(2))^2}[/tex]
Simplify values in the parenthesis
[tex]Distance =\sqrt{(0+5)^2+(4-2)^2}[/tex]
[tex]Distance =\sqrt{(5)^2+(2)^2}[/tex]
Simplify the exponents
[tex]Distance =\sqrt{25+4}[/tex]
Simplify values in the radical sign
[tex]\Large\boxed{Distance =\sqrt{29}\approx5.4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
2. The sum to infinity of an exponential sequence with a positive common ratio is 25 and the first two terms is 16. find fifth term
Answer:
0
Step-by-step explanation:
hi
hi
haha
and
and
are doing
dog food
0 answer
(scroll to bottom for answer)The equation you want to be using is A(n)+1=(A(n))r because this is a exponential sequence
r represents the ratio, which you said was 25, so basically you said
A(n)
____ = 25
A(n)-1
rthe sum of the first 2 terms are 16, the first two terms being A1 and A2, they need to follow the equation:
A2
__ = 25
A1
lets give them variables to make this a bit easier-
A1 will be x and A2 will be y
x+y=16(1st equation)
y/x=25, 25x=y(2nd equation)
(if you multiply y/x=25 by x you will get that 25x=y, which is where that other equation came from)
going back to x+y=16
subtract y from both sides
x=16-y
use substitution and solve for the second equation
25(16-y)=y
distribute
400-25y=y
add 25y to both sides to get rid of the -25y on the left side while keeping the equation equal
400=26y
divide both sides by 26 and you get 400/26 which simplifies to 200/13
after all that you need to multiply 200/13 by 25, 3 separate times
200 1875000
___ x 25 x 25 x 25= _________
13 13
pull it into a calculator and you get something like
142846.153846
Evaluate the following functions for the given value.
19. f(x) = -x3 + x2; -2
Answer:
12
Step-by-step explanation:
f(x) = -x^3 + x^2
Let x = -2
Evaluate the expression
f(-2) = -(-2)^3 + (-2)^2
= - (-2)*(-2) * (-2) + ( -2) * (-2)
= -(-8) + ( 4)
= 8 + 4
= 12
Suppose that the derivable functions x=x(t) and y=y(t) satisfy xcosy=2.
If dx/dt=−2, find dy/dt when y=π/4.
a-) -√2 / 2
b-) 4
c-) -2√2
d-) √2
e-) 2√2
Please, someone help me!
Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:
a-) -√2 / 2.
What is implicit differentiation?Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.
In this problem, the function is:
xcos(y) = 2.
The derivative is relative to t, applying the product rule, as follows:
[tex]\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0[/tex]
[tex]\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}[/tex]
Since dx/dt=−2, we have that:
[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]
When y = π/4, x is given by:
xcos(y) = 2.
[tex]x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}[/tex]
Hence:
[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]
[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}[/tex]
Since cot(pi/4) = 1, we have that:
[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}[/tex]
Which means that option a is correct.
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Please help, need for math hw and cant figure it out
The standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2
How to represent the quadratic function in standard form?The quadratic function is given as
f(x) = -3x^2 + 6x - 2
The standard form of a quadratic function is represented as:
f(x) = ax^2 + bx + c
When both equations are compared, we can see that the function f(x) = -3x^2 + 6x - 2 is already in standard form
Where
a = -3
b = 6
c = -2
Hence, the standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2
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