You will find it easiest if you write the integral in the form.
∫??∫??13 ,∫??∫??1r3drdθ ,that is, with θ on the "outside" integral. Looking at your diagram, the minimum θ value in the region of integration is =0θ=0, which occurs along the x axis. The maximum θ value occurs at the point (1,1)(1,1), giving =/4θ=π/4. So we have∫/40∫??13 .∫0π/4∫??1r3drdθ .For any fixed θ value, the values of r in the region go from the vertical line =1x=1 to the semicircle. At =1x=1 we have =secr=secθ as you have noted. The easiest way to get the maximum r value is to draw a line from the origin at angle θ until it hits the semicircle, and a line from there to (2,0)(2,0). Then you can see in the diagram a right-angled triangle (because the angle in a semicircle is a right angle) with hypotenuse 22, and so we get max=2cosrmax=2cosθ. So the integral is∫/40∫2cossec13 .∫0π/4∫secθ2cosθ1r3drdθ .For sketching the graph,=2−2‾‾‾‾‾‾‾√⇒2−2+2=0⇒(−1)2+2=1 ,y=2x−x2⇒x2−2x+y2=0⇒(x−1)2+y2=1 ,and not forgetting that ≥0y≥0.
NEED HELP! WILL MARK BRAINLIEST
Answer:
im pretty sure its 27.
Step-by-step explanation:
if g(x) = 20 then the new problem is 20=x-7
20=x-7 . add 7 to both sides
+7=+7 . +7 cancels out the -7
27=x . <<<answer
8 (4 x 2.3)
A 8 x 2.3
B 4 x 2.3
C 8 x 9.2
D 8 x 4
Answer:
8 x 9.2
Step-by-step explanation:
The sum of the measures of the angles of any triangle is 180. In a particular triangle, one angle is 40 greater than the smallest angle, and the third angle is 10 less than three times the smallest angle. Find the measure of the three angles.
Answer:
The smallest angle is 30 degrees, the second angle is 80 degrees and the third angle is 70 degrees
Step-by-step explanation:
let x = the smallest angle
This means that one angle is x+40, and the third angle is 3x-10. This make our equation:
x + 40 + 3x - 10 + x = 180
Combine like terms
5x + 30 = 180
Subtract 30 from both sides
5x = 150
Divide both sides by 5
x = 30
Plugging this in:
3x - 10 =
90 - 10 =
80
And for the other:
x + 40 =
30 + 40 =
70
A car has four wheels. How many wheels are there for three cars?
Answer:
I think it would be 12! :)
Step-by-step explanation:
[tex]4 x 3=12[/tex]
Please help. Have a good day
PLEASEEEEEEEEEEEEEE HELPPPPPPPPPPPPPPPPPPPP find the number if 2.5 of it is .75
Answer:
3.332
Step-by-step explanation:
take 2.5/3=0.833
0.833*4=3.332
hopefully this is right
im 95% sure its right
Whats the constant term for y=3x + 5
1. 3
2. 5
3 is the constant/ slope
5 is the y intercept
I believe it's the first answer. I would just like to receive confirmation.
Thank you.
Answer
c
Step-by-step explanation:
Given the definitions of f(x) and g(x) below, find the value of (fog)(-3).
f(x) = -4x + 7
g(x) = 2x2 + 5x – 8
Answer:
-93
Step-by-step explanation:
Step one:
given the expressions
[tex]f(x) = -4x + 7\\\\g(x) = 2x^2 + 5x- 8[/tex]
we want (fog)(-3).
but (fog) is
[tex]f(x) = -4x + 7\\\\\ (fog)=-4(2x^2 + 5x -8) + 7\\\\ (fog)=-8x^2-20x+32+7[/tex]
Step two:
fog(-3)= put x= -3 in (fog)(-3)=-8x^2-20x+32+7
[tex](fog)(-3)=-8x^2-20x+32+7\\\\ (fog)(-3)=-8(-3)^2-20(-3)+32+7\\\\ (fog)(-3)=-8*9+60+32+7\\\\ (fog)(-3)=-72-60+32+7\\\\ (fog)(-3)=-93[/tex]
the number of home theatres a company sells varies directly as the money spent on advertising. How many home theatres does the company sell for each $500 spent advertising? [ direct variations ]
Negative ten is no less than two times a number plus fourteen
can you please solve it
Answer:
-12≥x
Step-by-step explanation:
-10≥2x+14
-24≥2x
-12≥x
List all the factors of the number 48.
O1,2,3,7,8, 12, 48
O2,3,4,6,8,16,24
0 1,2,3,4,6,8, 12, 16, 24, 48
O2, 3, 4, 6, 8, 9, 12, 16, 24
Use the triangle shown on the right to answer the question. Which equation can you use to solve for a?
Answer:
B
Step-by-step explanation:
The equation that can be used to solve for 'a' is a/sin35° = 30/sin60°.
What is a triangle?A triangle is a three-sided closed-plane figure form by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know sine rule of triangles which states,
a/sinA + b/sinB + c/sinC.
We also know that the sum of all the interior angles in a triangle is 180°.
Therefore, The measure of angle B is 180° - (35 + 85)°.
= 60°.
So, The equation can you use to solve for 'a' would-be,
a/sin35° = 30/sin60°.
asin60° = 30sin35°.
(√3/2)a = 30×0.5735.
a = (30×0.5735)/0.866.
a = 17.205/0.866.
a = 19.87.
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PLZ HELP THANK YOU BRAINLIEST IF CORRECT select all that apply (look at the photo)
PLEASE HELP ILL GIVE 5* AND THANKS.
Answer:
The numbers in the sequence are perfect squares
next number is 9
Jacob and Sarah are saving money to go on a trip. They need at least $1850 in order
to go. Jacob mows lawns and Sarah walks dogs to raise money. Jacob charges $15
each time he mows a lawn and Sarah charges $10 each time she walks a dog. The
number of dog walks that Sarah has scheduled is no more than five times the
number of lawns Jacob has scheduled to mow. Sarah will walk at least 65 dogs.
Answer:
[tex]\textsf{Constraint 1}: \quad 15x+10y\geq 1850[/tex]
[tex]\textsf{Constraint 2}: \quad y \leq 5x[/tex]
[tex]\textsf{Constraint 3}: \quad y \geq 65[/tex]
Step-by-step explanation:
Inequality signs:
< Less than.≤ Less than or equal to.> More than.≥ More than or equal to.Given variables:
x = Number of lawns mowed.y = Number of dogs walked.Constraint 1Given information:
$15 = Charge for mowing a lawn.$10 = Charge for walking a dog.$1850 = Minimum amount needed for the trip.Therefore, the amount earned from mowing the lawns and walking dogs should be more than or equal to $1850:
[tex]\boxed{15x+10y\geq 1850}[/tex]
Constraint 2Given information:
The number of dog walks that Sarah has scheduled is no more than 5 times the number of lawns Jacob has scheduled to mow:Therefore, Sarah will walk less than or equal to 5 times the number of lawns mowed:
[tex]\boxed{y \leq 5x}[/tex]
Constraint 3Given information:
Sarah will walk at least 65 dogs.Therefore, Sarah will walk more than or equal to 65 dogs:
[tex]\boxed{y \geq 65}[/tex]
K
State A contains the largest state population of Native Americans. This population is three times the Native American
population of State B. If the total of these two populations is 376 thousand find the Native American population in
each of these two states.
The Native American population in state A and B is 282,000 and 94,000 respectively.
Here, we are given that State A's population of Native Americans is three times the Native American population of State B.
Let the Native American population in state B be x
Thus, the Native American population in state A will be 3x
Total Native American population in state A and B = 376,000
Thus, we can get the following equation-
x + 3x = 376,000
4x = 376,000
x = 376,000/ 4
x = 94,000
⇒ 3x = 3 × 94,000
3x = 282,000
Thus, the Native American population in state A and B is 282,000 and 94,000 respectively.
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3kg 250g: 5kg pls tell me the answer I have exams
Answer:
Well if it made sense..
Step-by-step explanation:
please help me with my homework :)
In a group there are 10 owners and 20 workers. four workers are chosen what is the probability of choosing four worker sequentially
Answer:
15
Step-by-step explanation:
15
First year students in rolled at a college were asked whether they play video games. The responses, classified by whether the students were enrolled in the school of sciences the school of arts are shown in the table.
20 POINTS AND BRAINLIEST IF YOU GET ALL OF THIS RIGHT
Solve for x.
5x - 4 = -3x + 12
x = 2
x = 6
x = -4
Solve for x.
5x - = 4x +
x = 5/9
x = -1/3
x = 5/18
Solve for x.
12x - 17 = 5x + 19
x = 2/7
x = 7/5
x = 36/7
Solve for x.
7x + 17 = 3x + 21
x = 1
x = 3/4
x =4/3
Solve the system of equations by substitution.
3x - 4y = 13
5x + 4y = 11
The solution of the system is x = and y=
(Type integers or simplified fractions.)
Answer:
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=3,\:y=-1[/tex]
Step-by-step explanation:
[tex]3x - 4y = 13[/tex]
[tex]5x + 4y = 11[/tex]
isolate x for 3x-4y=13
[tex]\mathrm{Subsititute\:}x=\frac{13+4y}{3}[/tex]
[tex]\begin{bmatrix}5\cdot \frac{13+4y}{3}+4y=11\end{bmatrix}[/tex]
[tex]\frac{65+32y}{3}=11[/tex]
now isolate y for [tex]\frac{65+32y}{3}=11[/tex]
[tex]\frac{65+32y}{3}=11[/tex]
[tex]65+32y=33[/tex]
[tex]32y=-32[/tex]
Divide both sides by 32
[tex]\frac{32y}{32}=\frac{-32}{32}[/tex]
[tex]y=-1[/tex]
[tex]\mathrm{For\:}x=\frac{13+4y}{3}[/tex]
[tex]\mathrm{Subsititute\:}y=-1[/tex]
[tex]x=\frac{13+4\left(-1\right)}{3}[/tex]
[tex]=\frac{13-4\cdot \:1}{3}[/tex]
[tex]=\frac{9}{3}[/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{9}{3}=3[/tex]
[tex]=3[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=3,\:y=-1[/tex]
The radius of a semicircle is 5 yards. What is the semicircle's diameter?
r5 yd
yards
Submit
Answer:
Diameter: 10 Yards
Step-by-step explanation:
d = 2r
d = 2 ( 5 )
d = 10
-0.9 -1.2 which one is greatest
Answer:
-0.9
Step-by-step explanation:
it is closer to 0
state which theorem you can use to show that the quadrilateral is a parallelogram.
Answer:
Actually, there are two. They are the Parallelogram Opposite Sides Theorem and the Parallelogram Opposite Angles Theorem.
Step-by-step explanation:
POST means that if opposite sides of a quadrilateral are the same, it's a parallelogram.
POAT means that if opposite sides of a quadrilateral are the same, it's a parallelogram.
A quadrilateral has to meet both of these theorems to be a parallelogram.
help i’ll give brainiest thing !
Answer:
Yes, it is enough
[tex]y = -3x + 16[/tex]
Step-by-step explanation:
Given
[tex]Point = (6, -2)[/tex]
[tex]m = -3[/tex]
Required
Is the given info enough to find the equation?
Yes, it is enough and the proof is as follows:
And equation is solved using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (6,-2)[/tex]
[tex]m = -3[/tex]
Substitute these values in [tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - (-2) = -3(x - 6)[/tex]
[tex]y +2 = -3(x - 6)[/tex]
Open bracket
[tex]y +2 = -3x + 18[/tex]
Make y the subject
[tex]y = -3x + 18-2[/tex]
[tex]y = -3x + 16[/tex]
From the above, one can see that the given info is enough
Two expressions are shown below.
Expression 1: 0.25x - 12
Expression 2: 18- 0.55x
For which value of x will the two expressions have the same value?
A
-100
B
-20
С C
7.5
37.5
Answer:
0.25x -12= 18- 0.55x (subtract 0.25x from both sides)
-12= 18 -0.80x (subtract 18 from both sides)
-30= -0.80x (divide each side by -0.80)
x= 37.5 (this is your answer)
The value of x in which the two expressions have the same value is 37.5
Here,
Given that;
Two expressions are,
Expression 1 : 0.25x - 12
Expression 2: 18- 0.55x
We have to find the value of x.
What is Mathematical expression?
A sentence with a minimum of two numbers or variables and at least one math operation is present, is called Mathematical expression.
Now,
The value of x will be find after equating both expressions as;
0.25x - 12 = 18 - 0.55x
Subtract 0.25x from both sides, we get;
- 12 = 18 - 0.80x
Subtract 18 from both side, we get;
- 30 = - 0.80x
Divide each side by -0.80, we get;
x= 37.5
Hence, The value of x in which the two expressions have the same value is 37.5
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A 330-lb gorilla climbs a tree to a height of 21 ft. Find the work done if the gorilla reaches that height in the following times.
(a)
10 seconds
W =
(b)
W =
5 seconds
Need Help?
ft-lb
ft-lb
Read It
Watch It
According to the solving the work done if the gorilla reaches that height:
= 8400 ft lb.
What is meant by "work done"?The work performed by a force is defined as the sum of the displacement and or the component of both the applied force of both the object in the displacement direction. Work is accomplished when we push a block with a certain amount of force, "F," which causes the body to move more quickly. W = F stands for "work done."
The purpose of the work?Anytime a force transports something over a distance, work is performed. By multiplying the force by both the distance moved inside this direction of the force, you may determine the amount of energy transferred or work accomplished.
According to the given data:The effort put in by a 350-pound gorilla climbing a 24 foot staircase can be computed as:
(a) t = 10 sec
WF = (350 lb) (24 ft)
= 8400 ft lb (answer)
(b) t = 5 sec
WF = (350 lb) (24 ft)
= 8400 ft lb
work done does not depends on time.
According to the solving the work done if the gorilla reaches that height:
= 8400 ft lb.
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___% of $6,000 = $5,400
Pls tell me how to do this
Answer:
45
Step-by-step explanation:
jffjgnjfgnjgjfgjs
Answer:
90%
Step-by-step explanation:
1. We assume, that the number 5400 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 5400, so we can write it down as 100%=5400.
4. We know, that x% equals 6000 of the output value, so we can write it down as x%=6000.
5. Now we have two simple equations:
1) 100%=5400
2) x%=6000
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=5400/6000
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 6000 is what percent of 5400