Answers
Since DE is parallel to AC the ratio between the sides of the triangles should be the same.
From the small triangle we notice that 4:5; from the big triangle we notice that 10:AC, since this ratios have to be equatl this means that:
\(\begin{gathered} \frac{4}{5}=\frac{10}{AC} \\ AC=\frac{10}{\frac{4}{5}}=\frac{50}{4}=\frac{25}{2}=12.5 \end{gathered}\)Therefore, AC is 12.5 long.
To find AD we use the same principle. In the small triangle we have that 4:2; for the big triangle we have that 10:(2+AD). Then:
\(\begin{gathered} \frac{4}{2}=\frac{10}{2+AD} \\ 2=\frac{10}{2+AD} \\ 2(2+AD)=10 \\ 2+AD=\frac{10}{2} \\ 2+AD=5 \\ AD=5-2 \\ AD=3 \end{gathered}\)Therefore, AD is 3 long.
Related Questions
Calculate and plot the response of an undamped system to a step function with a finite rise time of t1 for the case m = 1 kg, k = 1 N/m, t1 = 4 s, and F0 = 20 N. This function is described by f(t) = Fosint = f(t) F. Plot of a pulse input of the form f(0) = Fo sin t. 0 TT 211Hint: You need to use the trigonometric relation sina sinB = [cos(a – B) – cos(a + 3)) = to solve the integration.
Answers
The response of the system to the step function with a finite rise time of t1 can be calculated and plotted using the equation F(t) = F0 sin(1/t1)t and the graph of f(t) = F0 sin t.
The response of an undamped system to a step function with a finite rise time of t1 can be calculated using the equation F(t) = F0 sin(1/t1)t. In this equation, F0 is the magnitude of the force, m is the mass of the system, k is the spring constant, and t1 is the rise time of the step function.
To calculate the response of the system, we need to solve the integral of F(t) from 0 to t. This can be done using the trigonometric relation sina sinB = [cos(a – B) – cos(a + B)]. By substituting F0, m, k and t1 into the equation, we get:
F(t) = F0 sin(1/t1)t = 20 sin(1/4)t = 5[cos(t/4 – 1/4) – cos(t/4 + 1/4)]
To plot the response of the system, we can use a graph of the form f(t) = F0 sin t. By substituting the calculated values of F(t) into the graph, we can see the response of the system to the step function with a finite rise time of t1.
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Anita incorrectly wrote z =w-18 to describe the pattern in the table. Choose the best description of Anitas error
Answers
Boxes of Valentine’s Day chocolate truffles come in a variety of sizes. The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches. If each truffle in this box has a volume of 2 cubic inches, how many truffles are included in the box?
A.
Answers
Answer:
135.
Step-by-step explanation:
Volume of the box = 15*12*1.5
= 270 in^3.
So the number of truffles = 270 / 2
= 135.
The number of truffles in the box is 135.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The dimensions of the box = 15 inches x 12 inches x 1.5 inches.
The dimension of each truffle = 2 cubic inches
The number of truffles included in the box.
= (15 x 12 x 1.5) / 2
= 270/2
= 135
Thus,
The number of truffles in the box is 135.
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Last year the Debate club had 17 members. This year there are 33 members in the club. Estimate the percent change in the number of club members.
Answers
We can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.
What is the percent change?
Percentage change is a way to describe the difference between an old value and a new value, expressed as a ratio and then multiplied by 100.
To estimate the percent change in the number of club members, we can use the percent change formula:
percent change = (new value - old value) / old value x 100%
where the "old value" is the number of club members last year and the "new value" is the number of club members this year.
Plugging in the numbers we have:
percent change = (33 - 17) / 17 x 100%
percent change = 16 / 17 x 100%
percent change ≈ 94.1%
Therefore, we can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.
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choose number between 49-95 that is a multiple of 2,4, and 5
Answers
Help Pleasee! On the track and field team, three eights
of the members do the hurdles.
Of the members who do the hurdles, four fifths also do the long jump.
If there are 40 members on the track team, how many do both the hurdles and the long jump?
There are ________ members that do both.
Answers
Answer:
12
Step-by-step explanation:
3/8 of 40 * 4/5
15 * 4/5
12
Answer:
12
Step-by-step explanation:
A 40 litres pail of paint costs $34. How much does 1 litre of paint cost?
Answers
Answer:
85 cents
Step-by-step explanation:
34÷40= .85
adding characters to get to 20
Triangle QRS is dilated according to the rule DO,2 (x,y). On a coordinate plane, (0, 0) is the center of dilation. Triangle Q R S has points (negative 3, 3), (2, 4), and (negative 1, 1). What is true about the image ΔQ'R'S'? Select three options. Which statements are true? DO,2 (x,y) = (2x, 2y) Side Q'S' lies on a line with a slope of -1. QR is longer than Q'R'. The vertices of the image are closer to the origin than those of the pre-image. The distance from Q' to the origin is twice the distance from Q to the origin.
Answers
Answer:
Options A, B and E are correct
Step-by-step explanation:
From the information given above, we would draw a dilation that produces an image that is the same shape as the original image, but has a different size.
The scale factor is 2
QRS → Q'R'S' = (x,y) → 2(x,y)
The coordinates of ∆QRS
Q (-3, 3)
R (2, 4)
S (-1, 1)
To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In order words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.
2 (x,y) = (2x, 2y)
The coordinates of ∆Q'R'S' becomes:
Q' (-6, 6)
R' (4, 8)
S' (-2, 2)
To determine the statements that are true about the image ΔQ'R'S,
we would graph the coordinates of the two triangles.
Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.
See attached the diagram for better explanation.
Let's check out each options and compare it with diagram we obtained:
a) DO, 2 (x,y) = (2x, 2y)
A dilation about the origin with a scale factor 2 is described using the above notation.
Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)
R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)
S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)
This option is correct
b) Side Q'S' lies on a line with a slope of -1
Q' (-6, 6)
S' (-2, 2)
coordinate (x, y)
Slope = m = (change in y)/(change in x)
m = (6-2)/[-6-(-2)]
= 4/(-6+2) = 4/-4
m = -1
This option is correct
c) QR is longer than Q'R'
Length of QR (-3 to 2) = 5
Length of Q'R' (-6 to 4) = 10
QR is not longer than Q'R'
This option is false
d) The vertices of the image are closer to the origin than those of the pre-image
The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. In a transformation, the final figure is referred to as the image. The original figure is referred to as the preimage.
From the diagram, the vertices of the preimage (original image) are closer to the origin than those of the dilation image.
This option is false
e) The distance from Q' to the origin is twice the distance from Q to the origin.
The distance from Q' to the origin (6 to 0) = 6
The distance from Q to the origin (3 to 0) = 3
The distance from Q' to the origin = 2(the distance from Q to the origin)
This option is correct
Answer:
A,B and E is correct
Step-by-step explanation:
Help please I don’t get
Answers
Answer:
answer: 5^36
Step-by-step explanation:
(5^9)^4
5^9x4
5^36
answer: 5^36
alternative form 1.45519x 10^25
Answer:
is 5^36
Exact Form:
14551915228366900000000000
Decimal Form:
1.45519152⋅10^\({25}\)
The bottom row of the pile has 25 apples and the top row has 9. Each row has 4 less apples than the row below. How many apples are in the pile?
Answers
There are 90 apples in the pile and the row has 4 fewer apples than the row below.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The sum of an arithmetic sequence is the sum of the first n terms of the sequence as
Sₙ = n/2(2a+(n−1)d)
In arithmetic, here a₁ is the first term and sequence d represents the common difference.
Sum of the apples = 25 + 21 + 17 + 14 + 13 + 9
This series is in AP where a = 25 , d = - 4 and n = 6
As per the given data, the sum of apples would be as:
S₆ = 6/2(2×25+(6-1)×-4)
S₆ = 3(50 + 5×-4)
S₆ = 3(50 - 20)
S₆ = 3(30)
S₆ = 90
Therefore, there are 90 apples in the pile.
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A cylindrical steel pipe with a liquid is 21 cm long with radius 0, 4 cm and its hollow part is of radius 0, 1 cm. What is the volume of liquid, in litres, in the pipe? A. 9000 litres B. 9400 litres C. 9900 litres D. 10100 litres
Answers
Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.
To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.
Given:
Length of the cylindrical steel pipe (hollow part) = 21 cm
Radius of the solid cylinder = 0.4 cm
Radius of the hollow cylinder = 0.1 cm
First, let's calculate the volume of the solid cylinder (hollow part):
V1 = π × \(r1^2\) × h
V1 = π × \((0.4 cm)^2\) × 21 cm
Next, let's calculate the volume of the hollow cylinder:
V2 = π × \(r2^2\) × h
V2 = π × \((0.1 cm)^2\) × 21 cm
Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:
Volume of liquid = V1 - V2
Let's calculate these values:
V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³
V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³
Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³
To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:
Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L
Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.
Therefore, none of the options A, B, C, or D provided is the correct answer.
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The slope is negative.
True
False
Answers
Answer: true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The slope provided on the screen shows the function of the graph going in a downward direction from left to right, which is how any slope is negative.
Mrs. Cowley purchases $32,000 worth of stock on her broker's advice and pays her broker a 0.75% broker fee. She is forced to sell it when it falls to $25,100 two years later, and uses a discount broker who charges $17 per trade. Compute her net loss after the broker fees are taken out.
Answers
Answer: $6,320.25
Step-by-step explanation:
Mrs. Cowley's broker fee is calculated by multiplying the purchase price by the broker fee percentage: $32,000 x 0.0075 = $240. Her total cost for the purchase is then $32,000 + $240 = $32,240. When she sells the stock for $25,100, she incurs another fee of $17 for using the discount broker. To calculate her net loss, we subtract her total cost from her selling price and subtract the two broker fees: $25,100 - $32,240 - $17 - $17 = -$6,320.25, which is rounded to $6,320.25 as a net loss.
Find the symmetric point of the given point (-2,-2) on a parabola with vertex (-3, 1).
Answers
The symmetric point on parabola is x = -3
What is symmetric point in parabola ?
The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.
The vertex form of a parabola's (or a quadratic) equations is given by the following formula:
y = a(x - h)² + k , where (h, k) is the vertex and the axis of symmetry is given by the line x = h.
Where, vertex is given (h, k) = (-3, 1)
so the axis of symmetry is,
=> x = -3
Therefore, The symmetric point on parabola is x = -3
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what are three ratios that are equivalent to 8 5
Answers
Answer:
15:24, 20:32 and 40:64.
Step-by-step explanation:
hope this helps
Answer:
The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and lastly 16:10 because they both have a 2 as factors.
Step-by-step explanation:
The ratios that work is 15:24 because 5 x 3= 15, 24 x 3 = 24 as they both have a 3 as factors. There's also 20:32 as they both have a 4 as factors and lastly 16:10 because they both have a 2 as factors.
Help with this problem!!!!
X/2-3=9
Answers
Answer:
pretty sure it's
2
−
3
=
9
\frac{X}{2}-3=9
2X−3=9
2
−
3
+
3
=
9
+
3
Verify the Identity!!
Answers
Answer:
Check the proof below
Step-by-step explanation:
try to verify from RHS to LHS
(Tan a + tan b) / (tan a - tan b)
= (sin a / cos a + sin b /cos b) / ( sin a/ cos a - sin b/ cos b)
= (sin a cos b + cos a sin b)/ (sin a cos b - cos a sin b)
= sin (a+b) / sin (a-b)
Fyi
sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB
underneath barbed wire. She will have to crawl underneath barbed wire between the next two checkpoints (E and F) as well.
What are the coordinates of Checkpoints E and F if EF⎯⎯⎯⎯⎯⎯⎯⎯ is located at CD⎯⎯⎯⎯⎯⎯⎯⎯’ location in a 180∘ rotation of the course?
Select two answers: one for Checkpoint E and one for Checkpoint F.
F(3,2)
E(4,−5)
F(3,−2)
E(−4,5)
E(−4,−5)
F(−3,2)
Answers
Answer:
did you get any of them
Step-by-step explanation:
The area of rectangle is 105cm².If it length is 21 cm,what is its length and perimeter.
Answers
Answer:
length of other side is 5cm and the perimeter is 52
Step-by-step explanation:
The area is side x times side y.
Knowing that the area A is 105cm2 and side x is 21cm
A= x*y
105cm2= 21 y /21
Arranging for y we get
y= 105/21
y= 5 cm
The perimeter is all sides added up
P= 21+21+5+5=52cm
Answer:
length 5cm and perimeter 52 cm
Step-by-step explanation:
length=area/breadth
=105/21
=5 cm
perimeter=2(length+breadth)
=2(5+21)
=52 cm
A number cube is rolled. Event A is rolling an odd number, and event B is rolling a factor of 12. What is P(AU B)?
Answers
Explanation:
A = set of odd numbers = {1,3,5}
B = set of factors of 12 = {1,2,3,4,6}
A U B = union of set A and set B
A U B = {1,3,5} union {1,2,3,4,6}
A U B = {1,3,5, 1,2,3,4,6}
A U B = {1,2,3,4,5,6}
The set union operation combines two sets into one bigger set. Duplicates are tossed out.
There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.
Therefore, the probability event A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.
Side notes:
A U B can be read out as "event A or event B"; so P(A U B) is "the probability event A happens or B happens or both".A intersect B = {1,3} = values that are in both set A and set B at the same time. These are both odd and a factor of 12.Question 2
No calculations are necessary to answer this question.
3/01
3/02
$1.7420 $1.7360
Date
July GBP Futures
Contract Price
O long; long
Based on the closing prices of July GBP Futures Contract over the 3-day period in March 20XX as shown above, you shou
position on 3/01 and a position on 3/02.
O long; short
O short; short
3/03
short; long
$1.7390
Answers
The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.
What is the slope of the line shown below?
(1,6) (-5,-7)
A. 13/6
B. -13/6
C. -6/13
D. 6/13
Answers
\((\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{1}}} \implies \cfrac{ -13 }{ -6 } \implies \cfrac{13 }{ 6 }\)
can I get help PLEEEEEEEEEEEEEASE
Answers
Answer:
what do you need help with? i can try to help you
Step-by-step explanation:
Answer:
Help with what, where is the ?
i really need help, can someone please help me with this math question
Answers
The functions for this problem are defined as follows:
(t + s)(x) = x³ + 5x².(ts)(x) = \(5x^5\)(t - s)(-2) = -28.How to obtain the functions?The functions for this problem are given as follows:
s(x) = 5x².t(x) = x³.The addition and subtraction functions for this problem are given as follows:
(t + s)(x) = x³ + 5x².(t - s)(x) = x³ - 5x².At x = -2, the numeric value of the subtraction function is given as follows:
(t - s)(-2) = -2³ - 5(-2)²
(t - s)(-2) = -28.
The product function for this problem is given as follows:
(ts)(x) = \(5x^5\)
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Complete the table representing a linear function
Answers
Answer:
10 ; 10
Step-by-step explanation:
( 1 , 0 )
( 5 , 40 )
m = \(\frac{40-0}{5-1}\) = 10
y = 10x - 10
( 2 , 10 )
( 10 , 90 )
Which of the following are solutions to the system of inequalities y<−x+5 and y≥3x+1?
A)
(1,0)
cross out
B)
(−2,2)
cross out
C)
(1,6)
cross out
D)
(0,1)
cross out
E)
(1,4)
cross out
F)
(−2,7)
Answers
From the graph attached below, the solution to the system of linear inequalities are (1, 4)
What is the solution to the system of linear inequalities?A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.
In the problem given;
y < - x + 5 ...eq(i)
y ≥ 3x + 1 ...eq(ii)
To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.
From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E
Kindly find attached graph below
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Heeeelp please, Can be zero or not?
with all steps and explanay.
Answers
The value of integral is 3.
Let's evaluate the integral over the positive half of the interval:
∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx
Let u = 4 + 3sin(x), then du = 3cos(x) dx.
Substituting these expressions into the integral, we have:
∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du
Using the power rule of integration, the integral becomes:
∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]
Evaluating the definite integral at the limits of integration:
(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))
(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0
So, the value of integral is
= 3-0
= 3
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Answer:
\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)
Step-by-step explanation:
First, compute the indefinite integral:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)
To evaluate the indefinite integral, use the method of substitution.
\(\textsf{Let} \;\;u = 4 + 3 \sin x\)
Find du/dx and rewrite it so that dx is on its own:
\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)
Rewrite the original integral in terms of u and du, and evaluate:
\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)
Substitute back u = 4 + 3 sin x:
\(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
Therefore:
\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)
To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.
Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.
\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)
Therefore, the curve of the function is:
Below the x-axis between -π and -π/2.Above the x-axis between -π/2 and π/2.Below the x-axis between π/2 and π.So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.
Integrate the function between -π and -π/2.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)
Integrate the function between -π/2 and π/2:
\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)
Integrate the function between π/2 and π.
As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:
\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)
To evaluate the definite integral, sum A₁, A₂ and A₃:
\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)
Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:
\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)
Therefore, the given expression cannot be zero.
Use the following picture to answer the following
questions.
concave or convex?
name of the polygon
regular or irregular
Answers
There is no picture provided.
if you could fly and every hour u loose 30 feathers in 14 days how many feathers did you loose?
Answers
The total number of feathers lost in 14 days if you lose 30 feathers every hour is 10,080 feathers.
How many feathers will you loose?Feathers lost every hour = 30 feathers
How many feathers is lost in 14 days?
1 day = 24 hours
14 days = 24 × 14
= 336 hours
Total number of feathers lost in 14 days = Feathers lost every hour × number of hours in 14 days
= 30 × 336
= 10,080 feathers
Therefore, the total number of feathers lost in 14 days is 10,080 feathers
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Match the coordinate pair with the point shown in the image
Answers
Answer:
A(-6,1) I(-6,-2) N(-3,4) H(5,-2) P(2,2) M(0,-4) O(-6,-4) E(-3,-3)
L(-4,0)
Step-by-step explanation:
Answer:
A = (-6,1)
B = (-1, 3)
C = (0,0)
D = (6,3)
E = (-3,-3)
F = (3,0)
G = (2, -3)
H = (5, -2)
I = (-6, -2)
J = (-5, 3)
K = (2, 4)
L = (-4, 0)
M = (0,-4)
N = (3, 4)
O = (6, -4)
P = (2, 2)
Step-by-step explanation:
For coordinates on a graph, the form is: (x,y) where x left-to-right position and y is the up-and-down position. For x, the left direction is negative and the right direction is positive. For y, down is negative and up is positive. For the coordinates start in the center (where C is) and count how many boxes in the x direction, and then the boxes in the y direction and record your answer.