Answer:
the answer is number 9 m1
Determine the equation of the circle graphed below.
-12-11-10-9-8-7 -5-4-3-2
11098765432-
hadis
-2
-9
-10
-11
123456
8 9 10 11 12
(8,-2)
Answer:
(x - 3)² + (y + 4)² = 29
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
we have the coordinates of the centre but require to find the radius r
the radius is the distance from the centre to a point on the circle.
using the distance formula to find r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (3, - 4 ) centre and (x₂, y₂ ) = (8, - 2) point on circle
r = [tex]\sqrt{(8-3)^2+(-2-(-4))^2}[/tex]
= [tex]\sqrt{5^2+(-2+4)^2}[/tex]
= [tex]\sqrt{25+2^2}[/tex]
= [tex]\sqrt{25+4}[/tex]
= [tex]\sqrt{29}[/tex]
then equation with centre (3, - 4 ) and r = [tex]\sqrt{29}[/tex] , is
(x - 3)² + (y - (- 4) )² = ([tex]\sqrt{29}[/tex] )² , that is
(x - 3)² + (y + 4)² = 29
100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
The equation is verified, and we have shown that E_0 = cos⁴θ is equivalent to E_0 = E_0 (1/2 + cos2θ/2)².
We have,
To verify the equation
E_θ = E_0 cos^4θ = E_0 (1/2 + cos2θ/2)², we can expand the right-hand side and simplify it.
Starting with the right-hand side of the equation:
E_0 (1/2 + cos2θ/2)²
Expanding the square using the binomial expansion:
E_0 [(1/2)² + 2(1/2)(cos2θ/2) + (cos2θ/2)²]
Simplifying:
E_0 [1/4 + cos2θ + (cos2θ)²/4]
Combining the terms:
E_0 [1/4 + 4cos²θ/4 + (cos²θ)²/4]
Simplifying further:
E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4]
Combining the terms again:
E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4] = E_0 [1/4 + 4cos²θ/4 + cos⁴θ/4]
Simplifying the expression yields:
E_0 cos⁴θ = E_0 cos⁴θ
Therefore,
The equation is verified, and we have shown that E_0 = cos⁴θ is equivalent to E_0 = E_0 (1/2 + cos2θ/2)².
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Use the conversion factor 1 gallon=3.785 to convert 4 liters into gallons
Using the conversion factor, we can convert the liters into the number of gallons of 1. 057 gallons.
How to convert the liters ?A conversion factor is a mathematical ratio that is used to convert one unit of measurement to another. It is a multiplier or divisor that relates two different units of measurement for the same quantity.
To convert 4 liters into gallons using the conversion factor 1 gallon = 3.785 liters, you divide the given value (in liters) by the conversion factor.
This means that the number of gallons in 4 liters would be:
= 4 liters ÷ 3. 785 liters/gallon
= 1. 057 gallons
Therefore, 4 liters is approximately equal to 1. 057 gallons.
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Giselle works as a carpenter and as a blacksmith.
She earns
$
20
$20dollar sign, 20 per hour as a carpenter and
$
25
$25dollar sign, 25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of
30
3030 hours, and earned a total of
$
690
$690dollar sign, 690.
How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.
Answer:
Giselle worked as a carpenter for 12 hours and as a blacksmith for 18 hours last week
Step-by-step explanation:
Let's assume that Giselle worked as a carpenter for x hours and as a blacksmith for y hours last week.
We know that she earns $20 per hour as a carpenter and $25 per hour as a blacksmith, and that she worked a total of 30 hours, so we can write two equations based on this information:
x + y = 30 (total hours worked)
20x + 25y = 690 (total earnings)
To solve for x and y, we can use substitution or elimination. Let's use substitution.
From the first equation, we can solve for x in terms of y:
x = 30 - y
Substitute this expression for x in the second equation:
20(30 - y) + 25y = 690
Simplify and solve for y:
600 - 20y + 25y = 690
5y = 90
y = 18
So Giselle worked as a blacksmith for 18 hours last week.
To find how long she worked as a carpenter, we can substitute y = 18 into the first equation and solve for x:
x + 18 = 30
x = 12
Therefore, Giselle worked as a carpenter for 12 hours last week.
prove that
(z^a/z^b)^c * (z^b/z^c)^a * (z^c/z^a)^b =1
Step-by-step explanation:
remember, when we multiply the same base, we add the exponents, when we divide the same base we subtract the exponents.
when we have exponent of exponent, we multiply the exponents.
so,
the expression is
(z^ac / z^bc) × (z^ab / z^ac) × (z^bc / z^ab) = 1
we have in there the commutative and associative properties of multiplication : the sequence of operands do not matter at all.
and therefore we have in there the terms :
z^ac / z^ac
z^bc / z^bc
z^ab / z^ab
all three are 1
and so the main expression is
1 × 1 × 1 = 1
which is true, of course, and therefore the original equation is true.
In Algebra, an expression could have all of the four arithmetic operations, which would include multiplying, dividing, adding and subtracting.
(a) True
(b) False
Answer:
It is true that in algebraic expressions there could have all four arithmetic operations
Identify the center and radius of a circle with equation (x-5)^2+(y+3)^2=25
The center and radius of the circle is (5, -3), and 5 respectively.
What is the center and radius of the circle?The standard form equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Given the equation of the circle in the question:
( x - 5 )² + ( y + 3 )² = 25
To identify the center and the radius.
Comparing this equation ( x - 5 )² + ( y + 3 )² = 25 to the standard form of a circle equation, which is (x - h)² + (y - k)² = r², we can easily identify the center and radius of the circle.
( x - 5 )² + ( y + 3 )²
(x - h)² + (y - k)² = r²
The center of the circle is given by the values (h, k), which correspond to the opposite signs of the terms inside the parentheses.
In this case, the center of the circle is (5, -3), as we have (x - 5)² and (y + 3)².
The radius of the circle is the square root of the value on the right side of the equation.
In this case, the radius is √25, which simplifies to 5.
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pleaseeeeee helppppppp
The statements that complete the function transformations are left, up, stretch and stretch
Completing the function transformationsFrom the question, we have the following parameters that can be used in our computation:
f(x) = (x + 94)²
Also, we have
f(x) = x²
This implies that f(x) = (x + 94)² is obtained by shifting f(x) = x² left by 94 units
Next, we have
f(x) = x² + 94
This implies that f(x) = x² + 94² is obtained by shifting f(x) = x² up by 94 units
Next, we have
f(x) = 94√x from f(x) = √x
This implies that f(x) = 94√x can be obtained from vertically stretching f(x) = √x by a factor of 94
Also, the graph of f(x) = √94x can be obtained from horizontally stretching f(x) = √x by a factor of 1/94
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NO LINKS!!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Sines
1. A = 29°, C = 63°, c = 24
2. A = 72°, B= 35°, c = 21
Answer:
1) B = 88°, a = 13.1, b = 26.9
2) C = 73°, a = 20.9, b = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Question 1Given values:
A = 29°C = 63°c = 24As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies B=180^{\circ}-A-C[/tex]
[tex]\implies B=180^{\circ}-29^{\circ}-63^{\circ}[/tex]
[tex]\implies B=88^{\circ}[/tex]
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
Solve for a:
[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
[tex]\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies a=13.0876493...[/tex]
[tex]\implies a=13.1[/tex]
Solve for b:
[tex]\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
[tex]\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies b=26.9194211...[/tex]
[tex]\implies b=26.9[/tex]
[tex]\hrulefill[/tex]
Question 2Given values:
A = 72°B = 35°c = 21As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies C=180^{\circ}-A-B[/tex]
[tex]\implies C=180^{\circ}-72^{\circ}-35^{\circ}[/tex]
[tex]\implies C=73^{\circ}[/tex]
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
Solve for a:
[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
[tex]\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}[/tex]
[tex]\implies a=20.8847511...[/tex]
[tex]\implies a=20.9[/tex]
Solve for b:
[tex]\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
[tex]\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}[/tex]
[tex]\implies b=12.5954671...[/tex]
[tex]\implies b=12.6[/tex]
Find the current balance for Jeff’s savings account if he had a balance of $396.80, made three $15 deposits, withdrew $125, and earned $1.04 interest.
The current balance for Jeff's savings account is $317.84.
To find the current balance for Jeff's savings account, we need to calculate the net effect of the deposits, withdrawals, and interest on his initial balance.
Initial balance: $396.80
Deposits: 3 × $15 = $45
Withdrawals: $125
Interest: $1.04
Adding the deposits and interest to the initial balance:
$396.80 + $45 + $1.04 = $442.84
Then, subtracting the withdrawal:
$442.84 - $125 = $317.84
Therefore, the current balance for Jeff's savings account is $317.84.
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PLEASE HELP!!!!!!
it’s a division equation
Answer:
x+1
DOMAIN: x [tex]\neq[/tex] -5
Step-by-step explanation:
We can factor [tex]x^{2}[/tex]+6x+5 as (x+1)(x+5) since this expands to [tex]x^{2}[/tex]+5*x+1*x+5*1, which is [tex]x^{2}[/tex]+6x+5.
Now, we have:
[tex]\frac{(x+1)(x+5)}{(x+5)}[/tex]
We can cancel out x+5, because this expression is the same as (x+1)*[tex]\frac{x+5}{x+5}[/tex], which is (x+1).
HOWEVER, the denominator cannot be equal to zero because that will make the expression undefined (you can't divide by zero). So, since x+5[tex]\neq[/tex]0, x[tex]\neq[/tex]-5.
Elon sent a chain letter to his friends, asking them to forward the letter to more friends.
The relationship between the elapsed time,
�
tt, in days, since Elon sent the email, and the total number of people who receive the email,
�
(
�
)
P(t)P, left parenthesis, t, right parenthesis, is modeled by the following function:
P(t)=4⋅3t
Complete the following sentence about the daily rate of change in the number of people who receive the email.
Every day, the number of people who receive the email
by a factor of
.
Every day, the number of people who receive the email grows by a factor of 3.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.Based on the information provided above, an exponential function for the total number of people who received the email is given by;
[tex]P(t) = 4(3)^t[/tex]
By comparison, we have the following parameters;
Initial value, a = 4.
Growth rate, b = 3.
In conclusion, the number of people who receive the email from Elon every day grow by a factor of 3.
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What is the greatest common factor of 6, 34, and 2?
Answer: 2
Step-by-step explanation:
List the factors(numbers that multiply to make that number for each number
6: 1, 2, 3, 6
34: 1, 2, 16, 34
2: 1, 2
Whichever is the factor that is the greatest that they all have in common is your greatest common factor.
2
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The shape of the fence is a rhombus.
Option C is the correct answer.
We have,
To determine the shape of the fence with the given coordinates, we can analyze the properties of different quadrilaterals.
Square: All four sides are equal in length, and all angles are right angles.
Rectangle: Opposite sides are equal in length, and all angles are right angles.
Rhombus: All four sides are equal in length, but the angles are not necessarily right angles.
Trapezoid: At least one pair of opposite sides are parallel.
Let's analyze the given coordinates to determine the shape of the fence:
Side 1: Distance between (-16, 1) and (-6, 5) = √(((-6) - (-16))² + (5 - 1)²) = √(10² + 4²) = √(116)
Side 2: Distance between (-6, 5) and (4, 1) = √((4 - (-6))² + (1 - 5)²) = √(10² + (-4)²) = √(116)
Side 3: Distance between (4, 1) and (-6, -3) = √((-6 - 4)² + (-3 - 1)²) = √((-10)² + (-4)²) = √(116)
Side 4: Distance between (-6, -3) and (-16, 1) = √((-16 - (-6))² + (1 - (-3))²) = √((-10)² + 4²) = √(116)
We can see that all four sides of the fence have equal lengths, which means it is either a square, rectangle, or rhombus.
To further differentiate between these shapes, we need to consider the angles.
The angle between side 1 and side 2:
tan(angle) = (5 - 1)/(-6 - (-16)) = 4/10 = 0.4
angle ≈ 21.8°
The angle between side 2 and side 3:
tan(angle) = (1 - 5)/(4 - (-6)) = (-4)/10 = -0.4
angle ≈ -21.8°
The angle between side 3 and side 4:
tan(angle) = (-3 - 1)/(-6 - (-16)) = (-4)/10 = -0.4
angle ≈ -21.8°
The angle between side 4 and side 1:
tan(angle) = (1 - (-3))/(-16 - (-6)) = 4/10 = 0.4
angle ≈ 21.8°
All four angles are approximately 21.8° or -21.8°. This indicates that the fence is a rhombus since its sides are equal in length but its angles are not right angles.
Therefore,
The shape of the fence is a rhombus.
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Sarah is setting up a garden plot in the shape of a right triangle. One leg of the triangle will be 7 feet longer than the other and the hypotenuse will be 1 foot longer than the longest leg. Find the length of each side of the garden plot. As a part of your work, include a sketch with the sides labeled. Show your work algebraically and be sure to use proper units in your answer.
value of the sides of the triangle are given as follows;
shorter leg = 5
longer leg = 12
hypotenuse = 13
What is Pythagoras theorem?Pythagoras Theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
If the short leg = x
the longer length = x+7
the hypotenuse = x+7+1 = x+8
Using Pythagorean theorem
(x+8)² = x² + (x+7)²
x² +16x +64 = x²+ x² + 14x +49
collecting like terms
x²-2x²+16x -14x+64 -49= 0
-x² + 22x +15 = 0
x² -2x -15 = 0
x² -5x +3x -15 = 0
(x² -5x) (3x -15) = 0
x(x-5) +3(x-5)
(x+3)(x-5) = 0
x= -3 or +5
Since length is discreet we choose the positive answer
therefore x = 5
shorter leg = 5
longer leg = 5+7 = 12
hypotenuse = 5+7+1 = 13
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start time:9:55
End time:?
Elapsed time:27 minutes
Answer: 10:22
Step-by-step explanation:
9:55 + :05 = 10:00
10:00+ :22 = 10:22
An art class has 63 minutes of painting for every 54 minutes of instruction. What is the basic ratio of minutes of painting to minutes of instruction
The basic ratio of minutes of painting to minutes of instruction is 7 : 6
What is the basic ratio of minutes of painting to minutes of instructionFrom the question, we have the following parameters that can be used in our computation:
Painting = 63 minutes
Instruction = 54 minutes
The ratio can be represented as
Ratio = Painting : Instruction
When the given values are substituted in the above equation, we have the following equation
Painting : Instruction = 63 : 54
Simplify
Painting : Instruction = 21 : 18
Simplify
Painting : Instruction = 7 : 6
This ratio cannot be simplified
Hence, the solution is 7 : 6
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Graph by completing the square x2+8x+y2-10y-32=0
The circle equation x² + 8x + y² -10y - 32 = 0 can be graphed using (x + 4)² + (y - 5)² = 73
Graphing the circle equation by completing the squareFrom the question, we have the following parameters that can be used in our computation:
x² + 8x + y² -10y - 32 = 0
Add 32 to both sides of the equation
This gives
x² + 8x + y² -10y = 32
Group the terms in two's
So, we have
(x² + 8x) + (y² -10y) = 32
When we complete the square on each group, we have
(x + 4)² + (y - 5)² = 16 + 25 + 32
Evaluate the like terms
(x + 4)² + (y - 5)² = 73
Hence, the circle equation can be graphed using (x + 4)² + (y - 5)² = 73
See attachment for the graph
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Prove that
(secx+tanx)² =CSCx+1/CSC x-1
To prove that (secx+tanx)² = (cscx+1)/(cscx-1), we will start with the left-hand side (LHS) of the equation and simplify it step by step until it matches the right-hand side (RHS) of the equation.
LHS: (secx+tanx)²
Using the trigonometric identities secx = 1/cosx and tanx = sinx/cosx, we can rewrite the LHS as:
LHS: (1/cosx + sinx/cosx)²
Now, let's find a common denominator and simplify:
LHS: [(1+sinx)/cosx]²
Expanding the squared term, we get:
LHS: (1+sinx)² / cos²x
Next, we will simplify the denominator:
LHS: (1+sinx)² / (1 - sin²x)
Using the Pythagorean identity sin²x + cos²x = 1, we can replace 1 - sin²x with cos²x:
LHS: (1+sinx)² / cos²x
Now, let's simplify the numerator by expanding it:
LHS: (1+2sinx+sin²x) / cos²x
Next, we will simplify the denominator by using the reciprocal identity cos²x = 1/sin²x:
LHS: (1+2sinx+sin²x) / (1/sin²x)
Now, let's simplify further by multiplying the numerator and denominator by sin²x:
LHS: sin²x(1+2sinx+sin²x) / 1
Expanding the numerator, we get:
LHS: (sin²x + 2sin³x + sin⁴x) / 1
Now, let's simplify the numerator by factoring out sin²x:
LHS: sin²x(1 + 2sinx + sin²x) / 1
Using the fact that sin²x = 1 - cos²x, we can rewrite the numerator:
LHS: sin²x(1 + 2sinx + (1-cos²x)) / 1
Simplifying further, we get:
LHS: sin²x(2sinx + 2 - cos²x) / 1
Using the fact that cos²x = 1 - sin²x, we can rewrite the numerator again:
LHS: sin²x(2sinx + 2 - (1-sin²x)) / 1
Simplifying the numerator, we have:
LHS: sin²x(2sinx + 1 + sin²x) / 1
Now, let's simplify the numerator by expanding it:
LHS: (2sin³x + sin²x + sin²x) / 1
LHS: 2sin³x + 2sin²x / 1
Finally, combining like terms, we get:
LHS: 2sin²x(sin x + 1) / 1
Now, let's simplify the RHS of the equation and see if it matches the LHS:
RHS: (cscx+1) / (cscx-1)
Using the reciprocal identity cscx = 1/sinx, we can rewrite the RHS:
RHS: (1/sinx + 1) / (1/sinx - 1)
Multiplying the numerator and denominator by sinx to simplify, we get:
RHS: (1 + sinx) / (1 - sinx)
Now, we can see that the LHS and RHS are equal:
LHS: 2sin²x(sin x + 1) / 1
RHS: (1 + sinx) / (1 - sinx)
Therefore, we have proven that (secx+tanx)² = (cscx+1)/(cscx-1).
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Need an answer quick!!
What is the volume of the shape on the next page?
Answer:
6 in³
Step-by-step explanation:
volume = width X length X height
= 3 X 1 X 2
= 6 in³
The bottom part says how many student tickets where brought? Can anyone pls help me PLSS
255 number of adults and 355 number of students bought ticket.
Here, we have,
Let the number of adults bought tickets are x and the number of students that bought tickets is (x + 100).
Since it is given that 100 more students brought tickets than adults.
Now, each adult ticket costs $5 and each student's ticket costs $3.5 and the total collected value of tickets is $2517.5.
So, 5x + 3.5(x + 100) = 2517.5
⇒ 8.5x + 350 = 2517.5
⇒ 8.5x = 2167.5
⇒ x = 255
So, 255 number of adults and (255 + 100) = 355 number of students bought ticket. (Answer)
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Answer this and I'll get you Brainlest!
The total cost of the meal if the meal costs $50 is $60
How to calculate the total cost of the mealFrom the question, we have the following parameters that can be used in our computation:
Tip percent = 20%
From the question, we can use any value as the cost of the meal
So, we can use the following
Meal cost = $50
So, we have
Tip amount = Tip percent * Meal cost
This gives
Tip amount = 20% * 50
Tip amount = 10
Next, we have
Total meal cost = Tip amount + Meal cost
This gives
Total meal cost = 10 + 50
Evaluate
Total meal cost = 60
Hence, the total cost of the meal is $60
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BTS-2 has coordinates (-8,6) and the edge connecting vertices P and Q has the equation y = 4.
(b) Write down the coordinates of BTS-4.
a. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4.
b. The coordinates of BTS-4 are (−8,4).
How to explain the informationa. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4. A Voronoi cell is a region of space that is closer to a given point than any other point. In this case, the given point is BTS-4. The Voronoi diagram is a partitioning of the plane into Voronoi cells, one for each point.
b. The edge connecting vertices P and Q has the equation y=4, which means that it is a horizontal line that intersects the y-axis at 4. The coordinates of BTS-2 are (−8,6), which means that it is located 8 units to the left of the origin and 6 units above the origin. Therefore, BTS-4 must be located 8 units to the left of the origin and 4 units above the origin, which gives it the coordinates (−8,4).
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Help me with this and expiation pls
The radius of the cylinder, considering it's lateral surface area, is given as follows:
r = 31.5 cm.
How to obtain the lateral surface area of a cylinder?
The lateral surface area of a cylinder of radius r and height h is given by the equation presented as follows:
Sl = 2πrh.
The parameters for this problem are given as follows:
Sl = 693π, h = 11.
Hence the radius of the cylinder, considering it's lateral surface area, is given as follows:
r = Sl/2πh
r = 693/22 (simplifying π in the numerator and denominator)
r = 31.5 cm.
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Question one
Let F be a Boolean function defined by the following Boolean expression:
F = (¬A ∧ ¬B ∧ ¬C ∧ D) ∨ (¬A ∧ B ∧ C ∧ D) ∨ (A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ ¬B ∧ C ∧ D) ∨ (A ∧ ¬B ∧ ¬C ∧ ¬D)
Where A, B, C, and D are Boolean variables.
a) Construct a truth table for F.
b) Find the minimal sum-of-products form of F using Quine-McCluskey method.
c) Using Boolean algebra, simplify the Boolean expression of F and state the simplified Boolean expression in terms of the three variables A, B, and C.
Answer:
a) The truth table for F is as follows:
A B C D F
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 0
0 1 0 1 1
0 1 1 0 1
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 1
1 0 1 1 0
1 1 0 0 1
1 1 0 1 0
1 1 1 0 0
1 1 1 1 1
b) Using the Quine-McCluskey method, we can find the minimal sum-of-products form of F:
F = ¬A ∧ ¬B ∧ D ∨ ¬A ∧ C ∧ D ∨ A ∧ B ∧ ¬C ∧ D ∨ A ∧ ¬B ∧ C ∧ D
c) Using Boolean algebra, we can simplify the Boolean expression of F as follows:
F = (¬A ∧ ¬B ∧ D) ∨ (¬A ∧ C ∧ D) ∨ (A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ ¬B ∧ C ∧ D)
= (¬A ∧ (¬B ∧ D ∨ C ∧ D)) ∨ (A ∧ (B ∧ ¬C ∧ D ∨ ¬B ∧ C ∧ D))
= (¬A ∧ (¬B ∨ C) ∧ D) ∨ (A ∧ ((B ∧ ¬C) ∨ (¬B ∧ C)) ∧ D)
= (¬A ∧ ¬B ∧ C ∧ D) ∨ (¬A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ B ∧ C ∧ D) ∨ (A ∧ ¬B ∧ ¬C ∧ D)
Therefore, the simplified Boolean expression of F in terms of the three variables A, B, and C is:
F = (¬A ∧ ¬B ∧ C ∧ D) ∨ (¬A ∧ B ∧ ¬C ∧ D) ∨ (A ∧ B ∧ C ∧ D) ∨ (A ∧ ¬B ∧ ¬C ∧ D)
Step-by-step explanation:
(HELP ME BRAINLIEST OF THE BRAINLESTS!!!!!!)
A 1. Some square tiles measure 3 1/2 inches on each side. Seven Tiles are placed in a row. How long is the row of tiles?
The row would be _____ inches long
B 2. Suppose that 10 tiles like those problem 1 were placed in a row. How long would that row of tiles be
It would be ______ inches long
The row of tiles would be 24 1/2 inches long.
B:The row of 10 tiles would be 35 inches long.
What is the length of the row?A 1. To be able to know the length of the row of tiles, one need to multiply the length of one tile by the number of tiles in the said row.
So, all tile measures 3 1/2 inches on each side, Hence the length of one tile is 3 1/2 inches.
Based on the fact that there are 7 tiles in a row, we have to multiply the length of one tile by 7:
Length of the row = 3 1/2 inches/tile x 7 tiles
= 24 1/2 inches
So, the row of tiles is 24 1/2 inches long.
B 2. Also, to find the length of a row of 10 tiles, we need to multiply the length of one tile by 10.
Note that:
Length of one tile = 3 1/2 inches
Number of tiles in the row = 10
Hence:
Length of the row = 3 1/2 inches/tile x 10 tiles
= 35 inches
So, the row of 10 tiles is 35 inches long.
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Select the correct answer from each drop-down menu.
(0.1² +20+15, z < 10
0.25³ +k, z 210
f(x)==
a) =
If the left-hand limit of f(z) is equal to the right-hand limit of f (x) as x approaches 10, the limit of f (x) as x approaches 10 is
the value of k is
and
The limit of f(x) as x approaches 10 is -25, and the value of k is -25.
For the left-hand limit,
lim(x->10-) f(x)
= lim(x->10-) (0.1x² + 20x + 15)
For the right-hand limit,
lim(x->10+) f(x)
= lim(x->10+) (0.25x³ + k)
Since we want the left-hand limit to be equal to the right-hand limit
lim(x->10-) f(x) = lim(x->10+) f(x)
lim(x->10-) (0.1x² + 20x + 15)= lim(x->10+) (0.25x³ + k)
0.1(10)² + 20(10) + 15= 0.25(10)³ + k
10 + 200 + 15 = 0.25(1000) + k
225 = 250 + k
k = 225 - 250
k = -25
Therefore, the limit of f(x) as x approaches 10 is -25, and the value of k is -25.
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will mark brainleist pls help me
we know that,
★ The sum of the angles in a triangle is always 180° ...
➺ 100° + 46° + x = 180°➺ 146° + x = 180°➺ x = 180°- 146° ➺ x = 34°__________________________________
Thus, the Value of x is 34°.
Answer:
34°Step-by-step explanation:
We know that,
Sum of three side of triangle is 180°
so,
100° + 46° + x = 180°
146° + x = 180°
x = 180° - 146°
x = 34°
[tex]\underline{\rule{190pt}{4pt}}[/tex]
Find the area of the given circle. Round your
answer to two decimal places. (Use pi = 3.14)
In this figure, we have been given a circle. The area of the circle is 314 sq ft.
The number of square units required to fill a circle is known as its area. The region occupied inside the boundaries of a round item or 2d figure is defined as the area in general. The measurement is done in square units, with square metres (m2) being the usual unit.
There are predefined formulas for calculating area for squares, rectangles, circles, triangles, and so on.
Area of a circle = πr²
We have been given r as 10 ft
and the value of π as 3.14, so we will just put it in the formula
Area of circle = 3.14 × 10²
= 3.14 × 100
314 sq ft.
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2. Evaluate (5+5√3i)^7 using DeMoivre’s theorem.
Write your answer in rectangular form.
Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i
How do we Evaluate (5+5√3i)⁷ using DeMoivre’s theorem?The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.
Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),
r = |z| magnitude of z
it becomes
r = √((5)² + (5√3)²) = 10
θ = arg(z) is the argument of z.
θ = atan2(b, a) = atan2(5√3, 5) = π/3
(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)
De Moivre's theorem to raise the complex number to the 7th power
(5 + 5√3i)⁷
= 10⁷× (cos 7π/3 + i sin 7π/3)
= 10⁷ × (cos 2π/3 + i sin 2π/3)
Convert this back to rectangular form:
Real part = r cos θ = 10⁷× cos (2π/3) = -5000000
Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i
∴ (5 + 5√3i)⁷ = -5000000 + 8660254.03i
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Answer:10^7 (1/2 - √3/2 i)
Step-by-step explanation:
To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:
Magnitude:
|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10
Argument:
arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3
So the number can be written in polar form as:
5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))
Now we can use DeMoivre's theorem:
(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))
To simplify, we need to find the cosine and sine of 7π/3:
cos(7π/3) = cos(π/3) = 1/2
sin(7π/3) = -sin(π/3) = -√3/2
Explanation:
So the final answer in rectangular form is:
10^7 (1/2 - √3/2 i)