Answer: To show that log5 7 = 1/(2n-1)(2mn-m-2), we'll start by using logarithmic properties and the given information.
First, let's express log9 75 in terms of the base 5 logarithm, using the change of base formula:
log9 75 = log5 75 / log5 9
Next, let's simplify the expression inside the logarithm by breaking down 75 and 9 into their prime factors:
log5 (3^2 * 5^2) / log5 (3^2)
Now, using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:
log5 (3^2) + log5 (5^2) - log5 (3^2)
Simplifying further, we have:
2 log5 3 + 2 log5 5 - 2 log5 3
The 2 log5 3 and -2 log5 3 terms cancel each other out, leaving:
2 log5 5
Now, let's substitute the value of m from the given information (log5 21 = m) into the expression:
2 log5 5 = 2 (log5 (5^2)) = 2(2 log5 5) = 4 log5 5 = 4m
Now, let's substitute the value of n from the given information (log9 75 = n) into the expression:
4m = 4(log5 5) = 4(1/2 log5 (5^2)) = 4(1/2 log5 25) = 4(1/2 log5 (5^2 * 5^2))
Using logarithmic properties, we can split the logarithm of a product into the sum of logarithms:
4(1/2 (log5 5^2 + log5 5^2)) = 4(1/2 (2 log5 5 + 2 log5 5)) = 4(1/2 (4 log5 5))
Simplifying further, we have:
4(1/2) (4 log5 5) = 4(2 log5 5) = 8 log5 5 = 8n
Finally, substituting the values of m and n into the expression:
log5 7 = 1/(2n-1)(2mn-m-2) = 1/(2(8) - 1)(2(4m) - m - 2) = 1/(16 - 1)(8m - m - 2) = 1/15(7m - 2)
Therefore, we have shown that log5 7 = 1/(2n-1)(2mn-m-2) = 1/15(7m - 2), using the given values of log5 21 = m and log9 75 = n.
The two ways to indicate an empty set are
please helpppppppppppppppppppppppppppppppppppppppp
Answer:
Step-by-step explanation:
It's c
-4 1/6
Plug in the number for a and you get -2 1/3 - 11/6
make the first number into a fraction, so -7/3
-7/3 - 11/6
common denominator, so, -14/6 - 11/6, which equals -25/6
simplify: -4 1/6
Hope that helps!
Answer:
The answer is
[tex] \frac{ - 25}{6} [/tex]
-4⅙
Step-by-step explanation:
[tex]a - \frac{ - 11}{6} [/tex]
[tex]a = - 2 \times \frac{1}{3} [/tex]
[tex] \frac{ - 7}{3} - \frac{ - 11}{6} [/tex]
[tex] = \frac{ - 25}{6} [/tex]
Identify a situation that would fit into this scenario and explain how would you organize this calculation to solve it without a calculator. Assume a 5% sales tax rate. For full credit, you will need the cost of the it, an explanation of how you would calculate the sales tax and the total cost.
You would add the sales tax amount to the cost of the meal to get the total cost. In this case, the sales tax amount is $1, so the total cost would be $26.
One situation that would fit into this scenario is calculating the total cost of a meal at a restaurant that costs $25. Firstly, to calculate the sales tax, you would need to convert the percentage of sales tax into a decimal.
In this case, the sales tax rate is 5%, so you would convert it to 0.05.Next, you would multiply the cost of the meal by the sales tax rate to calculate the sales tax amount.
To do this calculation without a calculator, you can use mental math or estimation techniques.For example, you could estimate 5% of $25 by breaking the 5% into a 1% and 4% calculation.
To calculate 1%, you would simply move the decimal point two places to the left, which gives you $0.25. Then, to calculate 4%, you could multiply $0.25 by 4, which equals $1.
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Multiply using the Vertical Method: (x+4)(2x^2−3x+5).
Using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.
What is vertical multiplication?
In vertical multiplication, the numbers to be multiplied are placed vertically over one another with their least significant digits aligned.
The top number is named the multiplicand and the lower number is the multiplier. The result of the multiplication is the product.
The given expressions;
(x+4)(2x² −3x+5).
We will multiply as follows;
2x² - 3x + 5
× x + 4
_________________
2x² - 3x + 5 (Multiply by x)
+ 8x² - 12x + 20 (Multiply by 4)
_________________
10x² - 15x + 25
Thus, using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.
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here is my algebra 13 homework, can someone please help me fast! Quick!!
The function h(x) = (2ˣ) + 1 does not have an x intercept.
A function has an x-intercept when the value of the function is equal to zero at some point on the x-axis.
(a) f(x) = -x + 2 is a linear function with a negative slope (-1) and a y-intercept of 2.
To find the x-intercept, we set f(x) equal to zero and solve for x:
0 = -x + 2
x = 2
Therefore, the function f(x) has an x-intercept at (2, 0).
(b) g(x) = -(x²) is a quadratic function that opens downward and has a vertex at (0, 0).
To find the x-intercept, we set g(x) equal to zero and solve for x:
0 = -(x²)
x²= 0
x = 0
Therefore, the function g(x) has an x-intercept at (0, 0).
(c) h(x) = (2ˣ) + 1 is an exponential function
To find the x-intercept, we set h(x) equal to zero and solve for x:
0 = (2ˣ) + 1
-1 = 2ˣ
However, there is no real value of x that satisfies this equation.
h(x) = (2ˣ) + 1 has no x intercept.
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Can I have answers for 2 a b c and d
Using the centimeter ruler:
a. 1 ÷ 1/10 and 4 ÷ 1/10 are 10 and 40b. multiplying by reciprocalc. 18 ÷ 1/10 is 180d. 4 ÷ 2/10 and 4 ÷ 8/10 are 20 and 5.For the quotients:
a. 50b. 16²/₃c. 5⁵/₉How to determine measurement?2.a. To find 1 ÷ 1/10, divide 1 by the fraction 1/10. Dividing by a fraction is the same as multiplying by its reciprocal, rewrite the problem as 1 × 10/1, which simplifies to 10. Therefore, 1 ÷ 1/10 = 10.
To find 4 ÷ 1/10, divide 4 by the fraction 1/10. Again, rewrite the problem as 4 × 10/1, which simplifies to 40. Therefore, 4 ÷ 1/10 = 40.
b. To find each quotient, we used the fact that dividing by a fraction is the same as multiplying by its reciprocal.
c. Following the same pattern, find 18 ÷ 1/10 by dividing 18 by 1/10. This is the same as multiplying 18 by the reciprocal of 1/10, which is 10/1. Therefore, 18 ÷ 1/10 = 180.
d. To find 4 ÷ 2/10, divide 4 by 2/10. Rewrite the problem as 4 × 10/2, which simplifies to 20. Therefore, 4 ÷ 2/10 = 20.
To find 4 ÷ 8/10, divide 4 by 8/10. Rewrite the problem as 4 × 10/8, which simplifies to 5. Therefore, 4 ÷ 8/10 = 5.
3. a. To divide 5 by 1/10, Rewrite the problem as 5 × 10/1, which simplifies to 50. Therefore, 5 ÷ 1/10 = 50.
b. To divide 5 by 3/10, Rewrite the problem as 5 × 10/3, which simplifies to 16 2/3. Therefore, 5 ÷ 3/10 = 16²/₃.
c. To divide 5 by 9/10, Rewrite the problem as 5 × 10/9, which simplifies to 5 5/9. Therefore, 5 ÷ 9/10 = 5⁵/₉.
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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, the period, phase shift, and vertical shift of the function. Then graph the function. Thank you!
For the function y = 3sin[2(θ-90°)] + 2, the amplitude is 3, the period is π, the phase shift is -45° and the vertical shift is 2 units up.
The amplitude of a sine function represents the maximum displacement from the midline.
The coefficient in front of the sine function is 3, so the amplitude is 3.
The period of a sine function is the length of one complete cycle. It can be calculated using the formula T = 2π/b, where b is the coefficient of θ inside the sine function brackets.
Here, b = 2, so the period is T = 2π/2 = π.
The phase shift of a sine function indicates a horizontal shift to the left or right.
In this case, c = 90°, so the phase shift is θ = 0° - 90°/2 = -45°.
The vertical shift indicates a shift up or down on the y-axis.
The constant term outside the sine function is 2, so the vertical shift is 2 units up.
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desperately need help!!!
The classification , symmetry , maximum r-values and the zeroes of the function are solved
Given data ,
a)
Let the function be represented as A
Now , the value of A is
r² = 25 sin( 2θ )
The equation represents a cardioid
It is symmetric about the polar axis.
The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.
The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0
b)
The equation represents a limaçon.
It is symmetric about the polar axis.
The maximum value of r is 7.
The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).
c)
The equation represents an Archimedean spiral.
It does not possess any symmetry.
There is no maximum r value.
The equation has a zero at θ = 1/2.
Hence , the zeroes of the function are solved
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Find the 15th term of the geometric sequence 2,6,18...
The first term of a geometric sequence is 2 and the common ratio is 3. The general term formula for the nth term of a geometric sequence is given by: an = a₁ × rⁿ⁻¹ Where, an is the nth term of the sequence, a₁ is the first term of the sequence, and r is the common ratio of the sequence. The 15th term of the sequence is 86,093,442.
To find the 15th term of the sequence, we need to use the above formula to find a₁ and r.The sequence is: 2, 6, 18, 54, ...Since the first term is 2, then a₁ = 2.The common ratio can be found by dividing any term by its preceding term. We will use the second and first term:6 / 2 = 318 / 6 = 3Again, the common ratio is 3. Now, we can use the formula to find the 15th term of the sequence: an = a₁ × rⁿ⁻¹a15 = 2 × 3¹⁵⁻¹a15 = 2 × 3¹⁴a15 = 2 × 43,046,721a15 = 86,093,442 The 15th term of the sequence is 86,093,442.
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x^2 -5x + 29 = 8x -6
Answer:
Step-by-step explanation:
x²-5x+29=8x-6
x²-13x+35=0
[tex]x=\frac{13 \pm\sqrt{(-13)^2-4(1)(35)} }{2(1)} \\x=\frac{13 \pm\sqrt{169-140} }{2} \\x=\frac{13 \pm\sqrt{29} }{2}[/tex]
Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house. One-half of the commission goes to the broker, and one-half of the remainder to another salesperson. Stevenson receives the rest. Find the amount she receives.
Answer:
Danielle Stevenson receives $2,600 from selling the $160,000 house.
Step-by-step explanation:
To find the amount Danielle Stevenson receives from selling the house, we'll follow these steps:
Calculate the commission earned by Danielle Stevenson: Commission = 6.5% * $160,000.
Commission = 0.065 * $160,000 = $10,400.
Determine the broker's share: Broker Share = 0.5 * Commission.
Broker Share = 0.5 * $10,400 = $5,200.
Calculate the remaining amount after the broker's share: Remaining Amount = Commission - Broker Share.
Remaining Amount = $10,400 - $5,200 = $5,200.
Determine the salesperson's share: Salesperson Share = 0.5 * Remaining Amount.
Salesperson Share = 0.5 * $5,200 = $2,600.
Finally, calculate the amount Danielle Stevenson receives, which is the remaining portion after the broker and salesperson's shares: Amount Danielle Receives = Remaining Amount - Salesperson Share.
Amount Danielle Receives = $5,200 - $2,600 = $2,600.
Therefore, Danielle Stevenson receives $2,600 from selling the $160,000 house.
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Can someone help me? Find the sum of the first 24 terms of the arithmetic series if the first term is 3 and the common difference is 3.
The sum of the 24 terms of the arithmetic series is 900
How to solve:
To find the sum of an arithmetic series, we can use the formular:
Sn = (n/2)(2a + (n-1)d)
Where;
Sn is the series sum, n is the number of terms, a is the first term, and d is the common difference.
The first term (a) in this scenario is 3, and the common difference (d) is 3. With n equal to 24, we want to find the sum of the first 24 terms.
When the values are entered into the formula, we get:
The sum of the first 24 terms of the arithmetic series is 900 because;
S24 = (24/2)(2(3) + (24-1)(3))
= 12(6 + 23(3))
= 12(6 + 69)
= 12(75)
= 900.
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A washer and a dryer cost $995 combined. The washer costs $95 more than the dryer. What is the cost of the dryer?
Answer:
$450
Step-by-step explanation:
995/2 = 497.5
95/2 = 47.5
497.5 + 47.5 = 545
495 - 95 = 450
Select ALL TRUE statements
A) There are no zeroes
B) There is one zero
C) There are two zeroes
D) The vertex is (1, 14)
E) The vertex is (14, 1)
F) The vertex is (2, 14)
G) The vertex is (14, 2)
H) The axis of symmetry is x = 1
I) The axis of symmetry is x = 2
J) The "a" of the parabola is positive
K) The "a" of the parabola is negative
M) The parabola has a minimum
N) The parabola has a maximum
O) The zeroes are -2 and 6
P) The zeroes are 1 and 6
Q) The zero is 6
R) The zero is 14
Answer:
The correct statements are:
A) There are no zeroes
D) The vertex is (1, 14)
H) The axis of symmetry is x = 1
J) The "a" of the parabola is positive
M) The parabola has a minimum
Therefore, the options B, C, E, F, G, I, K, N, O, P, Q, and R are all false.
Step-by-step explanation:
Step-by-step explanation:
Remember that, this is quadratic function graph.
Let's analyze fact the graph. We get :
There are two roots/zeroes
Two roots are x1 = -2 , x2 = 6
Vertex is maximum value of parabola (2,14)
Symmetry function is x = 2 (you can show that, x-axis from vertex)
"a" parabola indicated negative
The parabola with "a" negative, thus have maximum value (show that vertex is (2,14))
Conclusion :
The true statements are C,F,I,K,N,O (6 statements are shown)
Subject : Mathematics
Level : JHS
Chapter : Quadratic Functions
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x will be 16.
Given ,
Parallelogram with two sides:
side 1 = 3x + 20
side 2 = 5x - 12
In parallelogram the opposite side are equal and parallel.
Thus,
side 1 and side 2 will be equal and parallel.
Equating both sides to get the value of x,
3x + 20 = 5x - 12
x = 16
Hence the value of x can be found out by property of parallelogram.
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Can someone answer this question
Answer: 4th one is the correct one
Step-by-step explanation:
help me solve my math
Answer:
653.3 bacteria
Step-by-step explanation:
A continuously growing population of bacteria is modeled by the function:
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
where:
[tex]P(t)[/tex] is the population after [tex]t[/tex] time periods[tex]P_0[/tex] is the initial population[tex]r[/tex] is the relative rate of growthIn this problem, we are given the following values:
[tex]P_0 = 484 \text{ bacteria}[/tex][tex]r = 15\% = 0.15[/tex][tex]t = 2[/tex]We can plug these into the function to solve for [tex]P(2)[/tex].
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]
[tex]P(2) = 484 \cdot e^{0.3}[/tex]
Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.
[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]
On January 1 2019, a company reported assets of $1500000 and liabilities of $700000. During 2019, assets decreased by $100,000 and stockholders equity decreased $200,000. What is the amount of liabilities at December 31 2019? Enter your answer to the nearest whole number
The amount of liabilities at December 31, 2019, is $900,000.
To determine the amount of liabilities at December 31, 2019, we can use the accounting equation:
Assets = Liabilities + Stockholders' Equity
Given that the company reported assets of $1,500,000 and liabilities of $700,000 on January 1, 2019, we can set up the equation as follows:
$1,500,000 = $700,000 + Stockholders' Equity
During 2019, assets decreased by $100,000, so the new value of assets at December 31, 2019, would be $1,500,000 - $100,000 = $1,400,000.
Stockholders' equity decreased by $200,000, so the new value of stockholders' equity at December 31, 2019, would be $700,000 - $200,000 = $500,000.
Now we can substitute these values into the accounting equation to solve for liabilities:
$1,400,000 = Liabilities + $500,000
Rearranging the equation, we find:
Liabilities = $1,400,000 - $500,000
Liabilities = $900,000
Therefore, the amount of liabilities at December 31, 2019, is $900,000.
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Answer is option a, c, d
Ik it may seem like too easy question but how option C is answer since vector depend on both magnitude and 'direction' T-T
Won't direction will change?
The value of a scalar does not depend on the orientation.
The magnitude of a vector does not depend on the orientation of the axes.
(a) The value of a scalar does not depend on the orientation of the axes. Scalar is a quantity that has only magnitude and no direction, so it is independent of the coordinate system. Examples of scalars include temperature, mass, and time.
(b) Component of a vector depends on the orientation of the axes. If the coordinate axes are rotated or shifted, the components of a vector will change accordingly.
(c) A vector depends on the orientation of the axes. A vector has both magnitude and direction and changes when the orientation of the axes is changed.
(d) The magnitude of a vector does not depend on the orientation of the axes. The magnitude of a vector is defined as the length of the vector, which is independent of the coordinate system. For example, the magnitude of a velocity vector is the speed, which is the same regardless of the orientation of the axes.
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Graph the inequality y ≤1/3x+1
The graph of the inequality y ≤ 1/3x + 1 is added as an attachment and it is represented with option (c)
How to determine the graph of the inequalityFrom the question, we have the following parameters that can be used in our computation:
y ≤ 1/3x + 1
The above expression is an inequality that implies that
It is a linear inequalityIt has a slope of 1/3It has a y-intercept of 1The upper part and the left part of the graph is shadedNext, we plot the graph
See attachment for the graph of the inequality
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6 sinθ=5 to the nearest 0.1°
The value of the equation 6 sinθ=5 for θ is 56.4 degrees
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
6 sinθ=5
Express the equation properly
So, we have the following representation
6 sin(θ) = 5
Divide both sides of the equation by 6
This gives
sin(θ) = 5/6
Evaluate the quotient
sin(θ) = 0.833
Take the arc sin of both sides
θ = sin⁻¹(0.833)
Evaluate
θ = 56.4
Hence, the value of the equation for θ is 56.4 degrees
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Complete question
Approximate θ in the equation, to the nearest 0.1 degrees
6 sin(θ) = 5
Question: 4/8
Mr. Oswald, the head of human resources, has
been in the company for 24 years, which
corresponds to three times as many as the
number of years Mrs. Bright, the finance
director, is also employed there.
Considering neither of them leaves their jobs,
how many years will Mr. Oswald have worked for
the company when that corresponds to twice as
many as Mrs. Bright's number of years there?
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.
The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.
So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.
Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.
Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.
Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.
16 more years - 24 years = -8 years.
The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.
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Write a sine function that has a midline of y=4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right.
The sine function with a midline of y=4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2sin(2(x - π/4)) + 4.
To write a sine function with the given properties, we can use the general form of a sine function: y = A * sin(B(x - C)) + D, where A represents the amplitude, B represents the frequency (or inverse of the period), C represents the horizontal shift, and D represents the vertical shift (or midline).
In this case:
The midline is y = 4, so D = 4.
The amplitude is 2, so A = 2.
The period is π, so the frequency is B = 2π/π = 2.
The horizontal shift is π/4 to the right, so C = -π/4.
Plugging these values into the general form, we get the sine function:
y = 2 * sin(2(x - (-π/4))) + 4
Simplifying further:
y = 2 * sin(2(x + π/4)) + 4
Therefore, the sine function with a midline of y = 4, an amplitude of 2, a period of π, and a horizontal shift of π/4 to the right is y = 2 * sin(2(x + π/4)) + 4.
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evaluate 3x+5y when x=11 and y=4.
(a)23
(b)67
(c)53
(d)13
Answer:
(c):53
Step-by-step explanation:
Let's start with the equation:
3x+5y
Since we already have the values of x and y, we can just solve the equation.
3(11)+5(4)
33+20=53
The answer is (c)53
Regina is comparing two checking accounts. One has a monthly fee of $12
and a per-check fee of $0.10, and the other has a monthly fee of $9 and a per-
check fee of $0.25. What is the minimum number of monthly checks Regina
needs to write for the first account to be a better option?
A. 15
B. 30
OC. 21
OD. 20
The minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.
To solve this problemOn the basis of the quantity of checks written, we can compare the overall costs of the two accounts.
Let's calculate the total cost for each account based on the given information:
First Account:
Monthly fee: $12
Per-check fee: $0.10
Total cost = Monthly fee + (Per-check fee * Number of checks)
Second Account:
Monthly fee: $9
Per-check fee: $0.25
Total cost = Monthly fee + (Per-check fee * Number of checks)
We must determine the point at which the first account's total cost is less than the second account's total cost. Let's construct the formula:
$12 + ($0.10 * Number of checks) < $9 + ($0.25 * Number of checks)
Simplifying the equation
$12 - $9 < ($0.25 - $0.10) * Number of checks
$3 < $0.15 * Number of checks
Dividing both sides by $0.15:
$3 / $0.15 < Number of checks
20 < Number of checks
Therefore, the minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.
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Eight upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 7. The smallest domino, #0, is 4.00 cm tall and will be toppled by a person to start the chain reaction. Each subsequent domino is 12% taller than the one before. What is the height of domino #7?
The height of domino #7 is approximately 6.89 cm tall.
How to solve for the heightThe formula for the nth term of a geometric progression is:
[tex]a_n = a * r^(^n^-^1^)[/tex]
where:
a is the first term (the height of the smallest domino, 4.00 cm),
r is the common ratio (the growth rate, 1.12), and
n is the term number (for domino #7, n = 7 + 1 = 8, because the sequence starts with domino #0).
Let's plug these values into the formula:
[tex]a_8 = 4.00 cm * (1.12)^7[/tex]
(Note that we're using 7, not 8, because the first domino is #0, not #1.)
Now, compute the value:
[tex]a_8 = 4.00 cm * (1.12)^7[/tex]
= 6.89 cm
So, domino #7 is approximately 6.89 cm tall.
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Find the slope of the line through the points (4, 8) and (5, 10).
A. -1/2
B. 2
C. 1/2
D. -2
Answer:
2, answer choice B
Step-by-step explanation:
Slope = rise/run = (y2-y1)/(x2-x1).
You are given points (4,8) and (5,10).
slope = (8-10)/(4-5)
slope = (-2)/(-1)
slope = 2
(4,2)
I
5
(x, y)
Given that the circle to the left has a center at
point (4,2), and point (x, y) is on the
circle,write the equation for the distance (x, y)
is away from the center. Rearrange this
equation so it contains no radicals.
The equation for the distance of the point (x, y), from the center of the circle is; (x - 4)² + (x - 2)² = 5²
What is the general form of the equation of a circle?The general form of the equation of a circle with center (h, k) is; (x - h)² + (y - k)² = a², where the radius of the circle is; a
The radius of a circle is the distance from the center to a point (x, y) on the circumference, therefore, the equation for the distance of the point (x, y) from the center of the circle, is equivalent to the equation for a circle, where the distance of the point (x, y) from the center is the radius.
The coordinates of the center of the circle, (h, k) = (4, 2)
The radius of the circle, r = a = 5
The equation for the distance (x, y) from the center, which radius of the circle, with center (4, 2), is therefore;
Equation of a circle; (x - h)² + (y - k)² = a²
Equation from the center; (x - 4)² + (y - 2)² = 5²
Where;
5 = The radius, a = The distance from the center of the circle
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Two forces of 5N and 12N act at right angles to each other. Use a graph paper to determine the magnitude and direction of the resultant force graphically. State the scale you use to represent each vector. You will need a protractor to measure the angle the resultant makes with the 5N force.
The resultant of the force that acts in opposite directions is 7 N.
We have,
We know that the resultant force is the force that has the same effect in magnitude and direction as two or more forces that is acting together. We have to note that the force that is actinmg on an object is a vector quantity. The implication of this is that the magnitude and the direction of the forces that are acting on the body is very important.
By the use of the law of vectors we can be able to write in the case of the question that we have here, we can see that the forces are acting in the opposite directions. The implication of this is that we would have to subtract the forces so as obtain the resultant force.
We have to note that when we have opposite forces, one is said to be positive and the other negative and the resultant force can be found by subtraction. As such the resultant force can be obtained from;
Let the +B force be 12 N
Let the -B force be 5N
12 N - 5 N = 7 N
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1. If an object has a mass of 12kg, it has a weight of
Answer:
weight = gxg = 12kg to g = 0.12 and then using formula we get 0.12x0.12 = 1.44 is the weight
Step-by-step explanation:
Answer:
Therefore, the weight of the object is approximately 117.72 Newtons.
Step-by-step explanation:
The weight of an object is given by the formula:
weight = mass x acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.81 m/s².
So, the weight of an object with a mass of 12 kg is:
weight = 12 kg x 9.81 m/s² = 117.72 N
Therefore, the weight of the object is approximately 117.72 Newtons.