a uniform solid sphere of mass m1 and radius r1 is inside and concentric with a spherical shell of mass m2 and radius r2 (fig. p14.48). find the gravitational force exerted by the spheres on a particle of mass m located at (a) (b) and (c) where r is measured from the center of the spheres.
Answers
The gravitational force exerted by the spheres on a particle of mass m located at (a)r=a,(b)r=b, and (c)r=c are
[tex]F=\frac{Gm_1m_a}{R_1^2}\\\\F=\frac{Gm_1m}{b^2}}\\\\F=m(\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2} )[/tex]
Total gravitational Field at r=a
Total gravitational Field at r=a=Field due to solid sphere+ field due to spherical shell
we know the gravitational field inside the spherical shell is zero.
and gravitational field due to the solid sphere inside = [tex]\frac{GMr}{R^2}[/tex]
so here
Total gravitational Field=Field due to solid sphere+ field due to spherical shell
[tex]G=\frac{Gm_1a}{R_1^2} +0\\\\G=\frac{Gm_1a}{R_1^2}[/tex]
Force exerted on particle F=mG
[tex]F=\frac{Gm_1m_a}{R_1^2}[/tex]
when r=b:
we know the gravitational field inside the spherical shell is zero.
and gravitational field due to a solid sphere outside at a distance:
[tex]r=\frac{GM}{r^2}[/tex]
so here
Total gravitational Field=Field due to solid sphere+ field due to spherical shell
[tex]G=\frac{Gm_1}{b^2}}+0\\\\G=\frac{Gm_1}{b^2}}[/tex]
Force exerted on particle F=mG
[tex]F=\frac{Gm_1m}{b^2}}[/tex]
gravitational field due to a hollow sphere outside at a distance:
[tex]r=\frac{GM}{r^2}[/tex]
and gravitational field due to a solid sphere outside at distance:
[tex]r=\frac{GM}{r^2}[/tex]
so here
Total gravitational Field=Field due to solid sphere+ field due to spherical shell
[tex]G=\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2}[/tex]
Force exerted on particle F=mG
[tex]F=m(\frac{Gm_1}{c^2} +\frac{Gm_2}{c^2} )[/tex]
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Related Questions
A company wants to estimate the mean time it will take workers to complete a certain task. They reca the times to complete the task for a random sample of 30 workers. Match the following: ____ all workers from this company
____ 30 workers from this company
____ a worker from this company
____ mean time to complete a certain task for 30 workers from this company
____ mean time to complete a certain task for all workers from this company- time to complete a certain task
a. statistic b. individual c. variable d. sample e. population f. parameter
Answers
A. All workers from this company are the population (e)
B. 30 workers from this company is the sample (d)
C. Time to complete a certain task for a worker from this company is an individual (b)
D. Mean time to complete a certain task for 30 workers from this company is a statistic (a)
E. Mean time to complete a certain task for all workers from this company is a parameter (f)
The company wants to estimate the mean time it will take workers to complete a certain task, so they recall the times to complete the task for a random sample of 30 workers.
This sample represents a portion of the larger population of all workers from the company. The mean time to complete the task for this sample of 30 workers is a statistic, while the mean time to complete the task for the entire population of all workers is a parameter. The individual time to complete the task for each worker is a variable.
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What are 5 different ways to represent the number 329.01. Justify your work by showing how your representation mathematically represents the target number. Demonstrate your understanding of our work-in-place value.
Answers
Standard notation: 329.01
In standard notation, the digits are read from left to right, and each digit represents a different place value. The first digit, 3, represents the hundreds place, the second digit, 2, represents the tens place, the third digit, 9, represents the ones place, the fourth digit, 0, represents the tenths place and the fifth digit, 1, represents the hundredths place.
3100 + 210 + 91 + 00.1 + 1*0.01 = 329 + 20 + 9 + 0 + 0.01 = 329.01
Scientific notation: 3.2901 x 10^2
In scientific notation, the number is written as a decimal number multiplied by a power of 10. The decimal number, 3.2901, represents the coefficient and the power of 10, 10^2, represents the exponent.
3.2901 x 10^2 = 3.2901 x 100 = 329.01
Expanded notation: 3100 + 210 + 91 + 00.1 + 10.01
In expanded notation, the number is written as the sum of each digit multiplied by its corresponding place value.
3100 + 210 + 91 + 00.1 + 10.01 = 329 + 20 + 9 + 0 + 0.01 = 329.01
Fractional notation: 32901/10000
In fractional notation, the number is written as a ratio of two integers. The numerator represents the value of the number, and the denominator represents the place value of the last digit.
32901/10000 = 329.01
Decimal notation: 32901 in base 10
In decimal notation, the number is written as a whole number in base 10. The number can be represented as a combination of digits ranging from 0 to 9.
32901 = 329.01
All the 5 different ways of representation are mathematically equivalent and represent the same number 329.01, they are all different ways of expressing the same value and they all show the understanding of the place value system.
Thelma wants to buy a jacket that costs $60. She has $12 in her
savings account and plans to save an additional $10 per week. Which
of these shows a correct procedure Thelma could use to determine w,
the number of weeks she needs to save to have enough money to buy
the jacket?
A. 12+10w≥60
12+wz50
w≤4.17
B. 12+10w≥60
10wz48
w24.8
C. 12+10w≥60
12+w≥50
w24.17
D. 12+10w≥60
10wz48
w≤4.8
Answers
Thelma has to save by at least 4.8 weeks, according to the information we get. The proper course of action is B).
Which four sorts of money are there?According to economists, there are four basic sorts of money: commercial money, fiduciary funds, fiat money, and commodity money. Commodity money is money that derives its worth from the commodities from which it is created.
B. 12 + 10w ≥ 60
10w ≥ 48
w ≥ 4.8
Thelma must so set aside money over the past 4.8 weeks. Keep in mind this is the absolute minimum, so if she not save the entire $10 each week, she may require saving for longer.
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The Complete Question :
Thelma wants to buy a jacket that costs $60. She has $12 in her
savings account and plans to save an additional $10 per week. Which
of these shows a correct procedure Thelma could use to determine w,
the number of weeks she needs to save to have enough money to buy
the jacket?
A. 12+10w≥60
12+wz50
w≤4.17
B. 12 + 10w ≥ 60
10w ≥ 48
w ≥ 4.8
C. 12+10w≥60
12+w≥50
w24.17
D. 12+10w≥60
10wz48
w≤4.8
find the slope of the line that gores through the given points (5,1) and (2/3, -5)
Answers
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{\frac{2}{3}}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{\frac{2}{3}}-\underset{x_1}{5}}} \implies \cfrac{-6}{~~ -\frac{13 }{3 } ~~}\implies \cfrac{\frac{6}{1}}{~~ \frac{13}{3 } ~~}\implies \cfrac{6}{1}\cdot \cfrac{3}{13}\implies \cfrac{18}{13}[/tex]
Picture below has the question
Answers
a) At the beginning we have; 6 pCi/L
b) It would taken 2 days to have 4 pCi/L
What is the amount of the radon when first collected?We have to note that the radioactivity would have to do with the spontaneous disintegration of the material. In this case, we can see that we have the function that models the situation as;
R(t) = 6e^-0.18t Where t is the time that is taken
At first we have that the time is zero hence the R(t) is;
R(t) = 6e^-(0.18 * 0)
R(t) = 6 pCi/L
For us to have 4 pCi/L;
4= 6e^-0.18t
4/6 = e^-0.18t
0.67 = e^-0.18t
ln(0.67) = lne^-0.18t
t = ln(0.67)/-0.18
t = 2 days
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The cost of dress in a shop is 320.00 for more than more than the cast: If a customer of a pair of pays 305.00 for the turo items. How much does each cost.
Answers
The price of each of these be
A dress market at Rs.120 is 96A pair of shoes market at Rs.750 is 600A bag market at Rs.250 is 200.What is discount?The discount is determined by dividing the purchase price by the item's par value. Discount is a type of cost price reduction or deduction for a product. It is primarily employed in consumer interactions when discounts on various goods are offered to customers. A percentage represents the discount rate. (Discount List Price) 100 is the formula used to determine the rate of discount. The discount is the amount that is subtracted from the selling price in the formula. [(List price - Selling price)/List price] 100 is an additional formula for computing discount percentages.The simplest definition of a price is the sum of money exchanged by a buyer and seller for a good or service.A. Price [tex]}=\left(\frac{100 \%-20 \%}{100 \%}\right) * 120=\frac{80}{100} * 120=96 \\[/tex]
B. Price =[tex]\left(\frac{100 \%-20 \%}{100 \%}\right) * 750=\frac{80}{100} * 750=600 \\[/tex]
C. Price [tex]=\left(\frac{100 \%-20 \%}{100 \%}\right) * 250=\frac{80}{100} * 250=200[/tex]
The complete question is.
A shop gives 20% discount. What would the price of each of these be?
A dress market at Rs.120
A pair of shoes market at Rs.750
A bag market at Rs.250
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For what taxable income would a taxpayer have to pay $13,154.00 in taxes?
Answers
Therefore , the solution of the given problem of percentage comes out to be for the tax to be $13154.00, the income has to be around $84991.67 (around because taxes are rounded).
Define percentage.Any quantity that is expressed as a ratio of 100 is referred to as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." But it is commonly indicated by the "%" symbol. The percentage amount is flat with no dimensions. Percentages actually function as fractions because their numerator is 100. The percent symbol (%) should be used in front of a number to indicate that it is a percentage. If you correctly answered 75 out of total test questions, for example, you would score 75%.
Here,
Given :
The required range for income is $84200 to $160700 because the tax is over $12962 but under $31322.
The tax on the first $84202 is $12962, and the surplus, which we'll refer to as x, is subject to a 24% tax.
=> 24%*x = $13154 - $12962 = $190
=> x = $190/(24%) = $791.(6) (6)
Therefore, the total income is approximately $84,200 plus $791.
=> $84991.
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Answer the screenshot please.
Answers
As of December 21, the account's opening balance will be $ 4,000.66.
What is the rate of interest?An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
Given that, on December 18 of a leap year. Stacy opened a savings account by depositing $6000.
The account pays 1.45% interest, compounded daily.
To find the missing amounts in the table and determine what is her opening balance on December 21, the following calculations must be performed:
The interest rate must be divided by the number of days in the year.
0.0145 / 366 = 0.00003961748
December 18:
Opening balance = 0
Deposit = 6,000
Withdrawal = 0
Principal used to compute interest = 6,000
Day's interest rounded to the nearest cent = 0.24 ((6,000 x 0.00003961748) - 6,000)
Ending balance = $6000.24
On December 19 she deposited $500, and on December 20 she withdrew $2500.
December 19:
Opening balance = 6000.24
Deposit = 500
Withdrawal = 0
Principal used to compute interest = 6,500.24
Day's interest rounded to the nearest cent = 0.26 ((6,500.24 x 0.00003961748) - 6,500.24)
Ending balance = 6500.50
December 20:
Opening balance = 6500.50
Deposit = 0
Withdrawal = 2500
Principal used to compute interest = 4,000.50
Day's interest rounded to the nearest cent = 0.16 ((4,000.50 x 0.00003961748) - 4,000.50)
Ending balance = 4000.66
Therefore, as of December 21, the account's opening balance will be $ 4,000.66.
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Please help me with the following question.
Answers
(i) The average number of machinists being served or waiting to be served at any given time can be calculated as the average of the arrival rate and the service rate, which is (2 + 3) / 2 = 2.5.
What is an example of a unitary method?
We can use the unitary approach to calculate 100% of an amount. For instance, if 10% of the marbles in a pot are 35, then the total number of marbles in the pot will be 35 x 10%, or 350.
(ii) The average time a machinist spends waiting for service can be calculated as the difference between the average time between arrivals and the average service time, which is 1 / (2 - 3) = -0.5 hours. However, this result is not physically meaningful as service rate is higher than the arrival rate, which means that all customers can be served without waiting.
(iii) The total cost of operating the system for an eight-hour day can be calculated as the sum of the attendant's wage and the cost of the machinist away from his work, which is 8 * 21.50 + 8 * 4 = 172.
(iv) The cost of the system if there were two attendants working together as a team can be calculated as the sum of the wage of the two attendants and the cost of the machinist away from his work, which is 8 * (2 * 11.50) + 8 * 4 = 216.
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HELPP please!!!!!!!!!!!!
which expression is equivalent to (3/2)^3
A:3/2
B:3^3/2^3
C:3/2^3
D:3^3/2
Answers
The equivalent expression to (3/2)^3 is 3³/2³. Option B
What are index forms?The index form of a number is simply described as a number that is written as an exponential expression.
It is also described as a single number that is raised to another number.
Index forms explains the number of times the exponent contains another.
From the information given, we have that;
(3/2)³
expand the bracket, we get;
(3 ×3 × 3/ 2× 2 × 2)
Multiply the values
27/8
This is also written as;
3³/2³
Hence, the value is 3³/2³
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Round 52.476 to the nearest tenth.
Answers
Explanation: The 4 is in the tenths spot. The next digit over is 7, which fits the "5 or more" category. We'll bump the 52.4 up to 52.5 and ignore every other digit.
Answer:
52.5
Step-by-step explanation:
Tenths are the first decimal place to the right of the decimal.
Rounding to the nearest tenth means you have to look at the hundredth place, which is seven.
The rule is if your place value is five or more, you race the value up.
So rounding four up will be five
Lastly, get rid of any other place values on the right of your place
Therefore, your new number is 52.5
PLS help on number 9! Due today.
Answers
Answer:
For all graphs: Rate of change = 1/2
Step-by-step explanation:
To find the average rate of change for each function on the interval [1,5], all we have to do is find the slope between the points on the function with an x-value of 1 and 5. To find slope, we can use rise/run or (change in x)/(change in y)
Graph 1.)
Rise/Run
-2/4 = -1/2
Graph 2.)
Rise/Run
-2/4 = -1/2
Graph 3.)
Rise/Run
-2/4 = -1/2
Graph 4.)
Rise/Run
-2/4 = -1/2
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Landscaping A landscape company charges $55 per hour for the work of a designer, $40 per hour for the work of a foreman, and $25 per hour for the work of a laborer. A particular installation required 6 hours of design work, 11 hours from the foreman, and 33 hours of labor. Write out a mathematical statement for calculating the total labor cost and then compute this cost.
Answers
Answer:
Equation: 55D+40F+25L
Solution:$1595
Step-by-step explanation:
Equation: 55D+40F+25L
55(6)+40(11)+25(33)
330+440+825
Solution: $1595
Which statement about the end behavior of the logarithmic function f(x) = log(x+3)-2 is true?
A. As x decreases to the vertical asymptote at x = -3, y decreases to negative infinity.
B. As x decreases to the vertical asymptote at x = -1, y decreases to negative infinity.
C. As x decreases to the vertical asymptote at x = -3, y increases to positive infinity.
D. As x decreases to the vertical asymptote at x = -1, y increases to positive infinity.
Answers
Answer:
A
Step-by-step explanation:
As you should know, in a log function f(x) = a * log[k(x-d)] + c, the variable d would be your asymptote. Since the a value of the function is 1, nothing has been done to the graph and thus we can assume that it goes in the same direction of the parent function f(x) = log x. Therefore, as the x value gets closer to -3, the y value will continue to negative infinity.
A store has a sale on paper cups, 2 packs for $13.00. There are 100 cups in each pack. During the sale, what is the unit price per cup?
Answers
Answer:
Each cup cost 6.5 cents or 6 1/2 cents
Step-by-step explanation:
13/200- .065
Answer:
15 cents a cup
Step-by-step explanation:
divide 13.00 by 200 and round (*ゝω･*)
Please help me with this question.
Answers
The slope of the tangent will be 1280 and the equation of the tangent is y = 1280x - 3846.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that the equation is,
f(x) = 5x⁴ - 6
y = 5 x (4)⁴ - 6 = 1274
The slope of the tangent will be calculated as:-
f'(x) = 20x³ = 20 x ( 4 )³ = 1280
The equation of the line is,
y = mx + c
y = 1280x + c
1274 = 1280(4) + c
c = -3846
The equation is written as:-
y = 1280x - 3846
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What is the intermediate step in the form (x+a)^2 =b as a result of completing the square for the following equation?x^2−27x+31=−13x−14
Answers
The required step is adding 14 both sides of the equation to make it a whole square.
What are quadratic equations?A quadratic equation can be written in the standard form as ax² + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: The expression as x²-27x+31=-13x-14
Evaluating the expression we get
x²-27x+31=-13x-14
Adding both sides by 13x+14 we get
x²-27x+31+13x+14=-13x-14+13x+14
x²-14x+35=0
Again adding 14 both sides we get
x²-14x+35+14=14
(x-7)²=14
x-7=√14
x=√14+7
Hence, The required step is adding 14 both sides of the equation to make it a whole square.
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Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use S₁, S2, and S3, respectively, for the vectors in the set.) S = {(5, 4), (-1, 1), (4, 0)} (0, 0) Express the vector s₁ in the set as a linear combination of the vectors S2 and S3. S1 =
Answers
From the vector s₁ in the set as a linear combination of the vectors S2 and S3. S1 = 4S2 + S3 and (5, 4) can be expressed as a nontrivial linear combination of the vectors S2 and S3. Hence, the set is linearly dependent.
LD of Vectors SS1 = aS2 + bS3, where a and b are scalars.
Substituting the vectors from the set into the equation:(5, 4) = a(-1, 1) + b(4, 0)
Expanding both sides:5 = -a + 4b
4 = a
Solving for a and b:a = 4, b = 1
So, S1 = 4S2 + S3 and (5, 4) can be expressed as a nontrivial linear combination of the vectors S2 and S3. Hence, the set is linearly dependent.
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Which of the following are solutions to the inequality −2x+1>6? Select all that apply.
A. −52
B. –5
C. –2
D. −32
E. 0
F. –3
Answers
Answer:
ABDE
Step-by-step explanation:
plug in the values into the inequality
Solve x^2-7x=-12
Need help
Answers
Therefore the equation is x = 3.9275 or x = -5.8275.
What is equation?An equation is a mathematical statement that express the equality of two expression using of the equal sign or used to define relationship between differentiation variable and can be used to solve for the unknown's value when you from when you problem define equation you also use to describe the behavior of the physical system in the represent law of nature.
The given equation is an example of a quadratic equation, which has a form of ax^2 + bx + c = 0. In order to solve for x, we must use the Quadratic Formula, which states that x = [-b ± √(b^2 - 4ac)] / 2a.
In the equation given, a = 1, b = -7, and c = -12. Plugging these values into the Quadratic Formula, we get:
x = [7 ± √(7^2 - 4(1)(-12)] / 2(1)
x = [7 ± √(49 + 48)] / 2
x = [7 ± √97] / 2
x = (7 ± 9.855) / 2
Therefore, x = 3.9275 or x = -5.8275.
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Cameron is trying to figure out how far his home is from the park if 1/4 of the distance between Cameron's home and the park is 1/3 mile how long is the total distance
Answers
Answer:
4/3 miles
Step-by-step explanation:
First, let's turn the statement given to us into an equation:
1/4 of the distance between Cameron's house and the park is 1/3 miles
1/4 * x = 1/3 mile
Now, we need to solve for x.
[tex]\frac{1}{4}x=\frac{1}{3}[/tex] [Multiply by 4 to get x by itself]
x = 4/3.
So, if x is the distance between Cameron's house and the park and x=4/3, Cameron's house must be 4/3 of a mile away from the park.
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4.
units
a)
The lunch cost
The number of stickers collected by Maurice, Elle, and Justin is in the ratio 8:5:7.
If Maurice collected 960 stickers, how many stickers did Elle and Justin
each collect?
b)
If the three children have 1,500 stickers altogether, how many stickers did
they each collect?
Answers
a) For the ratio 8 : 5 : 7, if Maurice has 960 stickers then Elle collects 600 stickers and Justin collects 840 stickers.
b) For the ratio 8 : 5 : 7, if the total number of stickers is 1500 then Maurice collects 600 stickers, Elle collects 375 stickers and Justin collects 525 stickers.
What is ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
a) The ratio of stickers Maurice collects = 8
The number of stickers Maurice collects = 960
The ratio of stickers Elle collects = 5
The ratio of stickers Justin collects = 7
Let the number of stickers be x.
So, the equation for Maurice's collection will be -
8x = 960
x = 960/8
x = 120
So, Elle collects 5x stickers which is -
5 × 120 = 600 (substitute the value of x)
Justin collects 7x stickers which is -
7 × 120 = 840 (substitute the value of x)
Therefore, Elle and Justin have 600 and 840 stickers.
b) The total number of stickers is = 1500.
The ratio of stickers Maurice collects = 8x
The ratio of stickers Elle collects = 5x
The ratio of stickers Justin collects = 7x
The equation formed is -
8x + 5x + 7x = 1500
20x = 1500
x = 1500 / 20
x = 75
Substitute the value of x to find number of stickers.
So, Maurice collects = 8 × 75 = 600 stickers
So, Elle collects = 5 × 75 = 375 stickers
So, Justin collects = 7 × 75 = 525 stickers
Therefore, the number of stickers Maurice, Elle and Justin have is 600, 375 and 525 respectively.
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if e^y - e^-y= x, express y as an explicit function of x
Answers
[tex]e^y-e^{-y}=x\implies e^y-\cfrac{1}{e^y}=x\implies \cfrac{(e^y)^2-1}{e^y}=x \\\\\\ e^{2y}-1=xe^y \implies e^{2y}-xe^y=1[/tex]
now, we're going to do some "completing the square" on the left-side, that is, we'll make it a perfect square trinomial by using our very good friend Mr Zero, 0.
[tex]2\cdot n\cdot e^y=xe^y\implies n=\cfrac{xe^y}{2e^y}\implies n=\cfrac{x}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]e^{2y}-xe^y=1\implies e^{2y}-xe^y + n^2 - n^2=1\implies e^{2y}-xe^y+n^2=1+n^2 \\\\\\ (e^y)^2-xe^y+\left( \cfrac{x}{2} \right)^2=1+\cfrac{x^2}{4}\implies \left( e^y -\cfrac{x}{2} \right)^2=1+\cfrac{x^2}{4} \\\\\\ e^y -\cfrac{x}{2}=\sqrt{1+\cfrac{x^2}{4}}\implies e^y =\sqrt{1+\cfrac{x^2}{4}}+\cfrac{x}{2} \\\\\\ \ln(e^y)= \ln\left(\cfrac{x}{2}+ \sqrt{1+\cfrac{x^2}{4}} \right)\implies {\Large \begin{array}{llll} y=\ln\left(\cfrac{x}{2}+ \sqrt{1+\cfrac{x^2}{4}} \right) \end{array}}[/tex]
Based on the graph above, estimate to one decimal place the average rate of change from
Answers
-1.25 is the average rate of change from based on the graph.
What is average rate?
Average Rate — a single rate applying to property at more than one location that is a weighted average of the individual rates applicable to each location. To find the average rate of change, divide the change in y-values by the change in x-values. Finding the average rate of change is particularly useful for determining changes in measurable values like average speed or average velocity.
here, we have,
from the given graph we get,
f(x)= 8.5 at x= 1
f(x) = 3.5 at x= 5
we know that,
so, average rate = [f(b) - f(a)] / (b - a)
i.e. average rate = 3.5 - 8.5 / 5-1
= -5/4
= -1.25
Hence, -1.25 is the average rate of change from based on the graph.
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find 2 numbers whose product is -10 and whose sum is 3
Answers
Answer:
here
Step-by-step explanation:
Call the two integers a and b . We are given that a+b=−3, and ab=−10. Simple plug and chug yields the answers −5 and 2.
27. x = 9 and x = -5 it’s parallel or ?
Answers
The answer indicates that the lines at x = 9 & x = -5 both vertical and have no slope. They can't be parallel as a result.
Why is parallel important?Parallel in mathematics refers to two bars that never cross one another; picture an equal sign. Comparatively, the word "parallel" denotes similarity or simultaneous occurrence. Three close friends' similar lives might be shown in a tale.
Equal slope lines are parallel. The lines x = 9 & x = -5, on the other hand, are vertical and have no slope. They can't be parallel as a result. In actuality, vertical lines are never parallel to one another; rather, they always form a 90-degree angle (perpendicular).
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Which of the following statements is not true? A. The solution to a compound linear inequality involving the word "and" is the intersection of the solutions to each inequality. B. A compound linear inequality involving the word "and" must always have a solution. In other words, the solution is never the empty set. C. The solution to a compound linear inequality involving the word "or" is the union of the solutions to each inequality. D. A compound linear inequality involving the word "or" must always have a solution. In other words, the solution is never the empty set.
Answers
The statement that is not true is option B. A compound linear inequality involving the word "and" must always have a solution. In other words, the solution is never the empty set.
What is the linear inequality about?Option B is not true because a compound linear inequality involving the word "and" does not necessarily have a solution. The solution to a compound linear inequality involving the word "and" is the intersection of the solutions to each inequality.
This means that the solution is the set of values that satisfies both inequalities at the same time. However, if the solution to each inequality does not have any common values, then the solution to the compound inequality will be the empty set, which means there are no values that satisfy both inequalities.
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prove cot (3.14/2 -x) = tan x
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The proof of cot (3.14/2 -x) = tan x is given below.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
We have a trigonometric identity,
Cot (3.14/2 -x).
Simplifying,
Cot (π/2 - x),
= Cos(π/2 - x) / Sin (π/2 - x)
= (Cos π/2 Cos x + Sinπ/2 Sin x) / (Sinπ/2 Cos x - Cosπ/2Sin x)
= Sin x / Cos x
= Tan x
Hence proved.
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1/3 of 36 mutlitplied by the diffrence of 15 and 2
Answers
Answer:
156
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] of 36 = 36 ÷ 3 = 12
difference of 15 and 2 = 15 - 2 = 13
then
12 × 13 = 156
Which table shows a proportional relationship between x and y?
Answers
The only table that shows a proportional relationship is; Table C
How to Identify Proportional Relationships?Proportional relationships are defined as relationships between two variables where their ratios are equivalent to each other.
Option A: The ratios of each value of x and its' corresponding y-value are;
1.5/1, 3/2, 6/3, 9/6
This does not show a proportional relationship because they are not all equal.
Option B: The ratios of each value of x and its' corresponding y-value are;
1.5/3, 2.5/5, 3/7, 4.5/8
This does not show a proportional relationship because they are not all equal.
Option C: The ratios of each value of x and its' corresponding y-value are;
50/1, 150/3, 200/4, 250/5
This shows a proportional relationship because they are all equal.
Option D: The ratios of each value of x and its' corresponding y-value are;
6/2, 12/4, 18/5, 21/6
This does not show a proportional relationship because they are not all equal.
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