Answers
By putting the values the solution to the given Algebraic Equation is 9
What is Algebraic Equation?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
Solution:
[tex]c^{2} - a + 2a / b[/tex]
a = -3, b = 2, c = 3
Putting the values
3*3 - (-3) + 2(-3) / 2
We will use BODMAS
3*3 + 3 - 6 / 2
3*3 + 3 - 3
9 + 3 - 3
12 - 3
9
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Related Questions
A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each genre will be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If L is invited to speak on Friday, then on what days MUST a science fiction writer be invited? Possible Answers:Monday and Wednesday
Monday and Tuesday
Tuesday and Thursday
Only Wednesday
Monday and Thursday
Answers
As per the concept of probability, If L is invited to speak on Friday, then the science fiction writer be invited on Monday and Wednesday
Probability:
In statistics, probability refers the possible and favorable outcome of the particular event.
Given,
Here we need to find if L is invited to speak on Friday, then on what days MUST a science fiction writer be invited.
Here we know that the writers of the same genre may not speak on consecutive nights.
And here we have the only five slots to fill, two of the three science fiction writers must speak on Monday and Friday
So, If both X and J are invited, then at least one will be forced to speak on Monday or Friday, which is not allowed.
Then, modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.
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Find m<2
(Please help my test ends 12:50 west coast)
Answers
Answer:
40
Step-by-step explanation:
40
Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x 36 ( | error | < 0.01)
Answers
The Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is ( -0.0654 , 0.0654 ) .
Given :
Use the Alternating Series Estimation Theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error.sin x = x − x^3 / 6 ( | error | < 0.01 )
The next nonzero term in the Taylor series for sine is x^5 / 120 .
x^5 / 120 < .00000001
-0.00000001 < x^5 / 120 < .00000001
-0.0000012 < x^5 < .0000012
( -0.0000012 )^1/5 < x < ( .0000012 )^1/5
we have ( .0000012 )^1/5 ≈ .0654
= ( -0.0654 , 0.0654 )
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a 10-cmcm-long spring is attached to the ceiling. when a 2.0 kgkg mass is hung from it, the spring stretches to a length of 15 cmcm.
Answers
When a mass of 3 kg is hanged to it, the string will stretch 7.5 cm.
Given,
The length of the spring attached to the ceiling = 10 cm
The quantity of the mass hanged in the spring = 2 kg
The amount of stretching happened in the spring = 15 cm
We have to find the stretching of string when a mass of 3 kg is hanged to it;
Here,
Given that the force applied to the spring by the 2.0 kg is equal to the mass's weight:
F = mg = 2 kg × 9.8 m/s² = 19.6 N
Additionally, the stretching of:
Δx = 15 cm - 10 cm = 5 cm
So, applying Hooke's law:
F = kΔx
To determine the spring constant, k;
k = F/Δx = 19.6/5 = 3.92 N/ cm
The spring is now coupled to a new mass of m = 3.0 kg; the force this mass exerts on the spring equals
F = mg = 3 kg × 9.8 m/s² = 29.4 N
Thus, we may apply Hooke's law once more to determine the new stretching:
Δx = F/k = 29.4/3.92 = 7.5 cm
Therefore,
The string will be stretched 7.5 cm when a mass of 3 kg is hanged to it.
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When finding f(g(x)) what do you need to know about the domains and ranges
of f(x) and g(x)? Explain
Answers
All x-values that are within the scope of both f and g make up the domain of the (f g)(x).
How can the domain of f/g)(x be determined?All x-values that are within the scope of both f and g make up the domain of the (f g)(x). In this case, f has a domain of "x | x 0" and g has a domain of "all real numbers," thus (f g)(x) also has a domain of "x | x 0" since these values of x fall within both f and g's domains.Utilizing graphs is another method for determining the domain and range of functions. The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.To learn more about Domain refer to:
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Need help on this! (Many points!)
Answers
Answer:
[tex]\frac{-8}{9}[/tex]
Step-by-step explanation:
Substitute in 7 for x
[tex]\frac{7^{2}-5(7) -6 }{7^{2}-6(7) - 16 }[/tex]
[tex]\frac{49-35-6}{49-42-16}[/tex]
[tex]\frac{-8}{9}[/tex]
What is the horizontal shift for the absolute value function f(x)=3 |x+6| +9
Answers
Answer:
Left shift, 6 units
Step-by-step explanation:
In the equation:
f(x)=3 |x+6| +9
the " +6 " in close to the x represents the horizontal shift. X always tells us about horizontal or right/left moves. So an adjustment to the x is a horizontal adjustment.
But Caution! It is the opposite of what you might think. A PLUS6 is a LEFT shift. (While a MINUS6 would be a right shift, not the case here).
The parent function is:
f(x) = |x|
So our equation:
f(x)=3 |x+6| +9
has two changes made to it. LEFT6 because of the
" +6 " by the x. And the +9 tacked onto the end of the equation is a vertical shift UP9.
In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a .03 margin of error and use a confidence level of 90%. Complete parts (a) through (c) below.
a. Assume that nothing is known about the percentage to be estimated.
n=
b. Assume prior studies have shown that about 60% of full-time students earn bachelor's degrees in four years or less.
n=
c. Does the added knowledge in part (b) have much of an effect on the sample size?
Answers
The required sample sizes are given as follows:
a) n = 752.
b) n = 722.
c) The added knowledge in item b has an effect, as it decreases the sample size required. The decrease is not huge because the estimate is close to 0.5, but the farther the estimate gets from 0.5, the more the sample size decreases.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is calculated as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The margin of error in this problem is given as follows:
M = 0.03.
For item a, there is no previous estimate, hence we consider [tex]\pi = 0.5[/tex] and the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 752. (rounding up).
For item b, the estimate is [tex]\pi = 0.6[/tex], hence the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.6(0.4)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.6(0.4)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.6(0.4)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.6(0.4)}}{0.03}\right)^2[/tex]
n = 722. (rounding up).
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Three long wires (wire 1 wire 2 and wire 3 ) hang vertically. The distance between wire 1 and wire 2 is 23.0 cm On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 3.60 A. Wire 3 is to be located such that when it carries a certain current, each wire experiences no net force. (a) Is this situation possible? Is it possible in more than one way? Describe (b) the position of wire 3 and the magnitude and direction of the current in wire 3.
Answers
Based on the combination technique,
1. The position of wire 3
2. The magnitude and direction of current in wire 3
Combination method:
In statistics, the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter is know a combination method.
Given,
Here we have the three long wires hang vertically. The distance between wire 1 and wire 2 is 23.0 cm On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 3.60 A. Wire 3 is to be located such that when it carries a certain current, each wire experiences no net force.
And now we need to find the position of wire 3 and the magnitude and direction of the current in wire 3.
As per the given question, we know that the
=> Current in wire 1, i1 =1.2A upward
=> Current in wire 2, i2=5A downward
And the distance between wire 1 and 2 is calculated is
=> 20cm = 0.2m
Here the current is calculated as
=> F/l = μo•i1•i3/2πx
So,
=> F/l=6×10⁻⁶N/m
=> 6×10⁻⁶ = μo•i1•i3/2πx
=> 6×10⁻⁶ =4π×10⁻⁷×1.2×i3/(2π×0.0632)
When we do Cross multiply,
=> 6×10⁻⁶×2π0.0632=4π×10⁻⁷×1.2×i3
=> 2.383×10⁻⁶=4π×10⁻⁷×1.2×i3
=> i3= (2.383×10⁻⁶)/(4π×10⁻⁷×1.2)
Therefore, i3= 1.58A and it's direction is downward.
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If matrix M is of dimension 5 x 3, and matrix N is of dimension 5 x 5 then the dimension of NM is
Answers
A₂ₓ₃ matrix and B₃ₓ₄ matrix, The dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.
What are matrices?Matrices represent data in the form of rows and columns in an array form.
Suppose we have two matrices and their multiplication is possible only when the no. of columns in the first matrix is equal to the no. of rows in the second matrix.
Let A₂ₓ₃ matrix and B₃ₓ₄ matrix, Then the dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.
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.
Albert has a credit card with an APR of 20.7% and the following daily balances for this billing period: Days 1-3: $50 Days 4-10: $100 Days 11-25: $175 Days 26-30: $225 1. What is Albert’s daily rate? Round to the nearest ten thousandth.
Answers
Albert daily rate is 3.79%
How to determine Albert daily rate?We know that rate is the quantity or amount or the degree of a quantity measured with another quantity.
Albert's credit card APT = 20.7%
Daily balances are
Days 1-3 = (20.7*50)/100 = 10.35
Days 4-10 = (20.7*100)/100 =20.70
Days 11-25 = (20.7*175)/100 = 36.225
Days 26-30 = (20.7*225)/100 =46.575
Number of days in the month = 30 days
Total balance = $113.80
Daily rate = [tex]\frac{Total amount }{number of days}[/tex]
daily rate = [tex]\frac{113.80}{30}[/tex]
Dividing the figures we have 3.79
Therefore the daily rate is 3.79%
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Can someone help me with this, please?
Answers
π√π÷√π is an irrational number. So option (a) is required answer.
What is irrational number?A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number 2. Any irrational number, such as p/q, where p and q are integers, q, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.
Examples of irrational number: √3, ∛2, π
π is an irrational because it is neither ending nor recurrent.
Solving each part of options, we get
π√π÷√π = π
√25 = 5
√π÷π = 1
2√2 ÷ √2 = 2
As most of the option give rational number only one option gives irrational number which is π
We get π from option (a)
So, option (a) is correct option.
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simplify 1+1
[tex] \frac{1}{(1 - { \sqrt{ 5} )}^{2 } } + \frac{1}{(1 + \sqrt{ {5)}^{2} } } [/tex]
simplify
Answers
The value of the surd when simplified is 1/6
How to simplify the surd?We should recall that surd is the square root of all irrational numbers, simplification involves making it more simpler.
The given question is [tex]\frac{1}{(1-\sqrt{5 })^{2} } + \frac{1}{(1+\sqrt{5} )^{2} }[/tex]
We shall be simplifying the expression in parts
From difference of two squares
(1)/[(1-√5)(1+√5) = 1+5 = 1/6
The second part is 1/[(1+√5)(1+√5) = 1/(1+√10+5)
= 1/(6+√10)
Joining the two parts to get
1/6 + 1/(6+√10
Simplifying the fractions
(√10+1)/(6+√10)
= 1/6
Therefore the value of the expression is 1/6
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Change the circle equation into standard form then answer the following questions:
of the center?
of the vertices?
Coordinates
Coordinates
How long is the radius?
Domain?
Range?
X²+ y²-14X + 8Y+ 40 = 0
Answers
First, use the commutative property to rearrange and group x and y:
x^2+(-14x)+y^2+8y+40=0
Now, we will subtract 40 from both sides:
x^2+(-14x)+y^2+8y=-40
We can now complete the square for both x and y:
(x^2-14x+(-14/2)^2)+(y^2+8y+(8/2)^2)=-40+(-14/2)^2+(8/2)^2
Simplify:
x^2-14x+49+y^2+8y+16=-40+49+16
Factor and simplify:
(x-7)^2+(y+4)^2=25
Now, factor the 25 to a squared factor:
(x-7)^2+(y+4)^2=5^2
The circle is now in standard form, so let’s identify its features:
Center: (h,k) = (7, -4)
Radius: 5
Vertices: (7, 1), (7, -9), (2, -4), (12, -4)
Domain: [2, 12]
Range: [-9, 1]
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Find the measure of the arc or central angle indicated.
Answers
The central angle of the given arc LKJ is; 211°
How to find the length of an arc of a circle?
We want to find the length of the arc LKJ. The central angle for this arc length is; 115° + 96° = 211°
The formula for length of arc is;
L = θ/360 * 2πr
where;
θ is central angle
r is radius
We are not given the radius and as such, we can only find the central angle which is 211°
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Solve by using substitution. Express your answer as an ordered pair.
{4x+y=1
y=x−4
Answers
Answer:
The correct answer is (1, -3).
Step-by-step explanation:
To solve this question, we should use substitution. This means we can substitute the value given for y (as indicated by the second equation) into the first equation. This is shown below:
4x + y = 1
4x + (x - 4) = 1
We simplify the left side of the equation and then solve for x.
5x - 4 = 1
5x = 5
x = 1
We must also solve for y. To do this, we can plug in x = 1 into either of the given equations.
y = x - 4
y = 1 - 4
y = -3
Therefore, x = 1 and y = -3. The question asks us to express the answer as an ordered pair (x,y), so the answer is (1, -3).
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Callie took out a loan for $7000 to purchase a car. The loan must be repaod at the end of six years in one payment with interest of 5%. The total amount Callie has to pay back at the end of the loan is
A.$7350
B.$9100
C.$7900
D.$9700
Answers
The correct value of answer is B. $9100.The interest on the loan is 5% of the principal. So, the interest amount is:= $350
To calculate the total amount Callie has to pay back at the end of the loan, we need to add the principal amount (the original loan amount) and the interest accrued over the six-year period.
The interest can be calculated using the formula: Interest = Principal * Rate * TimeHere, the principal amount is $7000, the interest rate is 5% (or 0.05 as a decimal), and the time is 6 years.
Interest = $7000 * 0.05 * 6 = $2100
Adding the interest to the principal, the total amount Callie has to pay back is:
Total amount = Principal + Interest = $7000 + $2100 = $9100
Therefore, the correct answer is B. $9100.
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What is the solution set of the quadratic inequality x^2-5<0?
Answers
The solution set of the quadratic inequality x² - 5 < 0 is - √5 < x < √5
How to determine the solution set?From the question, we have the following parameters that can be used in our computation:
The quadratic inequality is:
x^2-5<0
Express properly
x² - 5 < 0
Add 5 to both sides of the inequality
x² < 5
Take the square root of both sides
x < ±√5
Expand the inequality expression
- √5 < x < √5
Hence, the solution is - √5 < x < √5
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Your sorority is preselling tickets for an end of year formal. You will save 22% off the door price by prepaying
$56.40 per ticket now.
How much will you pay if you wait to purchase tickets at the door?
Answers
Answer:
$68.81
Step-by-step explanation:
22% of 56.40 can be found by multiplying
.22 and 56.4, which equals 12.408
therefore, if you add 12.408, or 12.41, to 56.40 you will get 68.81
solve 2y=3x+12 for y
Answers
Answer: y=[tex]\frac{3x}{2}[/tex]+6
Step-by-step explanation:
isolate y by dividing both sides by 2
y=3x+12/2
y=[tex]\frac{3x+12}{2}[/tex]
y=[tex]\frac{3x}{2}[/tex]+6
The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron v(t) obeys the differential equation dv dt = −v[v2 − (1 + a)v + a] where a is a positive constant such that 0 < a < 1. (a) For what values of v is v unchanging (that is, dv/dt = 0)? (Enter your answers as a comma-separated list.) v = (b) For what values of v is v increasing? (Enter your answer using interval notation.) (c) For what values of v is v decreasing? (Enter your answer using interval notation.)
Answers
The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.
What is electric impulse?The strength of the field is shown by the distance between the lines; the closer they are to one another, the stronger the field.
In this scenario, the field weakens as we travel away from the charge because the distance between the lines widens (it actually obeys an inverse square law,
The electric field, which is pointed away from the core charge, is indicated by the direction of the lines.
This is due to the fact that a positive test charge would be repelled away from the electric field if it were placed there because the direction of the electric field corresponds to the direction of the force that a positive test charge would experience when immersed in the electric field.
Hence, The values of v for the electric impulse model in the Fitzhugh-Nagumo model are 0, 1, and a.
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For the following, find the length of AB:
(Use \large \pi=3.14 when necessary and round your final answer to the hundredths.)
Arc AB =
Answers
In the given diagram, the length of arc AB is 10.05.
Calculating the length of an arc ABFrom the question, we are to determine the length of arc AB.
From the formula for calculating the length of an arc, we have that
Length of an arc = θ/360° × 2πr
Where θ is the angle subtended by arc at the center of the circle
and r is the radius of the circle
In the given diagram,
Angle subtended by the arc = 48°
Radius, r = 12
Therefore,
The length of the arc = 48/360 × 2×3.14×12
Length of the arc = 2/15 × 1884/25
Length of the arc = 10.05
Hence, the length of AB is 10.05
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There are 1,295 students attending a small university. There are 714 women enrolled. What percentage of student are women?
Answers
Answer:
55.13 I'm sure is the answer
There are 714 women out of the total 1295 students:
[tex]\dfrac{714}{1295}\approx0.551351351351351[/tex]
About 55.14% of the students are women.
HELP ME QUICICICKCKC
Answers
Answer:
A.
Step-by-step explanation:
Multiply the x like terms than multiply the other like terms
At the time of her grandson's birth, a grandmother deposits 14000 in an account that pays 9.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
Answers
The value of the account at the child's twenty-first birthday is 102125.44
How to determine the value of the account at the child's twenty-first birthday?We can use the compound interest formula to determine the value of the account (A) on the child's twenty-first birthday:
A = P (1 + r/n)^(nt)
Where:
P is the initial amount of money deposited in the account
r is the interest rate
n is the number of times the interest is compounded per year
t is the number of years
Given: P = 14000, r = 9.5% = 0.095, t = 21, n = 12 (i.e. 12 months per year)
Substitututing into A = P (1 + r/n)^(nt):
A = 14000 (1 + 0.095/12)^(12×21)
A = 14000 (1 + 0.095/12)^(252)
A = 102125.44
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An element with a mass of 520 grams decays by 25.1% per minute. To the nearest tenth of a minute, how long will it be until there are 60 grams of the element remaining?
Answers
The total time for the mass of the element to be 60 grams is 7.5 minutes
What is exponential growth factor?
The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ for growth rate
x ( t ) = x₀ × ( 1 - r )ⁿ for decay rate
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units = n
Given data ,
Let the total mass of element be = 520 grams
So , the value of x₀ = 520 grams
Now , the decay rate of element is given by r = 25.1 %
To calculate the time at which the amount of element left is 60 grams = n
where n is the total time = t
So , x ( t ) = 60
The decay rate formula is given by the equation ,
x ( t ) = x₀ × ( 1 - r )ⁿ
Substituting the values in the equation , we get
60 = 520 ( 1 - 25.1/100 )ⁿ
On simplifying the equation , we get
60 = 520 ( 1 - 0.251 )ⁿ
Divide by 520 on both sides of the equation , we get
( 0.749 )ⁿ = 6/52
Taking logarithm on both sides , we get
n × log ( 0.749 ) = log ( 6/52 )
Divide by log ( 0.749 ) on both sides , we get
n = log ( 6/52 ) / log ( 0.749 )
n = -0.9378 / -0.1255
n = 7.47 minutes
Therefore , the value of n time t = 7.5 minutes
Hence ,
The total time for the mass of the element to be 60 grams is 7.5 minutes
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Find the derivative using the Fundamental Theorem of Calculus, part 1, which states that if f(x) is continuous over an interval [a, b], and the function F(X) is defined by F(X) - F'(x) = f(x) over [a, b]. [*re) or, then del tot Additional Materials eBook 4.
then Find the derivative using the Fundamental Theorem of Calculus, part 1, which states that if f(x) is continuous over an interval (a, b), and the function F(x) is defined by F(X) - F'(x) = f(x) over [a, b]. de la intu In(u) du 6.
Evaluate the definite integral using the Fundamental Theorem of Calculus, part 2, which states that iffis continuous over the interval [a, b] and F(x) is any antiderivative of f(x), then Giºrno dx = F(b) – Fla). [x?- ») 3x) dx Х
Answers
On solving the question, by the help of, Fundamental Theorem of Calculus, we got answer [tex]3xe^x[/tex]
What is fundamental Theorem of Calculus?A theorem that connects the ideas of differentiating a function from integrating a function is known as the fundamental theorem of calculus. The two processes are inverses of one another, with the exception of a constant number that is dependent on the starting point for computing area.
When asked to compute the derivative of an integral, utilize the calculus fundamental theorem rather than evaluating the integral.
FTOC informs us that:
[tex]\frac{d}{dx} [\int\limits^{3x}_t {3lnt} \, dxt] = 3xe^x[/tex]
(That is, the integral's derivative returns the original function to us.)
We are required to locate:
h'(x) where h(x)= [tex]\int\limits^{3x}_t {3lnt} \, dxt= 3xe^x[/tex]
what we want
[tex]h'(x) = \frac{d}{dx} [\int\limits^{ex}_t {3lnt} \, dxt] = 3xe^x.............................A[/tex]
(Note that the first integral's upper limits are not in the proper format for the FTOC to be applied immediately.) The chain rule and a replacement can be used to alter the definite integral. Let:
[tex]u = e^x = \frac{du}{dx} = e^x[/tex]
Using the chain rule and substituting into the integral [A], we obtain:
[tex]\frac{d}{dx} [\int\limits^{ex}_t {3lnt} \, dxt] =[/tex][tex]\frac{d}{dx} [\int\limits^{u}_t {3lnt} \, dxt] = 3xe^x[/tex]
= [tex]e^x \frac{d}{du} [\int\limits^{ex}_t {3lnt} \, dxt] = 3xe^x[/tex]
now we got answer - [tex]3xe^x[/tex]
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What is the circumcenter of a triangle formed by (4,2), (3,-3) and (2,2)?
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The circumcenter of a triangle formed by (4,2), (3,-3) and (2,2) is located at (3, -0.4).
The circumcenter of a triangle is the point of intersection of the three perpendicular bisectors of the sides of a triangle.
Let A = vertex at (4,2)
B = vertex at (3,-3)
C = vertex at (2,2)
Get the midpoint of each side.
midpoint = [(x₂ + x₁)/2 , (y₂ + y₁)/2]
side AB : midpoint = [(3 + 4)/2 , (-3 + 2)/2] = (3.5, -0.5)
side AC : midpoint = [(4 + 2)/2 , (2 + 2)/2] = (3, 2)
side BC : midpoint = [(3 + 2)/2 , (-3 + 2)/2] = (2.5, -0.5)
Get the slope of each side.
slope = (y₂ - y₁) / (x₂ - x₁)
side AB : slope = (-3 - 2) / (3 - 4) = 5
side AC : slope = (2 - 2) / (2 - 4) = 0/-2 = 0
side BC : slope = (2 - -3) / (2 - 3) = -5
Determine the equation of the line of each of the three perpendicular bisectors of the sides of a triangle, that passes through the midpoint and with a slope equal to the negative reciprocal of the slope of the side.
y = mx + b
perpendicular bisector of AB :
-0.5 = -1/5(3.5) + b ; b = 0.2 ; y = -1/5x + 0.2
perpendicular bisector of AC :
since AC is a horizontal line, x = 3
perpendicular bisector of BC :
-0.5 = 1/5(2.5) + b ; b = -1 ; y = 1/5x - 1
Since x is already equal to 3, substitute the value of x in the two other equation and solve for y.
y = -1/5x + 0.2
y = -1/5(3) + 0.2
y = -0.4
y = 1/5x - 1
y = 1/5(3) - 1
y = -0.4
Hence, the circumcenter of the triangle is located at (3, -0.4).
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write the following python function: asquare(k) takes k as a parameter and returns a list containing squares of first k integers. asquare(5) will return the list [1, 4, 9, 16, 25] print that list
Answers
The python function is, [1, 4, 9, 16, 25] [1, 4].
What is square of a number?
It is easy to determine a number's square. To determine the given number's square, we must multiply it by itself. A number raised to the power of 2 is always used to represent the square term.
For instance, the square of 6 is equal to 6 times 6, or 6 x 6 = 6^2 = 36.
A "Square Number" is the product of multiplying an integer or number (not a fraction) by itself.
For instance, 3 x 3 = 3^2, or 3 multiplied by 3 equals 3 squared. In essence, a square number is the result of multiplying an integer or number by itself exponentially.
Hence, the python function is, [1, 4, 9, 16, 25] [1, 4].
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f(x) = 3x² + 4x - 6
g(x) = 6x³5x² - 2
Find (f - g)(x).
O A. (f-g)(x) = 6x³ - 2x² + 4x - 8
O B. (f-g)(x) = -6x³ - 2x² + 4x - 8
O c. (f - g)(x) = 6x³ - 8x² - 4x + 4
O D. (f - g)(x) = -6x³ + 8x² + 4x - 4
Answers
The difference of the functions, f(x) = 3x² + 4x - 6 and g(x) = 6x³ - 5x² - 2, is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4.
How to Find the Difference of Two Functions?Finding the difference of two functions involves combining like terms together and then simplify.
Given the functions:
f(x) = 3x² + 4x - 6
g(x) = 6x³ - 5x² - 2
To find (f - g)(x), it implies that we find the difference between f(x) and g(x).
(f - g)(x) = f(x) - g(x)
Substitute
f(x) - g(x) = (3x² + 4x - 6) - (6x³ - 5x² - 2)
Open the parentheses:
f(x) - g(x) = 3x² + 4x - 6 - 6x³ + 5x² + 2
Combine like terms
f(x) - g(x) = - 6x³ + 8x² + 4x - 4
Therefore, the answer is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4
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