Simplify: √(5 + 2√6).
Answers
\(\large\underline{\sf{Solution-}}\)
Given that,
\(\sf\sqrt{5+2\sqrt6}\)
We can rewrite it as,
\(\sf\longmapsto\sqrt{5+2(\sqrt2)(\sqrt3)}\)
\(\sf\longmapsto\sqrt{2+3+2(\sqrt2)(\sqrt3)}\)
So,
\(\sf\longmapsto\sqrt{(\sqrt2)^2+(\sqrt3)^2+2(\sqrt2)(\sqrt3)}\)
We know that,
\(\sf\red⇛ a^2+b^2+2ab=(a+b)^2\)
Here, a = √2 and b=√3.
So,
\(\sf\longmapsto\sqrt{(\sqrt2)^2+(\sqrt3)^2+2(\sqrt2)(\sqrt3)}\)
\(\sf\longmapsto\sqrt{(\sqrt2+\sqrt3)^2}\)
So, the square root and the square get cancelled. So,
\(\sf\longmapsto\sqrt{(\sqrt2+\sqrt3)^2}\)
\(\sf\longmapsto\pm\sqrt2+\sqrt3\)
Therefore,
\(\bf\sqrt{5+2\sqrt6}=\pm\sqrt2+\sqrt3\)
Related Questions
A rectangle initially has dimensions 6 cm by 7 cm. All sides begin increasing in length at a rate of 3 cm/s. At what rate is the area of the rectangle increasing after 23 s?
Answers
Answer:
The area of the rectangle is increasing at a rate of 54 cm2/s.
Step-by-step explanation:
What is 42/66 written in lowest terms?
Answers
Answer:
7/11 or
7
--
11
Step-by-step explanation:
Hope this helps :)
1. 237 + 496 =
1. 600 - 321 =
7. 993 - 294 =
Answers
Answer:
237+496= 733
600-321= 279
993-294= 699
You recorded the actual expenses you incurred for a previous month in the above table. Determine your monthly budget based on the expenses given. a. $2,298.45 c. $2,205.24 b. $2,376.76 d. $1,879.12
Answers
Answer: Therefore, the closest option to the monthly budget based on the expenses given is (a) $2,298.45.
Step-by-step explanation:
$1,200.00 (rent) + $245.60 (electricity) + $80.00 (gas) + $60.00 (water) + $200.00 (groceries) + $150.00 (dining out) + $100.00 (entertainment) + $72.85 (internet) + $100.00 (miscellaneous) = $2,208.45
If Isabella has 1809 and Leah takes 27 how many will Isabella have left
1809/27=
Answers
Answer:
1809/27=67 is your answer........
A school has 800 students in Grade 6. Four fifths of those students avail the school bus facility. How many Grade 6 students travel by school bus?
Answers
Answer:
640 i believe
Step-by-step explanation:
can someone help me please
here is the picture
Answers
The composite result function of (f o g)(x) and the domain in the functions f(x) = x/( x + 1 ) and g(x) = 10/x are 10 / ( 10 + x ) and (-∞,-10) ∪ (-10,0) ∪ (0,∞) respectively.
What is the composite result function of (f o g)(x) and the domain?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = x/( x + 1 )g(x) = 10/x(f o g )(x) = ?First, set up the composite result function ( f o g ).
( f o g )(x) = f(g(x)) = g(x)/( g(x) + 1 )
( f o g )(x) = f(g(x)) = (10/x)/( (10/x) + 1 )
Simplify
( f o g )(x) = (10/x)/( (10/x) + 1 )
( f o g )(x) = (10/x) × 1/( (10/x) + 1 )
( f o g )(x) = (10/x) × ( x /(10 + x ) )
( f o g )(x) = 10 ( 1 /(10 + x ) )
( f o g )(x) = 10 / ( 10 + x )
To determine the domain, set the denominator in 10/x equals zero.
x = 0
Next, set the denominator in ( f o g )(x) = (10/x)/( (10/x) + 1 ) equals zero and solve for x.
(10/x) + 1 = 0
10/x = -1
10 = -x
-10 = x
x = -10
Therefore, the domain will be all values of x that makes the expression defined. (-∞,-10) ∪ (-10,0) ∪ (0,∞).
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Who knows how to solve this ??
Answers
The total of the original accounts was $2000.
suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000. a random sample of 400 house-holds has been chosen. in this sample, letxbe the number of households thatearn over 80,000, and letybe the number of households that earn over 450,000.use either the normal or the poisson approximation, whichever is appropriate ineither case, to nd the simplest estimates you can for the probabilitiesp(x48)andp(y2)
Answers
The probability of P(X = 48) and P(Y =2) is 0.1056 and 0.2642 respectively.
Suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000.
a random sample of 400 house-holds has been chosen
N = 400
P = 25%
n*p = 400*0.25 = 100
n(1-p) = 400 * 0.75 = 300
100 and 300 are greater than 5 so we use the normal distribution here to estimate further.
mean = n*p = 100
sd = √(np(1 - p))
sd = √(100(1 - 0.25))
sd = √(100 x 0.75)
sd = √75
sd = 8.66
p(X≥48)
= p(X≥47.5)
P(z < (47.5 - 40)/6)
P(z < 1.25)
= 0.8944
1 - 0.8944
= 0.1056
FOR Y
N = 400 p = 0.25% = 0.0025
400 * 0.0025 = 1
1 is less than 5 so we use poisson distribution.
using the excel function,
1 - BINOMDIST(1, 400, 0.0025, TRUE)
= 1 - 0.735759074
= 0.2642
Therefore, the probability of P(X = 48) is 0.1056 and P(Y =2) is 0.2642
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the number y divided by 100 y. ?
Answers
Answer:
1/100
Step-by-step explanation:
Evaluate the expression when m=3 and n=44.
1. n-6m
Answers
Answer: 35
Step-by-step explanation: PEMDAS n-6(3)
44-9
Answer:
26
Step-by-step explanation:
You just put it in, n- (6*m) 6m which is also equal to 44 - 6*3 = 44-18 = 26
I hope this helps!
25/5=60/12 do they form a proportion
Answers
Answer: YES
Step-by-step explanation: both equal 5 when divided.
Using L’Hôpital’s Rule, evaluate
Answers
By using L' hospital rule the value of lim(x→∞) x^(1/3x) is 0
The given limit is lim(x→∞) x^(1/3x)
Rewriting this expression in exponential form:
lim(x→∞) e^(ln(x^(1/3x)))
Using the properties of logarithms:
= lim(x→∞) e^((1/3x)ln(x))
Now, we can apply L'Hôpital's Rule by differentiating the numerator and denominator with respect to x:
= lim(x→∞) [(1/3x) × ln(x)]/ [1]
Differentiating the numerator and denominator:
= lim(x→∞) [(1/3x)×(1/x)×ln(x) + (1/3x) × (1)] / [1]
Taking the limit as x approaches infinity, the second term in the numerator ((1/3x)) approaches 0 as x tends to infinity.
Therefore, we are left with= lim(x→∞) [(1/3x^2) × ln(x)] / [1]
Again, taking the limit as x approaches infinity, the term (1/3x²) approaches 0 as x tends to infinity. Hence, we have:
= lim(x→∞) [0 × ln(x)] / [1]
= 0
Therefore, by using L' hospital rule the value of lim(x→∞) x^(1/3x) is 0
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sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12cm3/s . if the radius of the funnel is 8 cm and the altitude of the funnel is 16 cm, find
a) the depth of the salt water after 30 second
b)the rate of change of its depth at that instant
Answers
Answer:
h ≅ 16.29 cm
\(\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}\)
Step-by-step explanation:
From the conical funnel;
Let the adjacent line at the base of the cone be radius (r) and the opposite ( vertical length) be the height (h)
Then;
\(tan \theta= \dfrac{r}{h}\)
\(tan \theta= \dfrac{8}{16}\)
\(tan \theta= \dfrac{1}{2}\)
∴
\(\dfrac{r}{h} = \dfrac{1}{2}\)
\(r = \dfrac{h}{2}\)
The volume (V) of the cone is expressed as:
\(V = \dfrac{1}{3}\pi r ^2 h\)
\(V = \dfrac{1}{3}\pi (\dfrac{h}{2})^2 h\)
\(V = \dfrac{\pi h^3}{3\times 4}\)
\(\dfrac{dv}{dt} = \dfrac{3 \pi h^2}{3 \times 4} \dfrac{dh}{dt}\)
\(\dfrac{dv}{dt} = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}\)
Given that:
\(\dfrac{dv}{dt} = 12 \pi\)
Then:
\(-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}\)
\(- \int 48 \ dt = \int h^2 \ dh\)
\(\dfrac{h^3}{3}= -48 t + c\)
\(At \ t = 0 \ ; h = 0\)
∴
\(\dfrac{0^3}{3} = -48(0) + c\)
c = 0
So;
\(\dfrac{h^3}{3}= -48 t + 0\)
\(\dfrac{h^3}{3}= -48 t\)
t = 30
\(\implies h = (-48(30))^{1/3}\)
h = 16.2865
h ≅ 16.29 cm
Thus;
from \(-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}\)
\(\dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} } =\dfrac{dh}{dt}\)
\(\dfrac{dh}{dt} = \dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} }\)
\(\dfrac{dh}{dt}=\dfrac{-12 \times 4} { {16.29^2} }\)
\(\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}\)
1493600÷8 i need full steps
Answers
When 1,493,600 is divided by 8 the quotient is 186,700.
To divide 1,493,600 by 8, you can follow these steps:
We have to write down the dividend (1,493,600) and the divisor (8).
Now start with the largest place value in the dividend (the leftmost digit) and perform the division.
Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.
Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.
Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.
Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.
Divide 9 by 8. The quotient is 1, and the remainder is 1.
Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.
Divide 13 by 8. The quotient is 1, and the remainder is 5.
Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.
Divide 56 by 8. The quotient is 7, and there is no remainder.
Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.
Divide 70 by 8. The quotient is 8, and there is no remainder.
There are no more digits to bring down, and the division is complete.
The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.
Therefore, the result of 1,493,600 ÷ 8 is 186,700.
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Q1 ? Help Robert is 7 ½ years old. How many months old is he?
Answers
Answer:
Step-by-step explanation:
If Robert is 7 1/2 months old you need to multiply 7 1/2 by 12 because there are 12 months in a year.
7x12=84
1/2x12=6
6+84=90
Suppose a life insurance company sells a
$280,000
1-year term life insurance policy to a
20-year-old
female for
$270.
According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is
0.999544.
Compute and interpret the expected value of this policy to the insurance company.
Answers
Answer:
$142.32, profit on sale of the policy
Step-by-step explanation:
You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.
CostThe insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...
0.000456 × $280,000 = $127.68
ProfitThe company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...
$270 -127.68 = $142.32
The expected value of the policy to the company is $142.32.
This represents its profit from sale of the policy.
__
Additional comment
Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."
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Help Please.
The difference between two numbers is 9. Four times the larger number plus one-half the smaller is 45. What are the numbers?
Answers
Answer:
To solve this problem, we will use the following steps:
Step 1: Let's assume that the larger number is x and the smaller number is y, we know that the difference between the two numbers is 9, so we can write the equation: x-y = 9
Step 2: We know that Four times the larger number plus one-half the smaller is 45, so we can write the equation: 4x + 0.5y = 45
Step 3: Now we have two equations with two unknowns, we can solve for one of the unknowns by isolating it in one of the equations.
x-y = 9
x = y+9
Step 4: Now we can substitute the value of x in the second equation
4(y+9) + 0.5y = 45
4y + 36 + 0.5y = 45
4.5y + 36 = 45
4.5y = 9
y=2
Step 5: We can substitute the value of y in one of the equation, to find the value of x
x-2 = 9
x = 11
Final Answer: The two numbers are 11 and 2.
VPSB Social Studies 6 Q3-2022 (HOMEBOUND)
Which of the following buildings do you think represents the influence of ancient Greek culture?
SUPT.
Intro
Photo by Angus Cepka
0000
50f5
Photo by Daniel Schwen
O
Done
Bentley Dyson
Answers
The buildings that represent the influence of ancient Greek culture are -
THE PARTHENONTEMPLE OF OLYMPIAN ZEUSERECHTHEIONGREAT THEATER OF EPIDAURUSWhat is Ancient Greek Culture like?Greece is a collectivist society in the sense that there is strong loyalty shown to familial and social groups. The social life of many Greeks is usually kept to a close circle of family and friends. These personal relationships are deeply important to people's day-to-day life.Given are the buildings from Ancient Greek Culture.
The buildings that represent the influence of ancient Greek culture are -
THE PARTHENONTEMPLE OF OLYMPIAN ZEUSERECHTHEIONGREAT THEATER OF EPIDAURUSTherefore, the buildings that represent the influence of ancient Greek culture are -
THE PARTHENONTEMPLE OF OLYMPIAN ZEUSERECHTHEIONGREAT THEATER OF EPIDAURUSTo solve more questions on Ancient Greek Culture, visit the link below -
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Can someone help me please
Answers
Answer:
90,56,7867,45,89,45,24,67
Simplify csc(t)tan(t) to a single trig function or constant with no fractions.
Answers
Answer:
sec(t)
Step-by-step explanation:
\(\csc(t)\tan(t)=\frac{1}{\sin(t)}\times\frac{\sin(t)}{\cos(t)}=\frac{1}{\cos(t)}=\sec(t)\)
The single Trigonometric rate for csc( t) tan( t) is sec t.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in computations. There are six popular trigonometric functions for an angle. Sine( sin), cosine( cos), divagation( tan), cotangent( hut), secant( sec), and cosecant are their separate names and acronyms( csc).
Given:
csc( t) tan( t)
As, we know that csc t = 1/ sin t
and, tan t = sin t/ cos t
substituting the values in csc( t) tan( t) we get
csc( t) tan( t)
= 1/ sin t x sin t/ cos t
= 1/ cos t
= sec t
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What is the equation of a line, in general form, with a slope of -2 and a y-intercept of 8?
x + 2y - 8 = 0
2x + y - 8 = 0
2x - y + 8 = 0
Answers
\(2x+y-8=0\).
A state becomes good if its people are good justify this statement
Answers
Step-by-step explanation:
Yes, the statement is true "A state becomes good if its people are good". Government is one of the most important body for the good future of any country. The difference between a good and bad country occurs due to its government and governance. Similarly, citizens plays a vital role for the difference between good and bad state. The literacy rate of a state should be high for the sake of becoming good state. A state becomes good if its people are good, as they are representative of the state.
Step-by-step explanation:
The statement is correct because a state is made up of people. If people would only abide by the laws and be responsible citizens the state's image would also look good
A plane leaves an airport and flies due north. Two minutes later, a
second plane leaves the same airport flying due east. The flight
plan shows the coordinates of the two planes 10 minutes later. The
distances in the graph are measured in miles. Use the Pythagorean
Theorem to find the distance shown between the two planes.
(Example 2)
Answers
The distance between the two planes after 10 minutes is 10 miles.
Step by step explanationWe can use the Pythagorean Theorem to find the distance between the two planes. According to the theorem, the distance between two points in a plane is given by the equation:
d = √( (x2 - x1)^2 + (y2 - y1)^2 )
where (x1, y1) and (x2, y2) are the coordinates of the two points.
The first plane is flying due north, so its position after 10 minutes will be (0, 10). The second plane is flying due east, so its position after 10 minutes will be (10, 0).
We can plug these coordinates into the equation to find the distance between the two planes:
d = √( (10 - 0)^2 + (10 - 0)^2 )
d = √( 100 )
d = 10
So the distance between the two planes after 10 minutes is 10 miles
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A common multiple is 180 true or false
Answers
Answer:
False
Step-by-step explanation:
22647 inches to miles, please show work
Answers
Answer: 0.3574 miles
Step-by-step explanation:
22647 inches = 0.3574 miles
hurry this is a test please answer correctly
Answers
The Answer fam is.............5
Jack is shopping. Last week he bought $10 of groceries and ended up paying $10.07 after taxes. This week he's buying $15 of groceries. If the tax rate remains the same, how much will he end up paying after taxes?
Answers
Answer:
16.05
Step-by-step explanation:
first I realized 7 cents is .07% of 10 the I multiplied .07 times 15 then I added them up and got the answer
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The value of angle BCD is determined as 108⁰.
option B is the correct answer.
What is the value of angle BCD?The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc AB = m∠ACB
m∠ACB = 72⁰
The value of angle BCD is calculated as follows;
angle BCD = 180 - 72⁰ (sum of angles in a circle)
angle BCD = 108⁰
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Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answers
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.
