Answer:
First we write y and its derivatives as power series:
y=∑n=0∞anxn⟹y′=∑n=1∞nanxn−1⟹y′′=∑n=2∞n(n−1)anxn−2
Next, plug into differential equation:
(x+2)y′′+xy′−y=0
(x+2)∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0
x∑n=2∞n(n−1)anxn−2+2∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0
Move constants inside of summations:
∑n=2∞x⋅n(n−1)anxn−2+∑n=2∞2⋅n(n−1)anxn−2+∑n=1∞x⋅nanxn−1−∑n=0∞anxn=0
∑n=2∞n(n−1)anxn−1+∑n=2∞2n(n−1)anxn−2+∑n=1∞nanxn−∑n=0∞anxn=0
Change limits so that the exponents for x are the same in each summation:
∑n=1∞(n+1)nan+1xn+∑n=0∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−∑n=0∞anxn=0
Pull out any terms from sums, so that each sum starts at same lower limit (n=1)
∑n=1∞(n+1)nan+1xn+4a2+∑n=1∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−a0−∑n=1∞anxn=0
Combine all sums into a single sum:
4a2−a0+∑n=1∞(2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an)xn=0
Now we must set each coefficient, including constant term =0 :
4a2−a0=0⟹4a2=a0
2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an=0
We would usually let a0 and a1 be arbitrary constants. Then all other constants can be expressed in terms of these two constants, giving us two linearly independent solutions. However, since a0=4a2 , I’ll choose a1 and a2 as the two arbitrary constants. We can still express all other constants in terms of a1 and/or a2 .
an+2=−(n+1)nan+1+(n−1)an2(n+2)(n+1)
a3=−(2⋅1)a2+0a12(3⋅2)=−16a2=−13!a2
a4=−(3⋅2)a3+1a22(4⋅3)=0=04!a2
a5=−(4⋅3)a4+2a32(5⋅4)=15!a2
a6=−(5⋅4)a5+3a42(6⋅5)=−26!a2
We see a pattern emerging here:
an=(−1)(n+1)n−4n!a2
This can be proven by mathematical induction. In fact, this is true for all n≥0 , except for n=1 , since a1 is an arbitrary constant independent of a0 (and therefore independent of a2 ).
Plugging back into original power series for y , we get:
y=a0+a1x+a2x2+a3x3+a4x4+a5x5+⋯
y=4a2+a1x+a2x2−13!a2x3+04!a2x4+15!a2x5−⋯
y=a1x+a2(4+x2−13!x3+04!x4+15!x5−⋯)
Notice that the expression following constant a2 is =4+ a power series (starting at n=2 ). However, if we had the appropriate x -term, we would have a power series starting at n=0 . Since the other independent solution is simply y1=x, then we can let a1=c1−3c2, a2=c2 , and we get:
y=(c1−3c2)x+c2(4+x2−13!x3+04!x4+15!x5−⋯)
y=c1x+c2(4−3x+x2−13!x3+04!x4+15!x5−⋯)
y=c1x+c2(−0−40!+0−31!x−2−42!x2+3−43!x3−4−44!x4+5−45!x5−⋯)
y=c1x+c2∑n=0∞(−1)n+1n−4n!xn
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Drag each length to the correct location on the triangle. each length can be used more than once, but not all lengths will be used. what are the missing side lengths for the triangle? 10 5
Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
What is Trigonometry Ratios?Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.
According to the given information:Reference angle (∅) = 60
Adjacent = 4√3
Opposite = ?
Apply TOA:tan 60 = opp/adj
tan 60 = Opp/4√3
√3 = opp/4√3
Opposite = √3 × 4√3
Opposite = 12
Find the other missing side:Reference angle (∅) = 60
Adjacent = 4√3
Hypotenuse = ?
Apply CAH:cos 60 = adj/hyp
cos 60 = 4√3/hyp
hyp = 4√3/cos 60
hyp = 4√3/1/2
hyp = 4√3 × 2
hyp = 8√3
Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.
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B is the midpoint of segment AC. Which statement best describes the relationship between triangles ABD and CBD? (1 point)
The statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
What are similar triangles?
It is important to note the following;
"Two triangles are similar when their corresponding angles are equal and corresponding sides are in equal proportion."
The SSS congruence states that ; "Two triangles are congruent if all three sides of a triangle are congruent to corresponding three sides of other triangle."
SSS similarity postulates that; "Two triangles are similar if all the three sides of a triangle are in proportion to the three sides of another triangle."
SAS similarity postulates that ; "Two triangles are similar if the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle between the two sides in both the triangle are equal."
SAS congruence postulates that ; "Two triangles are congruent if two sides and the angle between these two sides of one triangle are congruent to the corresponding two sides and the included angle of a second triangle."
For given question,
We have been given triangles ABD and CBD.
B is the midpoint of line AC
⇒ AB = BC
For triangles ABD and CBD,
side AB = side CB; since, B is the midpoint of line AC
side BD = side BD ; they have common sides
side AD = side CD = 15 units each
So, by SSS postulates of triangle congruence triangles ABD and CBD are congruent triangles.
Therefore, the statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
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Please answer quickly! It would be great if you could include the question # and the answer in the answer section, and then explain it below. Thank you in advance!
Answer:
[tex]\textsf{19.} \quad S_{20}=1490[/tex]
33. None of these are correct.
Step-by-step explanation:
Question 19General form of an arithmetic sequence:
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven values:
[tex]a_n[/tex] = 27n = 20d = -5Substitute the given values into the formula and solve for a:
[tex]\implies 27=a+(20-1)(-5)[/tex]
[tex]\implies 27=a+(19)(-5)[/tex]
[tex]\implies 27=a-95[/tex]
[tex]\implies a=27+95[/tex]
[tex]\implies a=122[/tex]
Sum of the first n terms of an arithmetic series:
[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]
where:
a is the first term.d is the common difference.Given values:
a = 122n = 20d = -5Substitute the given values into the formula and solve:
[tex]\implies S_{20}=\dfrac{1}{2}(20)[2(122)+(20-1)(-5)][/tex]
[tex]\implies S_{20}=10[244-95][/tex]
[tex]\implies S_{20}=10[149][/tex]
[tex]\implies S_{20}=1490[/tex]
Question 33Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
where:
a is the first termr is the common ratioGiven values:
a₁ = 1458r = ¹/₃Substitute the given values into the formula and solve:
[tex]\implies S_6=\dfrac{1458\left(1-\frac{1}{3}^6\right)}{1-\frac{1}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456}{\frac{2}{3}}[/tex]
[tex]\implies S_6=\dfrac{1456 \cdot 3}{2}[/tex]
[tex]\implies S_6=2184[/tex]
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I need help cancelling units. please help
Hello and Good Morning/Afternoon:
Let's take this problem step by step:
Let's write out the equation we would hypothetically use to convert 410 kilometers to meters:
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}[/tex]
Let's see if there are any errors:
there are 1000 meters in 1 kilometerwhen converting kilometer --> meter⇒ we want to get rid of the kilometer symbol
⇒ which is done in this problem
[tex]410 kilometers * \frac{1000 meters}{1 kilometers}=\frac{410 kilometers}{1 kilometers}*1000 meters = 410000meters[/tex]
Thus the answer is true
Answer: True
Hope that helps!
What are the exact solutions of x2 − 5x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b squared minus 4 times a times c all over 2 times a?
Answer:
[tex]x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]
Step-by-step explanation:
So the question here is asking you to use the quadratic formula which is expressed as: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]
A quadratic can generally be expressed as: [tex]y=ax^2+bx+c[/tex]
So using the equation you gave: [tex]0=x^2-5x-1[/tex]
We can identify the following values: a=1, b=-5, c=-1
Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.
So plugging in the known values, we get the following equation:
[tex]x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]
The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.
Help me please im not good at math!
Answer:
12 square ft
Step-by-step explanation:
As given in the picture, the formula for the area of circles is A = pi*r*r. Since the radius is 2 ft and pi is approximately 3, A = 3*2*2 = 12 square ft.
Answer:
12 ft^2
Step-by-step explanation:
Since the formula to find the area of a circle is already up, we can use that to solve the question.
The image gave us the value of the radius right away, so the question will be a lot easier to solve.
--> The reason why the radius is needed is that the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.
Now, we can just replace r with 2.
--> A = 4[tex]\pi[/tex]
Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.
--> A = 4 x 3
--> A = 12
We can conclude that the area of the circle is 12 ft^2.
Question 9 of 25 a bookstore costs $105 a day to keep open, and it spends $12 for each book that it sells. if each book sells for $15, what is the break-even point for this bookstore?
The store will break even after selling 35 books.
What is the break-even point?The break-even point is the moment at which total cost and total revenue are equal, implying that your small firm has no loss or benefit. In other words, you've reached the point where the costs of production equal the revenues for a product.To find what is the break-even point for this bookstore:
Given:
The cost required per day to keep the store open = $105Amount spent on each book = $12Let, n be the number of books.
Total costs = 12n + 105
The selling price of each book = $15
Total revenue = 15n
For breaking even, costs = revenue.
12n + 105 = 15n105 = 15n - 12n105 = 3n3n = 105Dividing both sides by 3:3n/3 = 105/3n = 35Therefore, the store will break even after selling 35 books.
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A model train has a scale of 1 in :3 in. if the real trains is 12ft then how tall is the model train ?
If the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.
Given that the model train has a scale of 1:3 and the real train is 12 feet tall.
We are required to find the height of the model train.
Ratio shows how many times one number contains another number. A ratio is the relationship in quantity between two things. It expresses quantity of one thing in terms of another.
Ratio of model train to real train is 1 inches :3 inches.
Height of model train=12*1/4
=3 inches
Hence if the ratio of model train to real train is 1:3 and the real train is 12 feet then the model train is 3 feet long.
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In 2010 and 2012, gallup asked the same 50 people how many hours had they worked at a job in the past 7 days. Is there a difference in the population mean amount of hours worked at a job between 2010 and 2012? would this be an example of independent or dependent samples?.
The given case of Gallup asking the same 50 people how many hours had they worked at a job in the past 7 days. is an example of dependent sample.
What is dependent sample?The measured values in relation in a dependent sample (also called a paired sample).
Some characteristics of dependent sample are-
It is a dependent sample, for instance, if a sample of patients who have knee reconstruction is selected, and each patient is questioned during the procedure. The reason for this is that the identical person was questioned twice.If, for instance, you wish to examine if a new category of baseball bat really does have an impact on notable features and the same individuals play once from the old bat and once with new bat, you also have a dependent sample. Since each player utilized both bats, there are two measured values for each player, all measured values are likewise accessible in pairs.A variation is preselected based on the format wherein you insert your data. A series is typically a respondent and, more broadly, a case. Metric values in a sequence are therefore originally regarded as dependent.To know more about dependent sample, here
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A local school needs to paint the floor of its theater room, where the length of the floor, x, is at least 12 feet. The width of the floor is 4 feet less than the length. It will have a stage and a closet, and the remaining area of the floor will be painted. The dimensions are shown in the diagram:
rectangle with length of x ft and width of x minus 4 ft, right triangle inside labeled stage with height of x minus 4 ft and base of 8 ft, rectangle inside labeled closet with length of 8 ft and width of 4 ft, the rest of the rectangle is labeled floor
Let A represent the painted area, in square feet, of the floor. Choose the correct equation to solve for area (A).
The correct equation that shows the area of painted area is
A=[tex]x^{2} -8x-16[/tex].
Given that the length of the floor,x,is atleast 12 feet.The width of the floor is 4 feet less than the length.There is a right angle of height x-4 and base 8 feet. The rectangle inside has length of 8 feet and width be 4 feet.
We are required to find the painted area of the theater room in square feet.
To find the painted area of the theater the following steps must be followed:
1) Find the area of the theater room.
length =x
Breadth=x-4
Area=x(x-4)
=[tex]x^{2} -4x[/tex]
2) Area of the right triangle.
Height=x-4
Base=8
Area=1/2 *8*(x-4)
=4(x-4)
=4x-16
3) Find the area of the rectangle inside labeled closet.
Length=8
Width=4
Area=8*4
=32
Area=Area of theater room-Area of of right triangle-Area of closet.
=[tex]x^{2} -4x[/tex]-4x+16-32
=[tex]x^{2} -8x-16[/tex]
Hence the correct equation that shows the area of painted area is
A=[tex]x^{2} -8x-16[/tex].
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Answer:
A = x(x − 4) − 0.5(8)(x − 4) − 3(7)
Work:
x = length, making the width (x-4)
The stage closet will be (x-4)(8)(1/2)
The rectangle is 7(3)
which makes the painted area x(x-4) - 4(x-4)
thus giving us
x(x − 4) − 0.5(8)(x − 4) − 3(7)
Step-by-step explanation:
hope this helps :)
Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and
z ≥ 3.
There are 59 integer solutions
Such questions are best solved by writing cases and calculating the total number of cases. So beginning with
1) x = -3. The possible combinations are as follows:-
-3 2 13
-3 3 12
-3 4 11
-3 5 10
-3 6 9
-3 7 8
-3 8 7
-3 9 6
-3 10 5
-3 11 4
10 combinations
2) x = -2
-2 2 12
through
-2 11 3
10 combinations
3) x = -1
-1 2 11
through
-1 10 3
9 combinations
4) x = 0
0 2 10
through
0 9 3
8 combinations
as we can see from the pattern at x =1 we get 7 combinations, at x =2 we get 6 combinations, at x=3 we get 5 combinations and at x =4 we get 5 combinations.
Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.
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Distribute to create an equivalent
expression with the fewest symbols
possible.
2(3 – 8y)
=
Answer:
6 - 16y
Step-by-step explanation:
2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y
The area of the trapezoid is 40 square units.
A trapezoid is shown. The lengths of the bases are 6 and 10, and the height of the altitude is h.
What is the height of the trapezoid?
3 units
5 units
10 units
12 units
The altitude of the trapezoid, based on the given parameters is 5 units
How to determine the height of the trapezoid?From the question, we have the following parameters about the trapezoid
Base length 1 of the trapezoid = 6
Base length 2 of the trapezoid = 10
Area of the trapezoid = 40
Altitude of the trapezoid = h
The area of the trapezoid is calculated using
Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid
Substitute the given parameters in the above formula
40 = 0.5 * (6 + 10) * h
Evaluate the sum of 6 ad 10 (do not approximate)
40 = 0.5 * (16) * h
Evaluate the product of 0.5 and 16 (do not approximate)
40 = 8 * h
Divide both sides by 8 (do not approximate)
h = 5
Hence, the altitude of the trapezoid, based on the given parameters is 5 units
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Answer:
5 units
Step-by-step explanation:
Please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
[tex]t=5.825\sqrt[3]{w/p}[/tex]
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Step-by-step explanation:
Plug in known values
[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]
Divide both sides by 5.825
[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Cube both sides
[tex]12.1738 = \frac{3590}{P}[/tex]
Multiply both sides by P
[tex]12.1738P = 3590[/tex]
Divide both sides by 12.1738
[tex]P = 294.895[/tex]
Round to nearest hp
[tex]P = 295[/tex]
So if you look at the radical, it's possible for it to be mistake for a square root, and not a cube root. This was Daniels mistake, so his steps were
[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]
Divide both sides by 5.825
[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Square both sides
[tex]5.29197 = \frac{3590}{P}[/tex]
Multiply both sides by P
[tex]5.29197P = 3590[/tex]
Divide both sides by 5.29197
[tex]p\approx 678.385[/tex]
He also probably rounded during his steps, which would explain how he got 679 instead of 678 when rounding in the final, but either way his answer is completely off, and this is due to him mistakenly thinking the cube root was a square root.
CAN SOMEONE HELP ASAP WITH 7,8?!!??!
For triangle DEF,
m∠D = 21°
m∠E = 87°
DF = 16
For triangle RST,
m∠S = 68°
m∠T = 57°
Simple polygons with three sides and three internal angles make up triangles. It is one of the fundamental geometric shapes in which the three vertices are connected to one another.
For ΔDEF, it is given that, m∠F = 72°, DE=15,EF=17.
By the law of cosines,
side DF=(a2+b2﹣2abcosγ)1/2
DF=16
Similarly,
m∠D = 21°
As the sum of angles of triangle is 180,
m∠E = 87°
For ΔRST, it is given that, m∠R = 55°, RS=17,RT=9.
By the law of cosines,
side ST=(a2+b2﹣2abcosγ)1/2
ST=16
Similarly,
m∠S = 68°
As the sum of angles of triangle is 180,
m∠T = 57°
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4km^2= ? Mile^2
explain how
Answer:
See below
Step-by-step explanation:
An area of 2km x 2km = 4 km^2
1 km = .62137 miles
2 (.62137) x 2 (.62137) = 1.5444 mi^2
The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. on the bottom shelf are 3 fiction and 5 nonfiction books. choosing which 2 books describes a pair of dependent events?
The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true.To find which 2 books describe a pair of dependent events:
A pair of two dependent events are simply those in which the selection of the second item is contingent on the selection of the first item, causing the probability to change. Because the sample size is lowered when the initial item is taken without replacement, choosing the exact same item reduces the chance. Now, in regard to the question, this means that for two of the occurrences to be independent, they must be on the same shelf and of the same type of book, so that the second book cannot be selected until the first one is. Option D, where both books are on the same shelf and are of the same type, is the only option that fulfills this requirement.Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.
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how do i find x? pls tell me with working
Answer:
35
Step-by-step explanation:
Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.
Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.
Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.
6. Encik Azmi bought a locally made car for RM55 000. After 6 years, Encik Azmi wishes to sell the car. Based on the explanation from the used car dealers, the price of Encik Azmi's car will be calculated using the formula RM55 000 (8)". In this situation, n is the number of years after the car is bought. What is the market value of Encik Azmi's car? State your answer correct to the nearest RM. RM55 000
The result is 859,375,000.
What does multiplication mean?The result of two numbers being multiplied is known as the product. The multiplier is the number of such equal groups, and the multiplicand is the number of items in each group.Calculating the outcome of successive additions of two numbers is known as multiplication. The multiplication formula is 4 times 2 equals 8.Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests will be given in addition, subtraction, multiplication, and division. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.Multiplication has the following three characteristics: commutative, associative, and distributive.The market value of Encik Azmi's car:
Get the answer by multiplication.
[tex]=55000*8^{6}[/tex]
=55000*15625
=859,375,000
The market value of Encik Azmi's car is 859,375,000.
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Write an algebraic expression to match the graph
please help!
the graphed equation is:
y = -|x| + 1
How to find the algebraic expression that matches the graph?On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).
The general absolute value equation is:
y = a*|x - b| + c
Because the vertex is at the point (0, 1), we know that:
b = 0, c = 1
Replacing that we get:
y = a*|x| + 1
Now, this must be zero when we evaluate in x = 1, then:
0 = a*|1| + 1
a = -1
Then the graphed equation is:
y = -|x| + 1
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PLEASE HELP IM STUCK
Direct variation is modeled by the equation y = kx, where k is a constant and x and y vary based on the other's value.
We'll first need to find k, also known as the constant of variation, using our given values of x and y.
6 = k * -7
k = -6/7
Now that we have k, we can plug it in and substitute other values in for x or y. In this case, we'll plug in 4 for x and solve for y.
y = -6/7x
y = -6/7 * (4)
y = -24/7
y = -24/7
Hope this helps!
Answer:
y = -24/7
Step-by-step explanation:
We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.
When y = 6, x = -7, so the proportion will be 6 : -7.
We need to find the y when x is 4, so our equation will be:
6 : -7 = y : 4
Since the proportion will be the same.
Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.
-7y = 24
y = 24 / -7
y = - 24/7
So y = -24/7 will be our answer!
+ Since the '-' is already written down, the top box will contain 24, and the bottom box will contain 7.
each side of a 4ft x 6ft rectangular flower bed was lengthened by the same amount. the area of the new flower bed is twice the area of the old one. Find the new dimensions.
The new dimensions of the flower bed are 4√2 and 6√2
How to determine the new dimensions?The dimensions of the initial rectangular flower bed are given as:
Length = 4ft
Width = 6 ft
The area of the new flower bed is twice the area of the old one.
This means that
New Area = Old Area * 2
Substitute the dimensions of the old area in the above equation
New Area = 4 * 6 * 2
Express 2 as √2 * √2
This gives
New Area = 4 * 6 * √2 * √2
Rewrite the above equation as:
New Area = 4√2 * 6√2
The area of a rectangle is
Area = Length * Width
This means that:
Length = 4√2 ft
Width = 6√2 ft
Hence, the new dimensions of the flower bed are 4√2 and 6√2
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Answer: 6x8
Step-by-step explanation:
(4+x)(6+x)=2*24
x^2+10x+24=48
subtract 48 on both sides
x^2+10x-24=0
Solve using the quadratic formula
-10±√(100+96)÷2
simplifies to
-(10±14)÷2 = 2, -12
-12 doesn't work though because the sides can't be negative.
So x=2
To check, add both sides by 2:
2(4x6)=6x8=48
kelvin pumped 15.2 gallons of gas into his car. if he paid 59.13 for the total amount of gas, what was the rate per gallon that kelvin paid
Answer:
3.89
Step-by-step explanation:
if 15.2 gallons cost 59.13.What about 1
then we just divide 59.13 by 15.2 to get the cost of 1 gallon
In the following expression, both AAA and BBB are variables that can take positive values.
A+\dfrac{2}{B}A+
B
2
A, plus, start fraction, 2, divided by, B, end fraction
Which of these actions will cause the expression's value to increase?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
Keeping AAA constant and increasing BBB
(Choice B)
B
Keeping AAA constant and decreasing BBB
(Choice C)
C
Increasing AAA and keeping BBB constant
(Choice D)
D
Decreasing AAA and keeping BBB constant
The value to increase is keeping A constant and decreasing the value of B
What are fractions?Fractions are written as a ratio of two integers. For instance a.b is a fraction where a and b are integers.
In the fraction a/b, the numerator is and the denominator is b. If the value of the denominator is decreasing the fraction will increase but if the value of the denominator is increasing the fraction will decrease.
Given the expression A + 2/B, the higher the value of B provided such that that A is constant, the higher the expression. Hence the expression that will cause the value to increase is keeping A constant and decreasing the value of B
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Helppp!! pleasee i put a ss!
Answer:
-20
Step-by-step explanation:
He went back 20 and not forward 20. Everyone would want a penalty if you got to go forward.
NEED HELP ASAP
Which statement is correct?
OA) 7<√72<8
OB) 8<√72 <9
OC) 9<√72 <10
OD) 10<√72 < 11
Answer:
ur answer is B
Step-by-step explanation:
Answer:
B
As root over 72 is 8.48 and after we round off we get 8.5 so no B is correct
Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.A) 3 sec2(θ) − 4 = 0B) cot(θ) + 1 = 0
The solution of the assumed equation is
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
Assuming the equation is
csc^2(θ) = 2cot(θ) + 4
and not
Assuming the equation to be:
csc^2(θ) = cot^2(θ) + 1
Solving these equations usually begins with algebra and/or trigonometry. ID for transforming equations to have one or more equations of the form:
trigfunction(expression) = number
It is not always easy to understand how to perform the desired transformation. If it's not obvious, first use the trigonometric identity to reduce the number of different arguments or functions in the equation. In this expression, all arguments are θ. Therefore, there is no need to reduce the number of arguments. But he has two different functions, csc and cot.
csc^2(θ) = cot^2(θ) + 1
Substituting the right side of this equation into the left side of the equation, we get: :
cot^2 (θ) + 1 = 2 cot(θ) + 4
Now that we have only one function cot and one argument θ, we are ready to find the form we need. Subtracting the entire right-hand side from both sides gives:
cot^2(θ) - 2cot(θ) - 3 = 0
The left-hand side factorizes:
(cot(θ)-3)(cot (θ) ) + 1 ) = 0
Using the properties of the zero product,
cot(θ) = 3 or cot(θ) = -1
These two equations are now in the desired form.
The next step is to write the general solution for each equation. The general solution represents all solutions of the equation.
cot(θ) = 3
Note that 3 is not a specific angle value for cot. That's why you need a calculator. Your computer probably doesn't have the crib button, so you'll need to switch it to tan
Since tan is the reciprocal of cot, if cot = 3...
tan(θ) = 1/3
Inverse tan tan^-1(1/3) can be used to find the reference angle. You should get a reference angle of 18.43494882 degrees. Using this reference angle and cot (and tan) being positive in the 1st and 3rd quadrants, we get the general solutions
θ = 18.43494882 + 360k
and
θ = 180 + 18.43494882 + 360k
.
θ = 198.43494882 + 360k
where
cot(θ) = -1
-1 should be recognized as a special angle value for cot. So you don't need a calculator. This reference angle is 45 degrees. Using this reference angle, cot is negative in the 2nd and 4th quadrants, so
θ = 180 - 45 + 360k
and
θ = -45 + 360k (or 360 - 45 + 360k) the general solution for
must get. to:
θ = 135 + 360k
and
θ = -45 + 360k (or 315 + 360k)
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Me and mrs corrino can complete a job in 5 hours if mr corrino works twice as long as mrs corrino if each foes the job alone how long does it take mrs corrubi to complete the job alone
Mrs. Corrubi takes 7.5 hours to complete the job alone.
Directly proportional: as one amount increases, another amount increases at the same rate. Direct variation means when one quantity changes, the other quantity also changes in direct proportion
Inversely Proportional: when one value decreases at the same rate that the other increases. An increase in the quantity A leads to a decrease in quantity B and vice versa.
Let the number of hours taken by Mrs Corrubi to do a particular work be x.
∴ The number of hours taken by Mr Corrubi to do a particular work will be 2x.
So according to the condition,
1/x + 1/2x = 1/5
(2+1)/2x = 1/5
3/2x = 1/5
2x = 15
x = 7.5 hours.
Thus Mrs. Corrubi takes 7.5 hours to complete the job alone.
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If a diameter intersects a chord of a circle at a perpendicular, what conclusion can be made?
If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.
What is the relation between the chord and diameter of a circle?The segments of a circle whose endpoints are on its perimeter are called chords.A circle's diameter is the chord that passes across its center.The circle's longest chord equals its diameter.Any line that is perpendicular to a chord on the circle cuts it in half and goes through the center.The solution to the problem:
A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.
Therefore, the chord is bisected.
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(9⋅10
9
)⋅(−2⋅10
−3
)=left parenthesis, 9, dot, 10, start superscript, 9, end superscript, right parenthesis, dot, left parenthesis, minus, 2, dot, 10, start superscript, minus, 3, end superscript, right parenthesis, equals
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
-18\cdot 10^6−18⋅10
6
minus, 18, dot, 10, start superscript, 6, end superscript
(Choice B)
B
-18 \cdot 10^{5}−18⋅10
5
minus, 18, dot, 10, start superscript, 5, end superscript
(Choice C)
C
18\cdot 10^{-6}18⋅10
−6
18, dot, 10, start superscript, minus, 6, end superscript
(Choice D)
D
18\cdot 10^{-5}18⋅10
−5
Answer:
A. -18·10^6
Step-by-step explanation:
The rules of exponents apply to powers of 10 used in scientific notation. The associative and commutative properties of multiplication also apply.
Application(a^b)(a^c) = a^(b+c)
The numerical product is ...
[tex](9\cdot10^9)\cdot(-2\cdot10^{-3})=(9)(-2)(10^{9-3})=\boxed{-18\cdot10^6}[/tex]
__
Additional comment
Expressed in scientific notation, the result would be ...
[tex]-1.8\cdot10^7[/tex]
Your calculator can perform this multiplication for you.
