. Find the general solution to
d²y/dx²= 49y. Enter your answer as an equation y = ..

Note: d²y/dx²=k^2y

Answer: The graph of g(x) is the graph of f(x) shifted 3 units down.

The sum of the geometric series will be 1/4. And the sum of the series will be the negative 0.13.

The complete question is attached below.

Let a be the first term and r be the common ratio. Then the sum of the geometric series will be

S = a / (1 – r)     if r < 1

S = a / (r – 1)     if r > 1

The series is given below.

1/16 + 3/64 + 9/256 + 27/1024 ....

Then we have

a = 1/16

r = (3/64) / (1/16) = 3/4

Then the sum of the series will be

S = (1/16) / [1 – (3/4)]

S = (1/16) / (1/4)

S = 1/4

Let [tex]\rm S = (-0.13)^m[/tex], where m = 1

Then the value of S will be

S = (-0.13)¹

S = -0.13

Hence, the sum of the series will be the negative 0.13.

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The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].

A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:

[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex]      (1)

Now we prove that given expression contains the pattern:

n = 0

7

n = 1

7 + (- 1)² · 2² = 7 + 4 = 11

n = 2

7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2

n = 3

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18

n = 4

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].

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Answer:

P(Event) = N(Favorable Outcomes) / N (Total Outcomes)

P(sum of 10 or 11) = 5/36

Step-by-step explanation:

Probability states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

The higher or lessen the probability of an event, the more likely it is that the event will occur or not respectively. For example – An unbiased coin is tossed once. So the total number of outcomes can be 2 only i.e. either “heads” or “tails”. The probability of both outcomes is equal i.e. 50% or 1/2.

So,

P(Event) = N(Favorable Outcomes) / N (Total Outcomes)

Sample Space:

All the possible outcomes of an event are called Sample spaces.

Examples-

• If two dice are rolled together then total outcomes will be 36 and

Sample space will be

[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)  

  (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

  (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

  (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

  (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

  (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]

Probability of rolling a sum of 10 or 11 with two dice:

When two dice are rolled together then total outcomes are 36 and

Sample space is

[ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

  (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

  (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

  (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)  

 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)  

 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) ]

So, pairs with sum 10 or 11 are (4, 6) (5, 5) (6, 4) (5,6) (6,5) i.e. total 5 pairs

Total outcomes = 36

Favorable outcomes = 5

Probability of getting the sum of 10 or 11 = Favorable outcomes / Total outcomes

                                                               = 5 / 36

So, P(sum of 10 or 11) = 5/36

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The solution of the given quadratic equation is x=-2 or x=-3.

The given quadratic equation is x²+5x+6=0.

The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.

By using the splitting middle term method we can solve x²+5x+6=0.

That is, x²+2x+3x+6=0

⇒x(x+2)+3(x+2)=0

⇒(x+2)(x+3)=0

⇒(x+2)=0, (x+3)=0

⇒x=-2 or x=-3.

Therefore, the solution of the given quadratic equation is x=-2 or x=-3.

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An expression is defined as a set of numbers, variables, and mathematical operations. The solution of (4 x 3)² ÷ 6 is 24.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The solution of the expression (4 x 3)² ÷ 6 is,

(4 x 3)² ÷ 6

= (12)² ÷ 6

= 144 ÷ 6

= 24

Hence, the solution of (4 x 3)² ÷ 6 is 24.

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Answer: 119°

Step-by-step explanation:

From the positive y-axis, all angles are measured clockwise

PR = PQ + QR = 5[150°] + 3[60°]

X = 5*sin150 + 3*sin60 = 5.1

Y = 5*Cos150 + 3*Cos60 = -2.83

TanA = X/Y

A = -61° = 61° East of South = 119° Clockwise

Therefore, the bearing of R from P is 119°

Answer:

60°

Step-by-step explanation:

since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there

Answer:

Step-by-step explanation:

Plan

7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.

Solution

7y + 5y = 180 degrees               Combine the left

12y = 180 degrees                      Divide by 12

12y/12 = 180/12

y = 15

3y + 5y + x = 180                         Combine the left side

8y + x = 180                                  Substitute 15 for y

8*15 + x = 180                               Combine

120 + x = 180                                Subtract 120 from both sides

120 -120 +x =180 - 120                 Combine

x  = 60

Answer

s = 60 degrees

<TRS = 5y = 75

Answer:

Answer is 6

Step-by-step explanation:

Let the number be ×

Twice a number is 2×

Twice a number increase by 8 is 2×+8

hence the equivalent will be

2×+8=20

2×=12

×6

Answer:

6

Step-by-step explanation:

Let n be the unknown number.

"Twice a number" means to multiply the number by 2:  

⇒ 2n

"Increase by 8" means to add 8:

⇒ 2n + 8

"Is 20" means equals 20:

⇒ 2n + 8 = 20

Therefore, the equation is:  2n + 8 = 20

To solve, subtract 8 from both sides:

⇒ 2n + 8 - 8 = 20 - 8

⇒ 2n = 12

Divide both sides by 2:

⇒ 2n ÷ 2 = 12 ÷ 2

⇒ n = 6

Therefore, the unknown number is 6.

Answer:

Step-by-step explanation:

The answer would be "me" as the indirect object

If Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Sasha's bank account earns 4% simple interest. Therefore, if she wants it to be worth $1,000 in 5 years then the principal amount must be,

Account balance = PRT + P

$1,000 = P[(0.04×5)+1]

$1,000 = 1.2 P

P = $833.34

Hence, if Sasha wants her account to be worth $1,000 in 5 years, then she must deposit $833.34.

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Answer:

12 minutes

Step-by-step explanation:

added in the picture

The correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.

Prime numbers:-

The prime number is defined as the number which is divided by 1 and itself.

Composite numbers:-

The number is defined as the composite number when the number is divided by 1 itself and any other numbers also.

From the given options we need to choose the pattern of the series { prime, prime, prime, composite, prime, prime } so we can see that in option A correct pattern is followed.

Pattern { 1, 5, 7, 9, 11, 13 }

1   → prime

5  → prime

7  → prime

9  → composite

11  → prime

13 → prime

Therefore the correct answer is option A which is the pattern {prime, prime, prime, composite, prime, prime} is followed by 1, 5, 7, 9, 11, 13.

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answer

Step-by-step explanation:

there are only one

painting, sculpture and photograph.

The domain is  {0, 1, 2, 3, 4, 5, 6} and range is {4, 4.5, 5, 5.5, 6, 6.5, 7}.

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

The complete question is

Ryan also found that he could model the height of his plan with the equation H = 0.5D + 4 where D is the number of days and H is the height in centimeters. Determine the domain and the range for this relationship.

Given:

h = 0.5d + 4

The Domain of the function is: {0, 1, 2, 3, 4, 5, 6}

and the Range is: {4, 4.5, 5, 5.5, 6, 6.5, 7}

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Answer:

A,C,E

(if you find a better answer choose that.)

Step-by-step explanation:

This one has two acute angles and one obtuse.

This one is a scalene.

So, tick A,C,E

If f(x)=x²+2 and g(x)=x²+5 then the domain of  the (fog) (x) is (-∞,∞).

Given the f(x)=x²+2 and g(x)=x²+5

We have to find the domain of  the (fog) (x)

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

then,(fog) (x)= (x²+5)²+ 2

                    =x⁴+25+10x²+2

                    = x⁴+27+10x²

Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.

So domain (fog) (x)= (-∞,∞).

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Answer:

2025 $

Step-by-step explanation:

275 multiply 3 +1200

Answer:

A.$2,025

Step-by-step explanation:

$275 x 3 years + $1,200

= $2,025

Step-by-step explanation:

On a polar plane, the shape will be a line that goes through the pi/2- pi quadrant , and 3pi/2- 2pi quadrant

On a Cartesian or rectangular plane, the shape will be a line as well passing through 2nd and 4th quadrant

Because we have an open circle at (1, 2), and then the line continues up, we conclude that the domain is:

D: x > 1.

Here we know that:

"The second line has an open circle at (1, 2)"

This means that the value x = 1 is not on the domain of the second line, and we know that the line "then continues up through (3, 4)"

(notice that these are two points on the line y = x + 1).

So we conclude that x = 1 is the lower bound of the domain of that line (and we can't tell that there is an upper bound).

Then we can just write the domain as:

D: x > 1.

So the last option is the correct one.

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Answer:

Step-by-step explanation:

Given is isosceles right triangle, since its interior angles are 45°, 45° and 90°.

The missing length is therefore same as the length of the other leg:

Note: This is not included in the answer choices.

Answer:

4 units

Step-by-step explanation:

We can use the converse theorem of the isosceles triangle to find the missing leg.

Converse Isosceles triangle theorem: If two angles are congruent in a triangle, then sides opposite to those angles are also congruent.

Therefore,

As there are two 45° angles, the opposite sides to those are also congruent.

∴ s = 4

The correct answer is option C which is the angle LMO is 50°

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Given that:-

∠O = 70°

∠L = 60°

∠LMO =?

As we know that the sum of the three angles are 180 degree applying this relation:-

∠LOM + ∠OLM  + ∠LMO = 180

70 + 60 +  ∠LMO = 180

∠LMO = 180 - 70 - 60 = 50

Therefore the correct answer is option C which is the angle LMO is 50°

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Step-by-step explanation:

Can you attach the questions please? Thanks

Answer:

ln(20) = 2.9957

Here given:

ln(4) = 1.3863

ln(5) = 1.6094

Evaluating with that:

[tex]\rm \Rightarrow ln\left(20\right)=ln\left(5\right)+ln\left(4\right)\\[/tex]

[tex]\rm \Rightarrow ln\left(20\right)=1.3863 \ + \ 1.6094[/tex]

[tex]\rm \Rightarrow ln\left(20\right)=2.9957[/tex]

The question was incomplete. Below you will find the missing parts of the question.

The company actually loses money on their first few products as it costs them more to make them, but once they hit  ?   they break even again. The worst case scenerio is that they produce  ?   items, as they will have a profit of  ?   dollars. The first root tells us that the profit will be 0 when  ?   products are sold.

Answer: The company actually loses money on their first few products as it costs them more to make them, but once they hit  150   they break even again. The worst case scenerio is that they produce  75   items, as they will have a profit of  10000   dollars. The first root tells us that the profit will be 0 when  0   products are sold.

Because the roots are x = 0 and 150, the vertex is (75, 10000).

So, the function is y = [tex]-\frac{10000}{5625}(x-75)^{2} +10000[/tex]

When, y = 0,

[tex]0=-\frac{10000}{5625} (x-75)^{2} +10000[/tex]

⇒ [tex]\frac{10000}{5625} (x-75)^{2}=10000[/tex]

⇒ [tex](x-75)^{2} = 10000(\frac{5625}{10000})[/tex]

⇒ [tex](x-75)^{2} = 5625[/tex]

⇒ [tex]x-75=75[/tex]

⇒ x = 150

When y=0, then x =150, their income was in balance.

When x = 75, then y=10000, they will have a profit of 10000 dollars.

The first root tells us that the profit will be 0 when 0 products are sold.

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Step-by-step explanation:

The graph of the cube root parent function y = RootIndex 3 StartRoot x EndRoot is translated to form f(x) shown on the graph.

On a coordinate plane, a cube root function goes through (negative 7, 0), has an inflection point at (negative 6, 1), and goes through (2, 3).

Which equation represents f(x)?

f(x) = RootIndex 3 StartRoot x + 6 EndRoot + 1

f(x) = RootIndex 3 StartRoot x minus 6 EndRoot + 1

f(x) = RootIndex 3 StartRoot x + 6 EndRoot minus 1

f(x) = RootIndex 3 StartRoot x minus 6 EndRoot minus 1

Answer:

Step-by-step explanation:

The translation of the parent function is:

g(x) = ∛(x + 6) + 1

How do translations work?

There are two types of translations, these are:

Horizontal translation:

For a function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the translation is to the left.

If N is negative, the translation is to the right.

Vertical translation:

For a function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive the translation is upwards.

If N is negative the translation is downwards.

Here we start with the parent function:

f(x) = ∛x

And we apply two translations such that:

g(x) = ∛(x + a) + b

Such that:

g(-7) = 0

g(2) = 3

Then we have the system of equations:

∛(-7 + a) + b = 0

∛(2 + a) + b = 3

From the options, the only ones that make the first option true are:

g(x) = ∛(x + 6) + 1

Such that when evaluated in x = -7 we get:

g(-7) =  ∛(-7 + 6) + 1 =  ∛(-1) + 1 = 0

When evaluated in x = 2 it gives:

∛(2 + 6) + 1 =  ∛(8) + 1 = 2+ 1 = 3

So the only option that meets these conditions is:

g(x) = ∛(x + 6) + 1

Which is a translation to the left of 6 units and up 1 unit.

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Answer:

-4  option (c)

Step-by-step explanation:

Cramer rule : In this method, the values of the variables in the system are to be calculated using the determinants of matrices

if , D :determinant of the coefficient matrix

[tex]{D}_{x}:[/tex]determinant of the matrix with coefficients except x

then,

[tex]x=\frac{{D}_{x}}{D}[/tex]

similarly,

[tex]y=\frac{{D}_{y}}{D}[/tex]

[tex]z=\frac{{D}_{z}}{D}[/tex]

given,

D = -23

[tex]D_{y}[/tex]  =           [tex]det\left[\begin{array}{ccc}5&7&-1\\2&6&-2\\3&-7&2\end{array}\right][/tex]

[tex]D_{y}[/tex] = 92

therefore, y = 92/(-23)

   y = -4 answer

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Using linear functions, it is found that the airplane and the helicopter will be at the same altitude after 20 minutes.

A linear function is modeled by:

y = mx + b

In which:

The functions that gives the height of the airplane and the helicopter, after t minutes, is given by:

They will be equal when:

A(t) = H(t).

Hence:

30000 - 1000t = 500t

1500t = 30000

t = 30000/1500

t = 20 minutes.

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