Which quadratic has a maximum?
a. y = x2 + 2x + 2
b. y = - 2x² – 3x + 5
c. y = 0.5(x – 3)2 + 1
d. y = 2x + x2 - 1

Answer:21 obviously it’s actually (19) don’t tell anyone

Step-by-step explanation:

The general form of a solution of the differential equation is already provided for us:

[tex]y(x) = c_1 \textrm{e}^x + c_2\textrm{e}^{-x},[/tex]

where [tex]c_1, c_2 \in \mathbb{R}[/tex]. We now want to find a solution [tex]y[/tex] such that [tex]y(-1)=3[/tex] and [tex]y'(-1)=-3[/tex]. Therefore, all we need to do is find the constants [tex]c_1[/tex] and [tex]c_2[/tex] that satisfy the initial conditions. For the first condition, we have:[tex]y(-1)=3 \iff c_1 \textrm{e}^{-1} + c_2 \textrm{e}^{-(-1)} = 3 \iff c_1\textrm{e}^{-1} + c_2\textrm{e} = 3.[/tex]

For the second condition, we need to find the derivative [tex]y'[/tex] first. In this case, we have:

[tex]y'(x) = \left(c_1\textrm{e}^x + c_2\textrm{e}^{-x}\right)' = c_1\textrm{e}^x - c_2\textrm{e}^{-x}.[/tex]

Therefore:

[tex]y'(-1) = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e}^{-(-1)} = -3 \iff c_1\textrm{e}^{-1} - c_2\textrm{e} = -3.[/tex]

This means that we must solve the following system of equations:

[tex]\begin{cases}c_1\textrm{e}^{-1} + c_2\textrm{e} = 3 \\ c_1\textrm{e}^{-1} - c_2\textrm{e} = -3\end{cases}.[/tex]

If we add the equations above, we get:

[tex]\left(c_1\textrm{e}^{-1} + c_2\textrm{e}\right) + \left(c_1\textrm{e}^{-1} - c_2\textrm{e} \right) = 3-3 \iff 2c_1\textrm{e}^{-1} = 0 \iff c_1 = 0.[/tex]

If we now substitute [tex]c_1 = 0[/tex] into either of the equations in the system, we get:

[tex]c_2 \textrm{e} = 3 \iff c_2 = \dfrac{3}{\textrm{e}} = 3\textrm{e}^{-1.}[/tex]

This means that the solution obeying the initial conditions is:

[tex]\boxed{y(x) = 3\textrm{e}^{-1} \times \textrm{e}^{-x} = 3\textrm{e}^{-x-1}}.[/tex]

Indeed, we can see that:

[tex]y(-1) = 3\textrm{e}^{-(-1) -1} = 3\textrm{e}^{1-1} = 3\textrm{e}^0 = 3[/tex]

[tex]y'(x) =-3\textrm{e}^{-x-1} \implies y'(-1) = -3\textrm{e}^{-(-1)-1} = -3\textrm{e}^{1-1} = -3\textrm{e}^0 = -3,[/tex]

which do correspond to the desired initial conditions.

Answer:

acute

Step-by-step explanation:

its less then 90 degree

Answer:

-5

Step-by-step explanation:

The opposite would be 5, but since we need the opposite of the opposite, the opposite of 5 is -5. Hope this helped and wasn't too confusing!

Answer for 1.a is 6. 6 is in the thousands place.

Answer for 1.b is 9. 9 is in the thousandths place.

Answer:

14

Step-by-step explanation:

According to order of operations (PEMDAS), you should multiply the numbers on the two sides of the addition sign first. So:

-4 x -5 = 20

and

2 x -3 = -6

Then you add those two numbers together:

-6 + 20 = -14

Answer:

C

Step-by-step explanation:

Answer: c

Step-by-step explanation:

I just took the test and got it correct

Answer:

An animal or insect that only eats vegetation, such as grasses, fruits, leaves, vegetables, roots and bulbs.

Step-by-step explanation:

Answer:

Plant eating dinosaurs

Step-by-step explanation:

Herbivores have the word herb in it which refers to it being a plant eating dinosaur so a carnivore has the word carn which also refers to it being a meat eating dinosaur.

Hey there! I'm happy to help!

Let's call this number n. We can create the following equation.

(n+45)/2=5

Let's solve. We multiply both sides by 2.

n+45=10

We subtract 45 from both sides.

n=-35.

Have a wonderful day! :D

Answer:

n=-35

Step-by-step explanation:

Answer:

8.8

Step-by-step explanation:

speed=distance/time

speed- ?

distance- 200m

time- 22.75s

?=200/22.75

?= 8.791...

round it so that it becomes 8.8

Answer:

1.   75 degrees

2.  105 degrees

3.  35 degrees

Step-by-step explanation:

Hope this helps! :)

Answer:

37

Step-by-step explanation:

Answer:

[tex] \boxed{\sf x\degree = 67\degree} [/tex]

Step-by-step explanation:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

So,

⇒ 43° + 70° + x° = 180°

43° + 70° = 113°:

⇒ 113° + x° = 180°

Substracting 113° from both sides:

⇒ 113° - 113° + x° = 180° - 113°

113° - 113° = 0°:

⇒ x° = 180° - 113°

180° - 113° = 67°:

⇒ x° = 67°

Answer:

a) The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex], b) [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].

Step-by-step explanation:

a) The standard form of the complex number is [tex]z = a + i\cdot b[/tex], [tex]\forall \,a,b \in \mathbb{R}[/tex]. If we get that [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex], whose standard form is obtained by algebraic means:

1) [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] Given

2) [tex]z = (4\cdot \cos 60^{\circ})+i\cdot (4\cdot \sin 60^{\circ})[/tex] Distributive and Associative properties.

3) [tex]z = 2 + i\cdot 2\sqrt{3}[/tex] Multiplication/Result.

The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex].

b) The De Moivre's Theorem states that:

[tex]z = (a+i\cdot b)^{n}= r^{n}\cdot (\cos \theta + i\cdot \sin \theta)[/tex]

Where:

[tex]r =\sqrt{a^{2}+b^{2}}[/tex] and [tex]\theta = \tan^{-1} \left(\frac{b}{a}\right)[/tex].

If we know that [tex]z = (2+i\cdot 3)^{6}[/tex], then:

[tex]r = \sqrt{2^{2}+3^{2}}[/tex]

[tex]r =\sqrt{13}[/tex]

[tex]r \approx 3.606[/tex]

[tex]\theta = \tan^{-1}\left(\frac{3}{2} \right)[/tex]

[tex]\theta \approx 56.310^{\circ}[/tex]

The resulting expression is:

[tex]z = 3.606^{6}\cdot (\cos 56.310^{\circ}+i\cdot \sin 56.310^{\circ})[/tex]

[tex]z = 1219.585+i\cdot 1829.381[/tex]

Therefore, [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].

Answer:

The generated Taylor series is;

f(x) = 1/6 + (x-3)/36 + (x-3)^2/216 + (x-3)^3/1296......

Kindly note that the series here is truncated at the third derivative, but if wanted, evaluation could be more than this

Step-by-step explanation:

Here, we are to find the Taylor series generated by f at x = a

Mathematically;

f(x)= 1/(9-x)

The f(a) at this point is calculated below;

f(a) = 1/(9-3) = 1/6

The first derivative is calculated below;

f'(x) = 1/(9-x)^2

f'(3) = 1/6^2 = 36

The second derivative is calculated below;

f''(x) = 2/(9-x)^3

f''(3) = 2/(9-3)^3 = 2/6^3 = 2/216 = 1/108

The third derivative is calculated as follows

f'''(x) = 6/(9-x)^4

f'''(3) = 6/(9-3)^4 = 6/6^4 = 1/216..

The Taylor series is thus given by;

f(x) = f(a) + f'(a) (x-a) + f''(a) (x-a)^2/2! + f'''(a) (x-a)^3/3! +...

Substituting the values of 3 for a at each of the points , we obtain the Taylor series as shown below;

f(x) = 1/6 + (x-3)/36 + (x-3)^2*1/108*1/2 + (x-3)^3*1/216*1/6 +...

f(x) = 1/6 + (x-3)/36 + (x-3)^2/216 + (x-3)^3/1296......

Answer:

x is a 33° angle

Step-by-step explanation:

The two angles are supplementary meaning the measure of both angles adds up to 180°. You can tell they are supplementary because the angle is a straight line. so all you need to do is subtact 147 from. 180 to get the measure of x .

Answer:

x+147=180 ( sum of supplementary angle)

or, x = 180-147

or, x = 33

so the value of x is 33°

Answer: The answer is 17

Step-by-step explanation:

Because math is easy

Answer:

Hi there!

Your answers are:

1) 2^4 = 2×2×2×2 = 16

2) 2^3= 2×2×2= 8

3) 2^2 = 2×2 = 4

4) 2^1 = 2

5)2^0 = 1

6)2^ -1 = .5

7) 2^ -2 = .25

8) 2^ -3 = .125

9) 2^ -4= .0625

Hope this helps

Though I prefer to eat fruit, I enjoy vegetables too.

A homophone is a word that is pronounced the same as another word but differs in meaning.

Homophones may consist of two or more words, although pairs are more common than three or more words that sound the same. Examples of homophones that have three words are to, too, and two, and their, there, and they're.

here, we have,

Though I prefer to eat fruit, I enjoy vegetables too.

A homophone is a word that is pronounced the same as another word but differs in meaning.

Learn more about homophones here

brainly.com/question/7449238

#SPJ7

Answer:

12

Step-by-step explanation:

4+4+4=12

Answer:

A is point ( 6, -3, 6)

Step-by-step explanation:

Here in this question, we are concerned with finding the coordinates of point A.

Since we do not know the coordinates of point A, let’s represent them as (x,y,z)

By vector properties; Mathematically ;

AB = (7,4,4) - (x , y, z)

Thus; AB = (7-x)i + (4-y)j + (4-z)k

From the question, we are told that AB is also i + 7j -2k

By comparison;

(7-x)i = i

7-x = 1

x = 7-1

x = 6

(4-y)j = 7j

4-y = 7

4-7 = y

y = -3

and lastly

(4-z)k = -2k

4-z = -2

4 + 2 = z

z = 6

So the coordinates of A are (6, -3, 6)

Given:

Number  of Vegetarian Sandwich = 3

Number of Turkey Sandwich  = 7

Number  of  Pepperoni Pizza  = 8

Number  of  Cheese Pizza  = 10

To find:

The ratio which represents the number of orders for pepperoni pizza to cheese pizza.

Solution:

The ratio of number of orders for pepperoni pizza to cheese pizza is

[tex]\text{Ratio}=\dfrac{\text{Number of orders for pepperoni pizza}}{\text{number of orders for cheese pizza}}[/tex]

[tex]\text{Ratio}=\dfrac{8}{10}[/tex]

[tex]\text{Ratio}=\dfrac{4}{5}[/tex]

Therefore, the required ratio is 4:5 and option A is correct.

Answer:

4:5 and option A is correct.

Step-by-step explanation:

edge2020

Answer:

D

Step-by-step explanation:

An exponential model is appropriate because the relationship between period and the log of subscribers is roughly linear and the residual plot shows no distinct pattern.

Answer:

its D

Step-by-step explanation:

Answer:

Paloma and Abdul combined spent 4 hours more working on the project than Ben and Min combined.

Step-by-step explanation:

Note: This question is not complete as the bar chart is not included. The bar chart is therefore included before answering the question. Please, see the attached jpeg file for the bar chart.

The explanation to the answer is now given as follows:

From the bar chart, we have the number of hours each student spends working on the group project as follows:

Numbers of hours spent by Paloma = 21 hours

Numbers of hours spent by Adbul = 18 hours

Numbers of hours spent by Ben = 13 hours

Numbers of hours spent by Min = 22 hours

The number of hours each group spent working on the group project is calculated as follows:

Numbers of hours spent by Paloma and Abdul = Numbers of hours spent by Paloma + Numbers of hours spent by Paloma = 21 hours + 18 hours = 39 hours

Numbers of hours spent by Ben and Min = Numbers of hours spent by Ben + Numbers of hours spent by Min = 13 hours + 22 hours = 35 hours

Th number of hours Paloma and Abdul spend working on the project combined more than Ben and Min combined = Numbers of hours spent by Paloma and Abdul - Numbers of hours spent by Ben and Min = 39 hours - 35 hours = 4 hours

Therefore, Paloma and Abdul combined spent 4 hours more working on the project than Ben and Min combined.

Answer:

the degree is about 120

Step-by-step explanation:

b and a is about 60 something and so is b and c so add all that up and you get about 120 degrees.