Find the length of the curve.
x=3t² +5₁y = 2t³ +5,0 ≤t≤1

Answer:

  yes, it can be of odd degree

Step-by-step explanation:

The local maxima and minima correspond to zeros in the derivative of the function. The degree of the polynomial will be 1 more than some multiple of 2 greater than the number of zeros in the derivative.

__

For 2 each of local maxima and minima, the derivative will have 2+2 = 4 real zeros. The degree of the polynomial will be 1 greater, hence of degree 5 (or more). The polynomial must be of odd degree.

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The local extrema must alternate: a maximum must be followed by a minimum, or vice versa. When there are an even number of each kind, the end extrema will be of opposite kinds. The end behavior of the function will be upward from a minimum and downward from a maximum. Hence the end behaviors must be in opposite directions--characteristic of an odd-degree polynomial.

The polynomial must be of odd degree.

_____

Additional comment

A polynomial with real coefficients will have an even number of complex roots. The complex roots of the derivative of a polynomial have no effect on the number or kind of extrema.

__

Attached is an example of a polynomial with 2 maxima and 2 minima. It is of 5th degree.

Answer:

All of the following are answers:

B) It has a slope of 2

C) It goes through the origin

D) It is a straight line

Step-by-step explanation:

trust me

Because of the vertical asymptote and the change in concavity, we conclude that the correct option is B.

Remember that cot(x) = 1/tan(x).

Then we can rewrite:

cot(x) = cos(x)/sin(x).

We know that for x = 0, we have:

cot(0) = cos(0)/sin(0) = 1/0

Then we have a vertical asymptote that tends to ± infinity.

The only graph that meets this condition is the second and the third one, and by the curvature (we need to have a change of concavity/convexity) in the tangent function.

From that, we conclude that the correct option is B.

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Step-by-step explanation:

so, we have a large triangle made of the 2 cables as legs and the ground distance AB as baseline.

the tower is the height to the baseline of that large triangle.

let's call the top of the tower T.

and remember, the sum of all angles in a triangle is always 180°.

we know the angle A = 62°, and angle B = 72°.

assuming that AB is a truly horizontal line that means that the 2 legs (cables) have different lengths, the triangle is not isoceles, and the tower is not in the middle of the baseline.

so, the height (tower) splits the baseline into 2 parts. let's call them p and q.

p + q = 12 m

p = 12 - q

let's simply define that p is the part of the baseline on the A side, and q is the part of the baseline on the B side.

we have now 2 small right-angled triangles the large height (tower) splits the large triangle into.

one has the sides

AT, height (tower), p

angle A = 62°

angle T = 180 - 90 - 62 = 28°

the other has the sides

BT, height (tower), q

angle B = 72°

angle T = 180 - 90 - 72 = 18°

now remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with the sides and the associated angles being opposite.

p/sin(28) = height/sin(62)

q/sin(18) = height/sin(72)

we know from above that

p = 12 - q

so,

(12 - q)/sin(28) = height/sin(62)

height = (12 - q)×sin(62)/sin(28)

q/sin(18) = height/sin(72)

height = q×sin(72)/sin(18)

and therefore, as height = height we get

(12 - q)×sin(62)/sin(28) = q×sin(72)/sin(18)

(12 - q)×sin(62)×sin(18) = q×sin(72)×sin(28)

12×sin(62)×sin(18) - q×sin(62)×sin(18) =

= q×sin(72)×sin(28)

12×sin(62)×sin(18) = q×sin(72)×sin(28) + q×sin(62)×sin(18) =

= q×(sin(72)×sin(28) + sin(62)×sin(18))

q = 12×sin(62)×sin(18) / (sin(72)×sin(28) + sin(62)×sin(18))

q = 4.551603755... m

p = 12 - q = 7.448396245... m

height = q×sin(72)/sin(18) = 14.00839594... m ≈ 14 m

the cell tower is about 14 m tall.

Answer:

1,120 cm³

Step-by-step explanation:

Hello!

Think about it this way: There is a rectangular prism, with lengths of 20cm, 12cm, and 10cm, and another rectangular prism cut out of it with lengths, of 8cm, 8cm, and 20cm.

Volume = L * W * H

V = L * W * H

Subtract:

The total volume is 1,120cm³

Hey there!

Solve for x :

x = 6 ✅

3x - 2 = 16

>> Add 2 to both sides :

3x - 2 + 2 = 16 + 2

3x = 18

>> Divide each side by 3 :

3x / 3 = 18 / 3

x = 6

▪️Let's verify :

3(6) - 2 ⇔18 - 2 ⇔ 16

Therefore, your answer is x = 6

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3x−2=16

Add 2 to both sides.

3x=16+2

Add 16 and 2 to get 18.

3x=18

Divide both sides by 3.

x = 18 /3

Divide 18 by 3 to get 6.

x = 6 ===> Answer

Let x = 6

3×6−2=16

18-2= 16

16 = 16

Checked ✅

Answer:

a)b= 5

b)45

Step-by-step explanation:

a) 5 times ten is 50 . the two factors of 50 are 25 and 2. The square root of 25 is 5, so that's the answer.

b) 27 × 75 is 2025 and the base root is 45², then with the radical and exponent we reduce the index by 2 to get 45.

[tex]\textbf{a)}\\\\~~~\sqrt 5 \times \sqrt{10}\\\\=\sqrt{5} \times \sqrt{5 \times 2}\\\\=\sqrt{5} \times \sqrt 5 \times \sqrt 2\\\\=\left(\sqrt 5 \right)^2 \times \sqrt 2\\\\=5\sqrt 2\\\\\text{It is now in a form of} ~ b\sqrt2 ~ \text{where} ~b = 5.\\\\\\[/tex]

[tex]\textbf{b)}\\\\~~~\sqrt{27} \times \sqrt{75}\\\\=\sqrt{9 \times 3} \times \sqrt{25 \times 3}\\\\=\sqrt 9 \times \sqrt 3 \times \sqrt{25} \times \sqrt 3\\\\=3\times 5 \times \left(\sqrt 3 \right)^2\\\\=15 \times 3\\\\=45[/tex]

This function shows a horizontal translation of the parent function to the left and 2 units up.

The parent function of a square root function is expressed as:

f(x) = √x

According to the question, we are to plot the expression f(x) = √x+ 3 - 2

This function shows a horizontal translation of the parent function to the left and 2 units up. The required graph will be in the 2nd quadrant of the graph as shown;

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Answer:

It should be the first one.

Answer:

1) p ≥ -6

2) p ≤ -38/5

Step-by-step explanation:

3p + 4 ≥ -14

Subtract 4 to both sides

3p ≥ -14 - 4

3p ≥ -18

Divide 3 to both sides

p ≥ -18/3

p ≥ -6

[tex]\rule[225]{225}{2}[/tex]

1 - 5p ≥ 39

Subtract 1 to both sides

-5p ≥ 39 - 1

-5p ≥ 38

Divide -5 to both sides

p ≤ -38/5

[tex]\rule[225]{225}{2}[/tex]

Using the combination formula, it is found that there are 47,040 ways to form a soccer team.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]

A soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 6 midfield players and 8 defensive players

Since they are independent of each other, the total number of combinations will be;

[tex]^mC_k = \dfrac{8!}{3! \times (5)!} \times \dfrac{6!}{4! \times (2)!} \times \dfrac{8!}{3! \times (5)!} \\\\^mC_k =47,040[/tex]

Hence, There are 47,040 ways to form a soccer team.

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Answer:

y = 32.

Step-by-step explanation:

y = k/x^2    where k is the constant of variation

When y = 50 x = 4, so

50 = k / (4)^2

f = 50 * 4^2 = 800.

So the relation is

y = 800/x^2

When x = 5

y = 800/5^2

  =  32.

#1

Length in cm

Total length

#2

Total notes

Total money

|

Total suits per month=120

per year

#4

Total 5mins

total distance

Answer: See below

Step-by-step explanation:

Given:

AB = CD and BC = DE

To prove:

AC = CE

            Statements                                       Reasons

Therefore, AC = CE has been proved                

Using trigonometric ratios, the measure of side n to one decimal is 6.6 units.

Using the trigonometric principle

SOHCAHTOA,

cos 20 = adjacent / hypotenuse

adjacent side = n

hypotenuse side = 7

Therefore,

cos 20° = n / 7

cross multiply

n = 7 cos 20°

n = 7 × 0.93969262078

n = 6.5778483455

n = 6.6 units

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Answer:

50% to pull either a black or pink marble.

Step-by-step explanation:

The reason for this is due to the fact you have an equal amount of marbles of 2 different colors, so the chance of pulling one marble is not over another unless you remove say 1 pink marble, therefore the black marbles would have a higher percentage of being pulled instead of pink.

Answer:

{-12,0}

Step-by-step explanation:

first to solve this can collect like terms and add

X² +12x=0

and solve it by factorization method

X² +12x=0

x(x+12)=0

it means x multiplied by x = X² then x multiplied by 12 = 12x

so this means x or (x+12) equals to zero

x=0 and (x+12)=0

x+12=0

x=-12

so the solution set is {-12,0}

but can also be done by formula method

Answer:

19 cents or 0.199

Step-by-step explanation:

Hope it helped!

Answer:

19 cents

Step-by-step explanation:

divide total cost by amount of items

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

   L be the length of the rectangle

   w be the width of the rectangle

Formula: ‘area of a rectangle’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0  

Solving the quadratic equation w² + 3w - 10 =  0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]

  [tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]

-5 is not valid ,because w represents the width

which must be a positive number

Then  w = 2

Conclusion:

Width = 2

Length = 2 + 3 = 5

Answer:

1 is answer

Step-by-step explanation:

2*3/5*3___6/5

Work Shown:

A = area of the rectangle

A = length*width

A = 26*15

A = 390 square feet

B = area of the triangle

B = base*height/2

B = 8*9/2

B = 72/2

B = 36 square feet

C = total area

C = A+B

C = 390+36

C = 426 square feet

Im going to assume that you want the area of a circle.

We already have radius, which is the only variable that we need, now we just have to plug it into the area for the circle:

π(28²)

Multiplying this, you get 2461.76 cm³

Answer:

the prime numbers between 30 and 40 are 31 and 37 come on its so easy

Answer:

What exactly is the question here?

Answer:

2ax−2ay−2x2−2xy+2a+4x+2y

Step-by-step explanation:

Let's simplify step-by-step.

(x+y)(2)−2(x+y)(a+x)+(a+x)(2)

Distribute:

=(x)(2)+(y)(2)+−2ax+−2ay+−2x2+−2xy+(a)(2)+(x)(2)

=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x

Combine Like Terms:

=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x

=(−2ax)+(−2ay)+(−2x2)+(−2xy)+(2a)+(2x+2x)+(2y)

=−2ax+−2ay+−2x2+−2xy+2a+4x+2y

Answer:

=−2ax−2ay−2x2−2xy+2a+4x+2y

Answer:

[tex]\displaystyle \log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex] OR [tex]\displaystyle 3+\log\frac{z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]

Choose the more appropriate answer

Step-by-step explanation:

I read your problem as [tex]3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y[/tex]:

[tex]\displaystyle 3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y\\\\\log1000+\log z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log1000z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2}{(x+1)^2}+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}[/tex]

Answer: 134°

Step-by-step explanation:

Since angle ABC is equal to 75, we know that the arc in front of it (arc AC) is 150. We then start to add all the know arc angle measures together. So, our equation to finding arc BEC 360-150+76= BEC arc.

Answer:

134

Step-by-step explanation:

cause yeah

Answer:

zero

Step-by-step explanation:

pemdas

Answer:

I feel that is would be D

Step-by-step explanation:

This is the most reasonable awnser.

Answer:

$10955.6157151671

Step-by-step explanation:

Amount [A] = [tex]P(1+r)^{t}[/tex]

Here, P = principal (which is $5000)

r = rate of interest in decimal form(which is 0.04)

t = time in years (which is 20)

Substituting,

[tex]$5000(1+0.04)^{20}[/tex] = $10955.6157151671