Factorize cos²A+3cosA+2

Get the slope/tangent vectors for each line:

dP/dt = ⟨-2, -4, 5⟩

dQ/dt = ⟨3, 5, 4⟩

Take their cross product - I'll call it v :

v = ⟨-2, -4, 5⟩×⟨3, 5, 4⟩ = ⟨-41, 23, 2⟩

Normalize this vector by multiplying it by 1/||v|| :

n = v/||v|| = ⟨-41, 23, 2⟩/(3√246)

Then the distance d between P and Q is

d = |n • (⟨-2, -4, 5⟩ - ⟨4, 5, -4⟩)|

d = 1/(3√246) |⟨-41, 23, 2⟩ • ⟨-6, -9, 9⟩|

d = 1/(3√246) |246 - 207 + 18|

d = 57/(3√246)

d = 19/√246

Answer:

A. 1000/1 = x/2500

Step-by-step explanation:

1000 g = 1 kg

Using ratios

1000 g         x g

------------ = --------------

1 kg             25 00 kg

Answer:

A. 1000/1 = x/2500

Step-by-step explanation:

KHD - DCM

Kilo - Hecta - Deca - Base - Deci - Centi - Mili

*When moving from left to right, each spot you pass multiplis your number by 10.

2500 kilo → x grams (base)

Proportions:

grams/kilos = x/2500

*For every 1 kilo, there is 1000 grams.

1000/1 = x/2500

Answer:

x=7.23

Step-by-step explanation:

Brainliest please

9514 1404 393

Answer:

  1/8

Step-by-step explanation:

The percent symbol % can be thought of as being fully equivalent to /100.

  12 1/2% = (12 1/2)/100 = (25/2)/100 = 25/200 = 1/8

_____

Additional comment

It can be useful to memorize the decimal equivalents of the reciprocals of the numbers up to 12.

  1/12 = 0.0833...(repeating 3)

  1/11 = 0.0909...(repeating 09)

  1/10 = 0.1

  1/9 = 0.111...(repeating 1)

  1/8 = 0.125

  1/7 = 0.142857...(repeating the same 6 digits)

  1/6 = 0.1666...(repeating 6)

  1/5 = 0.2

  1/4 = 0.25

  1/3 = 0.333...(repeating 3)

  1/2 = 0.5

Of course, any of these is expressed as a percentage by multiplying by 100%. 1/8 = 12.5%, 1/6 = 16.6...% (repeating 6)

Answer:

a). 5√6

[tex] \sqrt{10} \times \sqrt{15} \\ = ( \sqrt{5} \times \sqrt{2} ) \times ( \sqrt{5} \times \sqrt{3} ) \\ = {( \sqrt{5}) }^{2} \times ( \sqrt{2} \times \sqrt{3} ) \\ = 5 \times ( \sqrt{6} ) \\ = 5 \sqrt{6} [/tex]

Answer:

-42/11

Step-by-step explanation:

x = y - 8

5x = 6 - 6y

So now solve the system of equations, divide everything in the second equation by 5 to get it to x = 6/5 - 6y/5

Now...

x = y - 8

x = 6/5 - 6y/5

Now substitute first equation into the second and x is gonna be -42/11 or the first number

Answer:

40

Step-by-step explanation:

Let x represent the mystery number.

Create an equation to represent the situation, then solve for x:

0.85x - 5 = 29

0.85x = 34

x = 40

So, the mystery number is 40.

Answer:

a) x^2-3x-4(you also can express it as (x+1)(x-4))

b)The length is 8 cm, the width is 3 cm

Step-by-step explanation:

a) The length is x+1

The width is (x+1-5)= x-4

The area is the product of the length and the width

(x+1)(x-4)= x^2-3x-4

b) The formula for counting the area is x^2-3x-4

It is equal to 24

S0 x^2-3x-4=24

x^2-3x-28=0

a=1 b=-3 c=-28

D= b^2-4ac= 3^2-4*(-28)= 9+112= 121

sqrtD= 11

x1= (-b-sqrtD)/2a=(3-11)/2=-4  The length is -4+1=-3<0, but the length must be positive, this root isn't suitable.

x2= (-b+sqrtD)/2a=(3+11)/2=7 The length is 7+1=8 (it is suitable)

8-5=3 - The width

Answer:

-6

Step-by-step explanation:

a1= -3

r= -(3/2)/-3 = 0.5

r>-3

s= a1/1-r

= -3/1-0.5

=-6

With a 10% profit the radio would be 2000 x 1.10 = 2,200

A 20 % discount means it would sell for 80% of the total price.

Divide the 2200 by 80% to get the fixed price:

2200/0.8 = 2750

Fixed price = 2750

Answer:

628 mi^3

Step-by-step explanation:

the volume of a cylinder is given by:

V = base area x height

thus,

V = (3.14)(5)^2(8)

V = (3.14)(25)(8)

V = 628 mi^3

the volume of the cylinder is 628 cubic miles

The volume of the cylinder is 628 cubic miles.

We have a cylinder of radius 5 mi and height 8 mi.

We have to find the volume of the figure and round it to nearest tenth.

The volume of cylinder is given by the formula -

Volume [tex]=\pi r^{2} h[/tex]

We can use the above formula to calculate the volume of cylinder. In our case -

r = 5 mi

h = 8 mi

Substituting the values in the formula -

Volume [tex]=\pi\times5^{2}\times 8\\\\[/tex] = 628 cubic miles.

Hence, the volume of the cylinder is 628 cubic miles.

To solve more questions on finding the volume of cylinder, visit the link below -

https://brainly.com/question/16134180?referrer=searchResults

#SPJ2

Answer:

0 ≤ d ≤ 20

Step-by-step explanation:

You mention that Manatees can swim in water up to 20 feet deep. So, this means that the largest depth that he can swim is 20 feet, not more than this. Also, keep in mind that the depth can't be negative, so ----> 0 ≤ d ≤ 20 feet

We want to write an expression (an inequality actually) that defines the depth at which a manatee can swim. The inequality is: 0ft ≤ d ≤ 20ft.

We know that the manatees can swim in water up to 20 feet deep. This represents the maximum deep at which manatees can swim, the minimum is trivial, it would be 0ft (when the manatees are on the surface of the water).

Then we can write the inequality:

0ft ≤ d ≤ 20ft.

This gives the range of possible values of d, depth at which the manatee can swim.

If you want to learn more, you can read:

https://brainly.com/question/17675534

Answer:- 10[tex]m^{2}[/tex] + 3m -9

Step-by-step explanation: Given ;  

  A= -3 -m

  B= 3m -5[tex]m^{2}[/tex]

 2B + 3A

        solution

     2B + 3A

substitute A and B in the formula

    2(3m - 5[tex]m^{2}[/tex]) + 3(-3 -m)

    6m - 10[tex]m^{2}[/tex] - 9 - 3m   group like terms

    - 10[tex]m^{2}[/tex] + (6m -3m) -9

     - 10[tex]m^{2}[/tex] + 3m -9

Answer: sorry

Step-by-step explanation:

767u6777

Answer:

B

Step-by-step explanation:

Pull in -4 and 0 into the variable x. and the 4 and -2 in the variable y and solve to get an equal answer.

Answer:

I believe it is 12,393.86

Answer:

Step-by-step explanation:

NO perimeter does not map directly to area....

take a square with side of 5 ... area is 5*5 which  is 25 perimeter is 20

if you now take a rectangle with long side 8 and short side 2

the perimeter is 20 but the area is 16

Answer:

the answer for this is 2.64575

√7=2.64

please mark this answer as brainlist

Answer:

I need points plsss

Step-by-step explanation:

Answer:

22,2

Step-by-step explanation:

average also known as mean

so you find it by adding all the numbers together and dividing them by how many there are

so 21,8 + 24,2 + 20.6 = 66,6 divided by 3 equals 22,2

Answer:

first term = -1/5

I cant see part b (sorry its too blurry)

thirteenth term = -0.2

part d: -19a/95a -0.2a

Step-by-step explanation:

socratic

Answer:

16 baskets

Step-by-step explanation:

Create a proportion where x is the number of baskets that Scott made:

[tex]\frac{14}{21}[/tex] = [tex]\frac{x}{24}[/tex]

Cross multiply and solve for x:

21x = 336

x = 16

So, Scott made 16 baskets.

Answer:

>

Step-by-step explanation:

the less negative the greater the number

Answer:

Step-by-step explanation:

a₁ = 15

a₂/a₁ = 45/15 = 3

a₃/a₂ = 135/45 = 3

...

It is a geometric sequence with a common ratio r=3.

Sum of first 12 terms = a₁·(1-r¹²)/(1-r)

= 15·(1-3¹²)/(1-3)

= 15·(-531,441)/(-2)

= 3,985,800