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3 years ago

If θ is an angle in standard position and its terminal side passes through the point (-4,-5), find the exact value of

Mathematics

1 answer:

NARA [144]3 years ago

7 0

9514 1404 393

Answer:

cot(θ) = 4/5

Step-by-step explanation:

In the polar/rectangular coordinate representation (x, y) ⇔ (r; θ), we know that ...

(x, y) = (r·cos(θ), r·sin(θ))

From the various trig definitions and identities, we also know that ...

cot(θ) = cos(θ)/sin(θ) = (x/r)/(y/r) = x/y

For the given (x, y) = (-4, -5), the cotangent is ...

cot(θ) = -4/-5 = 4/5

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a flat rectangular piece of aluminum has a perimeter of 64 inches. the length is 10 inches longer than the width. find the width

I am Lyosha [343]

Answer:

The width of the piece is 11 inches

Step-by-step explanation:

Let

x ----> the length of the rectangular piece of aluminum in inches

y ----> the width of the rectangular piece of aluminum in inches

we know that

The perimeter of the rectangular piece of aluminum is equal to

$P=2(x+y)$

we have

$P=64\ in$

$64=2(x+y)$

simplify

$32=x+y$ ----> equation A

$x=y+10$ ----> equation B

Solve the system by substitution

substitute equation B in equation A

$32=y+10+y$

solve for y

$32=2y+10$

$2y=32-10$

$2y=22$

$y=11$

therefore

The width of the piece is 11 inches

3 0

3 years ago

An = a1 + (n - 1)d

yarga [219]

Answer:

The car will travel 1980 meters in 15 minutes.

Hence, option 'D' is true.

Step-by-step explanation:

Given that a car travels 300 meters in the first minute, so

a₁ = 300

Each minute after, the car travels 120 meters. , so the sequence becomes

a₁, a₂, a₃, a₄, a₅, ...

300, 420, 540, 660, 780, ...

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$20-300=120,\:\quad \:540-420=120,\:\quad \:660-540=120,\:\quad \:780-660=120$

The difference between all the adjacent terms is the same and equal to $d=120$

now, we have

a₁ = 300

d = 120

so substituting a₁ = 300 and d = 120 in the nth term of the sequence

$a_n=a_1+\left(n-1\right)d$

$a_n=120\left(n-1\right)+300$

$a_n=120n+180$

Thus, the nth term of the sequence is:

$a_n=120n+180$

<u>Determining the distance the car travels in 15 minutes</u>

As we have already determined the nth term of the sequence such as

$a_n=120n+180$

now substituting n = 15

$a_{15}=120\left(15\right)+180$

$a_{15}=1800+180$

$a_{15}=1980$

Therefore, the car will travel 1980 meters in 15 minutes.

Hence, option 'D' is true.

6 0

3 years ago

the length of a rectangle is 4 unit less than the width. which expression represents the perimeter of the rectangle

WINSTONCH [101]

Answer:

Length: 11

Width: 5

Step-by-step explanation:

Let W = width

Let L = length

Length is 4 less than 3 times the width ==> L = 3*W - 4

Let P = Perimeter = 2*W + 2*L

Perimeter is 22 more than twice the width ==> P = 2*W + 22

Setting the 2 expressions for the perimeter equal to each other gives

2*W + 2*L = 2*W + 22

2*L = 22

L = 11

So 11 = 3*W - 4

3*W = 15

W = 5

The length is 11 and the width is 5

Check: 3*W - 4 = 11 = Length

Perimeter = 32 = 22 more than 2*5 = 10

3 0

3 years ago

A scale has a percent error of 7%. The scale reads the mass of a book as 450 g.

Hatshy [7]

500 grams I think it probably will be wrong but worth a try

7 0

3 years ago

Read 2 more answers

Find the value of x,y and z

Ierofanga [76]

Answer:

hope it helps, appreciate if you can give brainliests

3 0

3 years ago