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2 years ago

Solve the following, where 0° 0, then find cot

Mathematics

1 answer:

laila [671]2 years ago

3 0

Answer:

Nativism is the political position of preserving status for certain established inhabitants of a nation as compared to claims of newcomers or immigrants. It is characterized by opposition to immigration based on fears that the immigrants will distort or spoil existing cultural values.

Step-by-step explanation:

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Among all pairs of numbers (x,y)such that 6x+2y=36 find the pair for which the sum of squares, x^2+y^2 is minimum.

lora16 [44]

First, we simplify 6x+2y=36 into 3x+y=18 by dividing by 2. This means that y=-3x+18.

The sum $x^2+y^2$ can be written as: $x^2+y^2=(x+y)^2-2xy$ ,

from the binomial expansion formula: $(x+y)^2=x^2+2xy+y^2$ .

Thus, substituting y=-3x+18 and simplifying we have

 $x^2+y^2=(x+(-3x+18))^2-2x(-3x+18)$ $=(-2x+18)^2+6x^2-36x=4x^2-72x+18^2+6x^2-36x$ $=10x^2-108x+18^2$ .

This is a parabola which opens upwards (the coefficient of x^2 is positive), so its minimum is at the vertex. To find x, we apply the formula -b/2a. Substituting b=-108, a=10, we find that x is 108/20=5.4.

At x=5.4, the expression $10x^2-108x+18^2$ , which is equivalent to $x^2+y^2$ , takes it smallest value.

Substituting, we would find $10x^2-108x+18^2=10(5.4)^2-108(5.4)+18^2=291.6-583.2+324$ =32.4 This is the smallest value of the expression.

For x=5.4, y=-3x+18=-3(5.4)+18=1.8.

Answer: (5.4, 1.8)

8 0

2 years ago

Liam buys a motorcycle for $2,900. Its value depreciates annually at a rate of 12%. At the end of t years, it has a value of les

KIM [24]

It is given in the problem that

Liam buys a motorcycle for $2,900

Its value depreciates annually at a rate of 12%=0.12

At the end of t years, it has a value of less than $2,000

The exponential equation modeling this situation can be written as below

$2900(1-0.12)^t$

The inequality representing its value less than $2,000 can be written as below

$2900(1-0.12)^t$

4 0

2 years ago

Solve for xxx. Enter the solutions from least to greatest. (x -7)(-4x -2)=0(x−7)(−4x−2)=0left parenthesis, x, minus, 7, right pa

Lady bird [3.3K]

Answer:

-1/2, 7

Step-by-step explanation:

Given the expression

(x -7)(-4x -2)=0

This means that;

x - 7 = 0 and -4x - 2 = 0

x = 0+7 snd -4x = 2

x = 7 and x = -2/4

x = 7 and -1/2

Hence the solution from least to greatest is -1/2, 7

6 0

3 years ago

Ernesto Montenegro purchase a twelve 1000 Bonds having a quoted price of 100.75 he have to pay a 6% brokerage fee of the same pr

LenKa [72]

Answer: $106.8

Step-by-step explanation:

Given that the bond price is $100.75

With a 6% brokerage fee

Find the total cost to the nearest cent

First, we calculate the 6% brokerage fee= 6/100 × 100.75

= 0.06 x 100.75

= 6.045

Total cost therefore is the sum of brokerage fee and the cost of bond

= $6.045 + $100.75

= $106.795

To the nearest cent = $106.8

5 0

3 years ago

What is G if B = A × (1+G)T and B = 3,455, A = 1,969, and T = 8? Answer as a rate in decimal format so that 12.34% would be ente

zubka84 [21]

Answer:

G=0.0728

Step-by-step explanation:

The expression given is:

$B=A*(1+G)^T$

This expression has the format of a compounded interest at a rate G for a time T. If B = 3,455, A = 1,969, and T = 8, the value of the rate G is determined by:

$3,455=1,969*(1+G)^8\\G = \sqrt[8]{\frac{3,455}{1,969}}-1\\G=0.0728$

The rate G is 0.0728.

7 0

3 years ago