Graphs of the following equations are straight lines except :

Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

Dvinal [7]

Answer:

1.692 m/min

Step-by-step explanation:

Let $\theta$ be the angle between the two sides and x be the length of the third side. By cosine rule,

$x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta$

$x= \sqrt{340 - 336\cos\theta}$

We differentiate x with respect to $\theta$ by applying chain rule.

$\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}$

Rate of change of $\theta$ is 2

$\dfrac{\theta}{dt} = 2$

Rate of change of x is

$\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}$

$\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}$

At 60°,

$\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}$

4 0

2 years ago

ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ant legs L Elena w

barxatty [35]

Answer:

Neither are correct.

Step-by-step explanation:

The number of legs = the number of ants * 6.

The relationship is L = 6 a so neither are correct.

7 0

2 years ago

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Dahlia is trying to decide which bank she should use for a loan she wants to take out. In either case, the principal of the loan

vovangra [49]

Answer:

a. Loan Q’s finance charge will be $83.73 greater than Loan P’s.

Step-by-step explanation:

Loan P

Monthly payments for a 9-year 5.8% loan for $19,450 are $231.59, so the total repaid is ...

108 payments × $231.59 per payment = $25,011.72

Together with the service charge, the cost of the loan is ...

$25,011.72 + 925.00 - 19,450 = $6,486.72

__

Loan Q

Monthly payments for a 10-year 5.5% loan for $19,450 are $211.08, so the total repaid is ...

120 payments × $211.08 per payment = $25,329.60

Together with the service charge, the cost of the loan is ...

$25,329.60 +690.85 -19,450 = $6,570.45

__

Difference of charges

The cost of Loan Q exceeds that of Loan P by ...

$6,570.45 -6486.72 = $83.73 . . . . . matches choice A

_____

The payment values here were computed using a financial calculator. They can be found using the TVM Solver of a graphing calculator (TI-84), or by any spreadsheet. A number of web sites will also calculate loan payment values, or you can use the formula in your text to compute them yourself.

3 0

2 years ago

Jillian is selling boxes of cookies to raise money for her basketball team. the 10 oz. box costs $3.50, while the 16 oz. box cos

zhannawk [14.2K]

X + y = 24...y = 24 - x
3.50x + 5.00y = 97.50

3.50x + 5(24 - x) = 97.50
3.50x + 120 - 5x = 97.50
3.50x - 5x = 97.50 - 120
-1.5x = -22.50
x = -22.50/-1.5
x = 15....there were 15 ten oz boxes (x) sold

3 0

2 years ago

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If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.

nirvana33 [79]

Answer: Triangle LMN is an obtuse triangle.

The angle at vertex L is acute.

The angle at vertex N is acute.

Step-by-step explanation:

Here, triangle LMN has an obtuse angle at vertex M,

Thus, by the definition of obtuse angle triangle LMN is an obtuse triangle,

Now, Angle M is obtuse,

⇒ 90° < m∠ M < 180°

Since, by the property of a triangle,

m∠ L + m∠ M + m∠ N = 180°

⇒ m∠ M = 180° - ( m∠ L+ m∠ N )

⇒ 90° < 180° - ( m∠ L+ m∠ N ) < 180°

⇒ 90° - 180° < - ( m∠ L+ m∠ N ) < 0

⇒ -90° < - ( m∠ L+ m∠ N ) < 0

⇒ 90° > ( m∠ L+ m∠ N ) > 0 ( Since, a - b)

⇒ 90° > m∠ L and 90° > m∠ N

⇒ Both angle L and angle N are acute.

5 0

2 years ago

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