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4 years ago

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In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 3x – 1, and HE = 5y + 4. Find the values of x and y.

2 answers:

notsponge [240]4 years ago

8 0

Answer:

x=35 y=20

Step-by-step explanation:

earnstyle [38]4 years ago

4 0

The diagonals of a parallelogram bisect each other.

DH = HF and GH = HE

x + 5 = 2y
3x - 1 = 5y + 4

Solve the first equation for x.
x = 2y - 5

Now substitute 2y - 5 for x in the second equation.

3(2y - 5) - 1 = 5y + 4

6y - 15 - 1 = 5y + 4

6y - 16 = 5y + 4

y = 20

Now substitute 20 for y in the first original equation.

x + 5 = 2y

x + 5 = 2(20)

x + 5 = 40

x = 35

Answer: x = 35 and y = 20

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DaniilM [7]

The values of x and y are 70/22 and 30/22 respectively by using the first-order condition of differential calculus.

<h3>What is the first-order condition in differential calculus?</h3>

A first-order differential equation is represented by the equation $\mathbf{ \dfrac{dy}{dx} =f (x,y) }$ with 2 variables x & y, including its function f(x,y) specified on a xy-plane.

Given that:

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Let us first differentiate the above equation with respect to x, we have:

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$\mathbf{\implies -44x +22y+110=0}$ (multiply by -1)

44x - 22y = 110 ------ (equation 1)

Now, differentiating with respect to y, we have:

$\mathbf{\dfrac{\partial f(x,y) }{\partial y} =0 +22x-22y +0-40-0=0}$

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Now, we have a system of equations:

44x - 22y = 110

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<u> 22x - 22y = 40 </u>

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<u />

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44x - 22y = 110

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Learn more about the first-order conditions in differential calculus here;

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2 years ago

A trucking firm suspects that the mean life of a certain tire. it uses is less than 33,000 miles. To check the claim, the firm r

Mice21 [21]

Answer:

We accept the alternate hypothesis. We conclude that the mean lifetime of tires is is less than 33,000 miles.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 33,000 miles

Sample mean, $\bar{x}$ = 32, 450 miles

Sample size, n = 18

Alpha, α = 0.05

Sample standard deviation, s = 1200 miles

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 33000\text{ miles}\\H_A: \mu < 33000\text{ miles}$

b) Level of significance:

$\alpha = 0.05$

c) We use One-tailed t test to perform this hypothesis.

d) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$ Putting all the values, we have

$t_{stat} = \displaystyle\frac{32450 - 33000}{\frac{1200}{\sqrt{18}} } = -1.9445$

Now, $t_{critical} \text{ at 0.05 level of significance, 17 degree of freedom } = -1.7396$

Rejection area:

$t < -1.7396$

Since,

$t_{stat} < t_{critical}$

e) We fail to accept the null hypothesis and reject it as the calculated value of t lies in the rejection area.

f) We accept the alternate hypothesis. We conclude that the mean lifetime of tires is is less than 33,000 miles.

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