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3 years ago

Given that the measure of angle GHJ = 154 degrees find the angle of HIJ

Mathematics

1 answer:

vichka [17]3 years ago

6 0

Answer:

the correct answer is 77°

Step-by-step explanation:

Angle GHJ and IHJ form supplementary angles which add up to 180°

therefore angle IHJ=180-154

angle IHJ=26°

Triangle IHJ is an isosceles triangle whose base angles HIJand IJH are equal. Lets assign them the same value, x° each

since the sum of all interior angles of a triangle add up to 180°, then x°+x°+26°=180°

2x+26=180

2x=154°

x=77°

Therefore both HIJ and IJH measure 77°

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A rectangle initially has width 7 meters and length 10 meters and is expanding so that the area increases at a rate of 8 square

Tems11 [23]

Answer:

The length of rectangular is increasing at a rate 0.5714 meters per hour.

Step-by-step explanation:

We are given the following in the question:

Initial dimensions of rectangular box:

Length,l = 10 m

Width,w = 7 m

$\dfrac{dA}{dt} = 8\text{ square meters per hour}\\\\\dfrac{dw}{dt} = 40\text{ centimeters per hour} =0.4\text{ meters per hour}$

We have to find the rate of increase of length.

Area of rectangle =

$A = l\times w$

Differentiating we get,

$\displaystyle\frac{dA}{dt} = \frac{dl}{dt}w + \frac{dw}{dt}l$

Putting values, we get,

$8 = \dfrac{dl}{dt}(7) + (0.4)(10)\\\\\dfrac{dl}{dt}(7) = 8 -4\\\\\dfrac{dl}{dt} \approx 0.5714$

Thus, the length of rectangular is increasing at a rate 0.5714 meters per hour.

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3 years ago

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Rufina [12.5K]

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