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3 years ago

Explain why a + 2b = 110 in the triangle shown

Mathematics

1 answer:

Luda [366]3 years ago

3 0

Answer:

Step-by-step explanation:

According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180 degrees. For us, in our triangle:

a + 2b + 70 = 180 so

a + 2b = 180 -70 and

a + 2b = 110. That's why.

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A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

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3 years ago

What is 55x690-20+438x129=? <br> I will give brainliest.

frosja888 [35]

Answer:

don't know it sorry about tht

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3 years ago

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The two lines intersected by the transversal are parallel.what is the value of x?

sattari [20]

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3 years ago

Numbers are numbers of the form...

Olenka [21]

Answer: Third option.

Step-by-step explanation:

In order to solve the given exercise it is important to remember that:

1. Rational numbers are defined as those numbers that can be wrriten as a simple fraction.

2. The symbol for Rational numbers is: Q

3. Integers can be positive numbers, negative numbers and zero.

4. The symbol for Integers is: Z

5. Fractions have the following form:

$\frac{a}{b}$

Where:

"a" is the numerator and "b" is the denominator.

The numerator "a" and the denominator "b" are both Integers ( and $b\neq 0$ )

Therefore, based on the information given above, you can conclude that Rational numbers are numbers of the form $\{\frac{a}{b}|a,b$ ∈ $Z,b\neq0\}$

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3 years ago

Find the value of x.

Lynna [10]

Answer:

$here \: the \: two \: sides \: are \: equal \: so \: \\ the \: triangle \: is \: issosceles \\ then \: x = 40 \\ thank \: you$

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3 years ago

Explain why a + 2b = 110 in the triangle shown​

Explain why a + 2b = 110 in the triangle shown