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3 years ago

15

When m and I are cut by transversal n. if m<3=67° , determine m<6.

1 answer:

marshall27 [118]3 years ago

3 0

Answer:

113°

Step-by-step explanation:

Angles 3 and 6 are consecutive interior angles

<u>As per definition, consecutive internal angles add to 180°</u>

m∠3 = 67° ⇒
m∠6 = 180° - 67° = 113°

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I need help On This !!!!!!!!

bearhunter [10]

Answer:

Step-by-step explanation:

L'= 3, -3 M'= -3, -6 N'= -3, 3

7 0

3 years ago

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 $L\approx 15.57$ .

8 0

3 years ago

A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has an

lukranit [14]

ŷ= 1.795x +2.195 is the equation for the line of best fit for the data

<h3>How to use regression to find the equation for the line of best fit?</h3>

Consider the table in the image attached:

∑x = 29, ∑y = 74, ∑x²= 125, ∑xy = 288, n = 10 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (10×288 - 29×74) / ( 10×125-29² )

= 2880-2146 / 1250-841

= 734/409

= 1.795

x' = ∑x/n

x' = 29/10 = 2.9

y' = ∑y/n

y' = 74/10 = 7.4

b = y' - ax'

b = 7.4 - 1.795×2.9

= 7.4 - 5.2055

= 2.195

ŷ = ax + b

ŷ= 1.795x +2.195

Therefore, the equation for the line of best fit for the data is ŷ= 1.795x +2.195

Learn more about regression equation on:

brainly.com/question/29394257

#SPJ1

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1 year ago

This is a tricky one

IgorLugansk [536]

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3 years ago

Can someone help me with this problem [-64x(-5)-2x(3)]

galina1969 [7]

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