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3 years ago

14

What is the shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the

top vertex?
A a parallelogram that is not a rectangle

B a rectangle

C a triangle

D a trapezoid

2 answers:

topjm [15]3 years ago

8 0

Answer:

correct answer is trapezoid

Step-by-step explanation:

if im wrong plz correct me

bagirrra123 [75]3 years ago

7 0

Answer:

I'm pretty sure its a Trapezoid but don't quote me

Step-by-step explanation:

I don't really know

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Write an equation for a function that has vertical asymptotes at x=3 & x=-10

stepan [7]

Answer:

$\frac{5}{ {x}^{2} + 7x - 30}$

Step-by-step explanation:

We can write a rational function.

We need to make sure our denominator both have zeroes at 3 and 10.

Set an equation equal to zero to find the function

$0 - x = 3$

$0 - x = - 10$

$0 - ( - 3) = = 3$

$0 - 10 = 10$

So we would represent that's as

$x - 3$

and

$x + 10$

Multiply the two binomial together.

$(x - 3)(x + 10) = {x}^{2} + 7x - 30$

Let our numbetator be any interger.

Use any equation as long as the quadratic is the denominator and the interger is the numerator.

$\frac{5}{ {x}^{2} + 7x - 30 }$

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3 years ago

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3 years ago

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If the outliers are not included, what is the mean of the data set?

luda_lava [24]

The mean of the numbers is c. 67

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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

Sarah and Bridget have played 45 tennis matches.

Ainat [17]

Answer:

P(Sarah wins)= 1/3

P(Bridget wins)= 2/3

Step-by-step explanation:

15/45 = 1/3

1 - 1/3 = 2/3

8 0

3 years ago