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kap26 [50]
4 years ago
13

Solve the system by graphing 2x+y=4. y=3x+9

Mathematics
1 answer:
VMariaS [17]4 years ago
3 0

Answer

strech by 2 cordinate 1,4 then 2,8

second one is strech by 3 up 9

Step-by-step explanation:

x=-1

y=2

or thats what is see

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For what values of θ, −π ≤ θ ≤ π, is y = tan θ undefined?
pogonyaev

Answer:

The answer is II and IV ⇒ the 3rd answer

Step-by-step explanation:

* lets check the domain of angle Ф

∵ -π ≤ Ф ≤ π

∵ y = tanФ

∵ tanФ = sinФ/cosФ

* The effective term which makes tanФ undefined is cosФ

- If cosФ = 0, than tanФ will be undefined

* Lets check the angles that have cosФ = 0

∵ The unit circle intersect x-axis at point (1 , 0) and (-1 , 0)

∵ The unit circle intersect y-axis at point (0 , 1) and (0 , -1)

∵ cosФ = x-coordinates of the points

∵ The points of intersection with the y-axis have x- coordinates = 0

∴ The angles on the y-axis have cosФ = 0

* The angles on the +ve part of y-axis are π/2 and -3π/2

 The angles on the -ve part of y-axis are -π/2 and 3π/2

∴ The tan of π/2 , 3π/2 , -π/2 , -3π/2 undefined

* In the problem

I. -π ⇒ defined ⇒ on the -ve part of x-axis

II. -π/2 ⇒undefined

III. 0 ⇒ defined ⇒ on the +ve part of the x-axis

IV. π/2 ⇒ undefined

V. π ⇒ defined ⇒ on the -ve part of x-axis

∴ The answer is II and IV ⇒ the 3rd answer

3 0
3 years ago
In the figure, if CD = 15 cm, then BC ≈ cm.
Alona [7]
Check the picture below.

make sure your calculator is in Degree mode, since the angles are in degrees.

3 0
3 years ago
Read 2 more answers
What are the steps to solve 7÷2 1/3
igomit [66]
You have to make 7 into 21/3. Then change 2 1/3 into 7/3. Then divide 21/3 abd 7/3 which equals 3/3 which equals 1.
3 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
The diameter of a circle is 16 meters what is the area
KengaRu [80]

Answer:

201.1 meters squared

Step-by-step explanation:

A= pi*r squared

Diameter= 16, to find the radius we must divide by 2

16/2=8

Radius= 8

A= pi* (8)^2

A= 201.06

The area of the circle is 201.1 meters squared.

3 0
3 years ago
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