Given Data : Length = (7p - 10q) and Breadth = (2p - 9q)
Calculation :
⟹ Perimeter = 2(Length + Breadth)
⟹ Perimeter = 2(7p - 10q + 2p - 9q)
⟹ Perimeter = 2(9p - 19q)
⟹ Perimeter = <em>18p - 38q centimetres</em>
- <u>Answer : 18p - 38q centimetres</u>
Answer:
The height of the arch at its center is 250/9 or about 27.78 feet.
Step-by-step explanation:
We can write an equation to model the parabolic arch.
Let the left-most point of the arch be the origin (0, 0).
Since the bridge has a span of 100 feet, the right-most point must be (0, 100).
We can use the factored form of a quadratic:
![y=a(x-p)(x-q)](https://tex.z-dn.net/?f=y%3Da%28x-p%29%28x-q%29)
Where <em>p</em> and <em>q</em> are the <em>x-</em>intercepts.
Our <em>x-</em>intercepts are <em>x </em>= 0 and <em>x </em>= 100. Hence:
![y=ax(x-100)](https://tex.z-dn.net/?f=y%3Dax%28x-100%29)
At a point 40 feet from the center, the height of the arch is 10 feet.
The center is <em>x</em> = 50. So, a point 40 feet from the center can be either <em>x</em> = 10 or <em>x</em> = 90.
So, for instance, when <em>x</em> = 10, <em>y</em> = 10. Substitute and solve for <em>a: </em>
<em />
<em />
So:
![\displaystyle a=-\frac{1}{90}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D-%5Cfrac%7B1%7D%7B90%7D)
The same value will result if we let <em>x</em> = 90 and <em>y</em> = 10.
Hence, our equation is:
![\displaystyle y=-\frac{1}{90}x(x-100)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B1%7D%7B90%7Dx%28x-100%29)
The height of the arch at its center will be when <em>x</em> = 50. Hence:
![y(50)=\displaystyle -\frac{1}{90}(50)((50)-100)=\frac{250}{9}\approx 27.78\text{ feet}](https://tex.z-dn.net/?f=y%2850%29%3D%5Cdisplaystyle%20-%5Cfrac%7B1%7D%7B90%7D%2850%29%28%2850%29-100%29%3D%5Cfrac%7B250%7D%7B9%7D%5Capprox%2027.78%5Ctext%7B%20feet%7D)
Answer:
x = 40°
Step-by-step explanation:
105 = 3x - 15
105 + 15 = 3x
3x = 120
x = 120 : 3
x = 40°
The correct answer to this question would be answer choice B.
To convert the decimal 0.56 to a fraction, first set it to a fraction over 100 which would be 56/100.
Then, because the question asks for the fraction to be in simplest form, look for the greatest common factor of the numerator and denominator or 56 and 100.
To find it, list out all of their factors:
56: 1, 2, 4, 7, 8 , 14, 28, 56
100: 1, 2, 4, 5, 10,20,25,50,100
Notice that out of all the factors listed, the greatest common factor listed is 4. Because of this, divide both the numerator and denominator by 4 to simplify your fraction to your answer: 14/25
Applying the law of cosines, the measure of angle Y in the image below, to the nearest whole degree, is: B. 64°
<h3>What is the Law of Cosine:</h3>
Law of cosines is given as: y² = x² + z² – 2xz(cosY)
Given the following:
x = 12
y = 16
z = 17
Y = ?
Apply the law of cosines:
16² = 12² + 17² – 2(12)(17)(cosY)
256 = 433 - 408(cos Y)
256 - 433 = -408(cos Y)
-177 = -408(cos Y)
-177/-408 = cos Y
Y = cos^(-1)(177/408)
Y ≈ 64°
Learn more about law of cosines on:
brainly.com/question/7872492