Write y= - 4x on a graph
1 answer:
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Scale factor of area is the square of the scale factor of length
The required values are;
- The length of one sides of the garage was originally approximately <u>19.2 ft.</u>
- The length of one of the sides of the garage is now approximately <u>23.6 feet</u> long
- The percentage increase in length is approximately <u>22.5 %</u>
Reason:
The given parameters are;
The area of the square garage = 370 ft.²
The area of the new garage has 50% more space
Required;
Part A
The initial side length
The initial side length, given to the nearest tenth, <em>s</em>, is the square root of the area, <em>A</em>, given as follows;
- s = √(370 ft.²) ≈ 19.2 ft.
Part B
The side was increased by 50%, to give,
370 + 0.5×370 = 555
The new area of the garage = 555 ft.²
The side length of the new garage, s = √(555) ≈ 23.6
- The side of the garage now is 23.6 ft.
Part C
The percentage increase is given as follows;
- The percentage increase in length of the side of the garage is approximately 22.5 %
Learn more here:
Answer:
(1) Option A is correct , The measure of angle A = 26°
(2) Option D is correct, The measure of angle B =70°
Step-by-step explanation:
(1)
In a right angle triangle figure-1 ,
* Hypotenuse(H) is always opposite the right angle and it is always the longest side of the triangle.
* Adjacent side (B) is the non-hypotenuse side that is next to a given angle A.
* Opposite side(P) is across from a given angle A.
To find the Angle A we use the Cosine ratio:
Cosine ratio states that the ratio of the adjacent side of a right triangle to the hypotenuse.
By definition of cosine ratio we have;
....[1]
In the figure - 1 we have B = 18 in and H = 20 in
substitute these in [1] to find angle A
or
⇒
therefore, the measure of angle A is,
(2)P
In figure -2
Find the measure of angle B.
First find the side BC, using Pythagoras theorem;
Pythagoras theorem states that in the right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Apply Pythagoras theorem in rt. angle ABC;
Substitute the values of AB = 5.1 cm and AC =4.8 cm to solve for BC
Simplify:
or
Now, find the angle B, using tangent ratio;
Tangent ratio states that the ratio of the Opposite side of a right triangle to the adjacent side.
Therefore, the measure of angle B is; .
T = days passed
r = rate of growth
by 0 day, or t = 0, there are 2 folks sick,
by the third day, t = 3, there are 40 folks sick,
![\bf \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &40\\ P=\textit{initial amount}\to &2\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\to &3\\ \end{cases} \\\\\\ 40=2(1+r)^3\implies 20=(1+r)^3\implies \sqrt[3]{20}=1+r \\\\\\ \sqrt[3]{20}-1=r\implies 1.7\approx r\qquad \boxed{A=2(2.7)^t}](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BAmount%20for%20Exponential%20Growth%7D%0A%5C%5C%5C%5C%0AA%3DP%281%20%2B%20r%29%5Et%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5Cto%20%2640%5C%5C%0AP%3D%5Ctextit%7Binitial%20amount%7D%5Cto%20%262%5C%5C%0Ar%3Drate%5Cto%20r%5C%25%5Cto%20%5Cfrac%7Br%7D%7B100%7D%5C%5C%0At%3D%5Ctextit%7Belapsed%20time%7D%5Cto%20%263%5C%5C%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A40%3D2%281%2Br%29%5E3%5Cimplies%2020%3D%281%2Br%29%5E3%5Cimplies%20%5Csqrt%5B3%5D%7B20%7D%3D1%2Br%0A%5C%5C%5C%5C%5C%5C%0A%5Csqrt%5B3%5D%7B20%7D-1%3Dr%5Cimplies%201.7%5Capprox%20r%5Cqquad%20%5Cboxed%7BA%3D2%282.7%29%5Et%7D)
how many folks are there sick by t = 6?
r = rate of growth
by 0 day, or t = 0, there are 2 folks sick,
by the third day, t = 3, there are 40 folks sick,
how many folks are there sick by t = 6?