Step-by-step explanation:
FORMATION OF TABLE FOR THE FUNCTION ![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
As t represents the temperature in degrees Fahrenheit and c represents the number of cricket chirps per minute.
Considering the function
![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
when
then ![c = 4(40) - 150 = 160 - 150 = 10](https://tex.z-dn.net/?f=c%20%3D%204%2840%29%20-%20150%20%3D%20160%20-%20150%20%3D%2010)
when ![t = 50](https://tex.z-dn.net/?f=t%20%3D%2050)
then ![c = 4(50) - 150 = 200 - 150 = 50](https://tex.z-dn.net/?f=c%20%3D%204%2850%29%20-%20150%20%3D%20200%20-%20150%20%3D%2050)
when
then ![c = 4(60) - 150 = 240 - 150 = 90](https://tex.z-dn.net/?f=c%20%3D%204%2860%29%20-%20150%20%3D%20240%20-%20150%20%3D%2090)
when
then ![c = 4(70) - 150 = 280 - 150 = 130](https://tex.z-dn.net/?f=c%20%3D%204%2870%29%20-%20150%20%3D%20280%20-%20150%20%3D%20130)
when ![t = 80](https://tex.z-dn.net/?f=t%20%3D%2080)
then ![c = 4(80) - 150 = 320 - 150 = 170](https://tex.z-dn.net/?f=c%20%3D%204%2880%29%20-%20150%20%3D%20320%20-%20150%20%3D%20170)
when
then ![c = 4(90) - 150 = 360 - 150 = 210](https://tex.z-dn.net/?f=c%20%3D%204%2890%29%20-%20150%20%3D%20360%20-%20150%20%3D%20210)
when ![t = 100](https://tex.z-dn.net/?f=t%20%3D%20100)
then ![c = 4(100) - 150 = 400 - 150 = 250](https://tex.z-dn.net/?f=c%20%3D%204%28100%29%20-%20150%20%3D%20400%20-%20150%20%3D%20250)
So
Lets form the data table for this function based on the determined values
![t\:\:\:\:\:\:\:40\:\:\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:60\:\:\:\:\:\:\:\:\:\:70\:\:\:\:\:\:\:\:\:\:\:80\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:\:\:100](https://tex.z-dn.net/?f=t%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A40%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A60%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A70%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A80%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A100)
![c\:\:\:\:\:\:\:\:10\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:130\:\:\:\:\:\:\:\:\:170\:\:\:\:\:\:\:\:\:210\:\:\:\:\:\:\:\:\:\:250](https://tex.z-dn.net/?f=c%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A10%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A130%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A170%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A210%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A250)
PART 1)
Considering the function
![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
As we know that
when
then ![c = 4(60) - 150 = 240 - 150 = 90](https://tex.z-dn.net/?f=c%20%3D%204%2860%29%20-%20150%20%3D%20240%20-%20150%20%3D%2090)
- Meaning the number of chirps per minute would increase to
, when the temperature t in degrees Fahrenheit increase to 60.
The appropriate logic is that the speed at which cricket chirps is based on the temperature. The table table also indicates that as the temperature t increases, the number of cricket chirps also increases.
PART 2)
- A rate of change is a rate that determines how one quantity changes in relation to another quantity.
Considering the two points
![\mathrm{Slope\:between\:two\:points}:\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(40,\:10\right),\:\left(x_2,\:y_2\right)=\left(50,\:50\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%2840%2C%5C%3A10%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%2850%2C%5C%3A50%5Cright%29)
![m=\frac{50-10}{50-40}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B50-10%7D%7B50-40%7D)
![m=4](https://tex.z-dn.net/?f=m%3D4)
It logically means for every increase of
units in
(temperature in degrees Fahrenheit), the value of
(number of chirps) is increasing to
units.
Thus, the rate of change will be
.
Part 3)
Considering the function
![c\:=\:4t\:-\:150](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4t%5C%3A-%5C%3A150)
The data table for this function
![t\:\:\:\:\:\:\:40\:\:\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:60\:\:\:\:\:\:\:\:\:\:70\:\:\:\:\:\:\:\:\:\:\:80\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:\:\:100](https://tex.z-dn.net/?f=t%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A40%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A60%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A70%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A80%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A100)
![c\:\:\:\:\:\:\:\:10\:\:\:\:\:\:\:\:50\:\:\:\:\:\:\:\:\:\:\:90\:\:\:\:\:\:\:\:\:130\:\:\:\:\:\:\:\:\:170\:\:\:\:\:\:\:\:\:210\:\:\:\:\:\:\:\:\:\:250](https://tex.z-dn.net/?f=c%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A10%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A50%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A90%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A130%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A170%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A210%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A250)
Putting
in the function brings the value of
as
.
i.e.
![c\:=\:4\left(40\right)\:-\:150=160=10](https://tex.z-dn.net/?f=c%5C%3A%3D%5C%3A4%5Cleft%2840%5Cright%29%5C%3A-%5C%3A150%3D160%3D10)
Yes, it does make sense.
Its logical meaning is that at the start, when the value of
was
temperature in degrees Fahrenheit, then the value of
(number of chirps per minute) was
.
Answer:
1. D.
.
2. D.
.
Step-by-step explanation:
1.
, where,
r = Radius of the cone,
h = Height of the cone.
Upon substituting our given values we will get,
![\text{Volume of an oblique cone}=\frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
![\text{Volume of an oblique cone}=\frac{1}{3}\pi(8\text{ cm})^2\times 15\text{ cm}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%288%5Ctext%7B%20cm%7D%29%5E2%5Ctimes%2015%5Ctext%7B%20cm%7D)
![\text{Volume of an oblique cone}=\frac{1}{3}\pi(64\text{ cm}^2)\times 15\text{ cm}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%2864%5Ctext%7B%20cm%7D%5E2%29%5Ctimes%2015%5Ctext%7B%20cm%7D)
![\text{Volume of an oblique cone}=\pi(64\text{ cm}^2)\times 5\text{ cm}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D%5Cpi%2864%5Ctext%7B%20cm%7D%5E2%29%5Ctimes%205%5Ctext%7B%20cm%7D)
![\text{Volume of an oblique cone}=320\pi\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20an%20oblique%20cone%7D%3D320%5Cpi%5Ctext%7B%20cm%7D%5E3)
Therefore, the volume of our given oblique cone is
and option D is the correct choice.
2.
, where,
r = Radius of the cone,
h = Height of the cone.
Upon substituting our given values we will get,
![\text{Volume of right cone}=300\pi \text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20right%20cone%7D%3D300%5Cpi%20%5Ctext%7B%20cm%7D%5E3)
Therefore, the volume of our given right cone is
and option D is the correct choice.
Let's solve this problem step-by-step.
STEP-BY-STEP EXPLANATION:
Let's first establish that the origin is always ( 0, 0 ).
Next, as shown in the diagram attached, we can establish that there is a right-angle triangle formed when we connect the different points given from the problem. We can use this to solve the problem.
As the shape is a right-angle triangle, we can use Pythagoras' Theorem which is as follows:
a^2 + b^2 = c^2
Where c = hypotenuse of the right-angle triangle
Where a and b = other two sides of the right-angle triangle which aren't the hypotenuse
From this, we will substitute the values from the problem into Pythagoras' Theorem.
a^2 + b^2 = c^2
a = 12
b = 5
c = distance from the origin = d
THEREFORE:
( 12 )^2 + ( 5 )^2 = d^2
d^2 = 12^2 + 5^2
d^2 = 144 + 25
d^2 = 169
d = square root of ( 169 )
d = 13
FINAL ANSWER:
Therefore, the point ( 12, 5 ) is 13 units from the origin.
Hope this helps! :)
Have a lovely day! <3
The answer is 75. What I did to get my answer is divide 15 by 0.20
The area of a rectangle with a base of 5 feet and a height of 9 1/2 feet is 47.5ft