Answer:
Correct answer: V = 55.36 cm³
Step-by-step explanation:
Given:
a = 4 cm edge of the bases
H = 8 cm the height of the prism
Area of the base is equilateral triangle which area is:
B = a² · √3 / 4 = 4² · 1.73 / 4 = 16 · 1.73 / 4 = 6.92 cm²
Volume of the prism is:
V = B · H = 6.92 · 8 = 55.36 cm³
V = 55.36 cm³
God is with you!!!
P = 11
Add 20 to both sides to get 5p = 55.
Then divide by 5 to get 'p' by itself.
55 / 5 = 11.
Answer:
17
Step-by-step explanation:
Mission Information :
This question is incomplete this line is missing in the question " Rin reaches into the bag, pulls out a blue marble, and puts it in her pocket. Then Misaki reaches in and pulls out a marble. What is the total number of possible outcomes for Misaki’s marble"
Now coming to the solution ,
Given :
Red marbles=3
blue marbles=5
green marbles=2
yellow Marbles=8
Total number of outcomes can be determined by
=Red marbles + blue marbles + green marbles + yellow Marbles
![= 3\ +\ 5+2 +8=18](https://tex.z-dn.net/?f=%3D%203%5C%20%2B%5C%20%205%2B2%20%2B8%3D18)
As mention in the given question the Rin is pulling the 1 marble ,Now Total number of outcomes
![=18-1\\=17](https://tex.z-dn.net/?f=%3D18-1%5C%5C%3D17)
Therefore 17 is the correct answer
Answer:
x-intercept: (2,0)
y-intercept: (0,3)
Step-by-step explanation:
We are asked to graph our given equation
.
To find x-intercept, we will substitute
in our given equation.
![\frac{1}{2}x+\frac{1}{3}(0)=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%2B%5Cfrac%7B1%7D%7B3%7D%280%29%3D1)
![\frac{1}{2}x+0=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dx%2B0%3D1)
![2*\frac{1}{2}x=2*1](https://tex.z-dn.net/?f=2%2A%5Cfrac%7B1%7D%7B2%7Dx%3D2%2A1)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Therefore, the x-intercept is
.
To find y-intercept, we will substitute
in our given equation.
![\frac{1}{2}(0)+\frac{1}{3}y=1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%280%29%2B%5Cfrac%7B1%7D%7B3%7Dy%3D1)
![0+\frac{1}{3}y=1](https://tex.z-dn.net/?f=0%2B%5Cfrac%7B1%7D%7B3%7Dy%3D1)
![3*\frac{1}{3}y=3*1](https://tex.z-dn.net/?f=3%2A%5Cfrac%7B1%7D%7B3%7Dy%3D3%2A1)
![y=3](https://tex.z-dn.net/?f=y%3D3)
Therefore, the y-intercept is
.
Upon connecting these two points, we will get our required graph as shown below.
To find the tangent line we will need the slope of the tangent at x=-1 (the x-coordinate of the point given). We find the slope by using the derivative of the curve.
Th curve given is
![y^{2} =5 x^{4} - x^{2}](https://tex.z-dn.net/?f=%20y%5E%7B2%7D%20%3D5%20x%5E%7B4%7D%20-%20x%5E%7B2%7D%20)
which can be solved for y by taking the root of both sides. We obtain
![y=(5 x^{4}- x^{2} ) ^{1/2}](https://tex.z-dn.net/?f=y%3D%285%20x%5E%7B4%7D-%20x%5E%7B2%7D%20%29%20%5E%7B1%2F2%7D%20%20)
We find the derivative using the chain rule. Bring down the exponent, keep the expression in the parenthesis, raise it to 1/2 - 1 and then take the derivative of what is inside.
![y’=(1/2)(5 x^{4} - x^{2} )^{-1/2}(20 x^{3} -2x)](https://tex.z-dn.net/?f=y%E2%80%99%3D%281%2F2%29%285%20x%5E%7B4%7D%20-%20x%5E%7B2%7D%20%29%5E%7B-1%2F2%7D%2820%20x%5E%7B3%7D%20-2x%29)
Next we evaluate this expression for x=-1 and obtain:
![\frac{20(-1)^{3} -(2)(-1)}{2 \sqrt{5(-1 ^{4}-(-1 ^{2}) } }= \frac{-20+2}{2 \sqrt{5-1} }=-18/4=-9/2](https://tex.z-dn.net/?f=%20%5Cfrac%7B20%28-1%29%5E%7B3%7D%20-%282%29%28-1%29%7D%7B2%20%5Csqrt%7B5%28-1%20%5E%7B4%7D-%28-1%20%5E%7B2%7D%29%20%20%7D%20%7D%3D%20%5Cfrac%7B-20%2B2%7D%7B2%20%5Csqrt%7B5-1%7D%20%7D%3D-18%2F4%3D-9%2F2%20%20)
So we are looking for a line through (-1,2) with slope equal to -9/2. We use y=mx+b with m=-9/2, x=-1 and y=2 to find b.
![2=(-9/2)(-1)+b](https://tex.z-dn.net/?f=2%3D%28-9%2F2%29%28-1%29%2Bb)
2-(9/2)=b
b=-5/2
So the tangent line is given by y=(-9/2)x+(-5/2)