Answer:
Option (2).
Step-by-step explanation:
It is given in the question,
ΔLMN is a right triangle with base LM = 3a units
Hypotenuse MN = 5a
By applying Pythagoras theorem in ΔLMN,
MN² = LM² + NM²
(5a)² = (3a)² + MN²
25a² - 9a² = MN²
MN = √16a²
MN = 4a
Therefore, vertices of the triangle will be L(0, 0), M(3a, 0) and N(0, 4a).
Option (2) will be the answer.
Answer: (f-g)(2)=14
Step-by-step explanation:
(f – g) (-2) means the same as subtracting f(2) and g(2). Since we are given f(x) and g(x), we can use them to solve. There are two ways to solve. One is to find f(2) and g(2), and then subtract them. Another way is to do (f-g)(x), then plug in x=2. I will show both methods.
Method 1
f(2)=3(2)²+1 [exponent]
f(2)=3(4)+1 [multiply]
f(2)=12+1 [add]
f(2)=13
g(2)=1-(2) [subtract]
g(2)=-1
(f-g)(2)=13-(-1) [subtract f(2) and g(2)]
(f-g)(2)=14
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Method 2
(f-g)(x)=3x²+1-(1-x) [distribute -1]
(f-g)(x)=3x²+1-1+x [combine like terms]
(f-g)(x)=3x²+x
(f-g)(2)=3(2)²+2 [plug in x=2, exponent]
(f-g)(2)=3(4)+2 [multiply]
(f-g)(2)=12+2 [add]
(f-g)(2)=14
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Now, we know that (f-g)(2)=14. We confirmed this with both methods.
Answer:
-3/2
Step-by-step explanation:
Answer:
408 cm^3
Step-by-step explanation:
You have to find the volume of each object individually. You first find the volume of the sphere, so you input the radius, which is 3, into the equation which comes out to be 108 cm^3. You then have to find the volume of the cylinder, and since you have the diameter of the cylinder, and you need the radius, and the radius is half of the diameter, you would input 5 into the equation as the radius, since half of 10 is 5. That comes out to be 300 cm^3, so then you add the two volumes together, which is 408 cm^3
