Answer:8/12=2/3
Step-by-step explanation:
Answer: 6.3 years
Step-by-step explanation:
To find the time in years, we will use the Compound interest formula:
F = P( 1 + i/m)^mn
Where F = future value of investment ($8000); P = Amount invested ($5000); I
i = interest rate (7.5%); m = number of times money is compounded in a year (m = 4 for quarterly) and n = time of investment in years
Substituting;
8000 = 5000( 1 + 0.075/4)^4n
Divide both side by 5000 and simplify the bracket on the right hand side;
8000/5000 = (1.01875)^4n
1.6 = (1.01875)^4n
Since n is the power, to solve for it we can introduce the natural logarithm ( ln);
ln (1.6) = ln (1.01875)^4n
The power can betaken down according to the Laws of logarithms;
ln (1.6) = 4n x ln(1.01875)
To get n, divide both sides by 4ln (1.01875);
ln (1.6)/ 4ln(1.01875) = n
Therefore; n = 6.3 years
The right answer is Option 2: A right triangle with side length of √47 and hypotenuse of 10.
Step-by-step explanation:
We know that;
![a^2 + b^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2)
We will put the unknown length as √53 to check the solution.
Option 1: a = 6 , b = √53 , c = √91
![(6)^2+(\sqrt{53})^2=(\sqrt{91})^2\\36+53=91\\89\neq 91](https://tex.z-dn.net/?f=%286%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%28%5Csqrt%7B91%7D%29%5E2%5C%5C36%2B53%3D91%5C%5C89%5Cneq%2091)
Option 2: a=√47, b = √53, c = 10
![(\sqrt{47})^2+(\sqrt{53})^2=(10)^2\\47+53=100\\100=100](https://tex.z-dn.net/?f=%28%5Csqrt%7B47%7D%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%2810%29%5E2%5C%5C47%2B53%3D100%5C%5C100%3D100)
Option 3: a = √19, b=√53, c= √34
![(\sqrt{19})^2+(\sqrt{53})^2=(\sqrt{34})^2\\19+53=34\\72\neq 34](https://tex.z-dn.net/?f=%28%5Csqrt%7B19%7D%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%28%5Csqrt%7B34%7D%29%5E2%5C%5C19%2B53%3D34%5C%5C72%5Cneq%2034)
Option 4: a=√73, b=√53, c=20
![(\sqrt{73})^2+(\sqrt{53})^2=(20)^2\\73+53=400\\126\neq 400](https://tex.z-dn.net/?f=%28%5Csqrt%7B73%7D%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%2820%29%5E2%5C%5C73%2B53%3D400%5C%5C126%5Cneq%20400)
Option 2 satisfies pythagoras theorem.
Therefore;
The right answer is Option 2: A right triangle with side length of √47 and hypotenuse of 10.
Keywords: pythagoras theorem, square root
Learn more about pythagoras theorem at:
#LearnwithBrainly
Answer:
97°
Step-by-step explanation:
Usually measure of arc denotes to the central angle created by the arc at the centre of circle or peak of sector
Here. for AT arc the measure of central angle is <AOT
So our required answer is 97°