Answer:
757,576cents
Step-by-step explanation:
Given
Amount = $10000
Time = 4years
Rate = 8%
n = 1/4 year (compounded quarterly
Using the formula to get the principal
A = P(1+r/n)^nt
10000 = P(1+0.08/0.25)^4(1/4)
10000 = P(1+0.32)
10000= 1.32P
P = 10000/1.32
P = 7575.76
Hence he suppose to invest $7575.76 which is equivalent to 7575.76×100 cents i.e 757,576cents
Answer:
- 4x² - 13x + 8 = 0
- 4x² - 11x + 5 = 0
- 16x² - 41x + 1 = 0
- x² + 5x + 4 = 0
- x² - 66x + 64 = 0
Step-by-step explanation:
<u>Given</u>
- α and β are roots of 4x²-5x-1=0
<u>Then the sum and product of the roots are:</u>
- α+b = -(-5)/4 = 5/4
- αβ = -1/4
(i) <u>Roots are α + 1 and β + 1, then we have:</u>
- (x - (α + 1))(x - (β + 1)) = 0
- (x - α - 1)(x - β - 1) = 0
- x² - (α+β+2)x + α+β+ αβ + 1 = 0
- x² - (5/4+2)x +5/4 - 1/4 + 1 = 0
- x² - 13/4x + 2= 0
- 4x² - 13x + 8 = 0
(ii) <u>Roots are 2 - α and 2 - β, then we have:</u>
- (x + α - 2)(x + β - 2) = 0
- x² + (a + β - 4)x - 2(α + β) + αβ + 4 = 0
- x² + (5/4 - 4)x - 2(5/4) - 1/4 + 4 = 0
- x² - 11/4x - 10/4 - 1/4 + 16/4 = 0
- x² - 11/4x + 5/4x = 0
- 4x² - 11x + 5 = 0
(iii) <u>Roots are α² and β², then:</u>
- (x - α²)(x-β²) = 0
- x² -(α²+β²)x + (αβ)² = 0
- x² - ((α+β)² - 2αβ)x + (-1/4)² = 0
- x² - ((5/4)² -2(-1/4))x + 1/16 = 0
- x² - ( 25/16 + 1/2)x + 1/16 = 0
- x² - 33/16x + 1/16 = 0
- 16x² - 33x + 1 = 0
(iv) <u>Roots are 1/α and 1/β, then:</u>
- (x - 1/α)(x - 1/β) = 0
- x² - (1/α+1/β)x + 1/αβ = 0
- x² - ((α+β)/αβ)x + 1/αβ = 0
- x² - (5/4)/(-1/4)x - 1/(-1/4) = 0
- x² + 5x + 4 = 0
(v) <u>Roots are 2/α² and 2/β², then:</u>
- (x - 2/α²)(x - 2/β²) = 0
- x² - (2/α² + 2/β²)x + 4/(αβ)² = 0
- x² - 2((α+β)² - 2αβ)/(αβ)²)x + 4/(αβ)² = 0
- x² - 2((5/4)² - 2(-1/4))/(-1/4)²x + 4/(-1/4)² = 0
- x² - 2(25/16 + 8/16)/(1/16)x + 4(16) = 0
- x² - 2(33)x + 64 = 0
- x² - 66x + 64 = 0
Answer: 130 kg 920 g
Step-by-step explanation:
Given
The weight of the goat is 59 kg 720 g
The combined weight of goat and cow is 190 kg 640 g
Suppose, the weight of the cow is x kg
We know, 1 kg=1000 g
Converting weight into kg
Goat weight
Total weight
Then, the cow weight is given by
Answer:
688.7
Step-by-step explanation:
Top and Bottom
Area = 3/4 * pi * r^2
r = 6
Area = 3/4 * 3.14 * 6^2
Area = 84.78
Don't round yet.
Vertical surface
Vertical surface = 3/4 * pi * d * h
d = 12 inches (the diameter)
Vertical surface = 3/4 * 3.14 * 12 * 15
Vertical surface = 423.9
Two inner faces
They are both rectangles
Area = 2 * L * W
L = 15
w=6
Area = 2 * 15 * 6 <u> 180</u>
Total 688.68
Total = 688.7
