Ok what do u need help with?
Answer:
The value of Liam's investment at the end of 4 years is £9069.764
Step-by-step explanation:
Compound interest is interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods of an investment.
We multiply the principal amount by one plus the annual interest rate to the power of the number of compound periods to get a combined figure for principal and compound interest.
4.5% in the first year;
4.5/100 = 0.045
(1 + 0.045) × 8000 =
1.045 × 8000 = £8360.
2.75% for all subsequent year;
2.75/100 = 0.0275
1 + 0.0275=1.0275
Number of years is;
4-1=3years
Therefore,
8360 × (1.0275)^3 =
8360 × 1.0849 = £9069.764
Answer:
2x + 12y + 43 ≥ 40
17x + 12y + 8z ≥ 20
14x + 6y + z ≤ 50
x ≥ 0
y ≥ 0
z ≥ 0
Step-by-step explanation:
given:
Cost Eggs = $2
Cost of edema = $5
cost of elbow Macaroni = $3
Lets eggs = x,
edamame = y
elbow macaroni = z
TC = 2x+5y+3z
Therefore;
2x + 12y + 43 ≥ 40
17x + 12y + 8z ≥ 20
14x + 6y + z ≤ 50
x ≥ 0
y ≥ 0
z ≥ 0
the first objective is to make sure the total cost is subject to the required nutritional requirements.
So the total cost function (TC) is denoted by the number of servings multiplied for each costs. Eggs cost $2, edamame $5, and macaroni $3.
The problem subjects that each meal contains at least 40g of carbohydrates (this is the condition).
to get this we need to add what each meal component adds to the total, eggs add 2g of carbs, edamame 12g, and macaroni 43g.
Same should be done for protein, we require at least 20 grams of protein, Eggs add 17g, edamame adds 12g, and macaroni adds 8g.
and lastly we don't want more than 50 grams of fat, Eggs add 14g, edamame add 6g and macaroni 1g.
Answer: 0.0064683053
I just used a calculator..
You did ask for the EXACT value, which no one has posted yet. The exact value is √(2 + √3)/2. To three decimal places, that is .966.
As for how I got that, I started with a 30-60-90 triangle and extended the longer side by the length of the hypotenuse to get a 15-75-90 triangle, then used Pythagoragus. For some reason, though, most students have an easier time using a half-angle formula, so feel free to do it that way.
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OK, sorry, I see Awesome Sauce also gives an exact value. It is also correct, just looks a little different.
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From your comment in Additional Details, it appears you want to use the angle difference relation: cos(π/12) = cos(π/4 - π/6). That works also, but you need to get the formula right, which is:
cos(a - b) = cos a * cos b + sin a * sin b
For cos (45 - 30), this gives cos 45 * cos 30 + sin 45 * sin 30 = √2/2 * √3/2 + √2/2 * 1/2 = √2/4(√3 + 1). This is yet another expression for the same exact value.
