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3 years ago

Evaluate the expression when c=8 and d=7. 4d-c whats the answer?

Mathematics

1 answer:

11111nata11111 [884]3 years ago

8 0

Answer:

The answer is 20.

Step-by-step explanation:

4(d) - c

4(7) - c

28 - c

28 - 8

20 is the answer.

I hope this helps, have a nice day.

You might be interested in

What is the smallest integer k>2000 such that both 17k/66 and 13k/105} are terminating decimals?

Dvinal [7]

17k/66 and 13k/105 must reduce to fractions with a denominator that only consists of powers of 2 or 5.

For example, some fractions with terminating decimals are

1/2 = 0.5

1/4 = 1/2² = 0.25

1/5 = 0.2

1/8 = 1/2³ = 0.125

1/10 = 1/(2•5) = 0.1

1/16 = 1/2⁴ = 0.0625

and so on, while some fractions with non-terminating decimals have denominators that include factors other than 2 or 5, like

1/3 = 0.333…

1/6 = 1/(2•3) = 0.1666…

1/7 = 0.142857…

1/9 = 1/3² = 0.111…

1/11 = 0.09…

1/12 = 1/(2²•3) = 0.8333…

etc.

Since 66 = 2•3•11, we need 17k to have a factorization that eliminates both 3 and 11.

Similarly, since 105 = 3•5•7, we need 13k to eliminate the factors of 3 and 7.

In other words, 17k must be divisible by both 3 and 11, and 13k must be divisible by both 3 and 7. But 13 and 17 are both prime, so it's just k that must be divisible by 3, 7, and 11. These three numbers are relatively prime, so the least positive k that meets the conditions is LCM(2, 7, 11) = 231, and thus k can be any multiple of 231.

If you're familiar with modular arithmetic, this is the same as solving for k such that

13k ≡ 0 (mod 3)

17k ≡ 0 (mod 3)

17k ≡ 0 (mod 7)

13k ≡ 0 (mod 11)

and the Chinese remainder theorem says that k = 231n solves the system of congruences, where n is any integer.

Now it's just a matter of finding the smallest multiple of 231 that's larger than 2000, which easily done by observing

2000 = 8•231 + 152

and so k = 9•231 = 2079.

3 0

2 years ago

After sitting on a shelf for a while, a can of soda at room temperature (73 F) is placed inside a refrigerator and slowly cools.

Alona [7]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling here:

$T(t)=T_s+(T_0-T_s)^{-kt$

where T(t) is the temp of something after a certain amount of time, t, has gone by; Ts is the surrounding temp, and T0 is the initial temp. k is the constant of cooling. We need to first solve for this using the information given. Filling in what we know:

$53=35+(73-35)^{-35k$ which can simplify a bit to

$53=35+(38)^{-35k$ and $18=38^{-35k$

Take the natural log of both sides:

$ln(18)=ln(38)^{-35k$

Taking the natural log allows us to pull that exponent down out front:

$ln(18)=-35k*ln(38)$

and now we can divide both sides by ln(38) to get

-35k = .794585 so

k = -.023

Now that have the value for k, we can go on to solve the rest of the problem which is asking us the temp of the soda after 70 minutes. Filling in using the k value and the new time of 70 minutes:

$T(t)=35+(38)^{70(-.023)$ and