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KonstantinChe [14]
3 years ago
14

Simply the expression 3(2x+y)

Mathematics
1 answer:
Damm [24]3 years ago
4 0

Answer:

6x + 3y

Step-by-step explanation:

3(2x + y)

6x + 3y

Bet of Luck!

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3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt

Evaluate the integral to solve for y :

\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt

\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x

\displaystyle y = x^3+2x^2+kx - 2

Use the other known value, f(2) = 18, to solve for k :

18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}

Then the curve C has equation

\boxed{y = x^3 + 2x^2 + 2x - 2}

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2

The slope of the given tangent line y=x-2 is 1. Solve for a :

3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1

So, the point of contact between the tangent line and C is (-1, -3).

7 0
2 years ago
After earning interest, the balance of an account is $420. The new balance is 7/6 of the original balance. Write an equation tha
vredina [299]
<h3>Given</h3>

The current balance is $420.

The current balance is 7/6 of the original balance, b

<h3>Find</h3>

equation to use to find b

<h3>Solution</h3>

Equate the two descriptions of the current balance.

... $420 = (7/6)b . . . . . equation to use to find b

3 0
3 years ago
Can someone help me please.
Ket [755]

Answer:

28. the second and third one

29. 687.50 dollars

Step-by-step explanation:

2.49(2) + 1.79(2) + 0.89(4) = 12.12 no

2.49(3) + 1.79(2) = 11.05 yes

2.49(2) + 1.79(3) + 0.89 = 11.24 yes

2.49(4) + 1.79 + 0.89 = 12.64 no


area = length times width

a = 6.25 times 5

a = 31.25 square feet

31.25(22) = 687.50

3 0
3 years ago
What are you finding when you are asked what is 60% of 175? the part, the whole or the precent​
butalik [34]

Answer:

105 is the part.

Step-by-step explanation:

175 is the whole

60% is the percent

x is the part

175 * 0.60 = 105

3 0
2 years ago
Notebook paper is on sale for 50% off a package regularly sells for $0.58 a customer made by only two packages at the sale price
blagie [28]
Richard had to pay 0.87
7 0
3 years ago
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