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2 years ago

Domain, first element, and y -value all have the same meaning. True Or False

1 answer:

4 0

False;
Domain- The set of possible values of the independent variable or variables in a function.
y-Value is in a graph {y=mx+b} is the slope its the number "M" that is multiplied by x, and "b" is the y-intercept {That is the point where the line crosses the x axis.

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What is 91,284 rounded to the nearest hundred thousand

otez555 [7]

If this is asking for the nearest hundred thousand, and not ten thousand, than you would round up to 100,000. 91,284 is close to 100,000.

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3 years ago

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).

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2 years ago

What is 10 as a percentage?

Marta_Voda [28]

i think its 1000%

why?

''Convert the decimal to a percentage by multiplying the decimal by 100.''

8 0

2 years ago

Read 2 more answers

What fraction is bigger 1/4 or 16 1/3

Evgen [1.6K]

16 1/3 is bigger than 1/4

5 0

2 years ago

Justin buys a shirt that costs 24 dollars and a jacket that costs 54 dollars. If sales tax is 7%, what is the total purchase pri

andreyandreev [35.5K]

Answer:

$83.46

Step-by-step explanation:

24 + 54 =78

78 × 7% = 5.46

78 + 5.46 = $83.46

8 0

2 years ago