What root means to make or to do

1. f(x) = 3x – 2; f(4)??

netineya [11]

Answer:

the answer is 5

Step-by-step explanation:

f(4) = 3(4) -2

7 - 2 = 5

8 0

3 years ago

Read 2 more answers

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

Find the measure of < 1. m < 1 = degrees

Furkat [3]

<1 = 120/2 = 60

answer
60 degrees

8 0

4 years ago

Ignacio is curious about the average age of cars in the commuter lot at Mis large university. He takes a random

spin [16.1K]

Answer:

Between 12.614 years and 16.386 years

Step-by-step explanation:

Given that:

Mean age (μ) = 14.5 years, standard deviation (σ) = 4.6 years, number o sample (n) and the confidence interval (c) = 90% = 0,9

α = 1 -c = 1 -0.9 = 0.1

$\frac{\alpha }{2} = \frac{0.1}{2} = 0.05$

The z score of $\alpha /2$ is the same as the z score of 0.45 (0.5 - 0.05). This can be gotten from the probability distribution table. Therefore:

$z_{0.05}=1.64$

The margin of error (e) = $z_{0.05}\frac{\sigma}{\sqrt{n} }$ = $1.64*\frac{4.6}{\sqrt{16} }=1.886$

The interval = μ ± e = 14.5 ± 1.886 = (12.614 ,16.386)

4 0

3 years ago

A shipment of 11 printers contains 2 that are defective. Find the probability that a sample of size 2, drawn from the 11, will

svet-max [94.6K]

The required probability is $\frac{36}{55}$

Solution:

Given, a shipment of 11 printers contains 2 that are defective.

We have to find the probability that a sample of size 2, drawn from the 11, will not contain a defective printer.

Now, we know that, $\text { probability }=\frac{\text { favourable outcomes }}{\text { total outcomes }}$

Probability for first draw to be non-defective $=\frac{11-2}{11}=\frac{9}{11}$

(total printers = 11; total defective printers = 2)

Probability for second draw to be non defective $=\frac{10-2}{10}=\frac{8}{10}=\frac{4}{5}$

(printers after first slot = 10; total defective printers = 2)

Then, total probability $=\frac{9}{11} \times \frac{4}{5}=\frac{36}{55}$

7 0

3 years ago