Chuck needs to drive 400 miles on the highway.

Tcecarenko [31]

$c^2$ $2c^2 + 13c +21 \\4c^2 + 13(2)c + 42\\(2c + 6)(2c+7)\\(c+3)(2c+7)$

This is a way to factoring trinomials (there exist different equivalent methods).

Multiply the trinomial but the term accompanying $c^2$ . This is the second line. Then, you could take the square of the $4c^2$ , ant try to create a factor () () that will correspond to the expression in the second line. That is, we want $4c^2 + 13(2) c + 42 = (2c + ?) (2c + ?)$

In ? we put the corresponding numbers that, if we multiply them we will obtain 42, and if we add them we will obtain 13. This numbers are 6 and 7. Then, we have $(2c + 6) (2c +7)$

The last step is divide by the number that we multipy in the first step.

4 0

3 years ago

Resuelve el siguiente problema un buzo en una laguna decendio 8m en una hora.Si cada hora bojo la misma cantidad de metros, ¿cua

S_A_V [24]

Answer:

X = 32 meters.

Step-by-step explanation:

Let the unknown distance be X.

<u>Given the following data;</u>

Distance = 8 meters per hour
Time = 4 hours

To find how many meters he would cover in four hours;

1 hour = 8 meters

4 hours = X meters

Cross-multiplying, we have;

X = 8 * 4

<em>X = 32 meters.</em>

7 0

2 years ago

a 3 dimensional figure has a square base and 4 lateral faces that meet at a point. Explain the difference between the cross sect

Kruka [31]

Answer:

a slice is made perpendicular to the base through the vertex: triangle

slice is made perpendicular to the base and not through the vertex: trapezoid

Step-by-step explanation:

a slice is made perpendicular to the base through the vertex: triangle

slice is made perpendicular to the base and not through the vertex: trapezoid

8 0

2 years ago

Each friend received 5/4 of a pound of berries, how many friends are sharing berries?

Rudiy27

Answer:

2

Step-by-step explanation:

If 5 friends are sharing the berries, how many pounds of berries does each friend receive? Is the answer to 3/4 divided by 2/5 greater than or less than 1.

8 0

2 years ago

A golfball is hit from the ground with an initial velocity of 200 ft/sec. The horizontal distance that the golfball will travel,

algol13

Answer:

The golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of $\pi/4$ .

Step-by-step explanation:

The formula from the maximum distance of a projectile with initial height h=0, is:

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}$

Where $v_i$ is the initial velocity.

In the closed interval method, the first step is to find the values of the function in the critical points in the interval which is $[0, \pi/2]$ . The critical points of the function are those who make $d'(\theta)=0$ :

$d(\theta)=\frac{v_i^2\sin(2\theta)}{g}\\d'(\theta)=\frac{v_i^2\cos(2\theta)}{g}*(2)\\d'(\theta)=\frac{2v_i^2\cos(2\theta)}{g}$

$d'(\theta)=0\\\frac{2v_i^2\cos(2\theta)}{g}=0\\\cos(2\theta)=0\\2\theta=\pi/2,3\pi/2,5\pi/2,...\\\theta=\pi/4,3\pi/4,5\pi/4,...$

The critical value inside the interval is $\pi/4$ .

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\d(\pi/4)=\frac{v_i^2sin(2(\pi/4))}{g}\\d(\pi/4)=\frac{v_i^2sin(\pi/2)}{g}\\d(\pi/4)=\frac{v_i^2(1)}{g}\\d(\pi/4)=\frac{(200)^2}{32}\\d(\pi/4)=\frac{40000}{32}\\d(\pi/4)=1250ft$

The second step is to find the values of the function at the endpoints of the interval:

$d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\\theta=0\\d(0)=\frac{v_i^2sin(2(0))}{g}\\d(0)=\frac{v_i^2(0)}{g}=0ft\\\theta=\pi/2\\d(\pi/2)=\frac{v_i^2sin(2(\pi/2))}{g}\\d(\pi/2)=\frac{v_i^2sin(\pi)}{g}\\d(\pi/2)=\frac{v_i^2(0)}{g}=0ft$

The biggest value of f is gived by $\pi/4$ , therefore $\pi/4$ is the absolute maximum.

In the context of the problem, the golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of $\pi/4$ .

4 0

3 years ago