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3 years ago

1. The difference between the product of nine and a number and three times the number.

Mathematics

1 answer:

Alik [6]3 years ago

7 0

Answer:

Question 1:

• Let the number be x

${ \tt{9x - 3x}} \\ { \boxed{ \tt{ = 6x}}}$

Question 2:

${ \tt{5x - 4x}} \\ { \boxed { \tt{ = x}}}$

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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

Which of the following numbers is NOT a solution of the inequality 3x – 5>_4x – 3 ?

Arte-miy333 [17]

Answer:

A)-1

Step-by-step explanation:

3x-5≥4x-3

3x-4x≥-3+5

-x≥2

x≤-2

(-infinity,-2]

-1 x

-2,-3,-5 ✓

8 0

3 years ago

Which of these sequences is a geometric sequence?

Lera25 [3.4K]

The geometric sequence is 3, 9, 27, 81, 243, 729 because each time it is multiplied by 3.

6 0

3 years ago

a right triangle has one side that measures 4 in. the angle opposite that side measures 80° what is the length of the hypotenuse

lara [203]

Answer:

The length of the hypotenuse is 4.1 in

Step-by-step explanation:

By definition, the sine of an angle is:

$sin(x) = \frac{opposite\ side}{hypotenuse}$

In this case they tell us that the opposite side measures 4 inches and the angle x measures 80 °.

With this information we can find the length of the hypotenuse h

$sin(80\°) =\frac{4}{h}\\\\h = \frac{4}{sin(80\°)}\\\\h = 4.062\ in$

Finally the length of the hypotenuse is 4.1 in

6 0

3 years ago

What are the solutions of 2x^2 +3x = -8 ///// click picture for options!!!

vivado [14]

2x^2 + 3x + 8 = 0

Answer: B) -3 + I √55 over 4.

4 0

3 years ago