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3 years ago

Find the length of the third side to the nearest tenth.

Mathematics

1 answer:

Aliun [14]3 years ago

8 0

Answer:

5.3

Step-by-step explanation:

You use the Pythagoras theorem which is a^2+b^2=c^2.

Since you're solving for a side length that's not the hypotenuse you will manipulate the equation to c^2-a^2=b^2. From here you just plug in numbers.

8^2 - 6^2 = b^2

64 - 36 = b^2

b = sqrt(28)

b = 5.2915.... = 5.3

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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

For which problem do you need to regroup 1 ten as 10 ones? Fill in the bubble next to the correct answer. Subtract 16 from 38, s

Kaylis [27]

Answer:

subtract 27 from 85

Step-by-step explanation:

-27

———

7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracted from 15 and then the 8 tens becomes 7 tens so 7-2=5

58+27=85 to check your work

5 0

3 years ago

James had 508 books to put into 9 boxes. how many books were in each box?

SOVA2 [1]

Answer:

around 56-57

Step-by-step explanation:

8 0

2 years ago

Colins class had 15 girls and 12 boys. If there were 4 boys what would be an equivalent ratio of boys and girls?

Leni [432]

Answer:

there would be 5 girls, boys 1; girl 1.25

Step-by-step explanation:

there are 1.25 girls for every boy

8 0

3 years ago

Juan is on his way home and his new car. He has driven 36 miles so far which is 3/4 of the way home. What is the total length of

Anarel [89]

Answer:

48 miles

Step-by-step explanation:

36/3 = 12 so 4/4 would be 48

3 0

2 years ago