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3 years ago

At what projection angle will the range of a projectile equal to 6 times its maximum height?

Mathematics

2 answers:

slamgirl [31]3 years ago

6 0

I not sure but it might be 60 kilogrames

soldier1979 [14.2K]3 years ago

4 0

The formula for maximum height is:

H = v²sin²θ/2g

The formula for range is:

R = v²sin(2θ)/g

The relationship between the two is written as:
R = 6H
v²sin(2θ)/g = 6(v²sin²θ/2g)
v²sin(2θ)/g = 3v²sin²θ/g)
Cancelling out like terms,
sin(2θ) = 3sin²θ
Solving for θ using a scientific calculator,
<em>θ = 33.7°</em>

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If c(x)=4x-2 and d(x)=x^2+5 , what is (c o d) (x)

Nookie1986 [14]

Answer:

4x² + 18

Step-by-step explanation:

note that (c ○ d )(x) = c(d(x))

To evaluate substitute x = d(x) into c(x), that is

c(d(x))

= c(x² + 5)

= 4(x² + 5) - 2

= 4x² + 20 - 2

= 4x² + 18

3 0

2 years ago

The number of portable widgets produced weekly by Widget, Inc., is related to the weekly profit in the way:

mixer [17]

9514 1404 393

Answer:

22 widgets
$58,400

Step-by-step explanation:

The turning point (maximum or minimum) of quadratic function ...

f(x) = ax² +bx +c

is at x = -b/(2a).

Here, this means the maximum profit will be had when the number of widgets produced weekly is ...

x = -88/(2(-2)) = 22

The profit at that level of production is ...

P(22) = (-2·22 +88)(22) -384 = 44(22) -384 = 968 -384 = 584 . . . hundreds

22 widgets must be produced weekly for the maximum weekly profit of $58,400.

3 0

3 years ago

A line passes through the origin and has a slope of 1/2.

ArbitrLikvidat [17]

Answer:

(2, 1)

Step-by-step explanation:

A line that passes through the origin and has a slope of 1/2 can be best represented as y = 1/2x

it starts at the origin

goes 2 units to the right

1 unit above

2 units to the right + 1 unit above = (2, 1)

Final Answer: (2, 1)

8 0

2 years ago

Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mice21 [21]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

3 0

3 years ago

Read 2 more answers

Please solve this literal equation for the variable "f"

Tatiana [17]

$\frac{df+10}{6}= g$

Now, multiply both sides by 6 and you get.....

df+10=6g

now, subtract 10 on both sides and you get.....

df=6g-10

now divide both sides by d to get f by itself and you get........

$f= \frac{6g-10}{d}$

8 0

3 years ago