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2 years ago

Find the indicated values g(t)=t^2-t and f(x)=1+x g(f(2)+3)

Mathematics

1 answer:

Semmy [17]2 years ago

7 0

Answer:

g( f(2)+3) = 30

Step-by-step explanation:

<u>step(i)</u>:-

Given function g(t)=t²-t and f(x)=1+x

given f(x)=1+x

f(2) = 1 + 2 =3

<u><em>step(ii)</em></u>:-

g( f(2)+3) = g(3 + 3)

= g(6)

= (6)² - 6

= 36 -6

= 30

<u><em>Conclusion</em></u>:-

g( f(2)+3) = 30

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A particle is projected with a velocity of <img src="https://tex.z-dn.net/?f=40ms%5E-%5E1" id="TexFormula1" title="40ms^-^1" alt

Katena32 [7]

Answer:

$2\sqrt{55}\text{ m/s or }\approx 14.8\text{m/s}$

Step-by-step explanation:

The vertical component of the initial launch can be found using basic trigonometry. In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. Let the vertical component at launch be $y$ . The magnitude of $40\text{ m/s}$ will be the hypotenuse, and the relevant angle is the angle to the horizontal at launch. Since we're given that the angle of elevation is $60^{\circ}$ , we have:

$\sin 60^{\circ}=\frac{y}{40},\\y=40\sin 60^{\circ},\\y=20\sqrt{3}$ (Recall that $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ )

Now that we've found the vertical component of the velocity and launch, we can use kinematics equation $v_f^2=v_i^2+2a\Delta y$ to solve this problem, where $v_f/v_i$ is final and initial velocity, respectively, $a$ is acceleration, and $\Delta y$ is distance travelled. The only acceleration is acceleration due to gravity, which is approximately $9.8\:\mathrm{m/s^2}$ . However, since the projectile is moving up and gravity is pulling down, acceleration should be negative, represent the direction of the acceleration.

What we know:

$v_i=20\sqrt{3}\text{ m/s}$
$a=-9.8\:\mathrm{m/s^2}$
$\Delta y =50\text{ m}$

Solving for $v_f$ :

$v_f^2=(20\sqrt{3})^2+2(-9.8)(50),\\v_f^2=1200-980,\\v_f^2=220,\\v_f=\sqrt{220}=\boxed{2\sqrt{55}\text{ m/s}}$

3 0

3 years ago

A recipe uses 5 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be

kodGreya [7K]

16 servings

because there are 4 cups in a quart, and two quarts is 8 cups.. if 5 cups of milk makes 10 servings there is half a cup in each serving.. so 8/.5 is 16

4 0

3 years ago

Read 2 more answers

List the next four multiples of fraction 7/12

Sidana [21]

<h2>Hello!</h2>

The answer is:

$\frac{14}{12}=\frac{7}{12}*2\\\\\\\frac{21}{12}=\frac{7}{12}*3\\\\\\\\\frac{28}{12}=\frac{7}{12}*4\\\\\\\\\frac{35}{12}=\frac{7}{12}*5$

A multiple of a number is the repeated sum of itself, for example:

Multiple of the number 1 are: 1, 2, 3, 4, 5 and so...

Multiple of the number 3 are: 3, 6, 9, 12, 15 and so...

From the example we have:

Multiple of the number 3 are: Itself, (3+3), (3+3+3), (3+3+3+3), (3+3+3+3+3) and so...

So,

Multiple of $\frac{7}{12}$ are:

$\frac{14}{12}=\frac{7}{12}*2=\frac{7}{12}+\frac{7}{12}\\\\\\\frac{21}{12}=\frac{7}{12}*3=\frac{7}{12}+\frac{7}{12}+\frac{7}{12}\\\\\\\\\frac{28}{12}=\frac{7}{12}*4=\frac{7}{12}+\frac{7}{12}+\frac{7}{12}+\frac{7}{12}\\\\\\\\\frac{35}{12}=\frac{7}{12}*5=\frac{7}{12}+\frac{7}{12}+\frac{7}{12}+\frac{7}{12}+\frac{7}{12}$

Have a nice day!

6 0

3 years ago

The ages of two brothers are in the ratio two to three, but in eight years, the ratio of their ages will be three to four. What

grigory [225]

3(3x+8)=4(2x+8)
9x+24=8x+32
x=8

2(8)=16
3(8)=24

that means that the younger brother is 16 years old

8 0

2 years ago

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determin

egoroff_w [7]

Answer:

The mean phenotype code is 2.72

The median phenotype code is 2.52

The mode phenotype code is 2.

The midrange of the phenotype codes is 2.52

B Only the mode makes sense since the data is nominal.

Step-by-step explanation:

5 0

2 years ago