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3 years ago

1. Mary has a mass of 40 kg and sprints at 1 m/s. How much kinetic energy does she have?

Mathematics

1 answer:

ZanzabumX [31]3 years ago

8 0

Answer:

The kinetic energy of Mary is 20 Joules

Step-by-step explanation:

Given

Mass = 40 kg

Velocity = 1 m/s

Required

Calculate the kinetic energy.

The kinetic of any body is calculated by using the following formula.

K.E = ½mv²

Where K.E represent kinetic energy

m represent the mass of the body

v represent the velocity of the body.

To solve the kinetic energy, in this case, we simply substitute 40kg for m and 1m/s for v.

This gives us

K.E = ½ * 40 * 1²

K.E = ½ * 40 * 1

K.E = 0.5 * 40

K.E = 20

Hence, the kinetic energy of Mary is 20 Joules

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If the function f(x) = -1/2x - 7 were graphed, which of the following would be true?

Fittoniya [83]

ANSWER

D. As the x-values increase, the y-values would decrease

EXPLANATION

The given function is
$y = - \frac{1}{2} x - 7$

The slope of this function is
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Since the slope is negative, there is a negative or an inverse relationship between x and y.

As the values of x increases, the values of y decreases.

Also, as the values of x decreases, the values of y increases.

The first option is not true because as x is becoming bigger and bigger negatively, y will become positive.

For instance, when
$x = - 40$
$y = - \frac{1}{2} ( - 40) - 7$

This implies that,

$y = 20 - 7 = 13$

Options B is obviously not true because the function has a negative relationship between x and y.

Option C is also false because, x can be positive since it is the independent variable.

See graph

Therefore, the correct answer is option D.

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3 years ago

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shtirl [24]

Answer:

$3y-2x=16+12i$

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$x \cdot 2y=-4-32i$

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Step-by-step explanation:

Given:

$x=-2-3i$

$y=4+2i$

---

1st problem:

$3y-2x$

$3(4+2i)-2(-2-3i)$

Distribute:

$12+6i+4+6i$

Combine like terms:

$16+12i$

---

2nd problem:

$-3x \cdot y$

$-3(-2-3i) cdot (4+2i)$

$-3(-2-3i)(4+2i)$

Distribute -3 to first factor:

$(6+9i)(4+2i)$

Use foil to simplify:

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Replace $i^2$ with -1:

$24+48i-18$

Combine like terms:

$6+48i$

---

3rd problem:

$x \cdot 2y$

$(-2-3i) \cdot 2(4+2i)$

Distribute 2 to the second factor:

$(-2-3i) \cdot (8+4i)$

$(-2-3i)(8+4i)$

Use foil to simplify:

$-16-8i-24i-12i^2$

Replace $i^2$ with -1:

$-16-32i+12$

Combine like terms:

$-4-32i$

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4th problem:

$(-2-3i)-(4+2i)$

Distribute:

$-2-3i-4-2i$

Combine like terms:

$-2-4-3i-2i$

Simplify:

$-6-5i$

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3 years ago

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ratelena [41]

Each of the members must raise at least $69.46.

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