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3 years ago

Simplify the expression 10h + 6 - 5h +3 Please show your steps.

Mathematics

1 answer:

leonid [27]3 years ago

7 0

ANSWER:Simplifying

10h + 6 + -5h + 3 = 0

Reorder the terms:

6 + 3 + 10h + -5h = 0

Combine like terms: 6 + 3 = 9

9 + 10h + -5h = 0

Combine like terms: 10h + -5h = 5h

9 + 5h = 0

Solving

9 + 5h = 0

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-9' to each side of the equation.

9 + -9 + 5h = 0 + -9

Combine like terms: 9 + -9 = 0

0 + 5h = 0 + -9

5h = 0 + -9

Combine like terms: 0 + -9 = -9

5h = -9

Divide each side by '5'.

h = -1.8

Simplifying

h = -1.8

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The displacement of a 500 g mass, undergoing simple harmonic motion, is defined by the function :

Valentin [98]

To solve this problem, we have to write out the simple harmonic motion equation and then use the respective formula to solve. The maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.

<h3>Simple Harmonic Motion</h3>

The given equation of the simple harmonic motion is

$x = 3.5sin(\frac{\pi}{2t} + \frac{5\pi}{4})\\$

Data;

ω = π/2
k = 1.254N/m

Solving this

$\frac{dx}{dt} = \theta = -3.5 * \frac{\pi}{2} cos (\frac{\pi }{2}t + \frac{5\pi}{4})\\$

Let's calculate the maximum velocity.

$V_m = \frac{3.5\pi}{2}$

This is only possible when cos θ = -1

The maximum kinetic energy is

$K_m = \frac{1}{2}mv_m^2 = \frac{1}{2}* \frac{500}{1000} * (\frac{7\pi}{4} )^2\\K_m = 7.56J$

The maximum kinetic energy is 7.56J

The maximum potential energy can be calculated as

$\omega^2 = \frac{k}{m} \\k = \omega^2 m \\k = \frac{\pi^2}{4} * \frac{500}{1000}\\ k= 1.254 N/m$

Using the value of spring constant, we can find the maximum potential energy

$P.E = \frac{1}{2}kx^2\\P.E = \frac{1}{2} * 1.234 * 3.5^2\\P.E = 7.56J$

The maximum potential energy is 7.56J

The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.

$ME = P.E + K.E\\ME = 7.56J$

The reason ME is equal to 7.56J is because when x is at maximum, v = 0 and makes kinetic energy equal to zero.

ME = 7.56J

From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.

Learn more on simple harmonic motion here;

brainly.com/question/15556430

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3 0

2 years ago

table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and G

Mariulka [41]

1. To solve this problem, you must make a System of equations.

2. The equations are:

d+g=22 (i)
0.75d+1.25g=21 (ii)

3. If you clear "d" from the equation (i), you have:

d+g=22
d=22-g

4. Now, you must substitute d=22-g into the equation (ii):

0.75d+1.25g=21
0.75(22-g)+1.25g=21

5. When you clear "g", you obtain its value:

16.5-0.75+1.25g=21
16.5+0.5g=21
0.5g=21-16.5
g=4.5/0.5
g=9 <span>Golden Delicious apples
</span>
6. If you also want to know the value of "d", you can substitute g=9 into the equation (i) and clear "d":

d+g=22
d+9=22
d=22-9
d=13 <span>Delicious apples
</span><span>
How many Golden Delicious apples did Mary buy?
</span>
The answer is: Mary bought 9 Golden Delicious apples.

5 0

3 years ago

Read 2 more answers

17/18 - 8/9 equal out to

Nutka1998 [239]

$\frac{17}{18}$ - $\frac{8}{9}$ =x
You must find a common denominator(bottom)
$\frac{8}{9}$ × $\frac{2}{2}$ = $\frac{16}{18}$
$\frac{17}{18}$ - $\frac{16}{18}$ = $\frac{1}{18}$
Your answer is x= $\frac{1}{18}$

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4 years ago

A table can be used to show the relationship between the number of hours a painter works painting and the total amount the paint

kkurt [141]

Try Adding $25 Dollars To 13 Hours Multiply Them And Your Answer Is Gonna Be 325

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3 years ago

Solve 6 + 5 √ 2 4 9 − 2 x = 7

NISA [10]

$6+5\sqrt{249}-2x=7 \\-2x=7-6-5\sqrt{249} \\-2x\approx-77.9 \\x\approx\frac{-77.9}{2}\approx38.95$

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4 years ago