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3 years ago

Find the solution of ×\2-1/5=×\3+1/4 please help me with this

Mathematics

1 answer:

ale4655 [162]3 years ago

4 0

Answer:

$x=\frac{27}{10}$

Step-by-step explanation:

Assuming that the beginning equation is $\frac{x}{2} -\frac{1}{5} =\frac{x}{3} +\frac{1}{4}$

First, we should find the common denominator of each of fractions. For all of these denominators, 60 is the smallest common denominator

$\frac{x}{2}(\frac{30}{30}) -\frac{1}{5}(\frac{12}{12}) =\frac{x}{3}(\frac{20}{20}) +\frac{1}{4} (\frac{15}{15}) \\\\\frac{30x}{60}-\frac{12}{60} =\frac{20x}{60}+\frac{15}{60}$

Now, we can multiply each side by 60, which will remove the fractions

$30x-12=20x+15$

Now we can add 12 to each side

$30x=20x+27$

Now subtract 20x from each side

$10x=27$

And lastly, divide each side by 10

$x=\frac{27}{10}$

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On a coordinate plane, an exponential function has a horizontal asymptote of y = 0. The function curves up into the first quadra

aleksandr82 [10.1K]

Answer:

The graph will show an initial value that is lower on the y-axis

Step-by-step explanation:

The exponential function has the next general form:

$y = ab^x$

where a is the initial amount and b is the base.

If the a value in the function is decreased, but remains greater than 0, the y-intercept of the curve decrease.

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4 years ago

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The Candy Shack sells 138 pounds of candy on Tuesday. They sold 71.76 pounds of jelly beans. What percent of the candy sold was

Pepsi [2]

Answer:

<h2>52% were jelly beans!</h2>

Explanation:

Cross multiply the following:

$\frac{x}{100} = \frac{71.76}{138}$

x times 138 = 138x

100 times 71.76 = 7,176

Divide both sides by 138:

$\frac{138x}{138} = \frac{7176}{138}$

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3 years ago

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A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial pos

jeka57 [31]

Part A - The average value of v(t) over the interval (0, π/2) is 6/π

Part B - The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

<h3>Part A: Find the average value of v(t) on the interval (0, π/2)</h3>

The average value of a function f(t) over the interval (a,b) is

$f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx$

So, since velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval (0, π/2) is given by

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt$

Since v(t) = 3cost, we have

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}$

So, the average value of v(t) over the interval (0, π/2) is 6/π

<h3>Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?</h3>

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

<h3>Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)</h3>

The total distance the yo-yo travels from time t = 0 to time t = π is given by

$x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6$

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

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1 year ago

Solve for s. 0.5s +1= 7+ 4.58 S =?

Lana71 [14]

Answer:

s = 21.16

Step-by-step explanation:

0.5s +1= 7+ 4.58

Combine like terms

0.5s +1=11.58

Subtract 1 from each side

0.5s +1-1= 11.58-1

.5s = 10.58

Multiply by 2

.5s *2 = 10.58*2

s = 21.16

4 0

3 years ago

Read 2 more answers

Can I get help on numbers 4,6,24, and 34 please

irinina [24]

Step-by-step explanation:

4: To evaluate an algebraic equation, replace each variable with the given number, and carry out the computation.

-This is basically explained the steps of evaluating an equation. You are receiving a number for x, so you then simplify and find if ?=? is true.-

6. 8+r

8 more than a number.

A number increased by 8.

24. 8-y

(Just the opposite.)

A number less than 8.

8 decreased by a number.

34. (I don't see the problem for this one.)

Hope I helped!

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3 years ago

Find the solution of ×\2-1/5=×\3+1/4 please help me with this​

Find the solution of ×\2-1/5=×\3+1/4 please help me with this