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denis-greek [22]

3 years ago

13

The area of a playground is 12 square yards. The length of the playground is 3 times longer than its width. Find the length and

width of the playground.

1 answer:

marishachu [46]3 years ago

6 0

Answer:

Width is 2 and Length is 6

Step-by-step explanation:

As the data is given, the area of a playground is 12 square yards.
The length of the playground is 3 times longer than its width.
Let width is x, length is 3 times therefore, length = 3x

As we know the formula for area,

Area=length x width.

So by putting values in this formula,

12sq = (3x)(x)

=> 3x2 = 12

=> x2 = 12/3,

=> x2 = 4 ,

by taking square root we get x= 2,

the width is 2 and length is 3 times hence, length is 3(2) = 6.

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What is the solution to this system of linear equations? y − 4x = 7 2y + 4x = 2

erik [133]

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▹ Answer

<em>(-1, 3)</em>

▹ Step-by-Step Explanation

y - 4x = 7

2y + 4x = 2

<u>Substitute</u>

y - (2 - 2y) = 7

<u>Solve</u>

y = 3

<u>Substitute</u>

4x = 2 - 2 * 3

<u>Solve</u>

x = -1

<u>Final Answer</u>

(x, y) = (-1, 3)

Hope this helps!

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4 0

4 years ago

What fraction is equal to 3 1/9 ?

Masteriza [31]

Answer:

28/9

Step-by-step explanation:

We will have to convert the given question into improper fraction before solving

So let's solve the question

3 1/9

Can be written as 28/9 which is improper fraction

Since there's nothing that can be used to divide both the numerator and denominator

Then our final answer is 28/9

But in the case where the fraction can be divided we can actually solve further

7 0

3 years ago

Read 2 more answers

The surface area of a cylinder is increasing at a rate of 9 pi square meters per hour. The height of the cylinder is fixed at 3

Alekssandra [29.7K]

Answer:

$9\pi \text{ cubic meters per hour}$

Step-by-step explanation:

Since, the surface area of a cylinder,

$A= 2\pi r^2 + 2\pi rh$ ................(1)

Where,

r = radius,

h = height,

If $A= 36\pi\text{ square meters}, h = 3\text{ meters}$

$36\pi = 2\pi r^2 + 2\pi r(3)$

$18 = r^2 + 3r$

$\implies r^2 + 3r - 18=0$

$r^2 + 6r - 3r - 18 = 0$ ( by middle term splitting )

$r(r+6)-3(r+6)=0$

$(r-3)(r+6)=0$

By zero product property,

r = 3 or r = - 6 ( not possible )

Thus, radius, r = 3 meters,

Now, differentiating equation (1) with respect to t ( time ),

$\frac{dA}{dt}= 4\pi r\frac{dr}{dt} +2\pi(r\frac{dh}{dt} + h\frac{dr}{dt})$

∵ h = constant, ⇒ dh/dt = 0,

$\frac{dA}{dt} = 4\pi r \frac{dr}{dt} +2\pi h \frac{dr}{dt}$

We have, $\frac{dA}{dt}=9\pi\text{ square meters per hour}, r = h = 3\text{ meters}$

$9\pi = 4\pi (3) \frac{dr}{dt}+2\pi (3)\frac{dr}{dt}$

$9\pi = (12\pi + 6\pi )\frac{dr}{dt}$

$9\pi = 18\pi \frac{dr}{dt}$

$\implies \frac{dr}{dt} =\frac{1}{2}\text{ meter per hour}$

Now,

Volume of a cylinder,

$V=\pi r^2 h$

Differentiating w. r. t. t,

$\frac{dV}{dt}=\pi ( r^2 \frac{dh}{dt}+h(2r)\frac{dr}{dt})=\pi ((3)(6) (\frac{1}{2})) = 9\pi \text{ cubic meters per hour}$

6 0

3 years ago

What is the awnser to this question because I don't understand

Virty [35]

Pemdas 1. parentheses: everything is already in parentheses. so next is exponents. 10×-2 is -20. and 10×6 is 60. so 4×-20 is the next step. it equals -80. and then 3×60 is 180. lastly,add -80 and 180 together. the answer should be 100 if i did that correctly.

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3 years ago

For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm

saveliy_v [14]

We have been given an equation $ae^{ct}=d$ . We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

$\frac{ae^{ct}}{a}=\frac{d}{a}$

$e^{ct}=\frac{d}{a}$

Now we will take natural log on both sides.

$\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})$

Using natural log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})$

We know that $\text{ln}(e)=1$ , so we will get:

$ct\cdot 1=\text{ln}(\frac{d}{a})$

$ct=\text{ln}(\frac{d}{a})$

Now we will divide both sides by c as:

$\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}$

$t=\frac{\text{ln}(\frac{d}{a})}{c}$

Therefore, our solution would be $t=\frac{\text{ln}(\frac{d}{a})}{c}$ .

5 0

3 years ago