From a rope 15m long, 4 1/3 m is cut off and 3/5 of the remaining is cut off again. Find the length of the remaining part of the rope.

Answers

Answer 1

Answer: 15 - 4 1/3 = 10 2/3
10 2/3 * 3/5 = 6 4/10
10 2/3 - 6 4/10 = 4 4/15

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Can someone help me with this pattern? And the rule.

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Each output is (double the input) plus 1 .

3x(5x2)=(3x5)x2 which property of multiplication does the equation show

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The Associative Property

a cylinder has a volume of 321 cubic units. if a cone has the same height and radius as the cylinder, what is its volume in cubic units

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1. First, let us write out the formula for the volume of a cylinder:

V = πr^(2)h

Now, given that the cylinder has a volume of 321 cubic units, we can rewrite the above formula with this new information:

321 = πr^(2)h

2. The volume of a cone is given by the following formula:

V = (1/3)πr^(2)h

Now, we can substitute 321 = πr^(2)h into the formula above to find the volume of the cone (this will work as the cone and cylinder have the exact same radius and height). Thus we get:

V = (1/3)πr^(2)h

V = (1/3)*321

= 107 cubic units

Note that there is another method that is perhaps more intuitive and can be used quite effectively in multiple choice questions, where working isn't required. What you should notice from the general formulas for the volume of a cone and a cylinder is that the volume of a cone is actually 1/3 of the volume of a cylinder (given that they have the same radius and height). Thus, if we know that the cone in our situation has the exact same radius and height as the cylinder, we can use this method as such:

Volume of cone = (1/3)*Volume of cylinder

Volume of cone = (1/3)*321

= 107 cubic units

PLEASE HELP ME FAST!The balance in two separate bank accounts grow each month at different rates. The growth rates for both accounts are represented by the functions f(x)=3^x and g(x)=5x+25. In what month is the f(x) balance greater than the g(x) balance? Show your work!
P.S Whoever gives me a good answer and shows their work I will make as Brainliest!

Answers

Answer:

From fourth month onwards, the growth rate of $f(x)$ is greater than that of $g(x)$ .

Step-by-step explanation:

Given:

The growth rates of both bank accounts are given as:

$f(x)=3^x\ng(x)=5x+25$

Now, as per question, we need to find the value of 'x' when the value of $f(x)>g(x)$ . Or,

$3^x>5x+25$

Now, we can do this by checking the values of 'x' by hit and trial method.

Let $x=1$ . The inequality becomes:

$3^1>5(1)+25\n3>30(False)$

Let $x=2$ . The inequality becomes:

$3^2>5(2)+25\n9>35(False)$

Let $x=3$ . The inequality becomes:

$3^3>5(3)+25\n27>40(False)$

Let $x=4$ . The inequality becomes:

$3^4>5(4)+25\n81>45(True)$

Therefore, the value of 'x' for which $f(x)>g(x)$ is 4.

So, from the fourth month onwards, the balance in $f(x)$ becomes greater than $g(x)$ .

The graphical solution is shown below to support the same.

From the graph, we can conclude that after the 'x' value equals 3.4, the graph of $f(x)$ lies above of $g(x)$ . Hence, $f(x)>g(x)$ for $x>3.4$

I need to know if this can make a triangle

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That can't make a triangle. First of all, to make a triangle the length of 2 side add together should be greater than the bigger number of the triangle. So, 45+8=53. The bigger triangle is 90.

Evaluate cot 120° without using a calculator by using ratios in a reference triangle.

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The reference angle for $120\degree$ is $60\degree$ .

Recall that $cot(120\degree) = (1)/(tan(120\degree))$

This implies that $cot(120\degree) = (1)/(tan(60\degree))$

Recall also from $30\degree - 60\degreee - 90\degree$ triangle that

$tan(60\degree)=\sqrt(3)$ and also since $120\degree$ is the in the second quadrant, the tangent ratio is negative.

Putting all together we have

$cot(120\degree) = (1)/(-\sqrt(3))$

Rationalizing the denominator gives

$cot(120\degree) = (-\sqrt(3))/(3)$

Answer:

The value of cot 120° is $-(√(3))/(3)$ .