IF AB measures 115° what is the length of the radius of the circle to the mearest hundredth

The real roots of the function using false-position method are 1/2 and 5/8

The real root of the function f(x) = x³ - 2x - 5 = 0 using the False-Position method can be calculated as;

1. Choose two initial guesses, a and b, such that f(a) and f(b) have opposite signs. In this case, we can choose a = 0 and b = 1.

[tex]c = \frac{(a * f(b) - b * f(a))}{(f(b) - f(a)}[/tex]

If f(c) = 0, then c is the root of the equation. Otherwise, replace a with b and b with c.

[tex]c = \frac{(0 * f(1) - 1 * f(0))}{(f(1) - f(0))} = \frac{1}{2}[/tex]

Since f(1/2) = -0.25, we can replace a with 1 and b with 1/2.

[tex]c = \frac{\frac{1}{2} * f(1) * f(\frac{1}{2}) }{(f(1) - f(\frac{1}{2}) } = \frac{5}{8}[/tex]

Since f(5/8) = 0.0625, we can stop here and say that the root of the equation is 5/8, which is approximately 0.625.

Where the roots of the equation are 1/2 and 5/8

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Answer:

26.74 degrees!

Step-by-step explanation:

The formula you can plug the numbers into is:

angle = L / r

Angle = the central angle

L = the length of the arc

r = radius of the circle

Answer: Answer is seen below (sorry if its confusing, this is what I got though)

Step-by-step explanation:

Answer:

We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1

Now we can substitute this value into the original equation and simplify:

y = -3 + tan(1/2 (0 + π/2))

y = -3 + 1

y = -2

The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down

The height of the cone in this problem is given as follows:

h = 16.4 units.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

The parameters for this problem are given as follows:

V = 2325 π, r = 15.

Hence the height is obtained as follows:

2325 = π x 15² x h/3

h = 2325 x 5/(15² x π)

h = 16.4 units.

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The correct option is B, the total volume is 6 gallons, 2 quarts, and 1 pint.

Here we just need to add all the volumes that are in the question, we have.

So there are:

3 gallons.

8 quarts.

13 pints.

Now let's do the changes of units, we know that:

8 pints = 1 gallon

4 quarts = 1 gallon

1 quart = 2 pints

then:

13 pints = 1 gallon  and 5 pints

8 quarts = 2 gallons

5 pints = 2 quarts and 1 pint

Then the total volume is:

6 gallons, 2 quarts, and 1 pint.

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Answer:

Let x be the measure of the smaller angle.

The larger angle is 4x.

The sum of the angles in a kite is 360 degrees.

So, 100 + 100 + x + 4x = 360

6x = 160

x = 26.67

The larger angle is 4x = 106.67 degrees.

So the answer is 106.67

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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