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3 years ago

Use a calculator to find angle theta for which tan theta = 2. Round to the nearest hundredth.

Mathematics

1 answer:

Mashutka [201]3 years ago

3 0

Answer:

in degrees: theta = 63.43°

in radians: theta = 1.11 rad

Step-by-step explanation:

To find the value of the angle theta that gives us tan(theta) = 2, we should use the inverse function of the tangent in the calculator, that is, the arc tangent function.

Then, if we use the arc tangent function (in some calculators, it may be shown as 'atan' or 'tan^-1') in the value 2, we would find:

atan(2) = 63.435°

So the angle theta that gives us tan(theta) = 2 is theta = 63.43°.

Be sure to check in the calculator if the answer is given in degrees or radians.

In radians, we would find theta = 1.1071 rad (rounded to nearest hundredth: theta = 1.11 rad)

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20 cm

lawyer [7]

The area of the arrow given in the figure is 610 square cm

<h3>Area of composite figure</h3>

The given figure is made up of rectangle and triangle. The area is expressed as:

Area = Area of rectangle + area of triangle

Substitute the given parameters

Area of the arrow = (15*20) + 0.5(31 * 20)

Area of the arrow = 300 + 310
Area of the arrow = 610 square cm

Hence the area of the arrow given in the figure is 610 square cm

Learn more on area of composite figures here: brainly.com/question/21135654

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7 0

2 years ago

Jerome burns 4 cal/min walking and 10 cal/min running. He walks between 10 and 20 min each day and runs between 30 and 45 min ea

erik [133]

Answer:

20 minutes should spend on walking and 30 minutes on running.

Step-by-step explanation:

Let x represents the minutes spent on walking and y represents the minutes spent on running,

∵ He burns 4 cal/min walking and 10 cal/min running,

So, the total calories burnt,

Z = 4x + 10y

Which has to be maximised.

Now, he walks between 10 and 20 min each day,

i.e. 10 < x < 20,

Also, he runs between 30 and 45 min each day,

i.e. 30 < y < 45,

By graphing 10 < x < 20 and 30 < y < 45,

We obtained the vertices of feasible region,

(10, 45), (20, 45), (10, 30) and (20, 30)

At (10, 45),

Z = 4(10) + 10(45) = 40 + 450 = 490,

At (20, 45),

Z = 4(20) + 10(45) = 80 + 450 = 530,

At (10, 30),

Z = 4(10) + 10(30) = 40 + 300 = 340,

At (20, 30)

Z = 4(20) + 10(30) = 80 + 300 = 380

Hence, maximum calories is 530 when 20 minutes spent on walking and 30 minutes spent on running.

5 0

3 years ago

Please help me its about Solving by substitution

Vera_Pavlovna [14]

Answer:

x=-2 y=3

Step-by-step explanation:

The substitution is basically given to you. Exchange x from the second equation with y-5

Once that is done and you combine the parentheses you get:

2y-10+y=-1

Add 10 on both sides of the equal sign

You get:

3y=9

Divide both sides by 3

You get:

y=3

To check your work you can substitute y in the second equation with 3 and solve it that way to get x=-2 (x equals negative two)

3 0

2 years ago

beaus recipefor granola bars calls for 3 1/2 cups of oatmeal. he only have 1/6 cup scoop.how many scoops of oatmeal will he need

Stells [14]

<h2>Answer:</h2>

The number of scoops of oatmeal he will need for the recipe is:

21 scoops.

<h2>Step-by-step explanation:</h2>

It is given that:

Beaus recipe for granola bars calls for 3 1/2 cups of oatmeal.

i.e. the cups of oatmeal required is:

$3\dfrac{1}{2}\ cups=\dfrac{3\times 2+1}{2}\ cups$

i.e.

$\dfrac{7}{2}\ \text{cups\ of\ oatmeal\ is\ required}$

Also, he has:

$\dfrac{1}{6}\ \text{cup scoop}$

This means that:

$\text{Number of scoops of oatmeal he need}=\dfrac{\text{Number of cups of oatmeal}}{\text{Number of cup scoop he has}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{\dfrac{7}{2}}{\dfrac{1}{6}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{7\times 6}{1\times 2}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=21\ \text{scoops}$