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In a right triangle, Angle A and B are acute. If tan B= 2, what is cos B? Round to three decimal places.Show work plzzz!!!

Answers

Answer 1

Answer:

The value of cosB ≅ 0.447 to three decimal places.

Since angle A and angle B are acute and tanB = 2, we find cosB from the trigonometric identity

tan²B + 1 = sec²B

Find SecB

So, substituting the value of tanB into the equation, we have

tan²B + 1 = sec²B

2² + 1 = sec²B

4 + 1 = sec²B

5 = sec²B

Taking square root of both sides, we have

√sec²B = ±√5

secB = ±√5

Find CosB

Since secB = 1/cosB, we have that

1/cosB = ±√5

⇒cosB = ±1/√5

Since B is acute, cosB will be positive.

So, cosB = 1/√5

cosB = 1/2.2361

cosB = 0.4472

cosB ≅ 0.447 to three decimal places.

So, the value of cosB ≅ 0.447 to three decimal places.

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Related Questions

Please help me please i really need help please
Please help me!! pel
A line passes through the points ( - 9, - 24) and (8, – 9).Calculate the slope of the line. Write your answer as a fraction.(If the slope is undefined, enter "DNE")
In the standard (x,y) coordinate plane below, the points ( 0,2), (8,2), (3,6), and (11,6) are the vertices of a parallelogram. What is the area, in square units, of the parallelogram
Please help me need it fast

You have a litre bottle of water and drink 375 millilitres.

How much is left?

Answers

The balance of water left in the bottle is 625 milliliters.

How Liters and Milliliters are calculated?

A liter exists as a unit of volume in the metric system.
A liter exists described as the volume of a cube that exists 10 centimeters on a side.
Liters and milliliters are metric units of volume which are used to measure the capacity of a liquid.
The capacity of a liquid can be measured in milliliters, centiliters, liters, and kiloliters.
There are about 3.785 liters in a U.S. gallon.

1 liter = 1000 milliliters

Let, 1000 milliliters - 375 milliliters = 625 milliliters

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Answer:

625 millilitres

Step-by-step explanation:

1 litre = 1000 millilitres

Left -> 1000 millilitres - 375 millilitres = 625 millilitres

Simplify. 4i√-24
Please and thank you!

Answers

The simplification of the given function as complex number would be -8√6 .

What is simplification of an expression?

Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

We have been given a function as complex number that is 4i√-24

We can also write it as;

4i√24 √-1

= 4i√2³ 3 √-1

= 4i (2) √6 (i)

Then simplify;

= 4 2i² √6

= 8 (-1)√6

= -8 √6

Therefore, the simplification of the given function as complex number would be -8√6 .

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Answer:

$-8√(6)$

Step-by-step explanation:

$4i√(-24) \n\n=4i√(24) √(-1) \n\n=4i\sqrt{2^(3)*3 } √(-1) \n\n=4i(2)√(6) (i)\n\n=4*2i^(2) √(6) \n\n=8(-1)√(6) \n\n=-8√(6)$

40% of the groups budget was spent on activities. If $64,000 was spent on the activities, what was the full budget? solve with the aid of a diagram. State what type of problem this is. if it's division, which type? Explain your reasoning, not just by using an equation.

Answers

Answer:

The full budget has a total value of $160,000

Step-by-step explanation:

This is a simple ratio problem and can be solved using the Rule of Three property. The Rule of Three is used to compare two ratios and find the missing part. In this case the ratios would be the following.

$(64,000)/(40 percent) = (x)/(100 percent)$

$(64,000 * 100 percent)/(40 percent) = \frac{x}$

$(6,400,000)/(40 percent) = \frac{x}$

$160,000= \frac{x}$

So now we know that 100% (The full budget) has a total value of $160,000.

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Grace's walking rate is 1.5 meters per second. Her house is 90 meters from the fountain. How many seconds will it take her to reach the fountain?

Answers

Grace's walking rate is 1.5 meters per second. Her house is 90 meters from the fountain. How many seconds will it take her to reach the fountain?

Answer: We know that Grace's walking rate is 1.5 meters per second

Number of meters Grace's house is from fountain is 90 meters.

Therefore, the time it will take Grace to reach the fountain is:

$(Distance-between-House-and-fountain)/(Grace's-walking-rate)$

$(90)/(1.5) =60 seconds$

Therefore, it will take Grace 60 seconds to reach fountain

Speed=1.5

Distance=90 meters

Time=?

Distance= time × speed

Thus,

T=distance/speed

=90/1.5

= 60 second

= 1 minute

Find the solutions to x2-2x+10=0. The quadratic formula has been started for you.

Answers

Answer

The solution to the quadratic equation is

$x=1\pm3i$

EXPLANATION

Problem Statement

The question gives us the beginning of the application of the Quadratic formula on a quadratic equation. We are required to simplify the expression and get in more certain terms, the values of x.

The expression given is:

$\begin{gathered} x^2-2x+10=0 \n \n x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \end{gathered}$

Solution

Let us begin to simplify the expression below:

$\begin{gathered} x=\frac{2\pm\sqrt[]{(-2)^2-(4)(1)(10)}}{2} \n \n x=\frac{2\pm\sqrt[]{(-2*-2)^{}-(4*1*10)}}{2} \n \n x=\frac{2\pm\sqrt[]{4-40}_{}}{2} \n \n x=\frac{2\pm\sqrt[]{-36}}{2} \n \n \text{From the laws of indices, we have:} \n \sqrt[]{a* b}=\sqrt[]{a}*\sqrt[]{b} \n \n x=\frac{2\pm\sqrt[]{-1*36}}{2} \n \n x=\frac{2\pm(\sqrt[]{-1})(\sqrt[]{36})}{2} \n \n \text{ We know that, } \n \sqrt[]{-1}=i \n \n x=(2\pm(i)(6))/(2) \n \n x=(2\pm6i)/(2) \n \n x=(2(1\pm3i))/(2) \n \n 2\text{ Crosses out} \n \n x=1\pm3i \end{gathered}$

Final Answer

The solution to the quadratic equation is

$x=1\pm3i$

What is the approximate radius of the disc if the area is 78.5 square inches?

Answers

78.5 = 3.14 * r^2

r^2 = 78.5 / 3.14 = 25

r = radius = 5 answer

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