Compute the area of the triangle. h = 8 cm b = 16 cm

1. Derive this identity from the sum and difference formulas for cosine:

kenny6666 [7]

Answer:

See below.

Step-by-step explanation:

1. (1 / 2)[cos(a – b) – cos(a + b)]

= 1/2 ( cosa cosb + sina sinb - (cosa cosb - sina sinb)

= 1/2 ( cosa cosb - cosa cos b + sina sinb + sina sinb)

= 1/2 ( 2 sina sinb)

= sina sinb.

(I used the 2 identities cos(a - b) = cosa cosb + sina sinb) and

cos (a + b) = cosa cosb - sina sinb.)

2. sin (π/2 - x) = sin (π/2) cos x - cos(π/2) sin x

= 1 * cos x - 0 * sinx

= cosx - 0

= cos x.

(I used the identity sin(a - b) = sina cosb - cosa sinb

and the fact that sin(π/2) = 1 and cos (π/2) = 0. )

7 0

3 years ago

Read 2 more answers

At The Old Home Fill'er Up and Keep on a-Truckin' Cafe, Mavis mixes two different types of coffee beans to produce a house blend

Alex Ar [27]

There are 45 pounds and 30 pounds of each type respectively.

Step-by-step explanation:

Since we have given that

Cost of first type = $2 per pound

Cost of second type = $7 per pound

Cost of mixture = $4 per pound

So, we need to find the quantity of each type to make 75 pounds of a blend.

We will use "Mixture and Allegations":

First type Second type

2 7

4

---------------------------------------------------

7 - 4 : 4 - 2

3 : 2

So, Quantity of first type would be

$\dfrac{3}{5}\times 75=3\times 15=45\ pounds$

Quantity of second type would be

$\dfrac{2}{5}\times 75=2\times 15=30\ pounds$

Hence, there are 45 pounds and 30 pounds of each type respectively.

3 0

3 years ago

Which equation has a vertex of (−6, 3)?

Vladimir79 [104]

Answer:

Are there answer choices?

Step-by-step explanation:

4 0

4 years ago

Information from a sample of 157 restaurant bills collected at the First Crush bistro is available in RestaurantTips. Two interv

wolverine [178]

Answer:

a) The 99% confidence interval is interval B: 3.35 to 4.35

The 90% confidence interval is interval A: 3.55 to 4.15.

b) Check Explanation.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value is obtained from either the t-distribution or the z-distribution tables. It depends on sample size and for smaller sample sizes, whether there is information provided for the population mean and standard deviation.

But whether z-distribution or t-distribution, the critical value increases as the confidence level increases.

Hence, the critical value for the 99% confidence level will be higher than the critical value for the 90% confidence level.

And since all the other parameters that determine the confidence interval and it's width (sample mean and the standard error of the mean) are the same for the 90% and the 99% confidence interval, the larger critical value for the 99% confidence interval means that it has the bigger width.

Hence, of the two intervals given,

Interval A: 3.55 to 4.15

Interval B: 3.35 to 4.35

The larger interval, (3.35, 4.35) is the 99% confidence interval and the smaller interval, (3.55, 4.15) is the 90% confidence interval.

b) The data required for this second part isn't available, but the answer for the confidence interval can be obtained using the steps I have given above and below.

Like I have given above,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error = (Critical value) × (standard Error of the mean)

The sample mean and the standard error of the mean are obtained from the sample data (which is missing).

Sample mean = (Σx)/N

x = each variable

N = number of variables = 20

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation (obtained from the sample data)

90% critical value for sample size of 20 = 1.73

99% critical value for sample size of 20 = 2.86

Hope this Helps!!!

4 0

4 years ago

What is the hight of a Building 1 Angle 71o Distance 20 meters

vlabodo [156]

The height of a building is 58.08 meters if the angle is 71 degree and the distance between A and B is 20 meters.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

Angle = 71 degree

Distance between A and B = 20 meters

Let's suppose the height of the building is x meters.

From the right angle triangle applying the tan ratio:

tan71 = x/20

x = 58.08 meter

Thus, the height of a building is 58.08 meters if the angle is 71 degree and the distance between A and B is 20 meters.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ1

6 0

2 years ago