MATHEMATICS COLLEGE

Answer the question in the picture

Answers

Answer 1

Answer:

Recall the angle sum identities:

$\sin(x+y)=\sin x\cos y+\cos x\sin y$

$\cos(x+y)=\cos x\cos y-\sin x\sin y$

Now,

$\tan(x+y)=(\sin(x+y))/(\cos(x+y))=(\sin x\cos y+\cos x\sin y)/(\cos x\cos y-\sin x\sin y)$

Divide through numerator and denominator by $\cos x\cos y$ to get

$\tan(x+y)=(\tan x+\tan y)/(1-\tan x\tan y)$

Next, we use the fact that $x,y$ lie in the first quadrant to determine that

$\sin x=\frac12\implies\cos x=√(1-\sin^2x)=\frac{\sqrt3}2$

$\cos y=\frac{\sqrt2}2\implies\sin x=√(1-\cos^2x)=\frac1{\sqrt2}$

So we then have

$\tan x=(\sin x)/(\cos x)=\frac{\frac12}{\frac{\sqrt3}2}=\frac1{\sqrt3}$

$\tan y=(\sin y)/(\cos y)=\frac{\frac1{\sqrt2}}{\frac{\sqrt2}2}=1$

Finally,

$\tan(x+y)=\frac{\frac1{\sqrt3}+1}{1-\frac1{\sqrt3}}=(1+\sqrt3)/(\sqrt3-1)=2+\sqrt3\approx3.73$

Related Questions

On a coordinate plane, the x-axis is labeled Number of Days and the y-axis is labeled Number of Computers. A line goes through points (3, 36), (4, 48), (5, 60). The graph shows a proportional relationship between the number of computers produced at a factory per day. In three days, 36 computers are produced; 48 computers are produced in 4 days; and 60 computers are produced in 5 days. Find the unit rate of computers per day using the graph. Unit rate: computers per day
I need help with this problem, please help!!!
Amanufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle can take no longer than 3 minutes. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)
Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a service facility. Suppose they are normal random variables with means of 50 minutes, 60 minutes, and 40 minutes, respectively. The standard deviations are 15 minutes, 20 minutes, and 10 minutes, respectively. a Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object.
The data set shows the number of practice free throws players in a basketball competition made and the number of free throws they made in a timed competition.Practice throws 312 614 2 710 8Free throws 10 22 9 35 4 11 28 20A. Use technology to find the equation AND coefficient of determination for each type of regression model. Use the number of practice throws for the input variable and the number of free throws for the output variable. Round all decimal values to three places. Equation of regression modelCoefficient of determinationLinear model Quadratic model Exponential model B. EXPLAIN, using the information you found above, which model best fits the data set. How did you come to your conclusion?Note: write exponents like this x^2 if you need to.

1. Maya has 24 baseball cards, and her grandfather gives her 6 baseball cards per week for earning good grades. Her brother, Marcus, has 0 baseball cards, but his grandfather gives him 12 baseball cards per week. After how many weeks will Maya and Marcus have the same number of baseball cards?

Answers

I think the answer is 4

Which expression equals
$9 \sqrt[3]{10}$

Answers

Answer:

B on edge

Step-by-step explanation:

5^3sqrt10+4^3sqrt10

If 6 bakers want to share a 45-pound bag of flour equally by weight, how many pounds of flour will each person get? Write an equation to solve and show your work.

Answers

Answer:

7.5 lbs

Step-by-step explanation:

We want to separate 45 pounds of flour by 6 people, which means we have to divide 45 by 6 to get 7 and 1/2 pounds or 7.5 lbs for each baker.

Answer:er./llllllll;tfph[n7j8ujhgedrsth5rdymu67igh8bn6[nmhylmnhhno9ooilhmny9yhju98y98079huj97

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Step-by-step explanation:sfrnb kds 3i4huygr4vfb 4rf413qgweb31Y

Tasia’s bank account balance was -$25.64. She deposited a check into her bank account and her new balance is $152.29. How much was the check that Tasia deposited into her account?

Answers

Answer:

$177.93

Step-by-step explanation:

Answer:

The check is 177.93$

Step-by-step explanation:

I did 25.64+152.29= 177.93

U can check it by doing -25.64+177.93

Find the prime factorization of
72

Answers

Answer:

72 = {2,2,2,3,3}

Step-by-step explanation:

2433

Need help asap
Graph f(x) = 3x + 4 and h(x) = f(x) +1

Answers

The coordinatepoints to plot on the graph are (0, 5) and (1, 8). The graph for the given functions are plotted below.

The given functions are f(x) = 3x + 4 and h(x) = f(x) +1.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, h(x)=3x+5

The graph of f(x) = 3x + 4 is as follows:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept: (0, 4)

The coordinatepoints to plot on the graph are (0, 4) and (1, 7)

The graph of h(x)=3x+5 is as follows:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept: (0, 5)

The coordinate points to plot on the graph are (0, 5) and (1, 8)

The coordinatepoints to plot on the graph are (0, 5) and (1, 8). The graph for the given functions are plotted below.