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3 years ago

Need 3 and 4 for those who are up to the task

Mathematics

1 answer:

Nikolay [14]3 years ago

6 0

Answer:

x = 18.4

y = 35º

Step-by-step explanation:

cos∅ = adj/hyp

cos49 = x/28

28cos49 = x

x = 18.4

tany = opp/adj

tany = 19/27

y = arctan19/27

y = 35º

You might be interested in

Please help me find x and explain.

strojnjashka [21]

Answer: x=11

Step-by-step explanation:

This is an isosceles triangle. It has 2 congruent sides and congruent angles. First, It is a given that an angle measure 42. Since that is the vertex angle, it not equal to the other angles. Using the converse of base angles isosceles triangle, we now the two angles at the bottom are congruent since the lines are equal so both of the bottom angles measure (5x+14). Next, Using Triangle Interior Theorem, a triangle 3 degrees adds up to 180 degrees so we set it equal to that.

42+ 5x+14+ 5x+14=180

42+10x+28=180

10x+70=180

10x=110

x=11

4 0

3 years ago

The amount of time (in minutes) that a commuter train is late is a continuous random variable with the probability density funct

Maurinko [17]

Answer:

Mean waiting time = E(X) = 0 minute

Variance = Var(X) = 140

Step-by-step explanation:

f(x) = –3(25 – x²)/500 for –10 < x < +10

f(x) = (-75 + 3x²)/500 for -10 < x < 10

f(x) = (0.006x² - 0.15) for -10 < x < 10

a) The mean of a Probability distribution is given by its expected value

Mean = E(X) = Σ xᵢpᵢ

xᵢ = each variable In the sample space

pᵢ = probability of each variable In the sample space.

In integral terms,

E(X) = ∫ xf(x) dx (evaluating the integral all over the sample space; that is, for - 10 to 10)

E(X) = ∫¹⁰₋₁₀ xf(x) dx

E(X) = ∫¹⁰₋₁₀ x[0.006x² - 0.15] dx

E(X) = ∫¹⁰₋₁₀ [0.006x³ - 0.15x] dx

E(X) = [0.0015x⁴ - 0.075x²]¹⁰₋₁₀

E(X) = [0.0015(10⁴) - 0.075(10²)] - [0.0015(-10⁴) - 0.075(-10²)]

E(X) = [15 - 7.5] - [15 - 7.5] = 0 minutes

b) Variance is given as

Variance = Var(X) = Σx²p − μ²

where μ = mean = E(X)

In integral terms,

Var(X) = [∫¹⁰₋₁₀ x²f(x) dx] - μ²

∫¹⁰₋₁₀ x²f(x) dx = ∫¹⁰₋₁₀ x²(0.006x² - 0.15) dx

= ∫¹⁰₋₁₀ (0.006x⁴ - 0.15x²) dx

= [0.0012x⁵ - 0.05x³]¹⁰₋₁₀

= [0.0012(10⁵) - 0.05(10³)] - [0.0012(-10⁵) - 0.05(-10³)]

= [120 - 50] - [-120 + 50]

= 70 + 70 = 140

Var(X) = [∫¹⁰₋₁₀ x²f(x) dx] - μ²

Var(X) = 140 - 0² = 140.

Hope this Helps!!!

8 0

3 years ago

Task 2 a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a

Galina-37 [17]

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

$y = 10000 * 1.04^x$

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

$y = 12000* 0.97^x$

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A exceeds city B, we have the following inequality

$10000 * 1.04^x > 12000 * 0.97^x$

Divide both sides by 10000

$1.04^x > 1.2 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{0.97})^x > 1.2$

$1.07^x > 1.2$

Take the natural logarithm of both sides

$\ln(1.07)^x > \ln(1.2)$

This gives

$x\ln(1.07) > \ln(1.2)$

Solve for x

$x > \frac{\ln(1.2)}{\ln(1.07)}$

$x > 2.69$

This means that, the population of city A will exceed city B after 3 years

<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A is at least twice city B, we have the following inequality

$10000 * 1.04^x \ge 2 * 12000 * 0.97^x$

$10000 * 1.04^x \ge 24000 * 0.97^x$

Divide both sides by 10000

$1.04^x \ge 2.4 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{ 0.97})^x \ge 2.4$

$1.07^x \ge 2.4$

Take the natural logarithm of both sides

$\ln(1.07)^x \ge \ln(2.4)$

This gives

$x\ln(1.07) \ge \ln(2.4)$

Solve for x

$x\ge \frac{\ln(2.4)}{\ln(1.07) }$

$x\ge 12.9$

This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

brainly.com/question/11464095

3 0

3 years ago

Divide using synthetic division (3y^4-13y^3+12y^2-33y+9)/(y-4)

tatiyna

3y³-y²+8y-1+5/y-4. is that unless you want the answer smaller

3 0

3 years ago

Y=-3x+3

kondor19780726 [428]

Answer:

X Y

-6 1

-3 2

0 3

3 4

yea its literally that easy

Step-by-step explanation: If you plot this on a graphing calculator or just a graph in general this is the answer you get

Hope this helps have an amazing day

6 0

3 years ago