Please help me answer ASAP

\(Answer: \large\boxed{Cos(\theta_{1} )=\frac{84}{85}}\)

Step-by-step explanation:

Thinking about a triangle in Quadrant IV, we can imagine sin as opposite/hypotenuse. Therefore, the hypotenuse is 85 and the opposite angle is -13. To find the adjacent angle, we use the pythagorean theorum,

\(a^2+b^2=c^2\)

\(-13^2+b^2=85^2\)

\(169+b^2=7225\)

\(b^2=7056\)

\(b=\sqrt{7056}\)

\(b=\pm84\)

Taking only the positive number, the adjacent angle is 84

Now that we have all 3 sides, we can find the cosine.

Cosine is adjacent/hypotenuse

Therefore,

\(Cos(\theta_{1} )=\frac{84}{85}\)

See the attached picture:

Answer:

6) x=20.64

7) x=12.423

8) x=26.5

Step-by-step explanation:

Answer:

9.68 × 10-5

Step-by-step explanation:

Step-by-step explanation:

Hi there!

Given;

= 5(π\6)

We have;

π = 180°

Keeping value of π in the question;

= 5(180°/6)

= 5*30°

= 150°

Therefore, answer is option B.

Hope it helps!

The constant of variation is, \(\frac{2}{3}\).

Joint Variation states that it is jointly proportional to a set of variables i.e, it means that z is directly proportional to each variable taken one at a time.

Given the statement:

The quantity n varies jointly with the product of z and the square of the sum of x and y.

"The square of sum of x and y" means \((x+y)^{2}\)

"Product of z and the square of the sum of  x and z" means \(z \times (x+y)^{2}\)

then; by definition we have;

n ∝ \(z \times (x+y)^{2}\)

our equation will be of the form of:

n = k. z × \((x+y)^{2}\)--------[1] ; where k is constant of Variation.

Given: n =18 , x =2 , y= 1 and z = 3

Solve for k;

Substitute these given values in [1] we have;

\(18=k.3(2+1)^{2}\)

Simplify:

18 = k. (27)

Divide both sides by 27 we get;

\(k =\frac{18}{27}=\frac{2}{3}\)

Therefore, the constant of variation is, \(\frac{2}{3}\).

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Answer:b

Step-by-step explanation:

( a)ρ² = (5/6) sec² θ.

(b) ρ = ±√(5 - 5 cos² θ) / sin θ cos φ.

For part (a) 6z² = 5x² + 5y²

The spherical coordinates for the variables x, y, and z are as follows:

x = ρsinθcosφy = ρsinθsinφz = ρcosθ

Substitute the values of x, y, and z into the given equation:6 (ρ cos θ)² = 5(ρ sin θ cos φ)² + 5(ρ sin θ sin φ)²

Simplify:6ρ² cos² θ = 5ρ² sin² θ (cos² φ + sin² φ)6ρ² cos² θ = 5ρ² sin² θ

Substitute sin² θ = 1 - cos² θ:6ρ² cos² θ = 5ρ² (1 - cos² θ)6ρ² cos² θ = 5ρ² - 5ρ² cos² θ6ρ² cos² θ + 5ρ² cos² θ = 5ρ²6ρ² = 5ρ² / (cos² θ + 5cos² θ)6ρ² = 5ρ² / cos² θ(6/5)ρ² = sec² θρ² = (5/6)sec² θ

The equation in spherical coordinates is ρ² = (5/6) sec² θ.

For part (b) x² + 5z² = 5

The spherical coordinates for the variables x, y, and z are as follows:

x = ρsinθcosφy = ρsinθsinφz = ρcosθ

Substitute the values of x, y, and z into the given equation:

(ρsinθcosφ)² + 5 (ρ cosθ)² = 5ρ²ρ² sin² θ cos² φ + 5 ρ² cos² θ = 5ρ²

Rearrange:ρ² (sin² θ cos² φ + 5 cos² θ - 5) = 0sin² θ cos² φ + 5 cos² θ - 5 = 0sin² θ cos² φ = 5 - 5 cos² θsin θ cos φ = ±√(5 - 5 cos² θ)

The equation in spherical coordinates is ρ = ±√(5 - 5 cos² θ) / sin θ cos φ.

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Answer:

c

Step-by-step explanation:

A is x times 2=y, b is x times 3= y, and d is for every first number, it is multiplying 2, then 3, etc.

Answer:

(x+3)(x+5)

x( x + 5) +3 ( x + 5)

x² + 5x + 3x + 15

x² + 8x + 15

The length of CF is CF = 5y + 9, based on the given parameters, and the complete lengths are:. CD = 2y - 2, DF = 3y + 11 and CF = 5y + 9

The given parameters are:

CD = 2y - 2

DF = 3y + 11

To calculate the length CF, we use the following equation

CF = CD + DF

Substitute the known values in the above equation

CF = 2y - 2 + 3y + 11

Evaluate the like terms

CF = 5y + 9

Hence, the length of CF is CF = 5y + 9, based on the given parameters.

So, the complete lengths are:.

CD = 2y - 2

DF = 3y + 11

CF = 5y + 9

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Answer:

18

Step-by-step explanation:

There is two pints for every quart so multiply 9*2=18

Answer:

The answer is C The sales range for team 2 is greater than the sales range for team 1.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

Parallel lines don't intersect

Answer:

Neither parallel or perpendicular.

Step-by-step explanation:

For AB A(-1,-4) and B(2, 11)

x1,y1 x2,y2

Gradient = (y2 - y1)/(x2 - x1)

= (11 - (-4))/(2 - (-1))

= 15/3 = 5.

For CD C(1 , 1) and D(4 , 10)

x1, y1 x2, y2

Gradient = (y2 - y1)/(x2 - x1)

= (10 - 1)/(4 - 1)

= 9/3 = 3

from the above they are neither parallel or perpendicular.

To solve the initial value problem y" + 4y = 4u_n(t), where y(0) = 0 and y'(0) = 1, we will follow these steps:

a. Find the Laplace transform of the solution y(t).

The Laplace transform of the given differential equation can be obtained using the properties of the Laplace transform. Taking the Laplace transform of both sides, we get:

s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 4U_n(s),

where Y(s) represents the Laplace transform of y(t) and U_n(s) is the Laplace transform of the unit step function u_n(t).

Since y(0) = 0 and y'(0) = 1, the equation becomes:

s^2Y(s) - s(0) - 1 + 4Y(s) = 4U_n(s),

s^2Y(s) + 4Y(s) - 1 = 4U_n(s).

Taking the inverse Laplace transform of both sides, we obtain the solution in the time domain:

y''(t) + 4y(t) = 4u_n(t).

b. Find the solution y(t) by inverting the transform.

To find the solution y(t) in the time domain, we need to solve the differential equation y''(t) + 4y(t) = 4u_n(t) with the initial conditions y(0) = 0 and y'(0) = 1.

The homogeneous solution to the differential equation is obtained by setting the right-hand side to zero:

y''(t) + 4y(t) = 0.

The characteristic equation is r^2 + 4 = 0, which has complex roots: r = ±2i.

The homogeneous solution is given by:

y_h(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are constants to be determined.

Next, we find the particular solution for the given right-hand side:

For t < n, u_n(t) = 0, and for t ≥ n, u_n(t) = 1.

For t < n, the particular solution is zero: y_p(t) = 0.

For t ≥ n, we need to find the particular solution satisfying y''(t) + 4y(t) = 4.

Since the right-hand side is a constant, we assume a constant particular solution: y_p(t) = A.

Plugging this into the differential equation, we get:

0 + 4A = 4,

A = 1.

Therefore, for t ≥ n, the particular solution is: y_p(t) = 1.

The general solution for t ≥ n is given by the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

y(t) = c1cos(2t) + c2sin(2t) + 1.

Using the initial conditions y(0) = 0 and y'(0) = 1, we can determine the values of c1 and c2:

y(0) = c1cos(0) + c2sin(0) + 1 = c1 + 1 = 0,

c1 = -1.

y'(t) = -2c1sin(2t) + 2c2cos(2t),

y'(0) = -2c1sin(0) + 2c2cos(0) = 2c2 = 1,

c2 = 1/2.

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Of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. So, 136 students earned a C for the course.

To find the number of students who earned a C in the course, we'll follow these steps:

1. Determine the total number of students in the course.
2. Find out how many students earned an A and how many earned a B.
3. Subtract the number of A and B students from the total to find the number of C students.

We are given that there are 180 students in the course. It is also mentioned that 41 students earned an A and 3 students earned a B.

Now let's perform the calculations:

Step 1: We know that the total number of students is 180.

Step 2: We need to find the combined number of A and B students. We are given that 41 students earned an A, and 3 students earned a B. So, to find the total number of A and B students, we simply add these two numbers:

41 (A students) + 3 (B students) = 44 (A and B students)

Step 3: To find the number of C students, we subtract the total number of A and B students (44) from the total number of students (180):

180 (total students) - 44 (A and B students) = 136 (C students)

So, 136 students earned a C for the course.

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Answer:

276.3 sq ft

Step-by-step explanation:

\(2 \times \pi {4}^{2} + 2 \times 4 \times \pi \times 7 = 276.3\)

Answer:

When the dimensions of the shape, such as radius, height, or length change, both surface area and volume also change. However, the volume of the object always changes more than the surface area for the same change in dimensions.

Based on the information provided, Michelle likes 540 but not 250. Based on the given information, Michelle seems to like numbers that are divisible by both 2 and 3.

96 is divisible by 2 (48 times) and 3 (32 times), while 45 is not divisible by 2. Similarly, 540 is divisible by 2 (270 times) and 3 (180 times), but 250 is not divisible by 3. So, Michelle would likely prefer numbers that are divisible by both 2 and 3.

Additionally, this is because she likes numbers that have a 6 in the ones place (like 96 and 540), but she does not like numbers that have a 5 in the ones place (like 45 and 250). It's important to pay attention to the specific criteria that Michelle likes and dislikes in order to determine which number she prefers.

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Answer:

x = 10

y = 5

Step-by-step explanation:

Applying Trigonometry ratio

sin∅ = opposite/hypotenuse

cos∅ = Adjacent/hypotenuse

From the diagram,

sin60° = 5√3/x

make x the subject of the equation

x = 5√3/sin60°

But, sin60° = √3/2

x = 5√3/(√3/2)

x = (5√3)(2/√3)

x = 10.

Also, applying

cos60° = y/x

Where x = 10, cos60° = 1/2

y = xcos60°

y = 10(1/2)

y = 5

Answer:

3250

Step-by-step explanation:

50 x 65 = 3250

Answer:

B. x =  -3 or x = 2

Step-by-step explanation:

Answer: Options 2 and 4

Step-by-step explanation:

Option 1: The angles add to \(180^{\circ}\), so the angles can form a triangle. However, because there are no side lengths, the triangle is only defined up to similarity.

Option 2: The angles do not add to \(180^{\circ}\), so a triangle cannot be formed.

Option 3: The side lengths do not satisfy the triangle inequality, so a triangle cannot be formed.

Option 4: It is not specified what side the \(75^{\circ}\) is opposite of, so multiple triangles can be formed.

Answer:

3x - 1 = 0

Step-by-step explanation:

3x + 1 = 0

The perpendicular of a line has a slope that is the negative reciprocal of that lines slope.

So the answer is 3x - 1 = 0

Answer:

92.5%

Step-by-step explanation:

Real numbers include the positive and negative integers and fractions (or rational numbers) and also the irrational numbers.

In the given graph of functions, all of the functions have a domain (x values) of all real numbers.

Therefore, the answer is letter B.

Answer:My Favorite Thing About Christmas Is.

Step-by-step explanation:Famliy and food

Presents and getting together with my family and relatives;)

Answer:

$12.3

Step-by-step explanation:

61.50*1=61.50

61.50/5= $12.3

Answer:

x = 61°

Step-by-step explanation:

since the triangle is isosceles the two angles opposite 58° are equal so:

x = (180° - 58°)/2 = 61°