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2 years ago

For a particular angle Θ, the cosine function f(x) = a cos b(Θ) has the following values within one cycle of the function:

Mathematics

1 answer:

expeople1 [14]2 years ago

7 0

If f(θ) = a cos(bθ), then from the first condition we find

f(0) = 3 ⇒ a cos(0) = 3 ⇒ a = 3

Together with the other conditions, it's evident that f(θ) has a period of π, so

2π/b = π ⇒ b = 2

so that

f(θ) = 3 cos(2θ)

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the population of Watesville decreases at a 1.6% per year.If the population was 62,500 in 2014 what will it be in 2020

vichka [17]

The population in 2020 will be 57657.5 approximately

<u>Explanation:</u>

Given:

Population in 2014, P = 62,500

Rate of decrease, r = 1.6%

Population in 2020, Q = ?

Number of years between 2014 to 2020 = 5 years

Population in 2020 = $P(1 - \frac{r}{100} )^t$

Substituting the value we get:

$Q = 62500(1- \frac{1.6}{100})^5\\ \\Q = 62500 ( 0.92252) \\\\Q = 57657.46$

Therefore, the population in 2020 will be 57657.5 approximately

7 0

3 years ago

A windshield wiper is 50 cm long. In one sweep it turns through an angle of 115°. Calculate the distance (length) it covers in o

sergeinik [125]

Answer:

The distance in one sweep is 100 cm approximately

Step-by-step explanation:

Here, we want to calculate the distance the wiper covers in one sweep

Mathematically;

we have a structure like an arc of a circle. It is the length of this arc we want to calculate.

The formula for the length of an arc is;

theta/360 * 2 * pi * r

r is the radius which in this case is 50 cm

We have ;

115/360 * 2 * 3.1412 * 50 = 100 cm approximately

4 0

3 years ago

(GIVING BRAINLIEST!!)

Montano1993 [528]

Answer:

6450

Step-by-step explanation:

1kg = 1000g

6.45 x 1000 = 6450

3 0

3 years ago

What is the minimum value of C = 7x + 8y, given the constraints: 2x + y ≥ 8, x + y ≥ 6, x ≥ 0, y ≥ 0. A. 32 B. 42 C. 46 D. 64

marshall27 [118]

Answer: The minimum value of C is 46.

Step-by-step explanation:

Since, Here, We have to find out Min C = 7x+8y

Given the constraints are $2x+y\geq 8$ -------(1)

$x+y \geq 6$ ------------- (2)

$x \geq 0$ , $y \geq 0$ -------- (3)

Since, For equation 1) x-intercept, (4, 0) and y-intercept (0,8)

And, $2\times 0+0\geq 8$ ⇒ $0\geq 8$ ( false)

Therefore the area of line 1) does not contain the origin.

For equation 2) x-intercept, (6, 0) and y-intercept (0,6)

And, $0+0\geq 6$ ⇒ $0\geq 6$ ( false)

Therefore the area of line 2) does not contain the origin.

Thus after plotting the constraints 1) 2) and 3) we get Open Shaded feasible region AEB ( Shown in below graph)

At A≡(0,8) , C= 64

At E≡(2,4), C= 46

At B≡(6,0), C= 42

Thus at B, C is minimum, And its minimum value = 42

5 0

3 years ago

Read 2 more answers

A rectangle has a length of (x+5)and a with of x Write down the expression for the area of a rectangle If the area is 24cm²,find

ratelena [41]

Answer: Width = 3cm

Length = 8cm

Step-by-step explanation:

Length = x+5 cm

Width = xcm

Area = 24cm²

Area of a rectangle = length × width

x × (x + 5) = 24

x² + 5x = 24

x² + 5x - 24 = 0

x² + 8x - 3x - 24 = 0

x(x + 8) - 3(x + 8) = 0

x - 3 = 0

x = 3

Width = 3cm

Since length = x + 5 = 3 + 5 = 8cm

Length = 8cm

8 0

3 years ago