Find the value of the trigonometric ratio. Express your answer as a fraction in lowest terms.

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Since two-thirds of cups of sugar are needed for each jug of lemonade, The amount of sugar needed for the given Jugs of lemonade is as follows:

Jug of Lemonade      Cups of sugar

3                                       2

6                                       4

9                                       6

12                                      8

The ratio of the jugs of lemonade to the sugar required for each jug of lemonade is given below:

1 jug of lemonade : 2/3 cups of sugar

The amount of sugar needed for the given Jugs of lemonade is as follows:

3 Jugs of Lemonade:

Cups of sugar = 3 * 2/3

Cups of sugar = 2

6 Jugs of Lemonade:

Cups of sugar = 6 * 2/3

Cups of sugar = 4

9 Jugs of Lemonade:

Cups of sugar = 9 * 2/3

Cups of sugar = 6

12 Jug of Lemonade:

Cups of sugar = 12 * 2/3

Cups of sugar = 4

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Answer:

the answer is something

Step-by-step explanation:

x2-14+6

x+3

Answer:

k = ± 4

Step-by-step explanation:

Given

x² - kx + 4 = 0 ← in standard form

with a = 1, b = - k, c = 4

The equation has equal roots, thus the discriminant

b² - 4ac = 0, that is

(- k)² - (4 × 1 × 4) = 0

k² - 16 = 0 ( add 16 to both sides )

k² = 16 ( take the square root of both sides )

k = ± \(\sqrt{16}\) = ± 4

Answer:

5 feet 4.4 inches tall

Step-by-step explanation:

Answer:

∠ A = 50°

Step-by-step explanation:

The angle adjacent to 145° inside the triangle is

180° - 145° = 35°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

85° is an exterior angle of the triangle , then

∠ A + 35° = 85 ( subtract 35° from both sides )

∠ A = 50°

According to the conversion factor, 10 grams is equal to 0.0220462 pounds and 0.3527392 ounces.

Converting units can be a tricky task, but it's important to be able to do it correctly in order to make accurate measurements. In this case, we will be converting grams to pounds and ounces.

To begin the conversion, we need to know the conversion factor between grams and pounds. The conversion factor is 0.00220462, which means that one gram is equal to 0.00220462 pounds.

Now, to convert 10 grams to pounds, we simply multiply 10 by the conversion factor:

10 grams * 0.00220462 pounds/gram = 0.0220462 pounds

So 10 grams is equivalent to 0.0220462 pounds.

Next, we need to convert the remaining decimal to ounces. There are 16 ounces in a pound, so we can use the conversion factor of 1 pound equals 16 ounces to find out how many ounces are in 0.0220462 pounds.

0.0220462 pounds * 16 ounces/pound = 0.3527392 ounces

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Complete Question:

Find the equivalent value for 10 grams in pounds and ounces.

24 ounces of half-strength Sustacal can be made from a 12-ounce can of full-strength Sustacal (C)

To make half-strength Sustacal, you need to dilute the full-strength Sustacal with an equal amount of water. This means that a 12-ounce can of full-strength Sustacal will make a total of 24 ounces of half-strength Sustacal.

12 ounces of full-strength Sustacal mixed with 12 ounces of water will result in 24 ounces of half-strength Sustacal, with half the original concentration of active ingredients.

It's important to note that the preparation of half-strength Sustacal is crucial for patients who may have difficulty swallowing the full-strength product.

Half-strength Sustacal is also preferred by some patients who are looking for a less caloric or lower-concentration liquid nutrition option.

Preparation of half-strength Sustacal must be done carefully to ensure the correct dilution and to maintain the safety and efficacy of the product.

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Answer:

24

Step-by-step explanation:

24÷8=3

24÷6=4

Answer:

Step-by-step explanation:

To find the breadth use Pythagorean theorem

Breadth² = diagonal² - length²

               = 34² - 30²

               = 1156 - 900

               = 256

Breadth = √256 = 16 cm

Breadth = 16 cm

Perimeter = 2*(length + breadth) = 2*(30 + 16) = 2*46 = 92 cm

Area = length * breadth = 30 *16 = 480 cm²

S O L U T I O N:

Let's assume that the given rectangle be ABCD and in that let ∆ABC be the right angled triangle formed from it.

Now we've been asked to find out the breadth. By applying Pythagoras theorem here in our rectangle ABCD we have,

\(:\implies\tt{ {b}^{2} = {d}^{2} - {l}^{2} }\)

\(:\implies\tt{ {b}^{2} = {34}^{2} - {30}^{2} }\)

\(:\implies\tt{ {b}^{2} = 1156 - 900}\)

\(:\implies\tt{ {b}^{2} = 256}\)

\(:\implies\tt{b = \sqrt{256} }\)

\(:\implies\tt{b = 16}\)

For the formula of area (a) = ? it is given by,

\(:\implies\tt{a = l \times b}\)

\(:\implies\tt{a = 30 \times 16}\)

\(:\implies\tt{a = 480 {cm}^{2} }\)

For the formula of perimeter (p) = ? is given by,

\(:\implies\tt{p = 2 \times (l + b)}\)

\(:\implies\tt{p = 2 \times (30 + 16)}\)

\(:\implies\tt{p = 2 \times 46}\)

\(:\implies\tt{p = 92cm}\)

Answer:

slope = 0

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (8, 2 ) and (x₂, y₂ ) = (10, 2 )

m = \(\frac{2-2}{10-8}\) = \(\frac{0}{2}\) = 0

Answer:

They are equal

Both answer is 65

Step-by-step explanation:

5x -30 = 2x +27

5x -2x = 27 +30

3x = 57

x = 57/3 = 19

5x -30 = 5(19) -30 = 65

2x +27 = 2(19) +27 = 65

Answer:

g(- 6) = 11

Step-by-step explanation:

substitute x = - 6 into g(x) , that is

g(- 6) = - (- 6) + 5 = 6 + 5 = 11

Answer:

11

Step-by-step explanation:

g(x) = -x + 5

Let x = -6

g(-6) = -(-6) + 5

         =6+5

         =11

The equation of the directrix is y=5.

All points in a plane that are equally spaced out from a given point and a given line make up a parabola. The line is known as the directrix, and the point is known as the parabola's focus. A parabola's axis of symmetry is perpendicular to the directrix, which does not touch the parabola.

Knowing the axis and vertex of a parabola allows one to determine the directrix of the curve.

Given:

-8(y-3) = (x+4)²

Now,

y - 3 = (-1/8)(x + 4)2

y = (-1/8)(x + 4)4 + 3

So,

y = k - p

y = 3 - p

Also, p = 1/ 4a

p = 1 / 4(-1/8)

p = -2

So,

y = 3 - p

y= 3-(-2)

y = 3+ 2

y= 5

Hence, the equation of the directrix is y=5.

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Answer:

answer is really hard and small, but I can't help because I don't know,

sorry not sorry

lol

regards,

Rosemary

The next three terms in each geometric sequence is 72, 36, 18, 9, 4.5, 2.25.

The general form of Geometric Progression is: a, ar, ar 2, ar 3, ar 4,…,a n. Where,

a = First term.

r = common ratio.

a n = nth term.

General Term or Nth Term of GP.

Let a be the first term  

And, r be the common ratio for a G.P.

The general form of Geometric Progression is:

GP-series

Where,

a = First term

r = common ratio

arⁿ ⁻¹ = nth term

The next three terms of the GP is :

2.25 + 2.25 = 4.5

4.5 + 4.5 = 9

9 + 9 = 18

18 + 18 = 36

36 + 36 = 72

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Answer:

Refer to the attachment. :)

Answer:

f(x)-5 = g(x)

Step-by-step explanation:

We translate the function g(x) down 5 units from the function f(x)

g(x) = f(x) -5

Rewriting

f(x)-5 = g(x)

Answer:

Option A

Step-by-step explanation:

f(x) and g(x) are exponential functions

We can see that f(x) is shifted 5 units down

So change in y

hence 5 is to be subtracted

يريدون منك استخدام النقاط لتساعد نفسك في رسم صورة المكعبات. هذا ليس سؤالًا حقًا يمكن لأي شخص مساعدتك في الإجابة عليه حيث عليك فقط رسم الصورة. النقاط هي فقط للمساعدة في جعل الأمر أسهل من مجرد الرسم باليد.

Step-by-step explanation:

the area of a triangle is baseline×height/2

in case of such a right-angled triangle we can use the sides that enclose the 90 degree angle as baseline and height.

so,

B = 8×6/2 = 8×3 = 24 yd²

the height h is 8 yd (as the picture clearly shows).

the perimeter of the base is the sum of all three sides

P = 8 + 6 + 10 = 24 yd

The required length of the rectangle is 89 m.

Given that,
The area of a rectangular field is 6942 m. If the width of the field is 78 m, what is its length is to be determined.

Perimeter is the measure of the figure on its circumference.

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

The area of the rectangle = length * width
                                6942  = length * 78
                                length = 89 m

Thus, the required length of the rectangle is 89 m.

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Answer:

7 out of 10

Step-by-step explanation:

if you have 10 in the cup then you add

4 vanilla 3 chocolate = 7

and add all scoops together and you get 10

so your probability would be 7 out of 10

another way to say it is

the probability of getting chocolate or vanilla ice cream from the cup would be 7 out of 10

Answer:

2t+16

Step-by-step explanation:

this should 2t+16

because 2t contains a variable and there are no available numbers/figits that match up

and 9 +7 is 16

hope i could help

Answer:

2t +16

Step-by-step explanation:

2t + 9 + 7

Combine like terms

2t +16

Answer:

x = 4

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angles

46 + (-1 + 8x) = 18x + 5

46 - 1 + 8x = 18x + 5

45 + 8x = 18x + 5 export like terms to the same side

45 - 5 = 18x - 8x

40 = 10x divide both sides by 10

x = 4

Answer:

61 minutes and 36 seconds

Step-by-step explanation:

150 mph is equal to 2.5 miles per minutes divide miles by 2.5

Answer:

x > 6

Step-by-step explanation:

3x - 3 < 9

3x < 12

x < 4

Since x < 4 is not true, then the solution is x > 6

\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)