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3 years ago

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Jane is making a suit that requires 2 5/8 yards for a jacket and 1 3/4 yards for a skirt. What is the total amount of material s

he needs?
A. 4 yards.
B. 4 3/8 yards.
C. 3 2/3 yards.
D. 3 1/2 yards

1 answer:

Delvig [45]3 years ago

3 0

The total amount of material she needs is 4 3/8 yards

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1..A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 26

statuscvo [17]

Answer:

See below for answers and explanations (along with a graph attached)

Step-by-step explanation:

<u>Part A</u>

The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet

<u>Part B</u>

The graph's function would be in the form of $y=acos(bx+c)+d$ where $a$ is the amplitude, $\frac{2\pi}{b}$ is the period, $-\frac{c}{b}$ is the phase/horizontal shift, and $d$ is the average/midline.

We already know our amplitude of $a=3$ from part A.

Since our period is given to us as 26 seconds, then we can use the equation $\frac{2\pi}{b}=26$ to find $b$ , which happens to be $b=\frac{\pi}{13}$ .

Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity $sin(x)=cos(x-\frac{\pi}{2})$ which shifts the cosine graph $\frac{\pi}{2}$ units to the right. This means that $c=-\frac{\pi}{2}$ , making our phase shift $-\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5$ , or 6.5 feet to the right

Our average/midline would be $d=12$ as given as the average height by the problem.

Therefore, the function is $f(x)=3cos(\frac{\pi}{13}x-\frac{\pi}{2})+12$

<u>Part C</u>

Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).

5 0

2 years ago

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A scientist kept 100 grams of a radioactive material in a container. After 280 days, he observed that 25 grams of the radioactiv

Wittaler [7]

Answer:

B: About 50 grams of the material was left in the container after 140 days.

Step-by-step explanation:

Radioactive materials decay at a rate called "half-lives." After a certain amount of time, the grams of radioactive material will be reduced to half. After that same amount of time again, the material will be reduced to half of the half.

1/4 is equal to 1/2 times 1/2. So, when 1/4 of the material remains, two half-lives have elapsed.

The question states that after 280 days, 25 grams of the material was left in the container. 25 grams is 1/4 of the original 100 grams that the scientist started with at time = 0 days.

When 25 grams of material remain, two half-lives have elapsed. 280 days equals two half-lives for this material. So 140 days (half of 280 days) equals one half-life for this material.

After 280 days (two half-lives), one fourth of the material (25 grams) will remain.

After 140 days (one half-life), half of the material (50 grams) will remain.

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3 years ago

What is the change temperature from 12 degree F to -3 degree F

Mama L [17]

Answer:

13

Step-by-step explanation:

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3 years ago

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BRAINLIEST AND FIVE STARS FOR CORRECT ANSWER

sesenic [268]

The full sequence from 3 to 21 is...

3, 5, 7, 9, 11, 13, 15, 17, 19, 21

Now first add 3 and 5 to get 8. Then 8 and 7 to get 15. After, add 15 and 9 to get 24 and furthermore.

(24+11=35 --> 35+13=48 --> 48+15=63 --> 63+17=80 --> 80+19=99 --> 99+21=120)

So I believe the sum of the sequence is 120

I hope this helps!

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3 years ago

The given line segment has a midpoint at (3, 1).

boyakko [2]

Answer:

y = 1/3 x.

Step-by-step explanation:

The slope of the given line is

(4 - (-2) / 2 - 4)

= -3.

So the slope of the line perpendicular to it = -1 / (-3) = 1/3.

This line also passes through the point (3, 1) so its equation is ( by the point-slope form):

y - 1 = 1/3(x - 3)

y - 1 = 1/3x - 1

y = 1/3 x (answer).

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3 years ago

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