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Katarina [22]
4 years ago
14

A supermarket finds that the number of boxes of a new cereal sold increases each week. In the first week, only 26 boxes of the c

ereal were sold. In the next week, 57 boxes of the cereal were sold and in the third week 88 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence. What is the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n?
Mathematics
1 answer:
Thepotemich [5.8K]4 years ago
4 0

If the pattern goes 26, 57, 88 you can find the difference between each number to see how much it's going up by each time. 57 - 26 = 31 and 88 - 57 = 31

That means each week the number of boxes of a new cereal increases by 31, or +31

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The distance that an object falls from rest, when air resistance is negligible, varies directly as the square of the time that i
eimsori [14]

Since the distance varies directly as the square of time, then its expression looks like this:

d\text{ = k}\cdot t^2

Where d is the distance, "k" is the proportionality constant and t is the time the object is falling. We know that after 6 seconds the stone travels 304 feet. With this information we can determine the value of "k".

\begin{gathered} 304=k\cdot(6)^2 \\ 304=k\cdot36 \\ k=\frac{304}{36} \\ k=8.44 \end{gathered}

Therefore the complete expression is:

d=8.44\cdot t^2

We want to know the distance after 7 seconds, therefore t = 7.

\begin{gathered} d=8.44\cdot(7)^2 \\ d=8.44\cdot49=413.56\text{ feet} \end{gathered}

The stone will travell approximatelly 314 feet in 7 seconds.

7 0
2 years ago
If the temperature was 89 degrees Fahrenheit would you wear a bathing suit or a jacket
TEA [102]

Answer:

Bathing suit.

Step-by-step explanation:


5 0
4 years ago
Read 2 more answers
I really need help ASAP! thx<br><br> Let f(z)=z-8 and g(z)=4z-9<br> Find (f+g)(2)
Hitman42 [59]

Answer:

  (f +g)(2) = -7

Step-by-step explanation:

Functions are added by adding their values.

<h3>Application</h3>

  (f +g)(2) = f(2) +g(2)

  = (2 -8) +(4(2) -9) . . . . . evaluate f and g with z=2

  = -6 +(-1)

  (f +g)(2) = -7

3 0
2 years ago
In art class, Arthur has created a triangle painting 1/5 of his painting is purple. He decided he wants to Paint 4/8 of the purp
babymother [125]

\frac{1}{10} part of the whole painting is gold colored.

<u>Solution:</u>

Given that , In art class, Arthur has created a triangle painting \frac{1}{5} of his painting is purple.  

He decided he wants to Paint \frac{4}{8} of the purple area gold  

We have to find what fraction of the whole painting will be painting?  

Now, \frac{1}{5} part of whole painting is purple

And, \frac{4}{8} part of the purple area is gold ⇒ \frac{4}{8} part of the \frac{1}{5} part of whole painting is gold

\text { Then, fraction of gold color }=\frac{4}{8} \times \frac{1}{5}=\frac{1}{2} \times \frac{1}{5}=\frac{1}{10}

Hence, \frac{1}{10} part of the whole painting is gold colored.

4 0
3 years ago
I need step by step help solving these problems (not just answers).
balu736 [363]
Secθ=-25/24 so cosθ=-24/25, sinθ=7/25 (quadrant 2) [√1-(24/25)²=√(625-576)/625=√(49/625)=7/25]
sin2θ=2sinθcosθ=-2×7×24/625=-336/625=-0.5376.
cos2θ=1-2sin²θ=1-2×49/625=527/625=0.8432.
tan2θ=sin2θ/cos2θ=-336/527 (=-0.6376 approx.)

The length of the third side is 12 making the Pythagorean triangle 5-12-13 (5²+12²=13²).
Assuming sinθ=5/13, then cosθ=12/13. sin2θ=2sinθcosθ=120/169; cos2θ=1-2sin²θ=1-50/169=119/169.
tan2θ=120/119.

Pythagorean triangle is 7-24-25. sinθ=2sin(θ/2)cos(θ/2), cosθ=1-2sin²(θ/2).
sin²θ=4sin²(θ/2)cos²(θ/2)=4sin²(θ/2)(1-sin²(θ/2)).
49/625= 4sin²(θ/2)-4sin⁴(θ/2); 4sin⁴(θ/2)-4sin²(θ/2)+49/625=0.
sin⁴(θ/2)-sin²(θ/2)+49/2500=0=(sin²(θ/2)-49/50)(sin²(θ/2)-1/50).
cosθ=1-2sin²(θ/2); 24/25=1-2sin²(θ/2), sin²(θ/2)=1/50, sin(θ/2)=1/(5√2)=√2/10.
cos(θ/2)=√1-1/50=7√2/10; tan(θ/2)=1/7.

(sin(x)cos(x))²=sin²(2x)/4.

This can be written cot(x)(cot(x)+1)=0. So cot(x)=0, x=π/2, 3π/2; or cot(x)=-1=1/tan(x), x=3π/4, 7π/4.
3 0
3 years ago
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