All categories

3 years ago

What is the constant rate of change of (5,80) (4,64) and (6,96)

Mathematics

1 answer:

sveticcg [70]3 years ago

8 0

Answer:

Step-by-step explanation:

The existence of the constant rate of change is given the ratio of y to x is the same. Then:

$k_{1} = \frac{80}{5}$

$k_{1} = 16$

$k_{2} = \frac{64}{4}$

$k_{2} = 16$

$k_{3} = \frac{96}{6}$

$k_{3} = 16$

In consequence, the constant rate of change is 16.

You might be interested in

Julia's great dane weighs 45 kgand Jake's chihuahua weighs 15 kg. How much bigger, as a percentage, is julia's dog?

jarptica [38.1K]

45kg-15kg=30kg Percentage: 30kg=0.3% Percentage =0.3%

8 0

3 years ago

Read 2 more answers

Find the surface area of each shipping package. Which package has the greater surface area? Does the same package have a greater

Kryger [21]

Answer:

greater area: A
no, B has the greater volume

Step-by-step explanation:

The relevant area and volume formulas are ...

A = 2(LW +H(L +W))

V = LWH

When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.

Figure A has the larger area.

Figure B has the larger volume.

<em>Additional comment</em>

The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)

3 0

2 years ago

A sequence is constructed according to the following rule: its first term is 7, and each next term is one more than the sum of t

Iteru [2.4K]

Answer:

Step-by-step explanation:

According to the described rule, we have

$a_1=7\\ \\a_1^2=7^2=49\Rightarrow a_2=4+9+1=14\\ \\a_2^2=14^2=196\Rightarrow a_3=1+9+6+1=17\\ \\a_3^2=17^2=289\Rightarrow a_4=2+8+9+1=20\\ \\a_4^2=20^2=400\Rightarrow a_5=4+0+0+1=5\\ \\a_5^2=5^2=25\Rightarrow a_6=2+5+1=8\\ \\a_6^2=8^2=64\Rightarrow a_7=6+4+1=11\\ \\a_7^2=11^2=121\Rightarrow a_8=1+2+1+1=5\\ \\\text{and so on...}$

We can see the pattern

$a_5=a_8=a_{11}=a_{14}=...=5\\ \\a_6=a_9=a_{12}=a_{15}=...=8\\ \\a_7=a_{10}=a_{13}=a_{16}=...=11$

In other words, for all $k\ge 2$

$a_{3k-1}=5\\ \\a_{3k}=8\\ \\a_{3k+1}=11$

Now,

$a_{2018}=a_{3\cdot 673-1}=5$

7 0

3 years ago

HELP! WILL GIVE BRAINLIEST!

romanna [79]

Answer:

I Know it is B trust me

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

an open rectangular cardboard box with a square base is to have a volume of 256cm^3. Find the dimensions of the box if the area

Anit [1.1K]

Let
x------> the length side of the square base of the box
y-------> the height of the box

we know that
volume of the box=b²*h
b=x
h=y
volume=256 cm³
so
256=x²*y------>y=256/x²--------> equation 1

<span>The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.</span>

surface area of the cardboard=area of the base+perimeter of base*height
area of the base=x²
perimeter of the base=4*x
height=y
surface area=x²+4x*y-----> equation 2
substitute equation 1 in equation 2
SA=x²+4x*[256/x²]-----> SA=x²+1024/x

step 1
find the first derivative of SA and equate to zero
2x+1024*(-1)/x²=0------> 2x=1024/x²----> x³=512--------> x=8 cm
y=256/x²------> y=256/8²-----> y=4 cm

the answer is
the length side of the square base of the box is 8 cm
the height of the box is 4 cm

5 0

3 years ago