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Pani-rosa [81]
3 years ago
6

Does anyone else agree that the answer for this family of curves question is E, dy/dx = x + y?

Mathematics
1 answer:
neonofarm [45]3 years ago
6 0
Yes this is the correct answer. The slope field shown is the differential equation dy/dx = x+y

All points along the line x+y = k, for some constant k, will have the same tangent slope k. For example, the line x+y = 0 will have every point with tangent slope 0 for the solution y(x). It may not be 100% clear, but this graph has horizontal tickmarks on the line x+y = 0, or the tickmarks are close to being horizontal. Using geogebra, I checked the others and they produced completely different graphs, which allowed me to rule them out.
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1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the a
Rudik [331]

Answer:

Part A) \$42,888.48  

Part B) A=\$22,304

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12  

substitute in the formula above  

A=8,500(1+\frac{0.0812}{12})^{12*20}  

A=8,500(1.0068)^{240}  

A=\$42,888.48  

Part B) What if the deposit were compounded monthly with simple interest?  

we know that

The simple interest formula is equal to

A=P(1+rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=20\ years\\ P=\$8,500\\r=0.0812

substitute in the formula above

A=8,500(1+0.0812*20)

A=\$22,304

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

A(t)=8,500(1.0068)^{12t} ------> equation A

A(t)=8,500(1+0.0812t)  -----> equation B

using a graphing tool  

see the attached figure  

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.

5 0
3 years ago
PLEASE HELP!! BE AUICK AND EXPLAIN!Solve the system by graphing!
zubka84 [21]
The answer to the question is (2,-2) d

4 0
3 years ago
Jim's backyard is a rectangle that is 15 5/6 yards long and 10 2/5 yards wide. Jim buys sods in pieces that are 1 1/3 yards long
Ne4ueva [31]

We are given

Jim's backyard:

Length is

L=15\frac{5}{6} =\frac{95}{6} yards

width is

W=10\frac{2}{5} =\frac{52}{5} yards

Since, this is rectangle

so, we can find area of rectangle

A=L*W

A=(\frac{95}{6})*(\frac{52}{5})

A=\frac{494}{3} yard^2

Area of one sod:

length is

l=1\frac{1}{3} =\frac{4}{3} yards

width is

w=1\frac{1}{3} =\frac{4}{3} yards

Since, it is rectangle in shape

so,

Area=l*w

A=\frac{4}{3}*\frac{4}{3}

A=\frac{16}{9}yard^2

Number of pieces of sod:

we can use formula

Number of pieces of sod = (area of Jim's backyard)/(area of one sod)

N=\frac{\frac{494}{3} }{\frac{16}{9} }

now, we can simplify it

N=\frac{741}{8} pieces need ..............Answer

7 0
3 years ago
A rectangle has a length of 12 mm and a width of 15 mm. A new rectangle was created by multiplying all of the dimensions by a sc
solmaris [256]

Answer:

the new perimeter will be 1/3 time the perimeter of the original rectangle

Step-by-step explanation:

8 0
3 years ago
A storage space in a basement is in the shape of a rectangular prisim. The hieght of the storage space is 5 feet. The length is
Greeley [361]

Answer:

length is 28.86ft

width= 4.12ft

Step-by-step explanation:

<h2>This problem bothers on the mensuration of solid shapes, a rectangular prism.</h2>

The storage space takes the shape of a rectangular prism, and we are required to find the width and length  of the storage space.

let the width of the basement be "w"

Given data

volume v=595ft^{3}

length l = 7w ft

width w= w

height h= 5 ft

We know that the expression for the volume of a rectangular prism is

volume= length * width* height

substituting our data we have to find "w"

595= 7w*w*5\\595=7w^{2}*5\\ 595= 35w^{2} \\

dividing both sides by 35 we have

w^{2}= \frac{595}{35\\}  \\w^{2}= 17\\

find the square root of both sides we have

w=\sqrt{17} \\w= 4.12

since we know that length= 7w and width = w , we can substitute our value for w and find the length and width

length= 7*4.12= 28.86ft\\width = 4.12ft

6 0
3 years ago
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