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wolverine [178]
2 years ago
12

5x + 1 over 2y2

Mathematics
1 answer:
Oxana [17]2 years ago
4 0

Step-by-step explanation:

So for this question just substitute the value and work out. I thought it it to the power of 2 as I can't tell from the question.

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5 0
2 years ago
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A herd of dinosaurs made paintings in the sand with their claws. Each baby dinosaur made 1515 paintings and each adult dinosaur
mart [117]

Answer:

4 adult dinosaurs and 12 baby dinosaurs.

Step-by-step explanation:

Let the number of adult dinosaurs be x.

Number of baby dinosaurs = 3x

Number of paintings made by each baby dinosaur = 15

Number of paintings made by each adult dinosaur = 7

Total number of paintings made by 3x baby dinosaurs = Number of baby dinosaurs * Number of paintings made by each baby dinosaur

= 3x * 15

= 45x

Total number of paintings made by x adult dinosaurs = Number of adult dinosaurs * Number of paintings made by each adult dinosaur

= x * 7

= 7x

Total number of paintings made by both baby and adult dinosaurs = 45x + 7x

= 52 x

Again the problem says that the total number of paintings made  = 208

So, 52x = 208

Dividing both sides by 52

\frac{52x}{52}  = \frac{208}{52}

Cancelling out the 52's from the top and bottom on the left

x = 4

So, number of adult dinosaurs = 4

Number of baby dinosaurs = 3x = 3*4 = 12

8 0
3 years ago
Find the general solution to each of the following ODEs. Then, decide whether or not the set of solutions form a vector space. E
Ipatiy [6.2K]

Answer:

(A) y=ke^{2t} with k\in\mathbb{R}.

(B) y=ke^{2t}/2-1/2 with k\in\mathbb{R}

(C) y=k_1e^{2t}+k_2e^{-2t} with k_1,k_2\in\mathbb{R}

(D) y=k_1e^{2t}+k_2e^{-2t}+e^{3t}/5 with k_1,k_2\in\mathbb{R},

Step-by-step explanation

(A) We can see this as separation of variables or just a linear ODE of first grade, then 0=y'-2y=\frac{dy}{dt}-2y\Rightarrow \frac{dy}{dt}=2y \Rightarrow  \frac{1}{2y}dy=dt \ \Rightarrow \int \frac{1}{2y}dy=\int dt \Rightarrow \ln |y|^{1/2}=t+C \Rightarrow |y|^{1/2}=e^{\ln |y|^{1/2}}=e^{t+C}=e^{C}e^t} \Rightarrow y=ke^{2t}. With this answer we see that the set of solutions of the ODE form a vector space over, where vectors are of the form e^{2t} with t real.

(B) Proceeding and the previous item, we obtain 1=y'-2y=\frac{dy}{dt}-2y\Rightarrow \frac{dy}{dt}=2y+1 \Rightarrow  \frac{1}{2y+1}dy=dt \ \Rightarrow \int \frac{1}{2y+1}dy=\int dt \Rightarrow 1/2\ln |2y+1|=t+C \Rightarrow |2y+1|^{1/2}=e^{\ln |2y+1|^{1/2}}=e^{t+C}=e^{C}e^t \Rightarrow y=ke^{2t}/2-1/2. Which is not a vector space with the usual operations (this is because -1/2), in other words, if you sum two solutions you don't obtain a solution.

(C) This is a linear ODE of second grade, then if we set y=e^{mt} \Rightarrow y''=m^2e^{mt} and we obtain the characteristic equation 0=y''-4y=m^2e^{mt}-4e^{mt}=(m^2-4)e^{mt}\Rightarrow m^{2}-4=0\Rightarrow m=\pm 2 and then the general solution is y=k_1e^{2t}+k_2e^{-2t} with k_1,k_2\in\mathbb{R}, and as in the first items the set of solutions form a vector space.

(D) Using C, let be y=me^{3t} we obtain that it must satisfies 3^2m-4m=1\Rightarrow m=1/5 and then the general solution is y=k_1e^{2t}+k_2e^{-2t}+e^{3t}/5 with k_1,k_2\in\mathbb{R}, and as in (B) the set of solutions does not form a vector space (same reason! as in (B)).  

4 0
3 years ago
What is the surface area of this triangular prism shown above?
PIT_PIT [208]
To find the surface are of the base: 8 * 8 = 64/2(becasue its a triangle not a square base) = 32.
To find the surface are of the 3 other faces, 12 * 8 = 96/2 = 48 * 3(for the 3 sides) = 144.
The entire surface area is 176.
4 0
3 years ago
Robbie, has scored 120 so far this season. He has scored all of his points on 1-point extra point kicks and 3-point field goals.
joja [24]

Answer:

39 and 27

Step-by-step explanation:

GIVEN: Robbie, has scored 120 so far this season. He has scored all of his points on 1-point extra point kicks and 3-point field goals. He has made a total of 66 kicks.

TO FIND: How many of each kick has he made.

SOLUTION:

Lets extra point kicks made by Robbie be x

points scored using extra point kick =1

field goal kicks made by Robbie =66-x

point scored using field goal kick =3

Total points scored by Robbie =120

Total points scored are the sum of points scored by extra point kicks and field goal kicks.

1\times x+(66-x)3=120

198-2x=120

2x=78

x=39

total extra point kicks =39

total field goal kicks =66-39=27

Hence Robbie made 39 and 27 kicks of extra point kick and field goal kicks respectively.

6 0
3 years ago
Read 2 more answers
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