MATHEMATICS COLLEGE

Complete the standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).

Answers

Answer 1
Answer:

Answer:

((x-30)^(2))/(40^(2)) - ((y+15)^(2))/(3^(2)) = 1

Step-by-step explanation:

The equation of the horizontal hyperbola in standard form is:

((x-k)^(2))/(a^(2)) - ((y-k)^(2))/(b^(2)) = 1

The position of its center is:

C(x,y) = \left((-10 + 70)/(2), -15 \right)

C(x, y) = (30,-15)

The values for c and a are respectively:

a = 70 - 30

a = 40

c = 30 - (-11)

c = 41

The remaining variable is computed from the following Pythagorean identity:

c ^(2) = a^(2) + b^(2)

b = \sqrt{c^(2)-a^(2)}

b = \sqrt{41^(2)-40^(2)}

b = 3

Now, the equation of the hyperbola is:

((x-30)^(2))/(40^(2)) - ((y+15)^(2))/(3^(2)) = 1
Answer 2
Answer:

Answer:

The above answer is correct but the 3 should be a 9

Step-by-step explanation:

Plato

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What’s the correct answer for this?
5.5x10^9 times 2.3x10^7

Pls help, and don’t give random answers just so you can have points.

Answers

i believe it’s C! because it doesn’t start out as 4 like in answer B but it still doubles

Tyson and Ariana each invested $2,500 in separate accounts. Tyson’s interest rate is 5.75% and is compounded annually. Ariana’s simple interest rate is 5.75%. Neither will make any additional deposits or withdrawals. At the end of 6 years, how much more has Tyson earned? Round your answer to the nearest cent.

Answers

Answer:

Tyson's account will have $ 133.90 more than Ariana's account.

Step-by-step explanation:

In Tyson's case, he invests $ 2,500 in an account whose interest rate is 5.75% and is compounded annually. In turn, Ariana invests the same amount and for the same interest, but this is not compounded.

Thus, Ariana, at the end of her 6 years, will have a total amount in her account of $ 3,362.5 (((2,500 x 5.75 / 100) x 6) + 2,500), of which $ 862.5 will correspond to the interest generated.

Instead, Tyson's investment interests will be consolidated annually. Thus, in 6 years, this investment will evolve as follows:

-Year 1 --- 2,500 x 1.0575 = 2,643.75

-Year 2 --- 2,643.75 x 1.0575 = 2,795.76

-Year 3 --- 2,795.76 x 1.0575 = 2,956.52

-Year 4 --- 2,956.52 x 1.0575 = 3,126.52

-Year 5 --- 3,126.52 x 1.0575 = 3,306.29

-Year 6 --- 3,306.29 x 1.0575 = 3,496.40

Thus, at the end of the 6 years, Tyson will have $ 3,496.40 in his account. Thus, Tyson's account will have $ 133.90 more than Ariana's account.

Match the vocabvulary

Answers

Answer: The answers are in the steps I numbered it as a question from 1 to 12 hopes it helps.Read it carefully.

Step-by-step explanation:

(1)  Answer is RATIONAL NUMBERS.

(2) Answer is  Fraction  

(3) Answer is Terminating decimal

(4) Answer  is  Decimal

(5)  Answer is Integer  

(6) Answer  is Repeating Decimal

(7)  Answer is  Perfect Square  

(8) Answer   is CLASSIFY

(9) Answer is Real Numbers  

(10) Answer is Percent

(11) Answer   Whole numbers

(12) Answer is Irrational numbers

The rate of change of the temperature T(t) of a body is still governed bydT
/dt
= âk(T â A), T(0) = T0,

when the ambient temperature A(t) varies with time. Suppose the body is known to have

k = 0.2

and initially is at 32°C; suppose also that

A(t) = 20eât.

Find the temperature T(t).

Answers

Answer:

T(t)=5e^(-t)+27e^(-0.2t)

Step-by-step explanation:

QUESTION

The rate of change of the temperature T(t) of a body is still governed by

(dT)/(dt)=-k(T-A), T(0)=T_0  when the ambient temperature A(t) varies with time. Suppose the body is known to have  k = 0.2  and initially is at 32°C; suppose also that  A(t) = 20e^(-t). Find the temperature T(t).

SOLUTION

(dT)/(dt)=-k(T-A), T(0)=T_0, A(t) = 20e^(-t), k=0.2

(dT)/(dt)=-0.2T+20(0.2)e^(-t)\n(dT)/(dt)+0.2T=4e^(-t)\n\text{Integrating factor}=e^(0.2t)\n(dTe^(0.2t))/(dt)=4e^(-t)e^(0.2t)\ndTe^(0.2t)=4e^(-t)e^(0.2t)dt\n\int d[Te^(0.2t)]=4\int e^(-t(1-0.2))dt\nTe^(0.2t)=4\int e^(-0.8t)dt\nTe^(0.2t)=(4)/(-0.8) e^(-0.8t)+C, \text{C a constant of integration}\nTe^(0.2t)=-5 e^(-0.8t)+C\nT(t)=5 e^(-0.8t)e^(-0.2t)+Ce^(-0.2t)\nT(t)=5e^(-t)+Ce^(-0.2t)\nWhen t=0, T_0=32\n32=5+C\nC=27

Therefore:

T(t)=5e^(-t)+27e^(-0.2t)

ezekiel has $250 in his bank account he deposts $35 from his birthday and then buys clothes for school for $75

Answers

Answer:

$140

Step-by-step explanation:

i assume ur asking for how much is left over

250-35= 215

215-75= 140

$140 left

The sum of two intcgers is -6. If one of them is 2, then the other is(a) 4
(b) 4
(c) 8
(d) -8​

Answers

Answer:

D) -8

Step-by-step explanation:

If you add a positive and a negative, you end up subtracting. If your sum is lower than any of the numbers you are adding together, then there is a negative. In this case, your only negative number is -8, but if there were others, you could find this equation by doing negative six minus two (because the equation was originally addition, it would still be subtraction to check your work or find the answer in this case.)

Hopefully you find this useful :)

Answer:   -8

Step-by-step explanation:    lets take the unknown number as x,

so we have, 2 + x= -6

                 by using transposition method, x= -6-2( positive becomes  

                                                                       negative when transpositioning)

      so, x= -8                      
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