All categories

3 years ago

5a - (-9) - 7a - 12 6 - 7m^2 + 4n^2 - 8 - 9m^2 - n^2

Mathematics

1 answer:

Klio2033 [76]3 years ago

3 0

Answer:

ken Copland

Step-by-step explanation:

You might be interested in

The tangent of the graph of y=<img src="https://tex.z-dn.net/?f=e%5E%7Bax%7D" id="TexFormula1" title="e^{ax}" alt="e^{ax}" align

bearhunter [10]

a) The tangent to $y=e^{ax}$ at $x=p$ has slope

$y' = ae^{ax} \implies y'(p) = ae^{ap}$

and $y=e^{ap}$ at this point. It passes through the origin, so its equation is

$y - 0 = ae^{ap} (x - 0) \implies y = ae^{ap} x$

It also passes through the point $(p,e^{ap})$ on the curve, so

$y - e^{ap} = ae^{ap} (x - p) \implies y = e^{ap} + ae^{ap} x - ape^{ap}$

By substitution,

$ae^{ap} x = e^{ap} + ae^{ap} x - ape^{ap} \implies e^{ap} = ape^{ap} \implies ap=1 \\\\ \implies \boxed{p=\dfrac1a}$

b) The normal to $y=e^{ax}$ at $x=2p$ has slope

$-\dfrac1{y'(2p)} = -\dfrac1{ae^{2ap}} = -1 \implies ae^{2ap} = 1$

It follows that

$ae^{2ap} = ae^2 = 1 \implies \boxed{a = \dfrac1{e^2} \text{ and } p = e^2}$

c) The tangent line equation is then

$y = \dfrac1{e^2} e^1 x \implies \boxed{y = \dfrac xe}$

7 0

2 years ago

Susan just got a promotion that increased her annual salary from $52,000 to $68,000. Susan's monthly expenses included a mortgag

Veseljchak [2.6K]

Answer:

c. Susan's debt-to-income ratio decreased by about 15%

Step-by-step explanation:

Susan's previous salary = $52,000

Susan's new salary = $68,000

Susan's mortgage = $1,500

The total of three minimum credit card payment = $350

Her lease payment = $280

Her student loan payment = $250

Her personal loan payment = $325

Therefore, her total debt = $1,500 + $350 + $280 + $250 + $325 = $2,705

Her new Debt to loan ratio = (Her total deb)/(Her total new income) = 2705/68000 = 3.9779 %

Her previous to loan ratio = (Her total deb)/(Her total previous income) = 2705/52000 = 5.2%

The percentage change in her debt to income ratio = (5.202 - 3.9779)/5.202 ≈ 23% decrease

Therefore, the best option is Susan's debt-to-income ratio decreased by about 15%.

8 0

3 years ago

Read 2 more answers

A company puts 36 cans into each box they send to a store. Each can has a radius of

sashaice [31]

Answer:

First, we calculate for the volume of each can by using the equation,

V = πr²h

Substituting the known values,

V = π(1.5 in)²(6 in) = 42.39 in³ (that is if 3.14 is used in replacement of π)

Then, we multiply the volume by 36.

total volume = (42.39 in³)(36) = 1526.04 in³

Step-by-step explanation:

3 0

3 years ago

How many places do you need to move the decimal to the left to write the

NikAS [45]

Answer: 6 x 10^12

Step-by-step explanation:

Move the decimal to the left so there is one non-zero digit number left of the decimal point. This will be the exponent placed on 10

3 0

3 years ago

Amy got a $1,000 loan from her bank, and she had to repay $1,550. What are the principal and interest amounts in this transactio

chubhunter [2.5K]

Out of the choices given, the principle is $1,000 and the interest is $550. The correct answer is C.

3 0

3 years ago

Read 2 more answers