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3 years ago

Use the Chain Rule to find dw/dt. (Enter your answer only in terms of t.)

1 answer:

4 0

We substitute the values of x, y and z into w to get an equation only in terms of t.
w = x * exp(y)/z
w = t⁶ x exp(9 - t) / (4 + 4t)
Now, in order to differentiate, we must apply the product and quotient rule of differentiation:
dw/dt = 6t⁵ * exp(9 - t) / (4 + 4t) + t⁶ [-(4 + 4t)exp(9 - t) - 4(exp(9 - t))/(4 + 4t)²]
This can be simplified further to obtain an easier expression.

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Solve the quadratic equation for x. What is one of the roots? (x + 6)^2 = 49

stich3 [128]

Answer:

x equals -1 and it also equals -13. They are both considered the roots.

Step-by-step

(x+6)^2= 49 to get rid of the exponent square root each side of the equation.
(x+6)= √49 Find square root of 49.
(x+6)= ±7 It could be positive 7 or -7 because both of them squared equal 49. Now solve for each possible equation, (x+6)= 7 and (x+6)=-7.
(x+6)=7 subtract 6 from each side.
x= 1
(x+6)=-7 Subtract 6 from each side.
x=-13
So the answers are -13 and 1.

3 0

4 years ago

Read 2 more answers

The gratuity on a restaurant bill was $18. If a 20% tip was left, what was the original amount of the bill? To solve, use what e

quester [9]

Gratuity is the total tip given.

The tip is directly proportional to total cost:

18/0.20 = x/1.00

$90

4 0

3 years ago

Read 2 more answers

If using the method of completing the square to solve the quadratic equation x^2 - 9x - 8 = 0, which number would have to be add

V125BC [204]

Answer:

Number: 28.25

Solution to Quadratic: $x=\frac{9}{2}\pm\frac{\sqrt{113}}{2}}$

Step-by-step explanation:

$x^2-9x-8=0$

$x^2-9x-8+28.25=0+28.25$ <-- 28.25 is the number you need to add

$x^2-9x+20.25=28.25$

$(x-4.5)^2=28.25$

$x-4.5=\pm\sqrt{28.25}$

$x=4.5\pm\sqrt{28.25}$

$x=\frac{9}{2}\pm\sqrt{\frac{113}{4}}$

$x=\frac{9}{2}\pm\frac{\sqrt{113}}{2}}$

6 0

3 years ago

An auction website charges $1 for a bid. The bidding starts at 1¢ and goes up 1c at a time. A television that is worth

viktelen [127]

The expected value of the outcome of the bid is $0.18

So let's start by counting how many bids are placed up to a total of 160.

100*160 = 16000.

What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)

Your odds of winning are 1/16000 (1 bid out of 16000).

If you win, your profit is 1920 ($2000 minus $80.00).

1920/16000 is $0.12

Your cost to enter the auction is $1, and your average winning offer is $0.12.

The result is $0.18 (0.12-1=-0.88).

Thus the expected value of the outcome of the bid is $0.18

Learn more about expected value here :

brainly.com/question/23509883

#SPJ1

7 0

2 years ago

Find all of the points of the form (x, −x) which are 7 units from the origin.

Morgarella [4.7K]

Answer:

(-7, 0) and (7, 0)

Step-by-step explanation:

All the points that are 7 units from the origin are on the circle:

x² + y² = 7²

The maximum and minimum values of x obtained when y = 0:

x² = 7²
√x² = √7²
x = ± 7

min x = -7 and
max x = 7

The points are:

(-7, 0) and (7, 0)

3 0

3 years ago

Read 2 more answers