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3 years ago

If x^2 + xy = 20 and dx/dt = -4 when x = -5 and y = 1, what is dy/dt

Mathematics

1 answer:

SpyIntel [72]3 years ago

7 0

Answer:

3.2

Step-by-step explanation:

x² + xy = 20

Take the derivative with respect to time:

2x dx/dt + x dy/dt + y dx/dt = 20

(2x + y) dx/dt + x dy/dt = 20

Given x = -5, y = 1, and dx/dt = -4:

(2(-5) + 1) (-4) + (-5) dy/dt = 20

(-10 + 1) (-4) − 5 dy/dt = 20

36 − 5 dy/dt = 20

5 dy/dt = 16

dy/dt = 3.2

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The bricks are built to form a garden. The perimeter of the outer square is 264 centimeters. The area of the inner square is 900

zhenek [66]

Answer:

Length: 124.7875 cm

Width: 7.2125 cm

Step-by-step explanation:

The perimeter of this area can be calculated as:

P = 2L + 2W

Where P is the perimeter, L is the length and W is the width

If the perimeter is 264 centimeters, we have that:

2L + 2W = 264

L + W = 132

The area can be calculated as:

A = L*W

Where A is the area.

If the area is 900 cm2, we have that:

L*W = 900

From the first equation, we have that L = 132 - W

Using this value in the area equation, we have:

(132-W)*W = 900

132W - W2 = 900

W2 - 132W + 900 = 0

delta = b2 - 4ac = 17424 - 3600 = 13824

sqrt(delta) = 117.575

W1 = (132 + 117.575) / 2 = 124.7875 cm

W2 = (132 - 117.575) / 2 = 7.2125 cm

Using the smaller value for W, the length will be:

L + 7.2125 = 132

L = 124.7875 cm

4 0

3 years ago

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Pedro can drive 2 times as fast as Pablo can ride his bicycle. If it takes Pablo 2 hours longer than Pedro to travel 72 miles, h

galben [10]

Pablo can ride his bicycle with speed of 18 miles per hour

Solution:

Given, Pedro can drive 2 times as fast as Pablo can ride his bicycle.

Let the speed of Pablo be "n" miles per hour

Then the speed of the Pedro will be "2n" miles per hour

Now, If it takes Pablo 2 hours longer than Pedro to travel 72 miles,

We have to find how fast can Pablo ride his bicycle?

The formula for speed is given as:

$\text { distance }=\text { speed } \times \text { time }$

Let the time taken by Pedro to travel 72 miles be "t" hours, then time taken by Pablo will be "t + 2" hours

In case of Pablo:

$\begin{array}{l}{72 \text { miles }=\text { speed } \times (t+2) \text { hour }} \\ {\rightarrow 72=n \times(t+2) \rightarrow(1)}\end{array}$

In case of Pedro:

$\begin{array}{l}{72 \text { miles }=\text { speed } \times \text { thours }} \\ {\rightarrow 72=2 n \times t \rightarrow(2)}\end{array}$

Then, equate both (1) and (2)

$\begin{array}{l}{n \times(t+2)=2 n \times t} \\\\ {\rightarrow t+2=2 \times t} \\\\ {\rightarrow t+2=2 t} \\\\ {\rightarrow 2 t-t=2} \\\\ {\rightarrow t=2}\end{array}$

Now, substitute t = 2 in (2)

$\begin{array}{l}{\rightarrow 72=2 n \times 2} \\\\ {\rightarrow 72=4 n} \\\\ {\rightarrow n=18}\end{array}$

Hence, the speed of Pablo is 18 miles per hour.

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3 years ago

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borishaifa [10]

X to the power of two+81

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3 years ago

In the monthly payment formula M=Pr(1+r)n/(1+r)n-1, for r if the interest rate is 6.9%

Elden [556K]

Answer:

0.00525

Step-by-step explanation:

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3 years ago

45 POINTS AND BRANLIEST!!!

Marysya12 [62]

PART A:

The x-intercept at 0 shows the location where the ball was kicked. The x-intercept at x = 16 shows the location where the ball hit the ground.

The maximum value represents the highest point of the ball.

The interval where the function is increasing is 0<x<8. Between this interval, the height of the ball measured from the ground is increasing.
The interval where the function is decreasing is 0<x<16. Between this interval, the height of the ball is decreasing.

PART B:

Reading from the graph

When x = 8, y = 10 ⇒ let this be x₁ = 8 and y₁ = 10
When x = 13, y = 6 ⇒ let this be x₂ = 13 and y₂ = 6

The rate of change = (y₂-y₁) / (x₂-x₁)
The rate of change = (6 - 10) / (13 - 8)
The rate of change = -4 / 5 = -(4/5)

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3 years ago

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