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4 years ago

14

Jessica is going to paint her patio. It is a rectangle measuring 7ft x 4ft x 5ft what is the volume, if volume=length x width x

height

1 answer:

Phoenix [80]4 years ago

7 0

7×4= 28

28×5=140 and that's your answer

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A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high

Agata [3.3K]

Answer:

dy/dt = 1.02 m/s

Step-by-step explanation:

First of all, let the distance of the dock above the bow of the boat be represented by x.

Also, let the distance of the boat from the dock be represented by y.

Let z represent the length of the rope.

Now, we can use pythagoras theorem to find a relationship between x, y and z since they form a right angle triangle where the vertical part is the dock, the base represents the water and the hypotenuse represents the rope.

Thus;

x² + y² = z²

Using implicit differentiation, we have;

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

We are given that the dock is 1 meter above the bow. Thus, x = 1

Also, the height is not changing and so dx/dt = 0

We are told the dock is 5 feet away from the boat. Thus, y = 5

dy/dt is is the speed we are looking for which is the rate at which the boat is approaching the dock.

We are not given the value of z but we can find it by using pythagoras theorem since we know the dock is 1 meter above the bow and the boat is 5 m away.

Thus;

z = √(1² + 5²)

z = √26

We are told the rope is being pulled in at the rate of 1 m/s. Thus; dz/dt = 1

Plugging all relevant values into the differentiation equation above gives;

2(1)(0) + 2(5)(dy/dt) = 2(√26)(1)

10(dy/dt) = 2√26

Divide both sides by 10 to get:

dy/dt = (√26)/5

dy/dt = 1.02 m/s

5 0

3 years ago

What is the value of (-0.4)^3

Fittoniya [83]

Answer:

-(2/5)^3 or -8/125 or -0.064

Step-by-step explanation:

convert the decimal into a fraction

then use your calculator to find the exact answer

6 0

3 years ago

Read 2 more answers

M is the midpoint of segment GR. G has coordinates (11,-5) and M is (4,-4) Find the coordinates of R

7nadin3 [17]

Answer:

(3, -3)

Step-by-step explanation:

<u>Given:</u>

G = (11,-5)
M = (4,-4)
R = ?

<u>Solution</u>

R(x, y)

<u>As per midpoint formula;</u>

4 = (11 + x)/2 ⇒ x + 11 = 8 ⇒ x = 3
-4 = (-5 + y)/2 ⇒ y - 5 = -8 ⇒ y = -3
R = (3, -3)

4 0

3 years ago

Tori sells snow cones. His profit in dollars and high temperature in degrees Fahrenheit for two weeks are shown in the table bel

masya89 [10]

Sorry i cant answer if there is no table <3

6 0

3 years ago

If measure of angle 1 = 2x+6 and measure of angle 2 = 8x+4 where angles 1 and 2 are supplementary, then how much is the actual m

nlexa [21]

Answer:

The actual measure of ∠1 = 40°

Step-by-step explanation:

We are given: ∠1 = 2x+6 and ∠2 = 8x+4

and both angles are supplementary. we need to find the actual measure of ∠1

Supplementary angles: If the angles are supplementary their sum is equal to 180°

In our case ∠1 +∠2 = 180°

2x+6+8x+4=180

Solving the equation to find x, then we can find the actual measure of ∠1

$2x+6+8x+4=180\\10x+10=180\\10x=180-10\\10x=170\\x=170/10\\x=17$

So, value of x = 17

Now, finding actual measure of ∠1 by putting x=17 in equation 2x+6

$\angle1=2(17)+6\\\angle1=34+6\\\angle1=40$

So, the actual measure of ∠1 = 40°

8 0

3 years ago