1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lina2011 [118]
3 years ago
8

How do I do question 9 & 11? Please help thank you!

Mathematics
1 answer:
Novay_Z [31]3 years ago
5 0
<h2>9.</h2><h3>Given</h3>
  • sphere with radius 15 cm
<h3>Find</h3>
  • linear approximation to the volume when the radius increases 0.4 cm
<h3>Solution</h3>

The equation for volume of a sphere is

... V = (4/3)π·r³

Differentiating gives

... dV = 4π·r²·dr

Filling in the given numbers gives

... change in volume ≈ 4π·(15 cm)²·(0.4 cm)

... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick

<h2>11.</h2><h3>Given</h3>
  • an x by x by 2x cuboid with surface area 129.6 cm²
  • rate of change of x is 0.01 cm/s
<h3>Find</h3>
  • rate of change of volume
<h3>Solution</h3>

The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².

The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is

... dV/dt = (d/dt)(2x³) = 6x²·dx/dt

We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...

... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)

... dV/dt = 0.7776 cm³/s

You might be interested in
Please help me my life depends on it
sammy [17]

Your answer should be 17 inches.

2.5 + 2.5 = 5 7 + 3 = 10 + 5 + 2 = 17.

I hope this helps answer your question. Have a great day

8 0
3 years ago
Hey there! can you please help me posted picture of question
Fiesta28 [93]
False.
 An exponential growth is a function of the form:
 y = A (b) ^ (k * t)
 Where,
 k> 0
 b> 1
 Because the value of b> 1 means that the function grows.
 Therefore, the answer to the question is false, because if k = 2 but b <1 then the function decreases.
 Answer:
 
False
7 0
3 years ago
Joel earns $1,700 per month. If he spends $425 on rent each month, what percent of his income does he spend on rent?
a_sh-v [17]
The answer is 25%
you take (425/1700)*100
0.25 * 100% = 25%
4 0
3 years ago
It takes a hose 2 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 13 inches tall. How long will it take
nirvana33 [79]
To make it easier, you calculate the volume of the first aquarium.

1st aquarium:
V = L x W x H
V = 8 x 9 x 13
V = 72 x 13
V = 936 in.
Rate: 936 in./2 min.

Now that you've got the volume and rate of the first aquarium, you can find how many inches of the aquarium is filled within a minute, which is also known as the unit rate. To do that, you have to divide both the numerator and denominator by their least common multiple, which is 2. 936 divided by 2 is 468 and 2 divided by 2 is 1.
So the unit rate is 468 in./1 min. Now that you've got the unit rate, you can find out how long it'll take to fill the second aquarium up by finding its volume first.

2nd aquarium:
V = L x W x H
V = 21 x 29 x 30
V = 609 x 30
V 18,270 inches

Calculations:
Now, you divide 18,270 by 468 to find how many minutes it will take to fill up the second aquarium. 18,270 divided by 468 is about 39 (the answer wasn't exact, so I said "about").
 
2nd aquarium's rate:
18,270 in./39 min.

As a result, it'll take about 39 minutes to fill up an aquarium measuring 21 inches by 29 inches by 30 inches using the same hose. I really hope I helped and that you understood my explanation! :) If I didn't, I'm sorry. I tried. :(
7 0
3 years ago
Wich graph is the result of the reflection f(x) =1/4(8)^x across the y axis and then across the x- axis
Snowcat [4.5K]

Answer:

I assume that the function is:

f(x) = \frac{1}{4}*8^x

Now let's describe the general transformations that we need to use in this problem.

Reflection across the x-axis:

For a general function f(x), a reflection across the x-axis is written as:

g(x) = -f(x)

Reflection across the y-axis:

For a general function f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

Then a reflection across the y-axis, and then a reflection across the x-axis is just:

g(x) = -(f(-x)) = -f(-x)

In this case, we have:

f(x) = \frac{1}{4}*8^x

then:

g(x) = -f(-x) =  -\frac{1}{4}*8^{-x}

Now we can graph this, to get the graph you can see below:

6 0
3 years ago
Other questions:
  • Whats the pattern of -128 , 64, -32, 16
    12·1 answer
  • 1. What are the four orders of operations
    12·2 answers
  • Select the equation in point-slope form for the line that passes through the point (1, –1) and has a slope of 4.
    9·1 answer
  • Which matrix Is the product of a 3x3 identity matrix and the scalar 3
    15·1 answer
  • The price of bottles water at the concession stand was doubled. Scott says this is 50% increase, but David says it’s a 100% incr
    6·1 answer
  • Help please will mark brainlest!!
    9·1 answer
  • Is -27 greater than -28
    11·1 answer
  • The bases on a baseball diamond are 90 feet apurt John anding on 2nd base and throws a ball to Sam who is standing exactly halfw
    15·1 answer
  • How many different arrangements are there of the 3 letters chosen from the word combination
    8·1 answer
  • What is x to the nearest tenth? <br><br><br> Show work pls.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!