If a lead puck has a diameter of 7.5 cm and height of 2.3 cm and is floating in the mercury then the bottom of the lead puck is 1.9 cm below the mercury surface.
In order to solve this problem, we will make use of Archimedes’ principle. Archimedes’ principle states that the buoyant force on an object equals the weight of the fluid displaced by the object.
Let the bottom of the lead puck is d meter below the mercury surface.
So, the volume of the mercury displaced by the lead puck is equal to the volume of the puck under the mercury:
V(mercury displaced) = V(puck) = πr²d,
where r = 0.075 m (diameter = 7.5 cm)
V(mercury displaced) = π(0.075 m)²d,
We also know that the density of mercury is 13,600 kg/m³ and the density of lead is 11,300 kg/m³.
Mass of mercury displaces = Volume × density = π(0.075 m)²d × 13600
Mass of the lead puck = π(0.075 m)²×0.023 × 11,300
At equilibrium weight of the mercury displaces will be equal to the weight of the lead puck.
π(0.075 m)²d × 13600 × g = π(0.075 m)²×0.023 × 11,300 × g
d = (0.023 × 11,300)/13600
d = 0.019 m
d = 1.9 cm
Therefore, the bottom of the lead puck is 1.9 cm below the surface of the mercury.
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help i dont understand how to do this the question is "Put your answer in decimal form."
Answer:
x = 2.5
Step-by-step explanation:
Hypotenuse ² = opposite ² + adjacent ²
(x + 4)² = x² + 6²
x² + 8x + 16 = x ² + 6²
x² + 8x + 16 - x² = 6²
8x + 16 = 36
8x = 36 - 16
8x = 20
x = 20/8
x = 2.5
answer?answer?answer?answer?answer?answer?answer?
Answer:
y=6/2x-6
y=3x-6
Step-by-step explanation:
what kind of number is e?
a.) integer
b.) rational
c.) natural
d.) irrational
Answer:
c.natural
Step-by-step explanation:
The number e , sometimes called the natural number, or Euler's number, is an important mathematical constant approximately equal to 2.71828.
Help me please I am a idiot who doesn’t get math
To calculate the cuboid's volume, use height×width×length which is 11×11×16
For the cylinder's volume, use πr²h. in this case, it is 3.14×4²×9
Add up the two answers you get and that's the solution
math help me pls now now
Answer:
14/1
Step-by-step explanation:
16/3 –5/4
(16*4–5*3)/12
49/12
1 4/1
Answer: 4 1/12
Step-by-step explanation:
Hope this helps!
Write a similarly comparing the three triangles in the diagram
Answer:
ΔBCE similar to ΔECD similar toΔBED
Step-by-step explanation:
ΔBCE similar to ΔECD similar toΔBED
Please help me! 20 points!
Enter your answer and show all the steps that you use to solve this problem in the space provided.
simplify
(in attachment)
Answer:
12 1/4 or (Decimal: 12.25)
Step-by-step explanation:
(3 1/2) (3 1/2)
= 7/2 (3 1/2)
= 7/2 (7/2)
= 49/4
= 12 1/4
I hope I helped you!!
Step-by-step explanation:
When we multiplying, we find the sum of the exponents so
[tex]3 {}^{ \frac{1}{2} } \times 3 {}^{ \frac{1}{2} } \\ {3}^{ \frac{1}{2} + \frac{1}{2} } \\ = {3}^{ \frac{2}{2} } \\ = 3[/tex]
A cell phone costs $750 and loses 28% of its value each year. Write an exponential decay function to represent this situation.
1. f(x)= 750 • 0.72^x
2. f(x)= 0.72 • 750^x
3. f(x)= 750 • 0.28^x
4. f(x)= 0.28 • 750^x
Answer:
1. [tex]f(x) = 750\cdot 0.72^{x}[/tex]
Step-by-step explanation:
The cell phone experiments an exponential depreciation, which is defined by the following formula:
[tex]f(x) = C_{o}\cdot (1-r)^{x}[/tex], for [tex]0<r< 1[/tex]. (1)
Where:
[tex]C_{o}[/tex] - Initial cost, measured in monetary units.
[tex]r[/tex] - Depreciation rate, no unit.
[tex]x[/tex] - Time, measured in years.
[tex]f(x)[/tex] - Current value of the cell phone, measured in monetary units.
If we know that [tex]C_{o} = \$\,750[/tex] and [tex]r = 0.28[/tex], then the exponential decay function that represents the situation is:
[tex]f(x) = 750\cdot 0.72^{x}[/tex]
Which means that correct answer is 1.
the question is: The endpoints of ST are S(2,-2) and T(4,2) what are the coordinates of midpoint of ST?
Answer:
(3,0)
Step-by-step explanation:
If you use a graphing calculator and connect the two points then you would get (3,0) :))
Which statement(s) about the line
below are true? Select all that apply.
A The x-intercept is -8.
B The line has a positive slope.
C The y-intercept is 4.
D The line has a negative slope.
Answer: A, B, and C.
Step-by-step explanation: The answers you have selected in the picture are correct.
These are the actual claims made regarding the line:
The x-intercept is at - 8 because y = 0 when x = -8.
The line is growing and has a positive slope.
As soon as x = 0 and y = 4, the y-intercept is at 4.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The true statements about the line are,
The x-intercept is at - 8, as when x = - 8 y = 0.
The line has a positive slope as it is increasing.
The y-intercept is at 4 as when x = 0 y = 4.
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Model the unknown number problem by writing an
algebraic expression. Then complete the statements.
Juan doubled his workout time.
Replace the words 'workout time" with.
The word "doubled" means
The correct algebraic expression is
Answer:
Model the unknown number problem by writing an algebraic expression. Then complete the statements.
Juan doubled his workout time.
Replace the words “workout time” with.
✔ the variable w
.
The word “doubled” means
✔ multiplied by 2
.
The correct algebraic expression is
✔ 2w
.
Step-by-step explanation:
Answer:
Model the unknown number problem by writing an algebraic expression. Then complete the statements.
Juan doubled his workout time.
Replace the words “workout time” with.
✔ the variable w
The word “doubled” means
✔ multiplied by 2
The correct algebraic expression is
✔ 2w
Step-by-step explanation:
help me plz !!!!!!!!!!
Step-by-step explanation:
Since y = x + 3
Substitute the value of y for each one into the equation
1. y = 4
4 = x + 3
4 - 3 = x
x = 1
2. y = 8
8 = x + 3
8 - 3 = x
x = 5
3. y = 5
5 = x + 3
5 - 3 = x
x = 5
Hope you got it
Steve studies math for 7/8 of an hour and history for 2/3 of an hour. How many hours did he study?
Answer:
The answer is 1 13/24 hours or 1 hour, 32.5 minutes
Step-by-step explanation:
Find a common multiple of the denominators 3 and 8, which would be 24. Convert the fractions:
7/8 x 3/3 = 21/24.
2/3 x 8/8 = 16/24
Add the two numerators = 37/24 or 1 13/24.
1/24 of an hour is 2.5 minutes, so 13/24 is 32.5 minutes.
The answer is 1 13/24 hours or 1 hour, 32.5 minutes
Each pair of polygons is similar. Find each missing side measure. two polygons 12 on top 5 on bottom second polygon 48 on top x on bottom
Answer:
[tex]x = 20[/tex]
Step-by-step explanation:
Given
First Polygon:
[tex]Top = 12[/tex]
[tex]Bottom =5[/tex]
Second Polygon
[tex]Top = 48[/tex]
[tex]Bottom =x[/tex]
Required
Find x
Since both polygons are similar, then:
[tex]Ratio = Top:Bottom[/tex]
For the first:
[tex]Ratio = 12:5[/tex]
For the second
[tex]Ratio = 48:x[/tex]
Equate both ratios
[tex]12:5 = 48:x[/tex]
Express as fraction
[tex]\frac{12}{5} = \frac{48}{x}[/tex]
Cross Multiply
[tex]12 * x = 48 * 5[/tex]
Solve for x
[tex]x = \frac{48 * 5}{12}[/tex]
[tex]x = \frac{240}{12}[/tex]
[tex]x = 20[/tex]
What is the solution of the system of equations? Enter the solution as an ordered pair (use decimal rounded to the nearest hundredth if necessary)
=32+54−2+8=−25
The Milgram Family drove 440 miles on 20 gallons of gas. At this rate, how many miles can they drive on 25 gallons of gas? *
Answer:550
Step-by-step explanation: first you need to find the unit rate ( or how many miles per gallon) by dividing 440 by 20 which would get 22, then you would take that and multiply it by 25 to get 550. Hope this helps!
A scale model of a house is 1/10 the size of the actual house. One of the bedrooms in the house is 16 feet long. Which expression will help you find the length of the same bedroom in the model?
yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees
Select the three inequalities that have n = 3 in the solution set
A. n + 5 < 9
B. 13 n < 1
C. 3n + 1 >7
D. 3n > 9.5
E. n-2<5
Answer:
Its just E
I'm sorry if I'm wrong
Answer: A, C, E
Solve for all the inequalitites.
n + 5 < 9
n < 9 - 5
n < 4
∴ n = 3 is a part of the solution set.
13n < 1
n < 1/13
∴ This definitely doesn't include n = 3.
3n + 1 > 7
3n > 6
n > 2
∴ n = 3 is part of the solution because n is larger than 2.
3n > 9.5
n > 9.5 ÷ 3
n > 3.16666666
∴ n = 3 is not part of the solution set.
n - 2 < 5
n < 5 + 2
n < 7
∴ n = 3 is a part of the solution set.
PLEASE HELPP!!!!
ive been stuck on this for 3 days i feel clueless
Answer:
C.
Step-by-step explanation:
I think im right!
Hopefully it helps!
Answer:
the answer is letter C I'm sure
Solve the system of linear equations by elimination x + 2y = 13 --x+y=5
Answer:
{x,y} = {1,6} Have a great day
Answer: welp its already answred
Step-by-step explanation:
In class 10 out of 25 students ride the bus.what percent of students ride the bus?
Answer:
40%
Step-by-step explanation:
it's easiest to get a percentage from 100, multiplying 25 by 4 gives you 100 so if you do that then multiply 10 by four to make the equation even that will give you the answer
what is 3/7 as decimal
Answer:
0.428571429
Step-by-step explanation:
Which shows the numbers ordered from least to greatest? 9.129, 9.37, 9.3, 9.219
Answer:
9.129 then , 9.219 then , 9.3 then , 9.37
Step-by-step explanation:
h(x)=2x-4
g(x) = x² - 2
Find (h•g)(x)
Answer:
2x² - 8
Step-by-step explanation:
What is the value of x
Answer:
x=12the opposite side of parallelogram are equal
Answer:
8
Step-by-step explanation:
Since, intercepts made by parallel lines on transversals are in proportion.
Therefore,
[tex] \frac{x}{24} = \frac{12}{36} \\ \\ \frac{x}{24} = \frac{1}{3} \\ \\ x = \frac{24}{3} \\ \\ x = 8[/tex]
Write each ratio in three different ways based on the table. Party Mix Makes 8 Cups 3 cups pretzels 3 cups bagel chips 1 cup cheese crackers 1 cup peanuts
which of the given values will make the inequality n-93>175 true?
n=82
n=105
n=268
n=300
n=312
Answer:
n = 300 and n = 312
Step-by-step explanation:
n - 93 > 175
n > 175 + 93
n > 268
Therefore only the two last answers are are possible n values (n has to be more than 268, not equal)
The two numbers 300 and 312 will make the inequality n-93>175 true which are correct option (D)300 and (E)312.
What is inequality?Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
Given inequality as:
n - 93 > 175
n > 175 + 93
n > 268
Therefore, n must be greater than 268 and not equal.
Hence, the two numbers 300 and 312 will make the inequality n-93>175 true.
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the sum of the three terms consecutive terms of an ap is -6 and the product is 64, find the terms. using a, a + d, a + 2d
Answer:
-8, -2 and 4
Step-by-step explanation:
Let the terms of the AP be a-d, a and a+d
If the sum is 6, then;
a-d+a+a+d = -6
3a = -6
a = -6/3
a = -2
Hence the first term is 6
If the product is 64
(a-d)(a)(a+d) = 64
-2(a²-d²) = 64
-2(4-d²) = 64
4-d² = -64/2
4-d² = -32
-d² = -32-4
-d² = -36
d² = 36
d = 6 or -6
The first term is a-d = -2-6 = -8
second term is a = -2
third term is a+d = -2+6 = 4
Hence the required AP is -8, -2 and 4
Complete the sentence.
Answer:
50 more
Step-by-step explanation:
Answer:
50 more than............
A lumberjack needs to climb a tree to place a satellite tower in the tree top in the woods. The satellite signal needs to reach a horizontal distance of 3500 meters along the ground. If the angle of elevation from the farthest distance along the ground that the satellite reaches to the satellite in the tree is 18 degrees, what is the radius of the satellite signal? Round your answer to the nearest meter.
Radius of the satellite signal = meters
Answer: I use clickcaculators.com ;)
Step-by-step explanation: