Answer:75.7
Step-by-step explanation: If you round the 56.734 you get 56.7, the 15.93 equals 16 the 2.6 rounded equals 3 so if you add them all together you get 75.7
is b intersection c = to b union c
Answer:
no.
Step-by-step explanation:
b ∩ c is the values that appear in both b and c.
b ∪ c is all the values in b and c.
Express the solution of, x^3 + 3x^2 < x + 3, using interval notation.
Answer:
Step-by-step explanation:
x^3+3x^2<x+3
(-∞,-3)∪(-1,1)
Water is poured into a conical paper cup at the rate of 3 cubic centimeters
(cm) per second (s). The paper cup measures 8 cm tall and the top has a
radius of 4 cm.
a.) Use similar triangles to express the radius r in terms of the height h.
Be sure to solve your equation for r.
ANSWER: r =
<
b.) Determine how fast the water level is rising at the instant the water is 4
cm deep.(The volume of a cone is V = r2h.) Be sure to round your
answer to 3 Decimal Places.
ANSWER:
dh
dt
m/s
Answer:
The water level is rising at the rate 0.238 cm per second
Step-by-step explanation:
Let the radius and height of water at time t be r and h respectively.
Height of cup =H= 8 cm
Radius of cup = R = 4 cm
By symmetry
[tex]\frac{r}{h}=\frac{4}{8} \\r=\frac{1}{2}h ---1[/tex]
Volume of water at time t , [tex]V= \frac{1}{3} \pi r^2 h[/tex]
[tex]\frac{dV}{dt}=\frac{1}{3}\pi 2r \frac{dr}{dt} h+\frac{1}{3} \pi r^2 \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{3}\pi r (2 \frac{dr}{dt} h+ r \frac{dh}{dt})[/tex]
With 1
[tex]\frac{dr}{dt}=\frac{1}{2} \frac{dh}{dt}[/tex]
So,
[tex]\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) (2 (\frac{1}{2} \frac{dh}{dt}h)+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( \frac{dh}{dt}h+ r \frac{dh}{dt})\\\frac{dV}{dt}=\frac{1}{3}\pi (\frac{1}{2}h) ( h+\frac{1}{2}h) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi h(\frac{3h}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{6}\pi (\frac{3h^2}{2}) \frac{dh}{dt}\\\frac{dV}{dt}=\frac{1}{12}\pi 3h^2 \frac{dh}{dt}[/tex]
We are given that Water is poured into a conical paper cup at the rate of 3 cubic centimeters (cm) per second (s).
We are supposed to find how fast the water level is rising at the instant the water is 4 cm deep.
So,[tex]\frac{1}{12}\pi 3(4)^2 \frac{dh}{dt}=3\\\frac{dh}{dt}=\frac{3 \times 12}{\pi 3(4)^2 }=0.238[/tex]
Hence the water level is rising at the rate 0.238 cm per second
The radius in terms of height is [tex]\mathbf{r =\frac 12h}[/tex], while the water level increases at 0.239 cm per second when the height is 4 cm
(a) Radius in terms of height
The given parameters are:
[tex]\mathbf{h = 8cm}[/tex] --- height
[tex]\mathbf{r = 4cm}[/tex] --- radius
The above parameters can be written as:
[tex]\mathbf{r :h =4cm : 8cm}[/tex]
[tex]\mathbf{r :h =4 : 8}[/tex]
Express as fractions
[tex]\mathbf{\frac rh =\frac 48}[/tex]
[tex]\mathbf{\frac rh =\frac 12}[/tex]
Multiply both sides by h
[tex]\mathbf{r =\frac 12h}[/tex]
(b) How fast the water is rising
The volume of a cone is:
[tex]\mathbf{V = \frac 13 \pi r^2h}[/tex]
Differentiate with respect to time
[tex]\mathbf{V' = \frac 13 \pi(2rh\ \frac{dr}{dt} + r^2\frac{dh}{dt})}[/tex]
When the water is 4cm deep, then the radius is 2cm using [tex]\mathbf{r =\frac 12h}[/tex]
So, we have:
[tex]\mathbf{V' = \frac 13 \pi(2 \times 2 \times 4\times \frac{dr}{dt} + 2^2\frac{dh}{dt})}[/tex]
[tex]\mathbf{V' = \frac 13 \pi(16 \frac{dr}{dt} + 4\frac{dh}{dt})}[/tex]
Also, we have:
[tex]\mathbf{r =\frac 12h}[/tex]
Differentiate with respect to time
[tex]\mathbf{\frac{dr}{dt} = \frac{1}{2}\frac{dh}{dt}}[/tex]
So, we have:
[tex]\mathbf{V' = \frac 13 \pi(16 \times \frac{1}{2}\frac{dh}{dt} + 4\frac{dh}{dt})}[/tex]
[tex]\mathbf{V' = \frac 13 \pi(8\frac{dh}{dt} + 4\frac{dh}{dt})}[/tex]
[tex]\mathbf{V' = \frac 13 \pi(12\frac{dh}{dt})}[/tex]
Expand
[tex]\mathbf{V' = 4\pi\frac{dh}{dt}}[/tex]
The volume increases at 3 cm^3 per second.
So, we have:
[tex]\mathbf{3 = 4\pi\frac{dh}{dt}}[/tex]
Divide both sides by 4
[tex]\mathbf{0.75 = \pi\frac{dh}{dt}}[/tex]
Divide both sides by pi
[tex]\mathbf{0.239 = \frac{dh}{dt}}[/tex]
Rewrite as:
[tex]\mathbf{\frac{dh}{dt} = 0.239}[/tex]
Hence, the water level increases at 0.239 cm per second when the height is 4 cm
Read more about volumes at:
https://brainly.com/question/1984638
The price of a new car is $42,500. If sales tax is 9%, then how much will you pay in total for the car?
Answer:
$46325 in total for the car
Step-by-step explanation:
grandfathers age is 4 times abduls age. 10 years ago his age was 7 times abduls age. find their present ages
Answer:
20,80
Step-by-step explanation:
[tex]Let\ Abduls\ present\ age\ be\ x\\His\ Grandfather's\ present\ age\ = 4x\\\\Abdul's\ age\ before\ 10\ years=x-10\\His\ Grandfather's\ age\ before\ 10\ years =4x-10\\\\We\ are\ given\ that\ ,\\Abdul's\ Grandfather's\ age\ before\ 10\ years = 7 * Abdul's\ age\ before\ 10\ years\\Hence, \\4x-10=7(x-10)\\4x-10=7x-70\\-10+70=7x-4x\\60=3x\\x=20\\Hence,\\Abduls\ present\ age\ =20\\His\ grandfather's\ present\ age\ = 4*20=80[/tex]
Answer:
Abdul's age=20 y/o
Grandpa's age=80y/o
Step-by-step explanation:
let Abdul's age be 'x'
so, grandpa's age=4x
Grandpa's age 10 yrs ago= 4x-10
according to the question, grandpa's age 1o yrs ago=7(x-10)
so, 4x-10=7(x-10)
4x-10=7x-70
by substituting,
70-10=7x-3x
60=3x
60/3=x
20y/o=x
so, 4x=20*4=80 y/o
6. Find the value of r in the following triangle.
Answer:
Helpppppp
Step-by-step explanation:
Seth has two similar ice cream cones, Cone A and Cone B. The height of Cone A is 16 inches, and the height of Cone B is 4 inches. What is the ratio of the volume of Cone A to the volume of Cone B?
Answer:
64 : 1.
Step-by-step explanation:
Ratio of the volumes is 16^3 to 4^3
= 4096 : 64
= 64 : 1.
What expression is equivalent to (-4y-x)-(3y-9x
Answer:
-7y+8x
Step-by-step explanation:
-7y+8x
Error Analysis A contractor purchases 7 dozen pairs of padded work gloves for $93.24. He incorrectly calculates the unit price as $13.32 per pair for the expense report. What is the correct unit price? What is the error
Answer:
Step-by-step explanation:
i hopes this helps
someone please help me? i’m confused it would be appreciated
Answer:
(1,220,707,125) B
Step-by-step explanation:
In how many ways can the numbers 3,4,5,6,7,8,9, and 10 b
divided into two sets A and B such that the sum of the numbers in B is three times the sum of the numbers in A?
pls help quick! will mark brainliest!
Answer:
4 times
Step-by-step explanation:
Given that the sum of all the numbers => 3+4+5+6+7+8+9+10 = 52
And we are to divide it into two sets such that the sum of set B is three times the number of sum of set A => Sum B = 3 * Sum A
Hence Total sum = Sum B + Sum A
Total sum ÷ 4 = 52 ÷ 4 = 13.
Since Sum B = (3 * Sum A) => (3 * 13 ) = 39
Therefore Sum B = 39 and Sum A = 13
To divide them into two sets
Sum A = (10, 3) = 13: Sum B = ( 4, 5, 6, 7, 8, 9) = 39
Sum A = (9, 4) = 13: Sum B = (3, 5, 6, 7, 8, 10) = 39
Sum A = (8, 5) = 13: Sum B = (3, 4, 6, 7, 9, 10) = 39
Sum A = (7, 6) = 13: Sum B = (3, 4, 5, 8, 9, 10) = 39
Hence, the correct answer is 4 times
please help me with this question
Answer:
the slope is -3, the slope is negative, the y-intercept is 0
Step-by-step explanation:
this ones are the ones that apply to the graph
HELP ill give brailist
Answer:
x = 4.25 (A. 4.25)
Step-by-step explanation:
(For, 4x + 39) 4 times 4.25 = 17, then add 17 + 39, which gets you to 56.
( for 16x - 12) multiply 16 times 4.25 = 68. subtract 12 from 68 to equal 56.
Sushil and Fiona win some money and share it in the ratio 3:4. Sushil gets £39. How much did Fiona get?
Answer:
52
Step-by-step explanation:
Answer:
Step-by-step explanation:
3 / 4 = 39 / x
4*39 = 3*x
x = 42
cos²30° + cos²60° + cos²90° + 2 cos 30° cos 60° cos 90°
Answer:
1
Step-by-step explanation:
[tex]cos²30° + cos²60° + cos²90°\\ + 2 cos 30° cos 60° cos 90° \\ \\ = \bigg( \frac{ \sqrt{3} }{2} \bigg) ^{2} + \bigg( \frac{ 1 }{2} \bigg) ^{2} + \bigg( 0\bigg) ^{2} \\ + 2 \times \frac{ \sqrt{3} }{2} \times \frac{ 1 }{2} \times 0 \\ \\ = \frac{3}{4} + \frac{1}{4} + 0 + 0 \\ \\ = \frac{3 + 1}{4} \\ \\ = \frac{4}{4} \\ \\ = 1[/tex]
A store is having a sale where movies are 40% off their original price. A movie is on sale for $26.00. What was the original price of the movie?
Solve -4.m - 6 + 6-m = -5 + 2m - 1
Answer:
m= 6/7
decimal form m= 0.857
Step-by-step explanation:
hope this helps
Answer:
m=6/7
m=0.857...
Step-by-step explanation:
-4m - 6 + 6-m = -5 + 2m - 1
-5m-6+6=-5+2m-1
-5m=-5+2m-1
-5m=2m-5-1
-5m=2m-6
-5m-2m=2m-6-2m
-7m=-6
divide both sides by -7
x=6/7
NEED HELP FAST MARKING PEOPLE AS BRAINLIST
Answer:
sss
Step-by-step explanation:
since the problem dosent give angles its most likes sss
Answer:
so i cant really see it but it looks as if the two triangles are right angles and are congruent.
Step-by-step explanation:
so i hope this helps a little if so mark as brainleist pls have a nice day
What is the total price of a $60 restaurant tab if you leave a 15% tip?
Answer:
$69 is the total cost of the bill
Step-by-step explanation:
60(1.15)
60 is the cost of the bill, and the 1.15 is the added tax plus the previous $60.
Put 60(1.15) into a calculator and
$69
Find the slope of each line
Answer:
y= -1/2x
Step-by-step explanation:
The cost of 6 books is $20.46. What is the cost of 1 book
Answer:
3.41
Step-by-step explanation:
divided 20.46 by 6
Answer:
$3.41
Step-by-step explanation:
You divided the total cost by number of books.
20.46 divided by 6 = 3.41.
Which expression can be used to check the answer to 56-(-14)=-4?
O-14x-4
O4(-14)
O 56x(-14)
O-4-56
Answer:
B
Step-by-step explanation:
April took out a $600 loan from the bank. At the end of 5 years, she pays back the principal, plus $60 simple interest.
What was the interest rate?
Answer:
April took out a loan of $600 and paid it back with simple interest of $60 after 5 years. The formula to calculate interest is given the principal and the time and the interest rate is . For this problem we have to find the interest rate given . To archive that , we can just solve the equation making the interest rate the subject of the formula as shown below,
The interest rate is or 0.02 as a decimal. The interest rate is 2% as a percentage.
Step-by-step explanation:
Answer:
2%
Step-by-step explanation:
alice arranges 42 blocks in 7 equal rows how many blocks are in each row
I NEED THIS ACAP
Answer:
There are 6 blocks in each row
Step-by-step explanation:
The total number of blocks is 42 and the number of rows is 7. So the equation would be 42 ÷ 7.
So, 42 ÷ 7 = 6. There are 6 blocks in each row.
Hope this Helps!
Total number of row is 6 row.
Given that;
Total number of block = 42 block
Total number i=of block in each row = 7
Find:
Total number of row
Computation:
Total number of row = Total number of block / Total number i=of block in each row
Total number of row = 42 / 7
Total number of row = 6
Learn more:
https://brainly.com/question/12000324?referrer=searchResults
This is trigonometry please answer it :)
I'll give a ♡ if you answer it
Answer:
2(a) 30°
(b) 48,59°
(c) 31,4485°
(d) 33,005565°
question 10 pls help
Answer:
D
Step-by-step explanation:
A bricklayer supports a 5 meter ladder. Against a vertical wall. The foot of ther ladder is 3 meters from the wall. Calculate the heigth at which the top of ladder is
Answer:
4 meters
Step-by-step explanation:
Let the height at which the top of the ladder is be represented by h. The sketch of the question forms a right angled triangle. So that applying the Pythagoras rule,
[tex]/hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]5^{2}[/tex] = [tex]h^{2}[/tex] + [tex]3^{2}[/tex]
25 = [tex]h^{2}[/tex] + 9
[tex]h^{2}[/tex] = 25 - 9
= 16
⇒ h = [tex]\sqrt{16}[/tex]
= 4
Therefore, the height at which the top of ladder is placed is 4 meters.
−2(x + 3 − 4x) = 3x − 18
How many solutions for x does this equation have?
Answer:
3
Step-by-step explanation:
because there are 3 x's
The table and the graph show the height and weight of ten basketball players. Which
statement is true?
Answer: the data point for player G is an outlier.
Step-by-step explanation:
Answer:
The data point for player G is an outlier.
While Brayden is in
training, he has to drink 650
milliliters of water per day.
How many liters of water will
that be for one week?
Answer:
4,550
Step-by-step explanation: 7 x 650 is 4,550
