Answer:
Step-by-step explanation:
if we have 137 students, and out of this number 7 were in cars
137-7=130 students in buses
there are 5 buses
130/5=26
26 students in each bus
The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubic meters per minute. At the instant when the radius of the cone is 99 meters and the volume is 180 cubic meters, what is the rate of change of the height? The volume of a cone can be found with the equation V=\frac{1}{3}\pi r^2 h.V= 3 1 πr 2 h. Round your answer to three decimal places.
Answer:
The rate of change of the height is 0.021 meters per minute
Step-by-step explanation:
From the formula
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
Differentiate the equation with respect to time t, such that
[tex]\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)[/tex]
To differentiate the product,
Let r² = u, so that
[tex]\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)[/tex]
Then, using product rule
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}][/tex]
Since [tex]u = r^{2}[/tex]
Then, [tex]\frac{du}{dr} = 2r[/tex]
Using the Chain's rule
[tex]\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}[/tex]
∴ [tex]\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})][/tex]
Then,
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
Now,
From the question
[tex]\frac{dr}{dt} = 7 m/min[/tex]
[tex]\frac{dV}{dt} = 236 m^{3}/min[/tex]
At the instant when [tex]r = 99 m[/tex]
and [tex]V = 180 m^{3}[/tex]
We will determine the value of h, using
[tex]V = \frac{1}{3}\pi r^{2}h[/tex]
[tex]180 = \frac{1}{3}\pi (99)^{2}h[/tex]
[tex]180 \times 3 = 9801\pi h[/tex]
[tex]h =\frac{540}{9801\pi }[/tex]
[tex]h =\frac{20}{363\pi }[/tex]
Now, Putting the parameters into the equation
[tex]\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}][/tex]
[tex]236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)][/tex]
[tex]236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386][/tex]
[tex]708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}[/tex]
[tex]708 = 30790.75 \frac{dh}{dt} + 76.36[/tex]
[tex]708 - 76.36 = 30790.75\frac{dh}{dt}[/tex]
[tex]631.64 = 30790.75\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}= \frac{631.64}{30790.75}[/tex]
[tex]\frac{dh}{dt} = 0.021 m/min[/tex]
Hence, the rate of change of the height is 0.021 meters per minute.
Does anyone know this because clearly i dont
You need 3 sticks of butter for every 24 cookies. If you have 5 sticks of butter how many cookies is that?
Answer:
5:40
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
:)
stephanie has the same number of dimes and nickels. she has $6.10 in all. what an equation that you could use to find the number of dimes and nickes
How many lines of symmetry are in this snowflake design?
5
BS UDJD9AYW VS DHS EG EE S WCWVW W S FHRD DJE EHVEBE EBE
In the equation
(x-3)2+(y-2)2=16, the center of the circle is...
Answer:
The center circle of this question is (2,3)
I WILL GIVE BRAINLIEST IF SOMEONE GET THIS.......
The ratio of John's earning to Musa's earning is 5:3. If Johns earning increases by 12% his new figure becomes 5,600. Find the corresponding percentage change in musa's earning if the sum of their new earning is 9,800.
Answer:
37.6%
Step-by-step explanation:
You can use find John's original earnings by taking 12% off of 5600. You can do this by doing 0.78 x 5600, and you get 4368.
Now, we can use John's orignal earning to find Musa's original earning. Knowing that their earning's correspond, you can use the proportion 5/3 = 5600/x. You can use cross products to solve:
4368 x 3 = 5x
13104 = 5x
2620.8 = x
Musa's original earnings was 2620.8.
If the sum of their new earnings is 9800, we can take of John's new earnings to find Musa's new earnings. 9800 - 5600= 4200. That means Musa's new earnings were 4200. To find the percentage, we can use the following equation, and then solve:
2620.8 = 4200x
.624 = x
That means that 2620.8 is 62.4% of 4200, and that it increased by 37.6%.
Hope t helps! Have a great day! Sorry it took so long.... I was trying to give a good answer :)need help on worksheet
Answer:
-2, -1, 0, 1, 2
Step-by-step explanation:
PLEASE HELP
due today in 20 minutes
i will mark you brainliest
PLS HELP!!
What values of u and v make triangle XYZ = Triangle GFH
Answers:
u = 18
v = 20
========================================================
Work Shown:
The leg YZ is congruent to the left FH
This means YZ = FH and that leads to u+v-18 = 10u-8v
The hypotenuse ZX is congruent to the hypotenuse HG
This means ZX = HG and we get the equation 14v-14u+32 = v+u+22
----------------------
The system of equations we have so far is
u+v-18 = 10u-8v
14v-14u+32 = v+u+22
Let's get the equations into standard form
Start with the first equation
u+v-18 = 10u-8v
u+v = 10u-8v+18
u+v-10u+8v = 18
-9u+9v = 18
-9(u-v) = 18
u-v = 18/(-9)
u-v = -2
Note how we can solve for the variable u to get
u = v-2
which we'll use later
----------------------
Let's get the other equation into standard form as well
14v-14u+32 = v+u+22
14v-14u-v-u = 22-32
-15u+13v = -10
Now plug in u = v-2 and solve for v
-15u+13v = -10
-15(v-2) + 13v = -10
-15v+30+13v = -10
-2v+30 = -10
-2v = -10-30
-2v = -40
v = -40/(-2)
v = 20
Which means,
u = v-2
u = 20-2
u = 18
the probability of rolling an even number with a six-sided number cube is about 1/2. Choose the likelihood that bests describes the probability of this event.
Answer:
50/50 chance
Step-by-step explanation:
Simple
Answer:
50% chance likely
Step-by-step explanation:
Fill in the symbol to make the inequality match the statements.
There are more people than dogs at the park p____d
There are less cats than people in the house c___p
Answer:
p > d
c < p
Step-by-step explanation:
A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist's estimate? Round the percent to the nearest hundredth if necessary.
Answer:
The percent error of the cyclist's estimate is 5.63%
Step-by-step explanation:
Percentages
The cyclist estimates he will bike 80 miles this week, but he really bikes 75.5 miles.
The error of his estimate in miles can be calculated as the difference between his estimate and the real outcome:
Error = 80 miles - 75.5 miles = 4.5 miles
To calculate the error as a percent, we divide that quantity by the original estimate and multiply by 100%:
Error% = 4.5 / 80 * 100 = 5.625%
Rounding to the nearest hundredth:
The percent error of the cyclist's estimate is 5.63%
PLEASE HELP ASAP!!!!!!!!
A car dealer wants the ratio of 3 trucks to 11 cars on his lot. If he has 87 trucks on his lot, how many cars should he have on his lot?
Answer:
hi
Step-by-step explanation:
hell0
10+(−3.5)×2+(−9)÷(−3)
Answer:
6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
10 + (-3.5) × 2 + (-9) ÷ (-3)
Step 2: Evaluate
Multiply: 10 - 7 + (-9) ÷ (-3)Divide: 10 - 7 + 3Subtract: 3 + 3Add: 6Help pls I’m really stupid
Answer:
8
Step-by-step explanation:
[tex]x - y \\ \\ = 6 - ( - 2) \\ \\ = 6 + 2 \\ \\ = 8[/tex]
You are a genius and not a stupid.
6th Grade Math Homework!
Will give brainiest!
15 Points!!
Please solve
ONLY ANSWER IF YOU HAVE THE ANSWERS
Don't need to explain
Keep in mind there are 2 pictures!
PLEASE HELP!! AND FAST!!
Multiply.
(x−5)(3x+6)
Express the answer in standard form.
Answer:
[tex]3x^{2} -9x-30[/tex]
Step-by-step explanation:
(x - 5)(3x + 6)
[tex]3x^{2} +6x-15x-30\\3x^{2} -9x-30[/tex]
Answer:
3x² - 9x - 30
General Formulas and Concepts:
Algebra I
Expand by FOIL (First Outside Inside Last)Combining Like TermsStep-by-step explanation:
Step 1: Define
(x - 5)(3x + 6)
Step 2: Expand
Expand [FOIL]: 3x² + 6x - 15x - 30Combine like terms: 3x² - 9x - 303 A trainer for a soccer team keeps track of the amount of water players consume during practice. The trainer observes that the average amount of water consumed by the team is a linear function of the temperature. The graph and equation for this function are shown. Choose True or False for each statement. True у 7.8 a. For every degree increase in temperature, the average amount of water consumed increases by 0.0875 gallons. False 7.2 b. When the temperature is below 74 degrees, the team consumes no water. Water (gal) True 6.6 64 False 6.0 0 X True 0 74 76 78 80 82 84 86 88 90 92 94 C. When the temperature is 86 degrees, the team consumes somewhere between 7 gal and 7.2 gal of water. Temperature (°F) False w = 0.0875t – 0.45, where w represents the average amount of water consumed, and t represents the temperature on that day. True d. The amount of water consumed by the team decreases by 0.45 gallons for every degree the temperature falls, False S
Answer:
Step-by-step explanation:
true false true false
Plzzzzzz im not lying i really need help plz y'all
Answer:
8000
Step-by-step explanation:
7-7=0
2-2=0
6-6=0
take the 1 out of 14,000 and add that to the 4 as a ten so you get 14 and than subtract 6 to get 8
What are some basic psychological responses a person could have to the color red?
Answer:
It depends on the person mental state or past. But red often gives the person a sense of danger or fear
Step-by-step explanation:
please please help i’ll give brainliest tysm:))
Answer:
a
Step-by-step explanation:
a
Answer:
I would say between 9 and 13
80% would be about 10 gallons and the remaining 20% would be like 3 gallons making it 13, but I don't think that it could hold more than 13 gallons, making the answer between 9 and 13
Step-by-step explanation:
How do you solve this?
Look at attached file please...I'm really confused!
Answer:
X=18, Y=6
Step by Step Explanation:
This is a little long winded.. Let's solve for Y first.
First looking at the problem, you can note a few things. First of all, there is an Isosceles triangle, and there is an equilateral triangle. Where they connect, there is a 90° angle.
Now, all equilateral triangles have the same angle measurement. 60°. Now, if you look where the right angle is, it is showing a 60° angle, a total of 90°, and an unknown area. So simply subtract. 90-60=30. Divide that by 5, and you have your answer of 6.
Now let's solve X. X is very simple. On an isosceles triangle, the two top sides are the same length. And one of the top sides is the same size as the equilateral triangle. And on equilateral triangles, all sides are the same.
So the 11 transfers over to the X side. So let's make a small equation. 11=X-7. To make it even, let's add 7 to both sides. 11+7=X+7-7. Simplify to get 18=X, which is your answer.
Answer:
X=18 y=6
Step-by-step explanation:
explain and solve
Find the solution(s) for x in the equation below.
x^2 - 25 = 0
A. x = -5
B. no solutions
C. x = 5
D. x = 5; x = -5
Answer:
D) x=5, x=-5.
Step-by-step explanation:
x^2-25=0
factor
(x+5)(x-5)=0
x+5=0, x-5=0,
x=0-5=-5,
x=0+5=5.
Need help with number 8 and 9
Answer:
45° and 12
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
(8)
The polygon has n = 8, that is 8 exterior angles, thus
exterior angle = 360° ÷ 8 = 45°
(9)
The number of sides n is
n = 360 ÷ 30 = 12
Answer:
45° 12 sides
Step-by-step explanation:
1) Every polygons interior angles is equal to 180 times two less than the amount of sides it has (i.e 180•(4-2)=360:quadrilateral) So applying that here we have eight sides so 180(8-2)=1080. Now divide that by 8 to get the measure of one angle and subtract it from 180 to get the exterior angle 45°
2) if the exterior angle is 30° then the interior angle is 150°. For this part i guess and checked but you can refer to the equation above. (180(x-2)=y/150)
PLEASE HELP!! please!!
Answer:
1.a
2.b
3.e
4.f
Step-by-step explanation:
A ball is thrown vertically upward from the top of a 96-ft tower, with an initial velocity of 16 ft/sec. Its position function is s(t) = -16t2 + 16t + 96. What is its velocity in ft/sec when it hits the ground?
Answer:
80 ft/s
Step-by-step explanation:
Given that,
A ball is thrown vertically upward from the top of a 96-ft tower, with an initial velocity of 16 ft/sec. Its position function is given by :
[tex]s(t)=-16t^2 + 16t + 96[/tex] ...(1)
When it hits the ground, s(t) = 0
[tex]-16t^2 + 16t + 96=0\\\\t=3\ s[/tex]
At t = 3 s it will hit the fround.
We need to find its velocity when it hits the ground.
Differentiate equation (1) to find its velocity.
[tex]v=\dfrac{ds(t)}{dt}\\\\v=\dfrac{d(-16t^2 + 16t + 96)}{dt}\\\\v=-32t+16[/tex]...(2)
Put t = 3 in equation (2)
[tex]v=-32(3)+16\\\\v=-80\ ft/s[/tex]
Hence, when it will ground its velocity is 80 ft/s.
To find the quotient 4 divided1/5 multiply 4 by
Answer:
5
Step-by-step explanation:
When dividing numbers by fractions, we can simply multiply the umber by the reciprocal of the decimal. So,
4 ÷ 1/5 = 4 × (reciprocal of 1/5)
A reciprocal of a number is the same number written under 1. aka, 1 divided by that number, which simply is flipping the numerator and denominator of a number.
So the reciprocal of 1/5 is 5/1 = 5.
So 4 ÷ 1/5 = 4 × 5.
So your answer is 5.
hope it was useful!
A triangular entranceway has walls with corner angles of 50°, 70°, and 60°. The designer wants to place a tall bronze sculpture on a round pedestal in a central location equidistant from the three walls. How can the designer find where to place the sculpture?
Answer:
Look for the incenter and place it there.
Step-by-step explanation:
Since there are three angles of 50°, 70° and 60°. If the designer is to place a sculpture on a round central position equidistant from all three walls, then he is looking for the incenter.
The incenter is simply the point where the bisectors of all the three angles intersect. This point is also the center of the largest circle that can be drawn inside the triangle where it touches all three sides of the triangle. Definitely, if the incenter is the middle of the circle that touches all the three sides, then the incenter will be equidistant from the three walls due to the fact that radius will always be the same in a circle.
This is why, he is to look for the incenter.