Considering a linear function for the radius, we have that:
The volume of the sphere is modeled by [tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex].After 300 seconds, it is of 775,735 in³.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.What is the volume of a sphere?The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, radius r increases at the rate of 0.03 inches per second and that r=48, hence it is represented by the following linear function:
[tex]r(t) = 0.03t + 48[/tex]
Thus, the volume of the sphere is given by:
[tex]V = \frac{4\pi r(t)^3}{3}[/tex]
[tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex]
After 300 seconds, the volume in cubic inches is given by:
[tex]V(300) = \frac{4\pi(0.03(300) + 48)^3}{3} = 775735[/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
Can someone please help me with this thank you
Answer:
The skeletal system has many functions. Besides giving us our human shape and features, it:
Allows movement: Your skeleton supports your body weight to help you stand and move. Joints, connective tissue and muscles work together to make your body parts mobile.
Produces blood cells: Bones contain bone marrow. Red and white blood cells are produced in the bone marrow.
Protects and supports organs: Your skull shields your brain, your ribs protect your heart and lungs, and your backbone protects your spine.
Stores minerals: Bones hold your body’s supply of minerals like calcium and vitamin D.
Tan^2xsin^2x=tan^2x-sin^2x
Prove identity
Answer:
See below for proof
Step-by-step explanation:
[tex]\tan^2x\sin^2x\\\\(\sec^2x-1)(\sin^2x)\\\\(\frac{1}{\cos^2x}-\frac{\sin^2x}{\sin^2x})(\sin^2x)\\\\(\frac{\sin^2x-\sin^2x\cos^2x}{\sin^2x\cos^2x})(\sin^2x)\\\\\frac{\sin^2x-\sin^2x\cos^2x}{\cos^2x}\\\\\frac{\sin^2x}{\cos^2x}-\sin^2x\\\\\tan^2x-\sin^2x[/tex]
Hence, the identity is proven
Solve for X -3x + -6 = 21
Answer:
x= -13.5
Step-by-step explanation:
X-3x+(-6)=21
-2x-6=21
-2x=27
2x=-27
x=-13.5
How many terms are in the expression? 9a + 6b + 3c + 1 A) 1 B) 2 C) 3 D) 4
Answer:
D.) there is 9a and 6b ,3c and 1 thats four different terms
Step-by-step explanation:
Have a nice day! :D
Cassie has 10 1/2 feet of string to make 15 beaded bracelets. She needs 9 inches of string for each bracelet. Does she have enough string to make all the bracelets? Explain. (1 foot = 12 inches)
Answer:
unfortunately one person will be without a bracelet
Brand 1 Brand 2 Brand 3 Store 1 Store 2 Store 3 Laptop Comparison Chart Criteria for laptop search: Laptop specifications: • At least 3GB of memory • At least 250 GB hard drive • At least 14” Screen • Weigh at most 7 pounds • At least a 1 year manufacturer warranty • Built-in wireless router • Must be new, not used of refurbished Spending Limit: $800 • Includes laptop, sales tax, and shipping • For the purpose of this project, use 7.5% sales tax
The total amount that will be paid for the products with a sales tax of 7.5% will be $1290.
How to compute the amount from the sales tax?Your information isn't complete as the table denoting the appropriate values aren't given.
Let's assume that the price of a product A is given as $800 ane product B is $400. If the sales tax is 7.5%, the total amount that will be paid will be:
= ($800 + $400) + (7.5% × $1200)
= $1200 + $90
= $1290
Learn more about sales tax on:
https://brainly.com/question/9437038
A point located at (1, 8) is reflected over the x-axis. What are the coordinates of the image?
(-1, 8)
(8, 1)
(-1, -8)
(1, -8)
Answer:
(1, -8)
Step-by-step explanation:
In this case, we are reflecting. Since we are reflecting over the x axis, the only thing that will change will be the y.
----------------------------------------------------------------------------------------------------------
The x is staying the same because it is not moving. The y, however, is changing sides.
----------------------------------------------------------------------------------------------------------
Since the y is positive in its original spot, when you reflect over the x axis, you will have a negative y value, which is why it is a -8.
----------------------------------------------------------------------------------------------------------
I hope this helps!
-No one
what is the answer
how do i do it
Answer:
-8.9° C
Step-by-step explanation:
Question:
Doing a scientific experiment the temperature of a container decreased by 35.7° C at a constant rate over 8 1/2 hours.
What value represents the change in the temperature of the container each hour?
Answer:
-8.9° C
Combine like terms:
-3(4x + 3) - (2x - 5) + 6(3x - 4)
Make sure you put your x term first
Due in 6 hours
Answer:
4x - 28
Step-by-step explanation:
[tex]-3(4x + 3) - (2x - 5) + 6(3x - 4)[/tex]
[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a-b\right)=-a+b[/tex]
[tex]-\left(2x-5\right)=-2x+5[/tex]
[tex]=-3\left(4x+3\right)-2x+5+6\left(3x-4\right)[/tex]
[tex]=-12x-9-2x+5+6\left(3x-4\right)[/tex]
[tex]=-12x-9-2x+5+18x-24[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=-12x-2x+18x-9+5-24[/tex]
[tex]\mathrm{Add\:the\:numbers:}\:-9+5-24=-28[/tex]
[tex]=-12x-2x+18x-28[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:-12x-2x+18x=4x[/tex]
[tex]=4x-28[/tex]
~Learn with Lenvy~
1. quadrilateral with 4 right angles
Answer:
Square
Step-by-step explanation:
What is the average rate of change of the function y = 3 cos x on the interval [π/2, π]?
Answer:
¹
Step-by-step explanation:
Average Rate of Change is
ts
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
Here b is pi, a is pi/2,
[tex] \cos(\pi) = - 1[/tex]
[tex] \cos( \frac{\pi}{2} ) = 0[/tex]
So we have
[tex] \frac{ - 1 - 0}{ \frac{\pi}{2} } = \frac{ - 1}{ \frac{\pi}{2} } [/tex]
Answer:
-2/pi
Step-by-step explanation:
Write the recursive definition for the geometric sequence. Then write the exponential equation using regression
-
128,32,8,2
The geometric sequence 128,32,8,2 has a common ratio
The recursive definition of the geometric sequence is [tex]a_n = 4a_{n-1}[/tex] where a1 = 128
How to determine the recursive definition?The geometric sequence is given as:
128,32,8,2
Start by calculating the common ratio (r)
[tex]r = \frac{a_{n}}{a_{n-1}}[/tex]
Substitute 2 for n
[tex]r = \frac{a_2}{a_1}[/tex]
Substitute known values
[tex]r = \frac{128}{32}[/tex]
Evaluate the quotient
[tex]r = 4[/tex]
Substitute 4 for r in [tex]r = \frac{a_{n}}{a_{n-1}}[/tex]
[tex]4 = \frac{a_{n}}{a_{n-1}}[/tex]
Cross multiply
[tex]a_n = 4a_{n-1}[/tex]
Hence, the recursive definition of the geometric sequence is [tex]a_n = 4a_{n-1}[/tex] where a1 = 128
Read more about geometric sequence at:
https://brainly.com/question/24643676
Find the area of the figure
Answer:
88 cm²
Step-by-step explanation:
88 cm² is your answer
The measure of an angle is 107.4 what is the measure of its supplemental angle ?
Answer:
72.6
Step-by-step explanation:
180-107.4 = 72.6
100.2and 19.400 which is greater
Answer:
19.400
Step-by-step explanation:
19.400 equals out to 42769.67886386625
Convert to vertex form: f(x) = x2 + 16x + 64
Answer:
Step-by-step explanation:
hello :
note : the vertex form is :
ax²+bx+c = a(x+(b)/(2a))²- delta/4a² and delta = b²- 4ac
in this exercice you have : a =1 b = 16 and c=64
continu ..........
Is a 779 a good MI score
Answer:
yes
explanation:
Your score falls within the range of scores, from 740 to 799, that is considered Very Good. A 779 FICO Score is above the average credit score. Consumers in this range may qualify for better interest rates from lenders.
What is the area of the figure below?
A. 16
B. 45
C. 51
D. None of these
Answer:
C. 51
Step-by-step explanation:
For Square:
Length x Height
7 x 6 = 42
For Triangle:
Base x Height x 1/2
(6x3)1/2 = 9
42 + 9 = 51
Which of the following describes the solution to a system of linear inequalities?
A. The soultion is the region where both shaded parts overlap.
B. The solution is everything on the shaded graph.
Answer:
A. The solution is the region where both shaded parts overlap.
Step-by-step explanation:
The solution to a system of linear inequalities is the intersection region of the solution of both inequalities. Or you could also say that it's the region where the graphs of the inequalities in the system overlap.
The shaded area represents the solution and where the two inequalities overlap.
train covers 20 km in one hour then how much distance will it cover in 1 min?
[tex]\sf\large\underline{Given:-}[/tex]
Speed of the train = 20km / 1hr.
[tex]\rightarrow[/tex] 1 hour = 60 minutes.
So, speed of the train = 20km/60min.
[tex]\sf\large\underline{To\: Find:-}[/tex]
[tex]\rightarrow[/tex]Distance covered by train in 1min.
[tex]\sf\large\underline{Solution:-}[/tex]
Let the distance covered by train in 1 min be [tex]\sf{x}[/tex] m.
So, if train covers 20 km in 60min then it covers [tex]\sf{x}[/tex] m in 1 min.
It can be written as,
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}}[/tex] [tex]\sf{=\frac{x}{1}}[/tex](by cross multiplication)
[tex]\rightarrow[/tex][tex]\sf{20\: = \: 60x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{20}{60}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{1}{3}= x}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{0.33= x}[/tex](approx)
Therefore, distance covered by train in 1 min= 0.33km (approx).
_______________________________
Hope it helps you:)
Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 'of an inch, it is 4 3/4 'inches.
a) What is the largest the actual height the plant could be?
b) What is the smallest the actual height the plant could be?
c) How large could the percent error in Jada’s measurement be?
Answer:
See below.
Step-by-step explanation:
a) 4 7/8 inches
b) 4 5/8 inches
c) 12.5%
Find the actual area of the triangle below.
Can someone pls help?
Answer:
200 meters2
Step-by-step explanation:
4 * 5 = 20
20 * 20 ÷ 2 = 200
If two chords are the same distance from the center of a circle, then they are ______.
Answer:
1 is the answer to have the distance same
An AC generator produces an alternating current with a peak value of 18 V. The resistance of the lamp is 4 ohms. What is the effective current?
The effective current when an AC peak voltage of 18V is applied to a lamp with 4 ohm resistance is 3.18 A.
What is current?Current is the flow of electrons through a conductor when voltage is applied across the conductor.
Given the peak voltage of 18 V, hence:
[tex]V_{rms}=\frac{Peak\ value}{\sqrt{2} } =\frac{18}{\sqrt{2} } =12.73 V\\\\I_{rms}=\frac{V_{rms}}{resistance } =\frac{12.73}{4 } =3.18 A\\[/tex]
The effective current when an AC peak voltage of 18V is applied to a lamp with 4 ohm resistance is 3.18 A.
Find out more on current at: https://brainly.com/question/24858512
A flag is created by sewing together
Answer:
yes, a flag is created by sewing it together
The mean weight of three people in a lift was 62kg. If two of them weighed 55kg each, how much did the third person weigh?
Answer:
72 kg
Step-by-step explanation:
let weight of third person=x
62-55=x-62
7=x-65
x=7+65=72 kg
The recent price of a car is Rs.10,00,000. If its price reduces by 10% yearly, after how many years it's price will be Rs. 7,29,000? Find it.
Answer:
hope it helps
also do write the givens
B. To make salad dressing for the fruit salad, Mrs. Santos uses 2/4 cup oil, 1 cup orange juice, and 3/4 cup honey. How many cups of salad dressing does this make? Explain how you found your answer.
Answer:
[tex]\sf 2 \frac14 \ cups[/tex]
Step-by-step explanation:
Add the amounts together:
[tex]\sf \implies \dfrac24+1+\dfrac34[/tex]
Convert the whole number 1 into a fraction with denominator 4:
[tex]\sf \implies \dfrac24+\dfrac44+\dfrac34[/tex]
As all the denominators are the same, we can simply add the numerators:
[tex]\sf \implies \dfrac{2+4+3}4[/tex]
[tex]\sf \implies \dfrac94[/tex]
Finally, convert the improper fraction into a mixed number:
[tex]\sf \implies 2 \frac14 \ cups[/tex]
Add all
[tex]\\ \rm\rightarrowtail \dfrac{2}{4}+\dfrac{3}{4}+\dfrac{4}{4}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{2+3+4}{4}[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{9}{4}[/tex]
[tex]\\ \rm\rightarrowtail 2\dfrac{1}{4}cups[/tex]
If 12Kg of chicken feed cost 20 how much would 5kg cost?
and what is the unit rate? ( price per 1 kg)
Step-by-step explanation:
if you 12kg cost 20 what about 5kg that will be 5kg×20÷12kg= 8.33 when you round of to the nearest hundredth this is the price of 5kg
sorry but i dont think i know how to answer the other question i have done what i only know thankyou
Mr. Anderson decides to visit a childhood friend. His car gives him 24.82 miles to the gallon. Mr. Anderson has 4 gallons of fuel. Which of the following is true?
A.
Mr. Anderson can travel 83.28 miles.
B.
Mr. Anderson can travel 49.64 miles.
C.
Mr. Anderson can travel 115.28 miles.
D.
Mr. Anderson can travel 99.28 miles.
Answer:
D. Mr. Anderson can travel 99.28 miles.
Step-by-step explanation:
If Mr. Anderson has 4 gallons and each gallon moves him 24.82 miles you can multiply the number of miles per gallon by the gallon resulting in an equation that looks like 4*24.82=99.28.