Answer:
B
Step-by-step explanation:
i did the test
Given f(x)=7x+12 and Domain={3,6,9} find Range
{21,42,63}
{9,6,3}
{33,54,75}
{19,26,33}
Answer:
the answer is the 3rd option
range = { 33, 54, 75 }
The radius of a cone is decreasing at a constant rate of 5 centimeters per minute, and the volume is decreasing at a rate of 148 cubic centimeters per minute. At the instant when the radius of the cone is 222 centimeters and the volume is 21 cubic centimeters, what is the rate of change of the height? The volume of a cone can be found with the equation V=1/3πr^2h. Round your answer to three decimal places.
Answer:
The rate of change for the height of the cone is [tex]-2.849\times 10^{-3}[/tex] centimeters per minute.
Step-by-step explanation:
We derive an expression for the rate of change for the height of the cone by differentiating the volume formula given on statement:
[tex]\dot V = \frac{\pi}{3}\cdot (2\cdot r\cdot h \cdot \dot r + r^{2}\cdot \dot h)[/tex] (1)
Where:
[tex]\dot V[/tex] - Rate of change for the volume of the cone, measured in cubic centimeters per minute.
[tex]r[/tex] - Radius of the cone, measured in centimeters.
[tex]h[/tex] - Height of the cone, measured in centimeters.
[tex]\dot r[/tex] - Rate of change for the radius of the cone, measured in centimeters per minute.
[tex]\dot h[/tex] - Rate of change for the height of the cone, measured in centimeters per minute.
If we know that [tex]\dot V = -148\,\frac{cm^{2}}{min}[/tex], [tex]r = 222\,cm[/tex], [tex]V = 21\,cm^{3}[/tex], [tex]\dot r = -5\,\frac{cm}{min}[/tex], then the rate of change for the height is:
[tex]h = \frac{3\cdot V}{\pi\cdot r^{2}}[/tex] (2)
Where [tex]V[/tex] is the volume of the cone, measured in cubic centimeters.
[tex]h = \frac{3\cdot (21\,cm^{3})}{\pi\cdot (222\,cm)^{2}}[/tex]
[tex]h \approx 4.069\times 10^{-4}\,cm[/tex]
From (1):
[tex]\frac{3\cdot \dot V}{\pi} = 2\cdot r\cdot h\cdot \dot r + r^{2}\cdot \dot h[/tex]
[tex]r^{2}\cdot \dot h = \frac{3\cdot \dot V}{\pi}-2\cdot r\cdot h\cdot \dot r[/tex]
[tex]\dot h = \frac{3\cdot \dot V}{\pi\cdot r^{2}}-\frac{2\cdot h\cdot \dot r}{r}[/tex]
[tex]\dot h = \frac{3\cdot \left(-148\,\frac{cm^{3}}{min} \right)}{\pi\cdot (222\,cm)^{2}} -\frac{2\cdot (4.069\times 10^{-4}\,cm)\cdot \left(-5\,\frac{cm}{min} \right)}{222\,cm}[/tex]
[tex]\dot h = -2.849\times 10^{-3}\,\frac{cm}{min}[/tex]
The rate of change for the height of the cone is [tex]-2.849\times 10^{-3}[/tex] centimeters per minute.
PLEASE HELP ILL GIVE 17 POINTS AND BRAINLIEST
The angle of elevation from a point on level ground to the top of a 50-ft tree is 25". How much closer to the tree does a point on the ground need to be for the measure of the angle of elevation to be twice the measure of the original angle? Round to the nearest tenth
A. 653
B. 778
C. 416
D. 1072
The answer is A
In this problem, we're dealing with tan since we're working with the opposite and adjacent sides.
Remember SOH CAH TOA which means
Sin: Opposite over Hypotenuse,
Cos: Adjacent over Hypotenuse,
and Tan: Opposite over Adjacent
to remember what sin cos and tan means
So to set up a tan equation we have to do
tan(angle) = opposite side length/adjacent side length
The first equation is tan(25) = 50/x
because we have to find the length of the adjacent side so we can find how far away the tree is.
which is about 107.2 ft
The second equation is tan(50) = 50/x
because now we have to find how far away the tree is once the angle of elevation is twice the measure of the original angle (which is 50)
which is about 41.9 ft
After we subtract the two values, you get 65.3 so the answer is A.
I hope this helps!
Two make the angle from the top of the tree to the ground distance should be 41.95 ft.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given, The angle of elevation from a point on level ground to the top of a 50-ft tree is 25".
Since it makes a right-angle triangle with the tree that has a height of 50
Also given, At another angle from the ground that is twice the previous angle calculate the base.
Thus, the new angle will be 50°
thus, the base of the triangle:
Since. tan α = height/ base
in our case, α is 50°
height = 50 ft
tan α = 50 / base
base = 50/tan 50°
Base = 41.95 ft
therefore, Two make the angle from the top of the tree to the ground distance should be 41.95 ft.
Learn more about right-angle triangles here:
https://brainly.com/question/3770177
#SPJ2
A ball is thrown from the top row of seats in a stadium. The function h(t) = - 16t^2 + 80t + 96 gives the height, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?
Answer:
2s or 3s
Step-by-step explanation:
Given the function that models the height of the object as;
h(t) = - 16t^2 + 80t + 96
The ball reaches the ground when h = 0
Substitute
0 = - 16t^2 + 80t + 96
Divide through by -16
0 = t²-5t-6
t²-5t-6 = 0
t²-2t-3t+6 = 0
t(t-2)-3(t-2) = 0
(tt-2)(t-3) = 0
t - 2 = 0 and t-3 = 0
t = 2 and 3s
Hence it will take the ball 2s or 3s to reach the ground
graph the inequality y is less than -2x+4
(i just need the ordered pairs to graph it pls help)
A chef is filling one sink with water, while emptying another. The first sink is empty and is being filled at a rate of 4 gallons per minuet. The second sink is full and is being drained at a rate of 2 gallons per minute. If both sinks hold 24 gallons of water, how many minutes will it take for the two sinks to have the same amount of water?
Solve the triangle with the law of sines
Answer:
see below
Step-by-step explanation:
We can use the law of sines
sin 80 sin B
--------------- = -------------
31 14
Using cross products
14 sin 80 = 31 sin B
14/31 sin 80 = sin B
.984807753 = sin B
Taking the inverse sin of each side
sin ^ -1 ( .444751888) = B
26.41 = B
The sum of the angles of a triangle is 180
A+B+C = 180
80 + 26.41 + C =180
106.41 + C = 180
C = 73.59
We can use the law of sines to find c
sin 80 sin 73.59
--------------- = -------------
31 c
c sin 80 = 31 sin 73.59
c = 31 sin 73.59 / sin 80
c = 30.20
AB = 30.20
data collected showes that the more you water the larger your plant will grow if you use the following equation y=1/2×+2 how tall will a plant be at 25 weeks if x is the number of weeks waterd andby represents rhe height of the plant
SOMEONE PLEASE HELP DONT SKIP NO ONE EVERY HELPS ME AND MY GRADE DEPENDS ON THIS PLSSSSS
Tom is buying topsoil for the flower bed shown below. One bag of topsoil covers 151515 square meters. How many bags of topsoil does Tom need to cover his flower bed?
Answer:
2 bags of topsoil.
Step-by-step explanation:
The attached figure shows a flower bed.
One bag of topsoil covers 15 square meters.
We need to find how many bags of topsoil does Tom need to cover his flower bed.
The area of the flower bed is :
[tex]A=\dfrac{1}{2}\times 12\times 5\\\\=30\ m^2[/tex]
Let he has to cover x bags of topsoil. So,
x = Area of flower bed/Area of 1 bag of top soil
x = 30/15
x = 2
Hence, he will need 2 bags of topsoil to cover his flower bed.
Best answer gets brainliest hurry ASAP
Answer:
its b
Step-by-step explanation:
mark as brainliest plz im right
Answer:
b
Step-by-step explanation:
the ratio answer is b.
Her house is at (−4, 10). Her school is at (−4, 3). The community center is at (2, 3). The grocery store is at (−4, −6). Part A: Use absolute values to calculate the distance in units from Nina's house to her school
Answer:
7 units
Step-by-step explanation:
Given that :
house is at (−4, 10). Her school is at (−4, 3)
House location = (-4, 10)
School location = (-4, 3)
Distance from house to school (d) :
Distance between two points :
x = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
x1 = - 4 ; y1 = 10 ; x2 = - 4 ; y2 = 3
d = sqrt[(-4 - (-4))^2 + (3 - 10)^2]
d = sqrt[(-4 + 4)^2 + (-7)^2]
d = sqrt(0 + (-7)^2)
d = sqrt(49)
d = 7 units
Solve the system by elimination. {2x+y=13x−y=−4 A. (3, 7) B. (2, 6) C. (4, 8) D. no solution
Answer:
A
Step-by-step explanation:
Given the 2 equations
2x + y = 13 → (1)
x - y = - 4 → (2)
Add the 2 equations term by term to eliminate the y- term, that is
3x = 9 ( divide both sides by 3 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
2(3) + y = 13
6 + y = 13 ( subtract 6 from both sides )
y = 7
solution is (3, 7 ) → A
Answer:
Step-by-step explanation:
2x+y=13
x - y =-4 lets add both equations
3x=13-4
x=9/3 , x=3
3-y=-4, y=7
choice A
Simplify 5 to the power of negative 2 over 4 to the power of 6?
Answer:
Step-by-step explanation:
[tex]\frac{5^{-2} }{4^{6} } =\frac{1}{5^{2} 4^{6} }[/tex]
Find the measure of the exterior angle.
A rectangular prism is 12 cm long, 6 cm wideand 5 cm high. What is the volume of the rectangular prism?
Write the equation of a line perpendicular to y =
3
x-3 and whose y-intercept is (0,12).
Answer:
y=-1/3x+12
Step-by-step explanation:
The slope of a line that is perpendicular to another is the negative reciprocal of the first. The slope of the line is 3 so the negative reciprocal will be -1/3.
Using the point-slope formula we can solve for the equation of a line with a slope of -1/3 and a point of (0,12).
The point slope formula is
y-y1=m(x-x1).
y-12=-1/3(x-0) -------------->Distribute: y-12=-1/3x ---------------> Isolate the y by moving the 12 to the other side. y=-1/3x+12
Which of the following number(s) are rational? Select all that apply.
a 2.323232…
b 2.32222…
2.323148…
c -2.3
d Negative 2.ModifyingAbove 3 with bar
Answer:
A B DE on ed 2021
Step-by-step explanation:
Use the distributive property to evaluate the expression
4(9 + 1)
What is the domain of y=sqrtx+7+5
Answer:
c on edge 2020
Step-by-step explanation:
The area of rectangular kitchen tile is 6x^2-8x-30. The width is 2x-6.
A) what is the length of the kitchen tile?
B) Find the perimeter
Answer:
L=6x^2-4x+5
P=12x^2-4x-2
Step-by-step explanation:
A=WL
So, we know the area is 6x^2-8x-30 and the width is 2x-6
Substitute
(6x^2-8x-30)=(2x-6)(L)
L=(6x^2-8x-30)/(2x-6
Divide
L=6x^2-4x+5
P=2L+2W
Substitute
P=2(6x^2-4x+5)+2(2x-6)
P=12×^2-8x+10+4x-12
Simplify
P=12x^2-4x-2
report the following sentence He said to me,"He is a nice fellow." i said to him,"You look sad and tired." she said to me ,"You are a clever person."
she said to them ,"You can pass your exams if you work hard."
sabnam said,"I went to the hospital yesterday."
Arbind said,"I lost my keys in the train yesterday.,:
shilpa said,"I was extremely nervous last week."
Husaain said,"We went to bed early last night."
Rahul said ,"I didn't take a taxi home last night."
Answer:
He told me that he was a nice fellow
I told him that he looked sad and tired
She told me that I was a clever person
She told them that they could pass their exams if they worked hard
Sabnam said that she had gone to the hospital the previous day
Shilpa said that she had been extremely nervous the previous week
Husaain said that they had gone to bed early the previous night
Rahul said that he had not taken a taxi home the previous night
Find the area and perimeter of the shape below. Show your work.
I REALLY NEED HELP!! PLEASE CAN SOMEONE HELP ME?
Answer:
The Super Sleuths did not find all 100 ounces of gold, they only found 92 2/3 ounces, so they have 7 1/3 more ounces of gold to find left.
Step-by-step explanation:
Pirate hid 100 ounces of gold.
1. 19 1/2 ounces of gold was found.
2. 26 2/3 more ounces of gold was found.
3. 5 1/6 more ounces of gold was found.
4. 48 1/3 more ounces of gold was found.
First, we need to add up all of the ounces of gold that was found.
12 1/2 + 26 2/3 = 39 1/6
5 1/6 + 48 1/3 = 53 1/2
53 1/2 + 39 1/6 = 92 2/3
100 - 92 2/3 = 7 1/3
Jordan is makinga garden
with an area of x^2 2+13x+
30 square feet and a length
of x +3 feet. Find an
expression for the width of
Jordan's garden
Answer:
( x + 10 )
Step-by-step explanation:
→ Divide x² + 13x + 30 by x + 3
( x + 3 ) ( x + 10 )
help me please thank you
Answer:
Number 1. Hope you can read that
Step-by-step explanation:
Please help need this fast I’m timed.
-28
-3
3
15
Answer:
-28
Step-by-step explanation:
-28
A school conference room can seat a maximum of 83 people. The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements. If each student must bring a parent with them, what is the maximum number of students that can attend each meeting?
Answer:
40 students
Step-by-step explanation:
We do not count the counselors or the principal because they are not students, so we do 83 - 3 = 80, now it is just simple division, for every student there is a parent, so we divide 80 in half, 80 / 2 = 40 students :D
Write a logarithmic function that represents the following transformations applied to the parent function: Reflection over the y-axis, a vertical stretch by a factor of (5/3) a transformation right 2 units, and a transformation down 6 units.
Answer:
Original function;
y = logbX
Transformation;
y = -5/3logb(x + 2) - 6
Step-by-step explanation:
General form of a logarithmic function is given below;
y = logb X (log to base b)
Reflection over the y-axis
y value remains same, x becomes negative
y = - logb X
Vertical stretch by a factor of 5/3
This means that we multiply the whole function by 5/3
That will be;
y = -5/3logbX
Transformation right 2 units
This means that we add the value of 2 to the x-axis value
y = -5/3logb(x + 2)
transformation down 6 units
This means that we subtract 6 from the total y value
y = -5/3logb(x + 2) - 6
Help me please !!!!!!
Answer:
z = -44
Step-by-step explanation:
3/4 (x - 8) = 4
3(x - 8) = 16
3x - 24 = 16
3x = 40
x = 40/3
4 - 2x = -5x - z
4 = -3x - z
z = -3x - 4
z = -3(40/3) - 4
z = -40 - 4
z = -44
Answer:
Z=-44
Step-by-step explanation:
To figure out z. we have to figure out x first
So
3/4(x-8)=4
x-8=4÷3/4
x-8=4×4/3
x-8=16/3
3x-24=16
3x=16+24
3x=40
x=40/3
Now
4-2(40/3)=-5(40/3)-z
4-80/3=-200/3-z
z-68/3=-200/3
z=-200/3+68/3
z=-44
Ariana has a dimes and y nickels. She has at most 12 coins worth a minimum of
$0.85 combined. Solve this system of inequalities graphically and determine one
possible solution.
9514 1404 393
Answer:
see attached (7 dimes, 5 nickels)
Step-by-step explanation:
The inequalities are plotted in the attachment. The solution shown is ...
(x, y) = (7, 5)
7 dimes and 5 nickels are 12 coins worth $0.90. This is the maximum number of coins, worth more than $0.85.
