Answer:
3. [tex]\dfrac{4}{3 \pi}[/tex]
Step-by-step explanation:
Volume of a cone:
[tex]V=\dfrac13\pi r^2h[/tex]
(where r is the radius and h is the height)
Given:
h = 16 cmr = 4 cm[tex]\implies r=\dfrac14h[/tex]
Therefore, substitute [tex]r=\frac14h[/tex] into the volume formula to find the volume of the cone in terms of h:
[tex]\implies V=\dfrac13\pi \left(\dfrac14h\right)^2h[/tex]
[tex]\implies V=\dfrac{1}{48}\pi h^3[/tex]
Differentiate with respect to h:
[tex]\implies \dfrac{dV}{dh}=3 \cdot \dfrac{1}{48} \pi h^2=\dfrac{\pi h^2}{16}[/tex]
Volume is increasing at a constant rate of 3cm/s:
[tex]\implies \dfrac{dV}{dt}=3[/tex]
Use the chain rule to find [tex]\dfrac{dh}{dt}[/tex]
[tex]\implies \dfrac{dh}{dt}=\dfrac{dV}{dt}\times\dfrac{dh}{dV}[/tex]
[tex]\implies \dfrac{dh}{dt}=3\times\dfrac{16}{\pi h^2}[/tex]
[tex]\implies \dfrac{dh}{dt}=\dfrac{48}{\pi h^2}[/tex]
When h = 6:
[tex]\implies \dfrac{dh}{dt}=\dfrac{48}{\pi \cdot 6^2}=\dfrac{4}{3 \pi}[/tex]
a student is running a 3k race he runs 1 km race every 2 minutes select the function that describes his distance from the finish line
Answer:
-1/2 x + 3
Step-by-step explanation:
need help with this asap
Answer:
they are three I will explain
Step-by-step explanation:
x+4/3÷6/x
this 3 expressions are equivalent to the equation above
1. x+4/3{x/6}
2. {x/6}x+4/3
3. x^2 + 4x /18
so SU All wealthy people travel by air. Everyone who does not travel by air travels by road. Therefore, poor people always travel by road. Is the argument valid.
Answer:
no, its not because its showing an ad hominem fallacy.
Step-by-step explanation:
brainliest?
Answer:
wealthy people travel by plane
other people travel by road
poor people travel by road
is the argument valid ANS:no
other people who do not travel on plane travel on car
and people who are poor travel on feet
For each figure, find x. Then find the perimeter.
i need help with 9 and 10
Answer:
Step-by-step explanation:
If a = 9 and b = 4, what is the value of 2a
-b?
Answer:
14
Step-by-step explanation:
2(9)-4=14
help help meeeeeee dont understAND
Answer:
2776 is the surface area.
Step-by-step explanation:
19 x 48 = 912 x 2 = 1824. 7 x 19 = 133 x 2 = 266. 49 x 7 = 343 x 2 = 686.
Answer:
2762
Step-by-step explanation:
The formula is:
2*(width*length+height*lenght+height*width)
2*(19*48+7*48+7*19)
this equals 2762
Dominik uses 20 grams of filling for each dumpling he makes. He has 1500 grams of dumpling filling.
Answer:
Step-by-step explanation:
If you are asking how many dumnplings he can make well this is the answer:
1) 1500÷20= 75
So he can make 75 dumplings
what is the value of (-2)6
with the six as a small number like ³
Answer:
64
Step-by-step explanation:
(-2)^6
6 is an exponent and basically it tells us to multiply the base, -2 by itself 6 times
so (-2)^6 is the same as saying -2 × -2 × -2 × -2 × -2 × -2
-2 × -2 × -2 × -2 × -2 × -2 = 64 so the value of (-2)^6 is 64
If f(x) = 2x² - 4, find (-5) f(x).
A. -5x²-4
B. 2x²-20
C. -7x²-9
D. -10x² +20
Answer:
D
Step-by-step explanation:
(- 5)f(x)
= - 5(2x² - 4) ← multiply terms in parenthesis by - 5
= - 10x² + 20
Please help .!!!!!!!!!
Answer:
-60 = x
Step-by-step explanation:
(-1/4)x - 12 = x + 3
(-1/4)x = x + 15
-0.25x = x + 15
-60 = x
How many quartiles does a data set have?
Answer: Four (4)
Step-by-step explanation:
We have four quartiles. They can be labeled as Q1, Q2, Q3, and Q4. I have attached an example, this comes from mathbitsnotebook.com.
As shown in the example, the quartiles are broken up by the median, and then the median of the medians.
What is the slope of the line shown?
Answer:
slope = 1/2
Step-by-step explanation:
Pick two convenient integer coordinates
I'll use (0,-1) and (2,0)
slope = (y1-y2)/(x1-x2) = (-1-0) / ( 0-2) = 1/2
A right triangle has one angle that measures 48°. What is the measure of the other acute angle?
Answer:
minus 48 to 90 then divide the answer by 2
Answer:
42°
Step-by-step explanation:
The 2 acute angles in a right triangle add up to 90°
90° - 48° = 42°
Hope this helps
help please. this doesn't make sense
Answer:
a = 39.2650873379cm
b = 11.5529459767cm
Step-by-step explanation:
a - Use the area of a triangle equation - 1/2 * a * b * Sin(C)
1/2 * 8 * 10 * Sin(79) = 39.2650873379cm
b - Use the cosine rule - c^2 = a^2 + b^2 - (2 * a * b * Sin(C)
64 + 100 - (2 * 8 * 10 * Cos(79)) = 133.4705607398
c = square root of 6.9396506484 = 11.5529459767cm
Put to however many significant figures / decimal places required.
:)
Pls help quick i need it soon
Answer:
Area = 32m^2q
Step-by-step explanation:
Area = bh
Area = 8mq · 4m
Area = 32m^2q
Please help me with this math problem!! Will give brainliest if correct!! :)
Answer:
2.98
Step-by-step explanation:
Tan(40) = 2.5/x
x = 2.5/Tan(40)
x = 2.98
What is the volume of the figure below, which is composed of two cubes with side lengths of 7 units?
A.
343 cubic units
B.
686 cubic units
C.
490 cubic units
Answer:
B) 686 cubic units
Step-by-step explanation:
If one cube has a side length of 7, then it equals to 343 cubic units. Since there are 2 cubes, this translates to 686 cubic units.
The angle of elevation to a nearby tree from a point on the ground is measured to be 64^{
∘. How tall is the tree if the point on the ground is 49 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary
The height of the tree that forms an angle of 64 degrees and point from the tree is 49 feet is 100.46 ft
The situation forms a right angle triangle.
How to find the sides when given angle of elevationusing trigonometric ratios,
tan 64 = opposite / adjacent
Where
opposite side = height of the treeadjacent side = distance from the point on the ground from the tree.Therefore,
tan 64 = h / 49
cross multiply
h = 49 × tan 64
h = 49 × 2.05030384158
h = 100.464888237
h = 100.46 ft
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Tom pays $528.90 for a computer in a sale. The original price had been reduced by 18%. Calculate the original price of the computer
Answer:
624.102
Step-by-step explanation:
pls give brainliest im new and need points
Pls help i need this so I can pass
Answer:
i cant see the photo, but i would love to help
Step-by-step explanation:
Can someone see if my answers are correct!
Sorry i keep asking questions lol, im just really struggling with math and my teacher wont answer my emails! And my mom doesn't understand any of this even though she's good at math! :(
Answer:
Step-by-step explanation:
The cross sectional area of a basketball would indeed be a circle. The units for surface area would be meters squared. The units meters cubed would be volume. Area is inherently a 2-dimensional problem. Therefore, having 3-dimensional units makes no sense. In your case, the correct answer would be yards squared
-(-4)(-6)-3/5(10+15) divided by 1/3
Answer:
-117
Step-by-step explanation:
-(-4)(-6)-3/5(10+15)
=4(-6)-3/5(25)
=-24- 15
=-39
-39÷1/3
=-117
Which inequality best represents the phrase?
A number less then 0
A. n=0
B. n greater than n 0
C. n greater then n with a underscore on the bottom 0
D. n greater than 0 with a underscore 0
Im not sure what it is but my best bet would be on A because the rest of them all say greater than 0 and you are trying to find the least.
Answer:
n < 0
Step-by-step explanation:
Given that:
A number less than 0
Solve:
Since it saying that A number (n) is less than 0 it means it can't be greater.
From the following answer chioce:
[A] n=0
[B] n greater than n 0
[C] n greater then n with a underscore on the bottom 0
[D] n greater than 0 with a underscore 0
We can see that [B], [C], and [D] all saying greater than. While only [A] has a equal sign to 0.
I'm guess that [A] meant to be put as n < 0. Since the other are saying greater than. But if not. None of the above are correct.
< → less than
> → greater than
A number less than 0 ⇒ n < 0
Kavinsky
PLEASE ANSWER QICKLY AND EXPLAIN
Answer:
A reflection over the x-axis
Step-by-step explanation:
The X-axis is the horizontal line, and if G is the result of F, then figure F going up or down 6 units would make it uneven and it wouldn't look flipped.
Answer:
A, a reflection over the x-axis
Step-by-step explanation:
If you focus on one point of figure G (-5,5) you can apply the reflecting rule over the x-axis (change the y-coordinate's sign and leave the x-coordinate the same) and get the point (-5, -5) which fits the rule.
x^2 - 72 = 6x
how to complete the square?
Answer:
x = 12 and x = -6
Step-by-step explanation:
First subtract 6x on both sides to get a 2nd degree polynomial equal to zero:
[tex]x^2-6x-72=0[/tex]
To complete the square, the formula is to divide 'b' by 2 and square the result. The general form for a 2nd degree polynomial of the variable 'x' is as follows:
[tex]ax^2+bx+c=0[/tex]
For your case, b = 6. Therefore, the term that must be added and subtracted to our equation is:
[tex](6/2)^2=3^2=9[/tex]
Add and subtract 9 to our equation to get:
[tex]x^2-6x+9-9-72=0[/tex]
The first three terms form a perfect square, we have:
[tex](x^2-6x+9)-9-72=0[/tex]
[tex](x^2-6x+9)-81=0[/tex]
What multiplies to equal 9 but adds to equal -6? That would be -3 and -3. Therefore:
[tex](x-3)^2-81=0[/tex]
Add 81 to both sides to get:
[tex](x-3)^2=81[/tex]
We want to take the square root, but recall a square root has a positive and negative branch. Therefore we have two solutions:
[tex]x-3=9[/tex]
[tex]x-3=-9[/tex]
[tex]x=12[/tex]
[tex]x=-6[/tex]
A triangle has sides with lengths of 13ft, 82ft, and 83ft. Is it a right triangle
Answer:
NOT a right triangle
Step-by-step explanation:
IF it is a right triangle, then the Pythagorean theorem would apply
13^2 + 82^2 = 83^2 ?????
169 + 6724 = 6889
6893 = 6889 ? No...it is NOT a right triangle
Form NOON to
1:23 A.M. how much time has passed?
Answer:
13 hours and 23 minutesStep-by-step explanation:
We know that:
⇒ When it is noon, the time is 12:00 pm⇒ When it is midnight, the time is 12:00 amTherefore,
The provided time is 1 hour 23 minutes ahead than 12:00 am. It will also take 12 hours for midnight from noon.Thus, we obtained:
⇒ Passed time: 12 hours + 1 hour + 23 minutes⇒ Passed time: 13 hours + 23 minutes⇒ Passed time: 13 hours and 23 minutesWhat is the value of 4(x−2)(x−3)+7(x−2)(x−5)−6(x−3)(x−5) when x=5? Type the answer in the box below.
Answer:
24
Step-by-step explanation:
when x = 5,
4(5-2)(5-3) + 7(5-2)(5-5) - 6(5-3)(5-5)
= 4(3)(2) + 7(3)(0) - 6(2)(0)
= 24
Paul earns a yearly salary of $29,100. His salary is divided equally into the same amount each month. How much money will Paul earn in January?
Answer:
$2,425 in January
Step-by-step explanation:
$29,100/12 months in a year = $2,425 each month
What is the approximate length of y? round to the nearest tenth of an inch. 1.4 in. 2.0 in. 2.8 in. 3.5 in.
The approximate length of "y" from the given diagram is 2.0inches
Volume of prismsThe formula for calculating the volume of a prism is expressed as:
V = lwh
l is the length
w is the width
h is the height
Given that V =4 cubic inches, hence:
4 = x * x* x
4 = x^3
x = ∛4
x = 1.587
Using the pythagoras theorem;
y^2 =1.587^2 +1.587^2
y^2 = 5.037
y = 2.0in
Hence the approximate length of "y" from the given diagram is 2.0inches
Learn more on volume of prism here: https://brainly.com/question/1331127
Answer: B. 2.0
Step-by-step explanation:
edge 2023