Using implicit differentiation, it is found that the rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that [tex]\frac{dr}{dt} = 0.5, r = 17[/tex], thus:
[tex]\frac{dV}{dt} = 4\pi (17)^2(0.5) = 1815.84[/tex]
The rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.
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Answer:
So the answer would be (A.
Step-by-step explanation:
Make y the subject of this equation:
P-3=qy
Answer: (P - 3)/q = y
Solve the equation, y = 7x + 10, using the x-values, 3, 5, and 8.
Which of the following T-tables represents the ordered pairs?
Please help !!
Answer:
y=7%283%29%2B10
y=21%2B10
y=31
(3,31)
Step-by-step explanation:
Answer:
the answer is A
Step-by-step explanation:
What is the value of 5+6−32(8÷14)?
Answer:
-7.3
Step-by-step explanation:
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Answer:
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Answer:
I'll answer 6 to 10 cuz that's only what I'm able to see
Step-by-step explanation:
6.
Y-Z
= {6,4,7,2,8,3} - {2,7,8,9,10}
= {6,4,3}
7.
( Y ∪ Z ) ∩ X
= ( {6,4,7,2,8,3} ∪ {2,7,8,9,10} ) ∩ {1, 2,3,5,8}
= { 2,3,4,6,7,8,9,10} ∩ {1, 2,3,5,8}
= {2,3,5,8}
8.
( X ∪ Y ) ∩ ( Y ∪ Z )
= ( {1, 2,3,5,8} ∪ {6,4,7,2,8,3} ) ∩ ( {6,4,7,2,8,3} ∪ {2,7,8,9,10} )
= {1,2,3,4,5,6,7,8} ∩ {2,3,4,6,7,8,9,10}
= {2,3,4,6,7,8}
9.
( X ∩ Z ) ∪ ( X ∩ Y )
= ( {1,2,3,5,8} ∩ {2,7,8,9,10} ) ∪ ( {1,2,3,5,8} ∩ {6,4,7,2,8,3} )
= {2,8} ∪ {3,8}
= {2,3,8}
10.
( X ∪ Y ) ∩ Z
= ( {1,2,3,5,8} ∪ {6,4,7,2,8,3} ) ∩ {2,7,8,9,10}
= {1,2,3,4,5,6,7,8} ∩ {2,7,8,9,10}
= {2,7,8}
What's the answer guys?
Answer: 14.4p - 2.2q + 4.3r
Step-by-step explanation:
(8.8p + 5.6p) + (6.2q - 8.4q) + (-1.8r + 6.1r)
= 14.4p - 2.2q + 4.3r
please give me a brainliest answer
how do i write 5z in expanded notation
how do you do this, thanks for helping
Answer:
A: (-7, -4)
B: (-3, 8)
Step-by-step explanation:
Ordered pairs are (x,y).
Count the lines and see:
A is 7 to the left and 4 down so (-7, -4)
B is 3 to the left and 8 up so (-3, 8)
REMEMBER X IS ALWAYS FIRST!!
Does this answer make sense? YES! Because quadrant II all the pairs will be (-#, #) and in quadrant III the pairs will be (-#, -#)
Hope that helps!
Solve for x.
(x÷2)+6=50
x = 22
x = 28
x = 38
x = 88
The answer is x = 88
The points (18,21) and (42,49) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
Answer: 5/2
Step-by-step explanation: 49 - 42/ 21 - 18
Does the graph represent a function? Why or why not?
Answer:
The vertical line test can be used to determine whether a graph represents a function. ... If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.
Step-by-step explanation:
Can i get braineist pls
Martin finds a shirt on sale
If an area of a circle is 65.71cm*2 what is the radius? Round the answer to 2DP.
Answer:
4.57
Step-by-step explanation:
square root of 65.71 divided by pie
help is very much needed
Answer:
IT'S NEGATIVE 3. HOPE THIS HELPS...
What are the differences and similarities between the the graphs and equations of circles and ellipses?
-x^4+2x^3+8x=0. solve by factoring
2.93114246
Step-by-step explanation:
what is the ratio of 22 and 8
Which inequality best represents that icecream at -3⁰C is cooler than icecream at 1⁰C?
Answer:
Ice cream at -3 c is cooler than 1 C therefore since you are looking to know which one is cooler > would be the best option.
Step-by-step explanation:
Have a wonderful day!
Find the 11" term of the following geometric sequence.
5, 15, 45, 135, ...
Clay gave four friends seven ball cards
each. How many cards did he give to his
friends?
solve please :3 will mark brainliest !!
__________
[tex] \: [/tex]
6f = $15
8f = $20
10f = ?
Soo :
2f = 5
f = 2,5
10f = 10(2,5) = $25✔
The cost of the wire of the third length in the table is, 25 dollars
We have to give that,
The cost of a certain type of wire varies directly with its length.
Now, From the table the equation between cost and length is,
y - 15 = (20 - 15)/(8 - 6) (x - 6)
y - 15 = (5/2) (x - 6)
y - 15 = 2.5x - 15
y = 2.5x
Where y represents the cost and x represent the length.
Hence, At x = 10 feet
y = 2.5 (10)
y = 25 dollars
So, The cost of the wire is, 25 dollars
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Multiply and simplify
Answer and explanation:
1. 2 × 3/10 = 6/10 = 3/5
2. 8 × 4/8 = 32/8 = 4
3. 9 × 3/9 = 27/9 = 3
4. 12 × 2/11 = 24/11 = 2 2/11
5. 3 × 5/7 = 15/7 = 2 1/7
6. 2 × 3/5 = 6/5 = 1 1/5
7. 11 × 4/8 = 44/8 = 5 4/8 = 5 1/2
8. 10 × 1/4 = 10/4 = 2 2/4 = 2 1/2
9. 5 × 1/4 = 5/4 = 1 1/4
10. 11 × 2/7 = 22/7 = 3 1/7
Hope this helps!
Find the missing angle measures.
What is m∠2?
a 40
b 60
c 50
d 100
Jon is 3 years younger than Laura. The product of their ages is 1,330. If j represents Jon’s age and represents Laura’s age, what value of j could be Jon’s age?
Answer:
35
Step-by-step explanation:
The factors chosen are 35 and 38 which multiplied = 1330(the product) Laura is 3 years older than jon so she is 38 and Jon is 35.
Marc solves the equation Latex: (\sqrt[4]{x})^3=5\textsf{.} His work is shown below. Step 1: Latex: (\sqrt[4]{x})^3=5 ( √ [ 4 ] x ) 3 = 5 Step 2: Latex: x^{\frac{3}{4} }=5 x 3 4 = 5 Step 3: Latex: x^{\frac{3}{4} \cdot \frac{4}{3} }=5^{\frac{4}{3} } x 3 4 ⋅ 4 3 = 5 4 3 Step 4: Latex: x=\sqrt[3]{5 \cdot 5 \cdot 5 \cdot 5} x = √ [ 3 ] 5 ⋅ 5 ⋅ 5 ⋅ 5 Step 5: Latex: x=5\sqrt[3]{\not{5} \cdot \not{5} \cdot\not {5} \cdot 5} x = 5 √ [ 3 ] ¬ 5 ⋅ ¬ 5 ⋅ ¬ 5 ⋅ 5 Step 6: Latex: x=5\sqrt[3]{5} x = 5 √ [ 3 ] 5 Explain what Marc did in steps 4 and 5. Why did he do this? Create your own radical equation and explain how to solve it. Is there an extraneous solution to your equation?
Based on the calculation, we can say that there is an extraneous solution to the equation
Given the equation solved by Marc expressed as:
[tex](\sqrt[4]{x})^3=5[/tex]
We are to check if the indices equation has an extraneous equation.
According to the law of indices [tex](\sqrt[n]{m} )^a=m^{\frac{a}{n} }[/tex], the expression becomes:
[tex](\sqrt[4]{x})^3=5\\x^\frac{3}{4}=5\\[/tex]
Raise both sides to the power of 4/3 as shown:
[tex](x^\frac{3}{4} )^\frac{4}{3} = 5^\frac{4}{3}\\x^1 = 5^\frac{4}{3}\\x = 5^\frac{4}{3}\\[/tex]
This shows that there is an extraneous solution to the equation
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A square has a area of 121 square centimeters. what is the length of each side
Your classmate says the triangles below are not congruent by SSS. She explains that congruent sides do not correspond explain the error in her reasoning.
Congruent triangles are triangles with equal corresponding sides.
The triangles are congruent
From the question (see attachment), we have the following observations.
Two corresponding sides are marked with ITwo corresponding sides are marked with IITwo corresponding sides are marked with IIIThe above highlights mean that:
The corresponding sides are congruent by SSS theorem
Hence, your classmate's claim is incorrect.
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The period of the function, y=cos(4x)is how many degrees?
The table shows a set of values for x and y
a) Assume y = [tex]x^{2}[/tex]
[tex]1b=\frac{k}{1^{2} }[/tex] k = 1b
[tex]y=\frac{1b}{x^{2} }[/tex]
b) y = 25
[tex]x^{2}=\frac{16}{25}[/tex]
[tex]x=\sqrt{\frac{4}{5} ^{2} }[/tex]
x = ±[tex]\frac{4}{5}[/tex]
x > 0, x = 4/5
{ Equation }
y=16/x² is required equation for y in terms of x and x=4/5 when y=25.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The table of values are
x 1 2 3 4
y 16 4 16/9 1
Given that y is inversely proportional to square of x.
y=k/x²
Let us consider
y=16 and x=1
16=k/1
k=16.
y=16/x²
So y=16/x² is equation for y in terms of x
b) We need to find value of x when y=25
25=16/x²
Use cross multiplication
x²=16/25
Take square root on both sides
√x²=√16/25
x=±4/5
If x>0 , so x=4/5
Hence y=16/x² is required equation for y in terms of x and x=4/5 when y=25.
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