=============================================
Explanation:
The volume of a cylinder formula is
V = pi*r^2*h
where r is the radius and h is the height.
---------------
For the first cylinder, we have r = 2 and h = 7. This leads us to...
V = pi*r^2*h
V = pi*2^2*7
V = pi*4*7
V = pi*28
V = 28pi
This is the exact volume in terms of pi.
---------------
Repeat those steps for the other cylinder (r = 2 and h = 28)
V = pi*r^2*h
V = pi*2^2*28
V = pi*4*28
V = 112pi
---------------
To recap so far, we have these two cylinder volumes:
Cylinder A = 28piCylinder B = 112piWe see that cylinder B has the larger volume (since 112 > 28).
The ratio of the volumes from larger to smaller is 112pi : 28pi
Divide both parts by pi to have those terms cancel and we get the ratio 112:28
Lastly, we divide each part by the GCF 28
112/28 = 4
28/28 = 1
Therefore, the ratio 112:28 fully reduces to 4:1 which makes the final answer choice A.
The larger volume is 4 times that of the smaller volume.
----------------
A fairly quick way to see why we get this ratio is to notice the smaller height h = 7 jumps to the larger height h = 28 by a factor of 4.
In other words,
larger height = 4*(smaller height)
28 = 4*7
The fact that the radius is kept the same at r = 2 won't have an effect on the volume ratio. These parts effectively cancel out.
So this jump of "times 4" directly connects to the ratio 4:1
We multiplied the height by 4, so the volume is also multiplied by 4 (when going from the smaller cylinder to the larger one).
If you have 6 periods per day at school and math is 1 of them, what percentage of your school day is spent in math?
Answer:
16.67% of your day is spent in math class.
Step-by-step explanation:
The total would be 100% and then since you have 6 periods we divide 100 by 6 to get 16.67%. So 16.67% of your day is spent in math class.
Triangle ABC has an Area of 4 3/8 square feet. If the length of AC IS 1 2/3 feet, what is the length of BC?
Answer:
length of BC = 5 1/4 feet
Step-by-step explanation:
Area of a triangle = 1/2×base×height
Area = 4 3/8 square feet
Base = AC= 1 2/3 feet
Height = BC = ?
Area of a triangle = 1/2×base×height
4 3/8 = 1/2 × 1 2/3 × height
35/8 = 1/2 × 5/3 × height
35/8 = 5/6 × height
Height = 35/8 ÷ 5/6
= 35/8 × 6/5
= (35 × 6) / (8 × 5)
= 210 / 40
= 5 1/4 feet
Height = BC = 5 1/4 feet
length of BC = 5 1/4 feet
Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 EndFraction cups from the first orange, StartFraction 3 over 10 EndFraction cups from the second orange, StartFraction 9 over 20 EndFraction cups from the third orange, StartFraction 3 over 11 EndFraction cups from the fourth orange, and StartFraction 7 over 15 EndFraction cups from the fifth orange. Patel estimates that he needs 3 cups of orange juice for his family. About how much more orange juice does he need to reach his estimate?
Answer:A
Step-by-step explanation:this is not true
Answer:
It A
Step-by-step explanation:
I had the question hope this helps!!!!!
For the geometric series 2 + 6 + 18 + 54 + ... , find S8
Answer:
[tex]\displaystyle S_{8}=6560[/tex]
Step-by-step explanation:
We have the geometric sequence:
2, 6, 18, 54 ...
And we want to find S8, or the sum of the first eight terms.
The sum of a geometric series is given by:
[tex]\displaystyle S=\frac{a(r^n-1)}{r-1}[/tex]
Where n is the number of terms, a is the first term, and r is the common ratio.
From our sequence, we can see that the first term a is 2.
The common ratio is 3 as each subsequent term is thrice the previous term.
And the number of terms n is 8.
Substitute:
[tex]\displaystyle S_8=\frac{2((3)^{8}-1)}{(3)-1}[/tex]
And evaluate. Hence:
[tex]\displaystyle S_8=6560[/tex]
The sum of the first eight terms is 6560.
Answer:
S₈ = 6560
Step-by-step explanation:
The sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
where a is the first term and r the common ratio
Here a = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{6}{2}[/tex] = 3 , then
S₈ = [tex]\frac{2(3^{8}-1) }{3-1}[/tex]
= [tex]\frac{2(6561-1)}{2}[/tex]
= 6561 - 1
= 6560
Find the area of the trapezoid
Answer:
112
Step-by-step explanation:
add both bases the multiply by the height
Answer:
112
13 + 15
= 28 ÷ 2
= 14 × 8
= 112
14. Phyllis wants to hire a clown to entertain at her daughter's birthday party.
• The clown charges a $25 travel fee.
• The clown also charges $5.50 per hour to entertain.
Which equation describes the relationship between the cost, C, Phyllis must pay and the number of hours, n, the clown provides
entertainment?
Answer:
C=25+5.50n
Step-by-step explanation:
C=25+5.50n where c is the total cost and n is the number of hours the clown entertains.
5) Simplify the 1. (50x²+20xy)divide (-5x)
Answer:
-10x-4y
Step-by-step explanation:
Step-by-step explanation:
Explanation is in the attachment
your answer will be 10x(1+2y)
hope it is helpful to you ☺️
In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?
Two particles have positions at time t given by s1=4t-t^2 and s2=5t^2-t^3. Find the velocities
Step-by-step explanation:
Given that,
The positions of the first particle,[tex]s_1=4t-t^2[/tex]
Velocity,
[tex]v_1=\dfrac{ds_1}{dt}\\\\v_1=\dfrac{d(4t-t^2)}{dt}\\\\v_1=4-2t[/tex]
Position,
[tex]s_2=5t^2-t^3[/tex]
[tex]v_2=\dfrac{ds_2}{dt}\\\\v_2=\dfrac{d(5t^2-t^3)}{dt}\\\\v_2=10t-3t^2[/tex]
Hence, this is the required solution.
Find the area of a circle with radius, r = 5.72m.
Give your answer rounded to 2 DP.
r
The diagram is not drawn to scale.
Answer:
A≈102.79
Step-by-step explanation:
The formula for area of a circle is πr² so we need to substitute the r by 5.72.
π×5.7² = 102.79 m²
Answer:
Approximately 102.79 meters squared
Step-by-step explanation:
pi times 5.72 meters squared
Hope this helps!
In a triangle ABC, b=13cm c=17cm A=86 degree. Find B,C and a
Step-by-step explanation:
went to a calculator
it said
Side a = 20.66803
Side b = 13
Side c = 17
Angle ∠A = 86°
Angle ∠B = 38.863°
Angle ∠C = 55.137°
Devaughn is 7 years older than Sydney. The sum of their ages is 95. What is Sydney's age?
Answer:
44
Step-by-step explanation:
Let's say that Devaughn's age is D, and Sydney's age is S.
We know that D is 7 greater than S, so D = 7 + S.
We know that the sum of their ages, or D + S, is equal to 95, so D+S = 95
We have
D = 7 + S
D + S = 95
What we can do is plug D= 7 + S into the second equation to get
D + S = 95
= (7+ S) + S
= 7 + 2 * S
7+2 * S - 95
subtract 7 from both sides to isolate the coefficient and the variable
2 * S = 88
divide both sides by 2 to isolate the variable
S = 44
Sydney is therefore 44 years old
what are the x-coordinates of the solutions? Choose all that apply.
a. -2
b. 1
c. -1
d. 0
Answer:
a. -2
c. -1
Step-by-step explanation:
these are the only values for x, where the 2 equations deliver the same y value.
in case of a. y = -2×-2 - 1 = 4 - 1 = 3
and y = 3¹ = 3
c. y = -2×-1 - 1 = 2 - 1 = 1
y = 3⁰ = 1
Subtract 11.485-18.38
Answer:
-6.895
Step-by-step explanation:
11.485
-18.38
______
-6.895
A circular sheet covers 425cm on the table,find the area of the sheet.
solve this question plz.
Answer:
sorry i cannot help you
Find the area in mi^2
Answer:
27 mi^2
Step-by-step explanation:
The area of a triangle is always 1/2 (base times height) so it is 1/2 (9×6) = 27
i desperately need help with this one as well omg.. and i think it also needs a quadratic formula
Hello,
[tex]Formula:\ y=k*a^x+b\\\\ \lim_{x \to -\infty} y=-3 \Longrightarrow -3=k*a^{-\infty}+b=0+b \Longrightarrow b=-3\\\\if \ x=0\ then\ y=-2 \Longrightarrow -2=k*a^0-3 \Longrightarrow k=1\\\\if \ x=1\ then\ y=3 \Longrightarrow 3=a^1-3 \Longrightarrow a=6\\\\\boxed{y=6^x-3}\\[/tex]
evaluate 523 base7 - 65base7
If these are number systems then it will turn out like this [tex]\displaystyle\bf 523_7-65_7=\boxed{425_7}[/tex]
make v the subject of the relation f=vu/v+u
Answer:
v=fu/u-f
Step-by-step explanation:
the answer is explained in the diagram
Find the measure of the indicated angle to the nearest degree.
1)
A) 19°
C) 36°
B) 43°
D) 47°
Answer:
D
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan? = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{17}[/tex] , then
? = [tex]tan^{-1}[/tex] ([tex]\frac{18}{17}[/tex] ) ≈ 47° ( to the nearest degree )
A sea turtle can swim 13 kilometers in 5 hours at this rate speed how far can it travel in 9 hours
Answer:
23.4 km
Step-by-step explanation:
We can use a ratio to solve
13 km x km
-------- = ---------------
5 hours 9 hours
Using cross products
13*9 = 5x
117 = 5x
Divide each side by 5
117/5 = 5x/5
23.4 =x
Answer:
It travel 23.4 km in 9 hours.
Step-by-step explanation:
Given :-
A sea turtle can swim 13 km in 5 hours at this rate speed .
To find :-
How far can it travel in 9 hours.
Solution :-
Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.
Let us assume that In 9 hours turtle swim x km.
Now, We solve by using ratio for x.
In 5 hours it swim = 13 km
And, In 9 hours it swim = x km
Calculate for x
5 hours = 13 km
9 hours = x km
Use cross multiplication method , we get
5 × x = 9 × 13
5x = 117
Divide both side by 5
5x / 5 = 117 / 5
x = 23.4
Hence, It can travel 23.4 km in 9 hours.
The diagram shows a right angle triangle find the size of x give your answer to 1 decimal place
Answer:
34.9°
Step-by-step explanation:
SOH
CAH
TOA
SOH ... sin(x) = 8/14
arcsin(8/14) = 34.85°
Can someone help me with this math homework please!
Answer:
First dropbox: 7h + 43 = 64
Second dropbox: $3
Step-by-step explanation:
Here's what we know about the question so far:
$43 is the initial fee
The rototiller worked for 7 hours
$64 is the total cost (including initial fee)
h = hourly fee
The answer should be 7h + 43 = 64 because:
- It includes the initial fee of $43
- It sets the equation equal to $64, which is the total cost
- The hourly fee is being multiplied with 7 hours, which is correct since the h variable is hourly (not sure how to explain this part ;w; )
For the 2nd drop box, we will use basic algebra to solve for h:
7h + 43 = 64
(subtract both sides by 43)
7h = 21
(divide both sides by 7)
h = 3
There's your 2 answers!
Hope it helps (●'◡'●)
help me pls i don't ge this
Answer:
9. The area of rectangle S is four times bigger than rectangle R
10. (1, 3)
Step-by-step explanation:
To find the solution of the two linear equations:
y=x+2
y=-2x+5
x+2=y=-2x+5
3x=3
x=1
y=1+2
y=3
(1,3)
I need to find angle BAC
Answer:
m<BAC = 60°
Step-by-step explanation:
Theorem:
In a triangle, the measure of an exterior angle equals the sum of the measures of its remote interior angles.
m<ACD = m<A + m<B
130° = m<A + 70°
m<A = 60°
m<BAC = 60°
PICTURE INCLUDED NEED HELP!
Answer:
B
Step-by-step explanation:
7x root2 + x root 2 =8x root 2 and you just add the -4 root 2 on
Answer= B
How many subsets can be formed from the set F?
Answer:
32
Step-by-step explanation:
I'm very confirm with my answer mark me as brainliest plsssss
Iliana rotated trapezoid WXYZ 180° about the origin.
On a coordinate plane, trapezoid W X Y Z has points (negative 4, 2), (negative 3, 4), (negative 1, 4), (0, 2).
What is the correct set of image points for trapezoid W’X’Y’Z’?
W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
W’(4, 2), X’(3, 4), Y’(1, 4), Z’(0, 2)
W’(–2, –4), X’(–4, –3), Y’(–4, –1), Z’(–2, 0)
W’(2, 4), X’(4, 3), Y’(4, 1), Z’(2, 0)
Answer:
W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)
Step-by-step explanation:
Its A Your Welcome :)
Answer:
A.
Step-by-step explanation:
The level temperature of liquid in a thermometer is 28.60 lower than the boiling point of water. What is the thermometer reading? *
Answer:
71.4 degrees Celsius or 183.4 degrees Fahrenheit.
Step-by-step explanation:
The boiling point of water is 100 degrees Celsius.
I assume you mean the liquid's temperature is 28.60 degrees Celsius lower than the boiling point of water, so 100 - 28.6 = 71.4.
Therefore the liquid is 71.4 celsius.
If you wanted the temperature in Fahrenheit, the answer is 212 - 28.6 = 183.4 degrees Fahrenheit.
If f(a) is an exponential function where f(-3) = 18 and f(1) = 59, then find the
value of f(0), to the nearest hundredth.
Given:
For en exponential function f(a):
[tex]f(-3)=18[/tex]
[tex]f(1)=59[/tex]
To find:
The value of f(0).
Solution:
The general form of an exponential function is:
[tex]f(x)=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth/ decay factor.
We have, [tex]f(-3)=18[/tex]. Substitute [tex]x=-3,f(x)=18[/tex] in (i).
[tex]18=ab^{-3}[/tex] ...(ii)
We have, [tex]f(1)=59[/tex]. Substitute [tex]x=1,f(x)=59[/tex] in (i).
[tex]59=ab^{1}[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}[/tex]
[tex]3.278=b^{1-(-3)}[/tex]
[tex]3.278=b^{4}[/tex]
[tex](3.278)^{\frac{1}{4}}=b[/tex]
[tex]1.346=b[/tex]
Substituting the value of b in (iii).
[tex]59=a(1.346)^1[/tex]
[tex]\dfrac{59}{1.346}=a[/tex]
[tex]43.83358=a[/tex]
[tex]a\approx 43.83[/tex]
The initial value of the function is 43.83. It means, [tex]f(0)=43.83[/tex].
Therefore, the value of f(0) is 43.83.
