Suppose the sphere below with radius rhas a surface area equal to 45 units?Find the surface area of the sphere with twice the radius.21A. 180 units2B. 180 units3C. 90 units2D. 90 units 3
Answers
Solution
It is given that the small sphere with radius r has a surface area equal to 45 units square.
The surface area of a sphere with radius r is given by;
\(SA=4\pi r^2\)Since the surface area of the small sphere is 45 units square.
\(\begin{gathered} \Rightarrow45=4\pi r^2 \\ \\ \Rightarrow\frac{45}{4\pi}=r^2 \\ \\ \Rightarrow r=\sqrt{\frac{45}{4\pi}} \end{gathered}\)To find the Surface area with twice the radius, we need to multiply the value of r by 2;
\(\Rightarrow R=2r=2\sqrt{\frac{45}{4\pi}}\)Therefore, the surface area is of a sphere with a radius R is
\(\begin{gathered} SA=4\pi R^2 \\ \\ \Rightarrow SA=4\pi(2\sqrt{\frac{45}{4\pi}})^2=4\pi(4\times\frac{45}{4\pi})=4\times45=180\text{ unit}^2 \end{gathered}\)Hence, the correct option is A.
Related Questions
Plz help me if you're nice. If wrong answer i'll report you
Answers
Answer
z= 14
Step-by-step explanation:
4( 2z-3) -5(z-6) =3 *20
8z-12-5z+30=60
3z+18=60
3z=60-18
3z=42
z= 14
\( \frac{2z - 3}{5} - \frac{z - 6}{4} = 3 \\ = > \frac{4(2z - 3) - 5(z - 6)}{20} = 3 \\ = > \frac{8z - 12 - 5z + 30}{20} = 3 \\ = > \frac{3z + 18}{20} = 3 \\ = > 3z + 18 = 3 \times 20 \\ = > 3z + 18 = 60 \\ = > 3z = 60 - 18 \\ = > 3z = 42 \\ = > z = \frac{42}{3} \\ = > z = 14\)
Answer:
z = 14
Hope you could get an idea from here.
Doubt clarification - use comment section.
PLEASE HELP ON QUESTION ASAP !
hi ! I really need help understanding paragraph and I've also added a question about paragraph by me down below . Would like explanation in simple words.
If answers correct I'll rate you five stars a thanks and maybe even brainliest
Paragraph I needed help understanding:
If two or more cells are connected together side by side, the voltage across them is sum of the voltage of each cell. This is because both cells are pushing same way.
My Question about paragraph:
If the sum lets say was 4.5v would every individual cell be worth 4.5 as it says in question ' voltage across them is the sum of voltage of each cell ' or are they each a different value? And how would we be able to find value?.
Answers
If the sum of the voltage is 4.5V, it is possible that different cells have different voltages. For example, three cells with voltages 1V, 1.5V, and 2V could be connected together side by side to give a total voltage of 4.5V.
To find the voltage of each cell, we would need to know the voltage across each cell or the voltage of the other cells connected in the circuit. Then we could use the fact that the sum of the voltages across all cells in the circuit is equal to the total voltage of the circuit to solve for the voltage of each cell.
Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 90 feet of fencing to go around it, what dimensions will give him the maximum area in the garden.
Answers
Answer:
long side, semicircle diameter: 180/(4+π) ft ≈ 25.2 ftshort side: 90/(4+π) ft ≈ 12.6 ftStep-by-step explanation:
Let the rectangle dimensions be x and y. Assume that x represents the "short" side, so it is also the diameter of the semicircle. Then the perimeter is ...
P = x + 2y + πx/2 = 90
The area is the area of the rectangle added to the area of the semicircle:
A = xy + (1/2)π(x/2)^2 = x(π/8x +y)
Solving the perimeter equation for y, we get
y = (90 -x -π/2x)/2
and the area equation becomes ,..
A = x(π/8x +45 -x/2 -π/4x)
A = x(45 -x(1/2 +π/8))
The graph of A(x) is a parabola opening downward with zeros at x=0 and x=45/(1/2+π/8) = 360/(4+π).
The vertex (maximum) of the area curve will be halfway between the zeros, at ...
x = (0 +360/(4+π))/2 = 180/(4+π)
The value of y is then ...
y = (90 -x(1 +π/2))/2 = (1/2)(90 -(180/(4+π))(2+π)/2) = (1/2)(90)(1 -(2+π)/(4+π))
y = 45(4+π-2-π)/(4+π) = 90/(4+π)
The rectangle dimensions are 90/4+π) by 180/(4+π), with the semicircle diameter equal to 180/(4+π).
__
That's about 25.2 ft by 12.6 ft with the semicircle attached to the long side.
_____
Please note that the overall dimensions of the garden are the same in both directions. It is effectively "square" with two corners rounded into quarter circles.
In the diagram at right, DE is a midsegment of triangle ABC. If the area of triangle ABC is 96 square units, what is the area of triangle ADE? Explain how you know.
Answers
The area of triangle ADE is,
⇒ A = 48 square units
We have to given that,
In the diagram , DE is a midsegment of triangle ABC.
And, The area of triangle ABC is 96 square units
Now, We know that,
Since DE is a midsegment of triangle ABC, it is parallel to AB and half the length of AB. Therefore, DE is half the length of AB.
Hence, the area of triangle ADE is half the area of triangle ABC,
That is,
A = 96 / 2
A = 48 square units
Thus, The area of triangle ADE is,
⇒ A = 48 square units
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What is the area of a triangle
with the base of 20 inches and a
height of 6 inches?
Answers
Answer:
60 \(in^{2}\)
Step-by-step explanation:
Answer:
60.
Its pretty easy tbh. Well that is if you understand it.
34 miles
30 mph
How much time will it
take for these two
vehicles to meet?
55 mph
[?] hours
![34 miles30 mphHow much time will ittake for these twovehicles to meet?55 mph[?] hours](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/lJao5IqrAPJR8grB8BLa8305HMimCTar.png)
Answers
Answer:
0.4 hours
Step-by-step explanation:
or 24 minutes :D
Mrs. Santiago drinks 9 diet cokes in 3 days. If there are 24 diet cokes in a case, how many cases of diet coke
should she buy for the month of September? (*hint, you need to know how many days in September. You need
to figure out how many cokes she will need AND then how many cases that would be.)
Answers
Answer:
9=3 and 24=x 9x =24*3=8
Zoe says an equilateral triangle is always an acute triangle, but an acute triangle is never an equilateral triangle. Which statement explains whether Zoe is correct or not?
Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.
Zoe is not correct because equilateral triangles have three acute angles. Acute triangles have three acute angles, so acute triangles are always equilateral triangles.
Zoe is correct because equilateral triangles have three sides of equal length, and acute triangles have three sides of different lengths.
Zoe is correct because equilateral triangles have three acute angles. Acute triangles have one acute angle, so an acute triangle cannot be an equilateral triangle.
THE ANSWER IS NOT C
Answers
Answer:
Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.
Step-by-step explanation:
Logically, it makes no sense for Zoe to say, in effect, ...
"All E are A, but A are never E."
That is incorrect on its face. At least, it means that "sometimes A are E."
__
The appropriate choice is the first one:
Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.
Student Enrollment
The enrollment at a local college has been decreasing linearly. In 2004, there where 975 students enrolled. By
2009, there were only 730 students enrolled. Determine the average rate of change of the school's enrollment
during this time period, and write a sentence explaining its meaning.
The average rate of change=
The enrollment at the college has been [Select an answer at a rate of
Select an answer v
Answers
The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.
To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:
Average rate of change = (Change in enrollment) / (Change in time)
The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.
Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:
Change in enrollment = 730 - 975 = -245 students
The change in time can be calculated as:
Change in time = 2009 - 2004 = 5 years
Now we can calculate the average rate of change:
Average rate of change = (-245 students) / (5 years) = -49 students per year
Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.
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You have $319 of charges on your credit card. Then you charge $170 to buy Christmas presents. If your minimum payment if 6% of the balance, what will be your minimum payment?
Answer correctly and explain how you got the answer for brainliest.
Answers
Answer:
$29.34.
Step-by-step explanation:
To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:
Current balance = previous balance + new charge
Current balance = $319 + $170
Current balance = $489
The minimum payment is 6% of the current balance:
Minimum payment = 6% x current balance
Minimum payment = 6% x $489
Minimum payment = $29.34
Therefore, the minimum payment on the credit card would be $29.34.
Answer:
$29.34.
Step-by-step explanation:
To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:
Current balance = $319 + $170 = $489
Minimum payment = 6% x $489 = $29.34
The minimum payment on the credit card would be $29.34.
Hope this helped, have a GOOD DAY!!!!!
\((2x^{2} y3\)
Answers
Answer: Could you take a pic of the sheet because there is no sign ( x, +, etc.)
Step-by-step explanation:
The following table shows the number and type of properties available in three cities.
City
Key West
Orlando
Miami
Write a matrix that represents the number of each type of property available in Key West.
Answers
[ 3 9 13 ] is the Matrix showing all types of property available in key west .
What is matrix ?A matrix is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns to represent a mathematical object or an attribute of such an entity in mathematics.
Calculationgiven in the table that how many types of property are there in the table
its a simple matrix which u can directly see
its a 3 x 1 matrix ...
[3 9 13] this matrix shows the required value
hope this helps...
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Answer: [3 9 13]
Step-by-step explanation:
Need help please and thank you
Answers
Hey!
For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)
This way, it will be able to graph and get the answers quicker!
The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).
(-3,-2) (-4,0) ) slope = _
Answers
Answer:
-2
Step-by-step explanation:
[0-(-2)](rise) over [(-4) - (-3)](run)
2/-1 = -2 = slope
HOPE THIS HELPS!!!!
Best way to solve this type of equation Ax+by=c
Answers
The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.
Quadratic equation
The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.
The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.
Hence, either of the three methods are good ways to solve such equation.
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If you flip two coins 68 times, what is the best prediction possible for the number of times both coins will land on heads?the number of times it will land on tails?
Answers
If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is 17.
If you flip two coins 68 times, the best prediction for the number of times both coins will land on tails is 17.
What is the probability of getting two heads?The possible outcomes when two coins are flipped are;
head - head = HH
tail - tail = TT
Head and tail = HT
Tail and head = TH
The probability of getting two heads = 1/4
If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is calculated as;
Expected value = (68 flips) x (1/4 probability of getting HH) = 17
The probability of getting two tails = 1/4
Expected value = 68 x 1/4 = 17
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Toby has a strawberry lace that is 36 cm long ar He needs pieces 18 mm long to decorate a cake. How long is the lace in mm? How many 18 mm pieces can he cut from the lace? help⭐⭐⭐⭐⭐
Answers
Answer:
The lace is 36 cm long and 1 cm = 10 mm. So, 36 cm = 360 mm.
He can cut the lace into 18 mm pieces, so he can cut 360 mm / 18 mm = 20 pieces of 18 mm lace from the 36 cm lace.
What percent of cupcake sales were more than 3 cupcakes, but less than 7 cupcakes?
Answers
9% is the answer trust me on this
Write ln8t‾‾√ in expanded form. Note: When entering natural log in your answer, enter lowercase LN as “ln”. There is no “natural log” button on the Alta keyboard.
Answers
Answer:
Step-by-step explanation:
Find AC. FIND X USING THE PICTURE. BELOW. WILL MARK BRANLIEST FOR FIRST ONE TO ANSWER
Answers
Answer:
AC ≈ 50.5
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan29° = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AC}\) = \(\frac{28}{x}\) ( multiply both sides by x )
x × tan29° = 28 ( divide both sides by tan29° )
x = \(\frac{28}{tan29}\) ≈ 50.5 ( to the nearest tenth )
Answer:
50.5
Step-by-step explanation:
In the right triangle, focus on angle A. The side marked 28 is the opposite side, and the side marked x is the adjacent side. The trigonometric ratio that uses those two side is the tangent ratio.
tangent = (opposite) / (adjacent)
\(\tan{29^\circ}=\frac{28}{x}\)
Multiply both sides by x.
\(x\cdot \tan{29^\circ}=28\)
Divide by tan 29 degrees.
\(x=\frac{28}{\tan{29^\circ}}\)
Use a calculator (in degree mode!) to approximate x.
\(x \approx 50.5\)
A group of students stood in a circle to play a game. The circle had a diameter of 22 meters. Which measurement is closest to the area of the circle in meters?
Answers
The measurement closest to the area of the circle in meters is 379.94 sq. meters.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
The word "area" refers to a free space. A shape's length and width are used to compute its area. The majority of forms and things have corners and edges. When computing the area of a certain form, both the length and width of these edges are taken into account.
Given that,
diameter = 22m
radius = 22/2 = 11m
The area of the circle is:
A = πr²
Substituting the value of π = 3.14 and r = 11 we have:
A = (3.14)(11)²
A = 379.94
Hence, the measurement closest to the area of the circle in meters is 379.94 sq. meters.
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it's for hoooooooooy
Answers
Answer:
3.16666666667
Step-by-step explanation:
I think, if not sry. STAY SAVAGE
Answer:
1.45
Step-by-step explanation:
1/4 + 2 3/4 = 3
3 + 1/5 = 3 1/5
3 1/5 = 16/5
16/5 = 3.20
3.20 - 1.75 = 1.45
Help! Trying to figure out graph theory
Answers
Answer:
count the. dots i think bc thats what it have on it
please solve this question asap
Answers
Step-by-step explanation:
\(y = \sqrt{4x + 6} \)
\( {y}^{2} = 4x + 6\)
\( {y}^{2} - 6 = 4x\)
\( \frac{1}{4} ( {y}^{2} - 6) = x\)
Swap x and y
\( \frac{ {x}^{2} - 6 }{4} = y\)
Round 62394 to the nearest
Answers
Answer:
63000 or 62400. Didn't specify whether to the thousandth or hundredth
NO LINKS!! URGENT HELP PLEASE!!
Answers
Answer:
Step-by-step explanation:
1)
Congruency shortcuts:
HL, SSS, SAS, ASA, and AAS
where S=side
A=angle
H=hypotenule
L=leg
HL is only for a right triangle
If you can prove sides and angles are congruent according to those 5 rules, you have proven the triangles are congruent
Similarity shortcuts:
AA, SAS, SSS
We have triangle similarity if (1) two pairs of angles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS)
2)
BG ≅ GD >Given from image
IG ≅ GO >Given from image
<BGI ≅ <DGO >Vertical Angles
ΔBGI ≅ ΔDGO >SAS
You have proven that the triangles are congruent because you used the shortcut by proving a side and angle and a side are congruent so SAS makes them congruent
What is the value of g(2)
Answers
Answer:
Its value is 9.8 m/s2
Answer:
9.8 m/s2
Step-by-step explanation:
If the function y=sin(x) is transformed to y = sin(2x), how does the graph change?
It is stretched vertically.
It is compressed vertically.
It is stretched horizontally.
It is compressed horizontally..
Answers
Step-by-step explanation:
The transformation y = sin(2x) affects the graph of y = sin(x) by compressing it horizontally.
The function y = sin(2x) has a coefficient of 2 in front of the x variable. This means that for every x value in the original function, the transformed function will have half the x value.
To see the effect of this transformation, let's compare the graphs of y = sin(x) and y = sin(2x) by plotting some points:
For y = sin(x):
x = 0, y = 0
x = π/2, y = 1
x = π, y = 0
x = 3π/2, y = -1
x = 2π, y = 0
For y = sin(2x):
x = 0, y = 0
x = π/2, y = 0
x = π, y = 0
x = 3π/2, y = 0
x = 2π, y = 0
As you can see, the y-values of the transformed function remain the same as the original function at every x-value, while the x-values of the transformed function are compressed by a factor of 2. This means that the graph of y = sin(2x) appears narrower or more "squeezed" horizontally compared to y = sin(x).
Therefore, the correct statement is: It is compressed horizontally.
(30 points!)
which of the following is a true statement?
Answers
Answer:
B OR D
Step-by-step explanation:
A line passes through the points (0,1) and (13,-3). What is it’s equation in slope intercept form.
Answers
\(\huge\boxed{y=-\frac{4}{13}+1}\)
First, let's find the slope (\(m\)) of the line using the two points:
\(\begin{aligned}m&=\frac{y_2-y_1}{x_2-x_1}\\&=\frac{-3-1}{13-0}\\&=\frac{-4}{13}\\&=-\frac{4}{13}\end{aligned}\)
Now, we'll use point-slope form using the first point and the slope to get an equation for the line.
\(\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=-\frac{4}{13}(x-0)\end{aligned}\)
Now, we just need to get the equation to slope-intercept form, which is \(y=mx+b\).
\(\begin{aligned}y-1&=-\frac{4}{13}x\\y&=-\frac{4}{13}x+1\end{aligned}\)