Find the volume of the solid obtained by rotating the region enclosed by the curves y = 4x and y = x3 about the y-axis, where
Answers
The volume of the solid obtained by rotating the region enclosed by the curves y = 4x and y = x^3 about the y-axis is 64π cubic units.
The closest option provided is C. 128π/15.
To find the volume of the solid obtained by rotating the region enclosed by the curves y = 4x and y = x^3 about the y-axis, we can use the method of cylindrical shells.
First, let's determine the points of intersection between the two curves:
[tex]4x = x^3\\x^3 - 4x = 0\\x(x^2 - 4) = 0\\x(x - 2)(x + 2) = 0[/tex]
The curves intersect at x = 0, x = 2, and x = -2.
Next, let's consider a small vertical strip of width Δy and height y, located at a distance x from the y-axis. The volume of this cylindrical shell can be approximated as the product of its height (which is the circumference of the shell) and its width (Δy).
The radius of the shell is given by the distance from the y-axis to the curve y = 4x, which is x = y/4. Thus, the height of the shell is 2π(x)(Δy) = 2π(y/4)(Δy) = πy(Δy)/2.
To find the total volume, we integrate the volume of all these cylindrical shells from y = 0 to y = 16 (the range of y-values for the region enclosed by the curves):
V = ∫[0,16] πy(Δy)/2 dy
= π/2 ∫[0,16] y dy
= π/2 [[tex]y^2[/tex]/2] [0,16]
= π/2 × (1[tex]6^2[/tex]/2 - 0)
= π/2 × (256/2)
= π/2 × 128
= 64π
Therefore, the volume of the solid obtained by rotating the region enclosed by the curves y = 4x and y = [tex]x^3[/tex] about the y-axis is 64π cubic units.
The closest option provided is C. 128π/15.
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Question
Find the volume of the solid obtained by rotating the region enclosed by the curves y = 4x and y = x3 about the y-axis, where
A. 176\pi /15
B. 137 \pi/15
C. 128 \pi /15
D. 122\pi/15
Related Questions
Identify the domain of the function shown in the graph
Answers
Answer:
C. All real numbers.
Step-by-step explanation:
The domain is the set of all x values that are used by points on the graph. This is a sine wave, and we assume it extends infinitely far to the left and right. Even without that assumption, you can eliminate the other answers.
A. This describes the numbers on the x-axis between 0 and 5, inclusive. But the graph includes many more points with x-coordinates beyond that interval.
B. The same sort of thing: the graph extends well beyond the interval of x values between -5 and 5, inclusive.
D. This would mean the graph has only points with positive x-coordinates, but there are many with negative (or 0) x-coordinates.
Someone do this please
Answers
Answer: 102 degrees
Step-by-step explanation:
The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.
51 + 51 = Angle 4
Angle 4 = 102 degrees
1 1/5 · x/3 = 9/10
solve for x
Answers
The value of x in the equation 1 1/5 - x/3 = 9/10 is 9/10
Fraction1 1/5 - x/3 = 9/10
- x/3 = 9/10 - 1 1/5
- x/3 = 9/10 - 6/5
-x/3 = 9-12 / 10
-x/3 = -3/10
divide both sides by - 1/3x = -3/10 ÷ - 1/3
= -3/10 × -3/1
x = 9/10
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If x = false and y = false, is the statement: not x or not y
a) true
b) false
Answers
Answer:
false
Step-by-step explanation:
X is equal to Y
therefore,
X = Y
X= false
Y = false
so,
false = false
mean of four consecutive even numbers is 15. Enter each number separated by a comma
Answers
Therefore second number is (x+2).
Therefore third number is (x+4).
Therefore forth number is (x+6).
Hence,
(x+x+2+x+4+x+6+x+8)/4 = 15
(4x+12)/4 = 15
x+3 = 15
x = 12
So,
The number is 12, 14, 16, 18.
Hope it helps : )
Answer:
12, 14, 16, 18
Step-by-step explanation:
(x + (x+2) + (x+4) + (x+6))/4 = 15
^ solve algebraically
you'll get (4x+12)/4 = 15
then: 4x + 12 = 60
then 4x = 60-12
then 4x = 48
then x = 12
x is 12 so then do substitution
so you get
12 + (12+2) + (12+4) + (12+6)
12, 14, 16, 18
can someone please help mee
Answers
Answer:
[tex]\frac{\sqrt{731}}{30}[/tex]
Step-by-step explanation:
We first observe that the angle is located in quadrant III
This allows us to draw a triangle as attached in the attachments.
Using this triangle, we can find sin([tex]\theta_1[/tex]).
Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].
So our final answer is the answer shown above.
You may be wondering how did the side lengths appear on the triangle.
From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws and 2 pairs of appendages per body segment
Answers
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment: FALSE
What are Centipedes?Their bodies have an elongated, cylindrical form that can appear flat at times. Adults can range in size from half an inch to 6.5 inches. Despite its "thousand-legger" moniker, most have less than 100 legs. Despite having so many legs, these arthropods move slowly.Most centipedes can only bite with their poison claws just under the head, causing a bee-like sting; however, Scolopendra can harm a person with the sharp claws of its many walking legs.Centipedes have only one pair of legs on each body segment, which can be seen protruding from their flattened bodies. The number of body segments varies by species, and the number of pairs of legs ranges from 15 to 177, plus or minus one.As it is given in the description, centipedes have only one pair of legs on each body segment. So, the whole statement becomes False.
Therefore, the statement "centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment" is FALSE.
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Complete question:
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment. TRUE or FALSE
What number is represented by point B? A number line going from 1 to 2 with 5 equal spaces between 1 and 2. Point B is one mark to the left of 2. StartFraction 4 Over 5 EndFraction 1 and StartFraction 4 Over 5 EndFraction 1 and StartFraction 5 Over 4 EndFraction 2 and StartFraction 1 Over 5 EndFraction
Answers
Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2the number represented by point B is 1⁴/₅
The question has to deal with proportion
What is proportion?Proportion is the measure of a variable or quantity relative to another.
How to calculate which number represents point B?Since A number line going from 1 to 2 with 5 equal spaces between 1 and 2, the measure of a sub-unit between 1 and 2 is
= 1/5
So, each sub-unit measure 1/5
Since point B is one mark to the left of 2, we have that point B is y = 2 - 1/5 = (10 - 1)/5
= 9/5
= 1⁴/₅
So, the number represented by point B is 1⁴/₅
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What addition/subtraction equation should I put?
Answers
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
5 roses in a vase 12 flowers what is the ratio of all flowers in the vase of daisies
Answers
The ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.
The number of flowers in the vase = 12 flowers
The number of roses in the vase = 5 roses.
Therefore, the number of daisies in the vase = The number of flowers in the vase - The number of roses in the vase,
or, the number of daisies in the vase = 12 - 5 = 7.
Thus, the number of daisies in the vase = 7.
We are asked to find the ratio of the total number of flowers in the vase, to the number of daisies in the vase.
Thus, the ratio = The number of flowers in the vase/The number of daisies in the vase,
or, the ratio = 12/ = 12:7.
Thus, the ratio of the total number of flowers in the vase, to the number of daisies in the vase is 12:7.
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PQ has endpoints P(0, 0) and Q(8, 4). Find the coordinates of the midpoint of PQ
O
O
O
(4,4)
(2,4)
(4,2)
Answers
Geometry question need explanation on finding the answer
Answers
SinAngle = 13/14
Angle = Sin^-1(13/14)
Angle = 68.2132107017 degrees
Angle ≈ 68.2 degrees (1 decimal place)
Hope it helps : )
Please help! I'm giving 25 points!!
The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.
1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)
2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)
Answers
1. The number of gallons of water produced is 460 gallons
2. The amount in cm the sea would increase after 6 years is 392 cm
1. How to determine the number of gallons producedWe'll begin by by converting 1.9 m³ to cm³. This is illustrated below:
1 m³ = 1×10⁶ cm³
Therefore,
1.9 m³ = 1.9×10⁶ cm³
Next, we shall determine the volume of water produced from 1.9 m³ (i.e 1.9×10⁶ cm³) of ice. This is illustrated below:
From the question given,
1 cm³ of ice = 0.92 cm³ of water
Therefore,
1.9×10⁶ cm³ of ice = 1.9×10⁶ × 0.92
1.9×10⁶ cm³ of ice = 1.748×10⁶ cm³ of water
Finally, we shall determine the number of gallons produced. This is illustrated below:
From the question given,
3800 cm³ of water = 1 gallon
Therefore,
1.748×10⁶ cm³ of water = 1.748×10⁶ / 3800
1.748×10⁶ cm³ of water = 460 gallon
Thus, 460 gallons were produced
2. How to determine the amount in cm the sea would increase to after 6 yearsFrom the question given above,
1000 Km³ = 364 cm
Therefore,
179.4 Km³ = (179.4 × 364) / 1000
179.4 Km³ = 65.3016 cm per year
To obtain the increase after 6 years, multiply 65.3016 by 6 as shown below:
65.3016 × 6 = 392 cm
Thus, the sea will increase 392 cm after 6 years
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(08.01)Angela wants to know how many families in her neighborhood plan to attend the parade. She puts all 120 of the neighborhood addresses in a hat and draws a random sample of 30 addresses. She then asks those families if they plan to attend the parade. She finds that 40% of the families plan to attend the parade. She claims that 40% of the neighborhood families would be expected to attend the parade. Is this a valid inference?
A) Yes, this is a valid inference because the 30 families speak for the whole neighborhood
B)Yes, this is a valid inference because she took a random sample of the neighborhood
C)No, this is not a valid inference because she did not take a random sample of the neighborhood
D) No, this is not a valid inference because she asked only 30 families
Answers
Using sampling concepts, the correct option regarding the validity of the inference is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. If I had taken 1000 residents just from Buffalo, it would not be a representative sample.
In this problem, all addresses in the neighborhood are considered, hence a random sample was taken and the correct option is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
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Find the maximum or minimum value of the product of two numbers whose difference is 14.
Answers
The maximum value of the product of two number whose difference is 14 is 49.
What is the maximum or minimum value of a function?The maximum or minimum value of a function is the highest or lowest value of that function.
How to determine the maximum or minimum of the product of two numbers?Let the numbers be x and y
Their product f(x,y) = xy
Since their difference is 14, x - y = 14
So, x = 14 - y
Substituting x into f(x,y), we have
f(x,y) = xy
= (14 - y)y
= 14y - y²
To find the maximum or minimum value of f(x,y) we differentiate it with respect to y and equate to zero.
So, f(x,y) = f(y) = 14y - y²
df(y)/dy = d(14y - y²)/dy
df(y)/dy = d(14y)/dy - dy²/dy
df(y)/dy = 14 - 2y
Equating to zero, we have
df(y)/dy = 0
14 - 2y = 0
14 = 2y
y = 14/2
y = 7
To determine if this gives a maximum or minimum for f(y) = f(x,y), we differentiate f'(y) again
So, df'(y)/dy = d(14 - 2y)/dy
= d14/dy + d(-2y)/dy
= 0 - 2
= -2 < 0.
Since f"(y) = -2 < 0, then y = 7 gives a maximum for f(x,y)
So, since y = 7,
x = 14 - y = 14 - 7 = 7
So, f(x,y) is maximum at x = 7 and y = 7
So, f(7,7) = 7 × 7
= 49
So, the maximum value of the product of two number whose difference is 14 is 49.
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(17,-13),(17,8) finding slope from two points
Answers
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
There are really two ways to solve this problem. One of them is the slope formula. You can familiarise yourself with this formula
[tex]\sf{\dfrac{y2-y1}{x2-x1}}[/tex]
SUBSTITUTE the values
[tex]\sf{\dfrac{-13-8}{17-17}}[/tex]
[tex]\sf{\dfrac{-21}{\bf{0}}[/tex] (notice the zero was in bold-face)
Dividing by zero is an operation we cannot do.
So the slope of this particular line is not defined.
The other way is looking at the first co-ordinates of the points given
Notice that they are exactly the same. Whenever that happens, the slope of that line is not defined.
Hope that made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{\tt{calligraphy}}\star[/tex]
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits, we say the process is
Answers
The process is Capable.
According to statement
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits
and when these conditions are fulfilled then the process is to be called CAPABLE.
So, The process is Capable.
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help me please omg im in a rush
Answers
Answer:48
Step-by-step explanation:
Denise wants to enlarge her prom photo. She wants to increase the
size 4 times the original photo. If the original photo is 6 inches by 8 inches,
how many times larger is the new photo?
4
40
16
8
Answers
After enlargement, the new photo would be 16 times larger. The answer is C: 16.
What is an Enlargement?An enlargement can be described as a type of dilation in transformation which involves increasing the dimensions of an original image by a given scale factor, so that the new image is similar to the original image. Their sizes would be different while their shapes remain the same. Also, the ratio of their corresponding dimensions would be the same.
Given the following:
Dimension of original photo = 6 inches by 8 inches
Scale factor = 4
To find the new dimensions of the new photo, multiply the corresponding dimensions of the original photo by 4, thus:
6 × 4 = 24 inches
8 × 4 = 32 inches
New dimensions = 24 by 32
Area of original photo = 6 × 8 = 48 in.²
Area of new photo = 24 × 32 = 768 in.²
768/48 = 16
This means that the new photo is 16 times larger than the original photo.
The answer is: C. 16.
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if you were to solve the following system by substitution, what would be the best variable to solve for and what from what equation 3x 6y
Answers
so here you the answer is 9
a 90% confidence interval for a proportion is found to be (0.22,0.28). What is the sample proportion
Answers
The value of sample proportion is found to be 0.253.
What is the sample proportion?The sample proportion [tex]\hat{p}[/tex] indicates the percentage of people in a sample who exhibit a particular quality or attribute.
Divide the number of individuals (or items) who possess the desired attribute by the overall sample size to obtain the sample proportion.
Now, according to the question;
The 90% confidence interval for a proportion is found to be (0.22,0.28).
The confidence interval for the sample is given as-
Confidence interval = Sample proportion ± Margin of Error
Let [tex]\hat{p}[/tex] be the sample proportion.
The level of significance = 1 - 0.90
= 0.10 (10%)
From z-value table, at a significance level of 5% (two-sided), z has a critical value of 1.645.
90% confidence interval = [tex]\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Thus, 0.22 = [tex]\hat{p} - 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], and
0.28 = [tex]\hat{p} + 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Covert both equation in the form of [tex]\hat{p}[/tex] and equating to each other.
[tex]\begin{aligned}&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22\\&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06\\&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645}\\&\sqrt{\frac{\hat{\nu}(1-\hat{p})}{n}}=0.02\end{aligned}[/tex]
Take square root,
[tex]\begin{gathered}\frac{\hat{p}(1-\bar{p})}{n}=0.0004 \\n=\frac{\hat{p}(1-\bar{p})}{0.0004}\end{gathered}[/tex]
Substituting the value of 'n' in the receptive equation to get the value of [tex]\begin{aligned}0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{p(1-\hat{p})}} \times 0.0004 \\0.22 &=\hat{p}-1.645 \times \sqrt{0.0004} \\0.22 &=\hat{p}-(1.645 \times 0.02) \\0.22 &=\hat{p}-0.033 \\\hat{p}=& 0.22+0.033=0.253\\\end{aligned}[/tex]
Therefore, the value of sample proportion is 0.253.
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What is the size of exterior angle of regular polygon which has interior angle of 120 degree?
Answers
Answer: 60 degrees
Step-by-step explanation:
An interior angle of a polygon and its corresponding exterior angle are supplementary (add to 180 degrees).
5x=3125 how do i solve that
Answers
Answer:
just divide 3125 by 5 and your answer is 625
Step-by-step explanation:
Using division, 3125 by 5 and get answer 625.
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
If 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.
Division can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
Thus, a / b = a divided in b equal parts.
We have been given 5x = 3125
Divide by 5 each sides;
x = 3125/5
x = 645
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In your own words, explain the concept of a variable. Discuss how you can teach a class about the use of variables and how they can be used to create an algebraic expression.
Answers
VARIABLE is a symbol which is used for representation in a math.
According to the statement
we have to explain about the what is a variable.
So, VARIABLE is a symbol which is used for representation in a math.
It represent the so many things like Algebra, Matrix,Vector etc. and also so many things.
A variable may also be called a data item.
It is used to represent a data like country name, name, age, date of birth etc.
we know that the every thing is changeable. So, like ther things variables are also changeable.
The changing of variable parameters is called as variation. In problems relating to two or more variables, it is seen that the value of a variable changes with the change in the value.
So, VARIABLE is a symbol which is used for representation in a math.
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Hi having a bit of trouble.
Answers
Answer:
P = 160/A
Step-by-step explanation:
For P to vary inversely with A, we must have P be proportional to the reciprocal of A. The constant of proportionality is given.
Inversely proportionalTwo quantities are directly proportional if there is a constant of proportionality (k) that multiplies one of them to give the value of the other:
y = kx
They are inversely proportional if the inverse of one of them can be multiplied by a constant of proportionality to give the value of the other:
y = k(1/x) = k/x
In this problem, the variables P and A are said to be inversely proportional. That means the equation that relates them will be of the form ...
P = k/A
You are given such a form with k=160, which is an appropriate value for the relation given by the problem. All you need to do is fill in the variable:
P = 160/A
The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals? (5 points)
The measure of their corresponding angles is equal.
The ratio of their corresponding angles is 1:2.
The ratio of their corresponding sides is 1:2
The size of the quadrilaterals is different but shape is same.
Answers
The measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). This can be obtained by plotting the quadrilaterals on a graph paper and comparing the figures.
Which conclusion is true about the quadrilaterals?Given that,
vertices of quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)
vertices of quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4)
(x,y) ; (x, y-8)
ABCD is reflected across the line y=4 to get the quadrilateral EFCD.
Reflection means the size and shape of the quadrilaterals is same ⇒quadrilateral ABCD and quadrilateral EFCD are congruent.
Thus corresponding parts of congruent triangles are equal, corresponding angles will be equal.
Hence the measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).
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If the width of a rectangle can be represented by x and the length by x + 10, write an expression that can be used to represent the area of the rectangle. Simplify the expression as much as possible.
Answers
Answer:
The expression for area is (x)(x+10).
Step-by-step explanation:
Area=(w)(l)
Area=(x)(x+10)
(Note: This expression can be expanded, but then it wouldn't be fully simplified)
Hope this helps!
Which answer represents the following conditional statement in shorthand?
if megan is swimming, then it is warm outside.
Answers
The expression which represents the given conditional statement in shorthand is: S → W.
What is a conditional statement?A conditional statement can be defined as a statement that can be written to contain both a hypothesis and conclusion. Thus, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
If Megan is swimming = S
It is warm outside = W
Therefore, if Megan is swimming, then it is warm outside is represented by S → W.
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PLEASE ANSWER WILL GIVE YOU ALOT OF POINTS
Answers
The theorems that prove that lines are parallel includes:
Alternate interior angle theorem.Converse of corresponding angles postulate.How to prove lines are parallel?Parallel lines are the lines that do not intersect or meet each other at any point in a plane.
Theorems that prove that lines are parallel includes:
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what is the volume of the sphere shown below with a radius of 9
Answers
Answer:
972π or 3052.08 if π=3.14(remember to label the answer with your units)
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}\\[/tex]π[tex]r^{3}[/tex]. So, just plug the radius into the formula. [tex]r^{3}[/tex] in this case is [tex]9^{3}[/tex] which is 729. For, [tex]\frac{4}{3}[/tex]×729, the 3 and 729 cancel out to create 4×243 which is 972. Just add π to this and you get 972π. If π is 3.14 just multiple 972 and 3.14 to get 3052.08.