Find the equation of the ellipse with foci at (+-3,0) and major axis of length 12.
Answers
The equation of the ellipse with the foci is x²/36 + y²/(27) = 1.
What is the equation of the ellipse?
The distance between the foci of an ellipse is calculated using the following formula;
c² = a² - b²
Where;
a is half the length of the major axisb is half the length of the minor axisc is the distance between the fociFor this question, a = 6 and c = 3, the value of b is calculated as;
c² = a² - b²
3² = 6² - b²
9 = 36 - b²
b² = 27
b = √27
b = 3√3
The equation of the ellipse is calculated as;
x²/a² + y²/b² = 1
x²/36 + y²/(27) = 1
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Related Questions
Try it
Mrs. Chauvet has an unfair number cube that lands with 6 For how many of the outcomes does X = 0, meaning
facing up 40% of the time.
the outcome has no 6s?
Let X = the number of times that she rolls a 6 among 3
trials.
For how many of the outcomes does X = 1, meaning
the outcome has exactly one 6?
For how many of the outcomes does X=2, meaning
the outcome has exactly two 6s?
For how many of the outcomes does X=3, meaning
the outcome has exactly three 6s?
Answers
Answer:
The problem describes rolling an unfair number cube which lands with 6, and asks for the number of outcomes where X=0, X=1, X=2, and X=3.
X can be 0, 1, 2, or 3 if X equals the number of times she rolls a 6 over the course of three tries.
We must count the instances where none of the three trials yields a six in order to determine the number of occurrences where X = 0. Since there is a 0.4 percent chance that the cube will fall on 6, there is a 0.6 percent chance that it won't. Therefore, there are 0.6 * 3 = 0.216, or 21.6%, of outcomes where X = 0.
To find the number of outcomes where X=1, we need to count the number of outcomes where exactly one of the three trials results in a 6. There are three ways to choose which trial will result in a 6, and each of the other two trials must not result in a 6. Therefore, the number of outcomes where X=1 is 3 × 0.4 × 0.6^2 = 0.432 or 43.2%.
We must count the outcomes where precisely two out of the three trials yield a six in order to determine the number of events where X=2. There are three options for selecting the two trials that will end in a 6, and the third trial cannot also end in a 6. The proportion of outcomes where X=2 is therefore 3 0.4 2 0.6 = 0.288 or 28.8%.
Finally, to find the number of outcomes where X=3, we need to count the number of outcomes where all three trials result in a 6. This occurs with probability 0.4^3 = 0.064 or 6.4%.
Therefore, the number of outcomes where X = 0 is 21.6%, X=1 is 43.2%, X=2 is 28.8%, and X=3 is 6.4%.
Can I get some help in this question?
What value of x satisfies the equation (7q^3x)^3=343q^36
Answers
4 is the value of the variable x.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
We can simplify the left side of the equation by using the properties of exponents:
[tex](7q^{3x})^3 = 7^3 * (q^{3x})^3 = 343q^{9x}\\\\343q^{9x} = 343q^{36}\\\\q^{9x} = q^{36[/tex]
Now we can use the property that if [tex]a^b = a^c[/tex], then b = c. Therefore:
9x = 36
Dividing both sides by 9, we get:
x = 4
Therefore, the value of x that satisfies the equation is 4.
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Question 1 (1 point)
Write an inequality for the sentence.
The stadium held less than 25,000.
B
O a
O b
9ba580e611107c96c9efb866417dc160.webm 64 KB
s> 25,000
$≤25,000
Oc $<25,000
Answers
The inequality that represents the sentence "The stadium held less than 25,000 people" is given as follows:
c < 25,000.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.The amount is less than in this problem, hence the symbol is given as follows:
<.
As the amount is less than 25000, the inequality is given as follows:
c < 25,000.
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Please help on this asap!! 65 Points
Answers
No, It is not possible for 75% of the people surveyed at the park to purchase any two combination of the treats unless 14 people from the 'No preference group" decide to pick a treat. The two best frozen treat to pick will be Ice-cream sandwich and frozen fruit bar. With these two, 174 people are guaranteed to purchase the product.
How do we find the 75% chance of people surveyed buying any two combination of frozen treats?To find the 75% chance of people surveyed buying any two combination we say
58 + 95 + 79 + 17 = 250
75% of 250 = 187.5 which is 188
We need to see if 188 of people will pick up a treat based on the survey
58 + 95 = 153 < 188
95 + 79 = 174 < 188 however, if 14 people from no preference group purchase, then, this is the best combination.
58 + 79 = 137 < 188
The answer provided is based on the question below as seen in the picture;
Is it possible to select a combination of two frozen treats so that 75% of the people surveyed would be able to purchase their favorite? If so, which two types of frozen treats should you select? Use words and numbers to justify your answer
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A curve, described by x2 + y2 + 6y = 0, has a point A at (−3, −3) on the curve.
Part A: What are the polar coordinates of A? Give an exact answer.
Part B: What is the polar form of the equation? What type of polar curve is this?
Part C: What is the directed distance when theta equals 4 pi over 3 question mark Give an exact answer.
Answers
a) The polar coordinates of point A are (√(18), π/4).
b) The curve is a circle centered at the origin with radius 6.
c) The directed distance is the value of r, which is 6 √(3).
To find the polar coordinates of point A on the curve, we need to convert the point from Cartesian to polar coordinates. The conversion formula is:
r = √(x² + y²)
θ = arctan(y/x)
Using the values of point A, we have:
r = √((-3)² + (-3)²) = √(18)
θ = arctan((-3)/(-3)) = arctan(1) = π/4
To find the polar form of the equation x² + y² + 6y = 0, we need to convert it from Cartesian to polar coordinates. The conversion formulae are:
x = r cos(θ)
y = r sin(θ)
Using these formulae, we can rewrite the equation as:
r² cos²(θ) + r² sin²(θ) + 6r sin(θ) = 0
Simplifying this equation, we get:
r = -6 sin(θ) / (1 - cos²(θ))
To find the directed distance when θ equals 4 π over 3, we need to substitute this value of θ into the polar equation we found in Part B. Doing so, we get:
r = -6 sin(4 π/3) / (1 - cos²(4 π/3))
r = -6(-√(3)/2) / (1 - (-1/2)²)
r = 6 √(3)
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Need help pls and thank u!
Answers
Answer:
[tex]\sqrt[]{72}[/tex]
6.3141414141414...
[tex]\sqrt[4]{64}[/tex]
8.121 121 112 111...
Step-by-step explanation:
irrational numbers are real numbers that cannot be expressed as a ratio of integers.
example of irrational number [tex]\sqrt[]{2}[/tex]
example of rational number 2, 3, -4, etc.
Answers for these test question
Answers
The missing lengths and angles in the geometric systems are listed below:
Case 8: x = 60
Case 9: x = 48
Case 10: x = 5.535
Case 11: x = 5.665
Case 12: x = 9.103
Case 13: θ = 60°
Case 14: θ = 23.025°
How to find missing lengths and angles in triangles
In this problem we find two cases of geometric systems formed by triangles:
Systems of two similar triangles with a common unknown side.A triangle with an unknown side or an unknown angle.First case is analyzed by means of proportionality ratios and second case done by trigonometric functions:
Case 8
100 / x = x / 36
x² = 3600
x = 60
Case 9
x / 36 = 64 / x
x² = 36 · 64
x = 48
Case 10
x = 17 · sin 19°
x = 5.535
Case 11
x = 11 · cos 59°
x = 5.665
Case 12
x = 13 · tan 35°
x = 9.103
Case 13
cos θ = 7 / 14
cos θ = 1 / 2
θ = 60°
Case 14
tan θ = 17 / 40
θ = 23.025°
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Vanilla rent increased by 5%. The increase was $82. What was the original amount of Pavati's rent?
Answers
1.05x - x = 82
Simplifying the left side, we get:
0.05x = 82
Dividing both sides by 0.05, we get:
x = 1640
Therefore, the original amount of Pavati's rent was $1640.
A group consists of seven Democrats and eight Republicans. Four people are selected to attend a conference.
a. In how many ways can four people be selected from this group of fifteen?
b. In how many ways can four Republicans be selected from the eight Republicans?
c. Find the probability that the selected group will consist of all Republicans.
a. The number of ways to select four people from the group of fifteen is
b. The number of ways to select four Republicans from the group of eight Republicans is
c. The probability is
Answers
There 1365 ways to choose four people from the group of fifteen.
b. There are 70 ways to choose four Republicans from the group of eight Republicans.
C. The probability is about 0.0513, or 5.13%.
What is the probability about?a. To know the ways that four people can be selected from this group of fifteen is by:
nCr = n! / (r! x (n-r)!),
Where:
n = total number of items
r = is the number of items to be selected,
! = the factorial of a number.
Putting in the values into the the formula:
15C4 = 15! / (4! x (15-4)!)
(15-4)! = 11!
15C4 = 1365
B. Since:
n = 8
r = 4
Putting in the values into the the formula:
8C4 = 8! / (4! x (8-4)!)
(8-4)! = 4!
8C4 = 70
c. The Probability = Number of ways to choose four Republicans / Number of ways to choose four people
Hence Probability = 70 / 1365
= 0.0513
Therefore, the probability that the selected group will consist of all Republicans is about 0.0513, or 5.13%.
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David is trying to pick out an outfit for the first day of school. He can choose from 8 pairs of pants, 8 t-shirts, 4 sweaters or hoodies, and 3 pairs of shoes. How many different outfits does David have to choose from?
Answers
The number of the different outfits do David have to choose is 768.
Here we will use the concept of Combinations,
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Different outfits do Damian have to choose, will be;
⇒ 8C₁×4C₁×8C₁×3C₁
⇒ 8×4×8×3
⇒ 768
Hence, the number of the different outfits do David have to select is 768.
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Please help solve for x image attached!
Answers
Answer:
7 should go in the green blank.
10/x = x/7
A country recently had a GDP of $1000 billion. Its consumption expenditures were $650 billion, its government spent $250 billion, and it had domestic investment of $150 billion. What was the value of this country’s net capital outflow?
Answers
The value of this country's net capital outflow is $200 billion.
We have,
The formula for net capital outflow (NCO) is:
NCO = Domestic Investment - Foreign Investment
Since the problem only gives us information about domestic investment, we need to use another formula to calculate foreign investment.
The formula for national saving (S) is:
S = GDP - Consumption Expenditures - Government Spending
We can rearrange this formula to solve for foreign investment:
Foreign Investment = GDP - Consumption Expenditures - Government Spending - Domestic Investment
Substituting the given values, we get:
Foreign Investment = $1000 billion - $650 billion - $250 billion - $150 billion
Foreign Investment = $1000 billion - $1050 billion
Foreign Investment = -$50 billion
The negative sign indicates that there is a net capital inflow (i.e., foreign investment is greater than domestic investment).
Therefore, the value of this country's net capital outflow is:
NCO = Domestic Investment - Foreign Investment
NCO = $150 billion - (-$50 billion)
NCO = $150 billion + $50 billion
NCO = $200 billion
Thus,
The value of this country's net capital outflow is $200 billion.
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The distance between cities A and B on a map is 12.5 in. The distance from city B to city C, is 8.5 in, and the distance from C to A is 16.25 in. If the bearing
from A to B is N75°E, find the bearing from C to 4. Round to the nearest tenth of a degree.
16.25 in
12.5 in
8.5 in
The bearing from city C to city 4 is approximately (Choose one) (Choose one)
Answers
The bearing of C to A is 239⁰.
What is the bearing of C to A?
The bearing of C to A is calculated by finding the value of angle C using cosine rule since we know the value of all the sides of the triangle.
AB² = AC² + CB² - 2(AC)(CB) cosC
12.5² = 16.25² + 8.5² - 2(16.25 x 8.5) x cos C
156.25 = 336.3125 - 276.25cosC
276.25cosC = 180.06
cosC = 180.06/276.25
cos (C) = 0.6518
C = cos⁻(0.6518)
C = 49.3⁰
The value of angle A is calculated as follows;
Sin A/CB = Sin C/AB
sin A/8.5 = sin 49.3/12.5
sin A = 8.5 [sin 49.3/12.5]
sin A = 0.5157
A = sin⁻¹ (0.5157)
A = 31⁰
The bearing of C to A is calculated as;
= 270⁰ - 31⁰
= 239⁰
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How many times greater is the
value of the 4 in 2,849 than the
value of the 4 in 3,824?
Answers
Answer:
The value of the 4 in 2,849 is 4 x 100 = 400, while the value of the 4 in 3,824 is 4 x 10 = 40. Therefore, the value of the 4 in 2,849 is 400/40 = 10 times greater than the value of the 4 in 3,824.
Step-by-step explanation:
(Identifying Transformations LC)
Use the image to determine the type of transformation shown.
Preimage of polygon ABCD. A second image, polygon A prime B prime C prime D prime to the right of the first image with all points in the same position.
Horizontal translation
Vertical translation
Reflection across the x-axis
90° clockwise rotation
Answers
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
Option A is the correct answer.
We have,
A horizontal translation moves every point of a figure the same distance in the same direction.
In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.
A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.
A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.
A 90° clockwise rotation would rotate the figure 90 degrees to the right.
Thus,
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
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Determine the value of y, if x is 3.
y = x² + 11
Answers
Answer:
20
Step-by-step explanation:
just a substitute 3 in x so 3x3=9
11+9=20
A virus takes 5 days to grow from 180 to 230. How many days will it take to grow from 180 to 260? Round to the nearest whole number.
Answers
It will take approximately 8 days for the virus to grow from 180 to 260.
We can set up a proportion to solve this problem. Let "x" represent the number of days it will take for the virus to grow from 180 to 260.
The proportion can be set up as follows;
(Change in value) / (Time taken) = (Change in value) / (Time taken)
Using the given information, we have;
(260 - 180) / x = (230 - 180) / 5
Simplifying the fractions on both sides of the equation, we get:
80 / x = 50 / 5
Cross-multiplying, we have;
80 × 5 = 50 × x
400 = 50x
Dividing both sides of the equation by 50, we get;
x = 400 / 50
x = 8
Therefore, it will take 8 days.
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full method please
-6+28÷(-4)
Answers
Answer:
-13
Step-by-step explanation:
To add fractions, find the lowest common denominator and then combine
A towns government is looking into its residences opinion on rebuilding the boardwalk on the coast line.
two representatives from the town visit the existing boardwalk and randomly survey 50 people to see whether they support the new boardwalk, they find that 60% of those surveyed support the construction of the new boardwalk and conclude with 90% confidence the majority of residents support its construction, what aspects of the scenario brings the validity of this conclusion into doubt
Answers
The aspects of the scenario that bring the validity of the conclusion made by the representatives of the government would be:
Small sample sizeSampling biasWhat reduced the validity of the sample ?The sample size used by the representatives in the survey was only 50 individuals, which might not be sufficient to represent the views of the entire town's population accurately. A more extensive sample size would provide a more precise approximation of the public opinion.
Moreover, the conductance of the survey on the existing boardwalk presents the possibility of sampling bias since those who visit the boardwalk could hold different opinions towards the new construction than those that do not visit.
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Ayuda por favor es para mañana, fracciones equivalentes. Doy coronita
Answers
These fractions are equivalent fractions by algebraic property:
Case 1: YES
Case 2: NO
Case 3: YES
Case 4: NO
Case 5: YES
Case 6: YES
Case 7: NO
Case 8: YES
Case 9: YES
Case 10: YES
Case 11: NO
Case 12: YES
Case 13: NO
Case 14: YES
Case 15: YES
Case 16: YES
Case 17: NO
Case 18: YES
How to determine if two fractions are equivalent
In this question we must check 18 cases of equivalent fractions, two fractions are equivalent if the following algebraic property is met:
a / b = (a · c) / (b · c), where a, b, c are integers and c is nonzero.
Now we proceed to determine if each pair is equivalent:
Case 1
2 / 3 = (2 · 2) / (3 · 2)
2 / 3 = 4 / 6 (YES)
Case 2
2 / 6 = (2 · 3) / (6 · 3)
2 / 6 = 6 / 18 (NO)
Case 3
9 / 9 = (9 · 4) / (9 · 4) = 36 / 36 (YES)
Case 4
3 / 11 = (3 · 3) / (11 · 3) = 9 / 33 (NO)
Case 5
7 / 8 = (7 · 2) / (8 · 2) = 14 / 16 (YES)
Case 6
4 / 6 = (4 · 5) / (6 · 5) = 20 / 30 (YES)
Case 7
5 / 6 = (5 · 2) / (6 · 2) = 10 / 12 (NO)
Case 8
2 / 7 = (2 · 4) / (7 · 4) = 8 / 28 (YES)
Case 9
6 / 12 = (6 · 2) / (12 · 2) = 12 / 24 (YES)
Case 10
4 / 9 = (4 · 5) / (9 · 5) = 20 / 45 (YES)
Case 11
9 / 10 = (9 · 3) / (10 · 3) = 27 / 30 (NO)
Case 12
1 / 5 = (1 · 5) / (5 · 5) = 5 / 25 (YES)
Case 13
12 / 12 = (12 · 3) / (12 · 3) = 36 / 36 (NO)
Case 14
8 / 11 = (8 · 4) / (11 · 4) = 32 / 44 (YES)
Case 15
5 / 5 = (5 · 4) / (5 · 4) = 20 / 20 (YES)
Case 16
6 / 9 = (6 · 4) / (9 · 4) = 24 / 36 (YES)
Case 17
3 / 7 = (3 · 8) / (7 · 8) = 24 / 56 (NO)
Case 18
10 / 12 = (10 · 4) / (12 · 4) = 40 / 48 (YES)
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answers
Answer:
first option
Step-by-step explanation:
differentiate using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{dt}[/tex] × [tex]\frac{dt}{dx}[/tex] = [tex]\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
y = t² + 4t
[tex]\frac{dy}{dt}[/tex] = 2t + 4
x = t - 3
[tex]\frac{dx}{dt}[/tex] = 1
then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{2t+4}{1}[/tex] = 2t + 4
Answer:
2t + 4
Step-by-step explanation:
A parametric equation is one where x and y are defined separately in terms of a third variable (often the parameter t).
To find dy/dx from parametric equations, differentiate each equation with respect to the parameter t, then use the chain rule:
[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}}[/tex]
Differentiate the two parametric equations with respect to t:
[tex]x=t-3 \implies \dfrac{\text{d}x}{\text{d}t}=1[/tex]
[tex]y=t^2+4t \implies \dfrac{\text{d}y}{\text{d}t}=2t+4[/tex]
Use the chain rule to combine them:
[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}\\\\&=(2t+4) \times \dfrac{1}{1}\\\\&=2t+4\end{aligned}[/tex]
Therefore:
[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=2t+4}[/tex]
I need help as soon as possible please??
Answers
Answer:
4x² - 11xy - 3y²
Step-by-step explanation:
(4x + y)(x - 3y) =
Multiply each term of the first binomial by each term of the second binomial.
= 4x² - 12xy + xy - 3y²
Now combine like terms.
= 4x² - 11xy - 3y²
In parallelogram ABCD, AE =3x +7and CE=x+25.
What is AC?
O 68
O 34
O 18
09
D
C
B
Answers
An insurance company offers an ordinary annuity that earns 6.5% interest compounded annually. A couple plans to make equal annual deposits into this account for 30 years and then make 20 equal annual withdrawals of €25,000, reducing the balance of the account to zero.
(i) Compute the value of the fund based on the withdrawals required. [5 marks]
(ii) Compute the amount of each deposit needed in order to maintain the fund. [5 marks]
(iii) Compute the total interest earned over the entire 50 years. [5 marks]
Answers
Answer:
(i) To compute the value of the fund based on the withdrawals required, we can use the formula for the future value of an annuity due:
FV = P * ((1 + r)^n - 1) / r) * (1 + r)
where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, n is the total number of periods, and the extra (1 + r) factor is because the payments are made at the beginning of each period.
In this case, P = €25,000, r = 0.065, n = 20. We want to find the future value at the end of the 20-year period:
FV = 25000 * ((1 + 0.065)^20 - 1) / 0.065) * (1 + 0.065)
FV ≈ €743,704.96
Therefore, the value of the fund based on the withdrawals required is approximately €743,704.96.
(ii) To compute the amount of each deposit needed in order to maintain the fund, we can use the formula for the present value of an ordinary annuity:
PV = P * ((1 - (1 + r)^(-n)) / r)
where PV is the present value of the annuity, P is the annual payment, r is the interest rate per period, and n is the total number of periods.
In this case, PV = €743,704.96, r = 0.065, n = 20. We want to find the annual payment:
PV = P * ((1 - (1 + 0.065)^(-20)) / 0.065)
P ≈ €22,630.53
Therefore, the amount of each deposit needed in order to maintain the fund is approximately €22,630.53.
(iii) To compute the total interest earned over the entire 50 years, we can subtract the total deposits from the total withdrawals, and then subtract the initial balance. The total deposits are the annual deposit amount times the number of years (30), and the total withdrawals are the annual withdrawal amount times the number of years (20). The initial balance is the present value of the annuity that we calculated in part (ii).
Total deposits = €22,630.53 * 30 = €678,915.90
Total withdrawals = €25,000 * 20 = €500,000
Initial balance = €743,704.96
Total interest earned = Total withdrawals - Total deposits - Initial balance
Total interest earned = €500,000 - €678,915.90 - €743,704.96
Total interest earned ≈ -€922,620.86
Note that the negative sign indicates that the insurance company actually earned interest on this annuity, rather than the couple earning interest on their investment. This is because the withdrawals are greater than the deposits, and the interest rate earned by the insurance company is greater than the interest rate paid to the couple.
Step-by-step explanation:
Answer all questions please
Answers
The value of f(1) is 3.
An estimate of the value of f(-1) is -0.2.
The values of x for which f(x) = 1 are: x = (0, 3).
The value of x such that f(x) = 0 is x = -0.5.
The domain of f is {-2, 4}.
The range of f is {-1, 3}.
The interval over which f is increasing is {-2, 1}.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of the function shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-2, 4}.
Range = {-1, 3}.
In conclusion, we can logically deduce that this function is increasing over the [-2, 1] and decreasing over the interval [1, 4].
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i need help with this prblem
Answers
Answer:
y = x + 2
Step-by-step explanation:
y = mx + b
Point (0, 2) shows that the y-intercept is 2, so b = 2.
y = mx + 2
Now we find the slope using the 2 points, (0, 2) and (2, 4).
m = (4 - 2)/(2 - 0) = 1
y = x + 2
The radius, R, of a sphere is 9.5cm . Calculate the sphere's volume,V . Use the value 3.14 for , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
Answers
The volume of a sphere of radius 9.5 cm is approximately 3589.5 cm³
Calculating the volume of a sphereFrom the question, we are to calculate the volume of a sphere
The volume of a sphere is given by the formula
V = 4/3 πr³
Where V is the volume of the sphere
and r is the radius of the sphere
From the given information,
r = 9.5 cm
Thus,
Volume of the sphere = 4/3 × π × 9.5³
Put π = 3.14
Volume of the sphere = 4/3 × 3.14 × 9.5³
Volume of the sphere = 3589.54333 cm³
Volume of the sphere ≈ 3589.5 cm³
Hence,
The volume of the sphere is 3589.5 cm³
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find the area of the figure (hint don’t forget units!)
5.2 ft 3 ft 2.4
Answers
Answer:
A = 11.4 ft²
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the bases
here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²
7.35 km = _______ mm
Answers
Answer: 7.35 km = 7350000 mm
Step-by-step explanation:
Multiply km by 1000000
7.35 * 1000000 = 7350000 mm
Let u = -2i+9j, v = 2i- j, and w= -4i. Find 3u - (2v-w).
3u - (2v-w) =
(Type your answer in terms of i and j.)
Answers
The value of 3u - (2v-w) is -6i + 25j.
We have,
u = -2i+9j, v = 2i- j, and w= -4i.
Now, 3u - (2v - w)
= 3(-2i + 9j) - [ 2(2i - j) - (-4i)]
= -6i + 27j - [4i - 2j + 4i]
= -6i + 27j - 4i - 2j + 4i
= -6i + 25j
Thus, the value of 3u - (2v-w) is -6i + 25j.
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