Answers
Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:
p(x) = (x + 1) q(x)
for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:
p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0
So,
0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c
= -5 + 7 - 2 + 3 + c
= c = 3
So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.
Related Questions
Simplify:
9 – 3 x 2 + 4
Answers
Answer:
2
:
5STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 5-3x2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step
2
:
5 - 3x2 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : -3x2+5 = 0
Subtract 5 from both sides of the equation :
-3x2 = -5
Multiply both sides of the equation by (-1) : 3x2 = 5
Divide both sides of the equation by 3:
x2 = 5/3 = 1.667
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 5/3
The equation has two real solutions
These solutions are x = ±√ 1.667 = ± 1.29099
Two solutions were found :
x = ±√ 1.667 = ± 1.29099
(1 point) Find an equation of a line perpendicular to 2 = 10 and passing through the point (3,2). The line is
Answers
An equation for a line perpendicular to the line 2 = 10 can be found by finding the slope of that line and then finding the slope of the perpendicular line. The slope of the line 2 = 10 is 0, so the slope of the perpendicular line would be undefined.
The equation of a line with slope m passing through the point (x1, y1) can be written in the form:
y - y1 = m(x - x1)
Since the slope of the line is undefined, the equation of the line would be in the form:
x - x1 = constant
To find the equation of the line that passes through the point (3, 2), we substitute the values into the equation:
x - 3 = constant
So the equation of the line that is perpendicular to the line 2 = 10 and passes through the point (3, 2) is:
x - 3 = constant
or simply:
x = 3.
A differentiable function f(x,y) has the property that f(5,4)=7 and fx(5,4)=-3 and fy(5,4)=7. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=5, y=4
Answers
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) is z = -3x + 7y + 8.
In 3-space, the plane tangent to a surface at a point can be imagined similarly to how we can see the line perpendicular to a curve at a point in 2-space.
The equation of the tangent plane at the point (5,4,7) on the surface z=f(x,y) can be found using the following formula:
z - [tex]z_{0}[/tex] = fx([tex]x_{0}[/tex],[tex]y_{0}[/tex])(x - [tex]x_{0}[/tex]) + fy([tex]x_{0}[/tex],[tex]y_{0}[/tex])(y - [tex]y_{0}[/tex])
where ([tex]x_{0},y_{0},z_{0}[/tex]) is the point on the surface at which we want to find the tangent plane, and fx([tex]x_{0}[/tex],[tex]y_{0}[/tex]) and fy([tex]x_{0}[/tex],[tex]y_{0}[/tex]) are the partial derivatives of f with respect to x and y, respectively, evaluated at ([tex]x_{0}[/tex],[tex]y_{0}[/tex]).
In this case, we have [tex]x_{0}[/tex] = 5, [tex]y_{0}[/tex] = 4, [tex]z_{0}[/tex] = f(5,4) = 7, fx(5,4) = -3, and fy(5,4) = 7. Substituting these values into the formula, we get:
z - 7 = (-3)(x - 5) + (7)(y - 4)
Simplifying this equation, we get:
z = -3x + 7y + 8
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The area of a rectangular living room is 192 square feet. The length of the room is 8 feet less than twice the width. What is the width of the living room in feet?
Answers
Answer:
The width of the living room is 10 feet.
Step-by-step explanation:
Let the width of the living room is w.
And the length of the room is 2w - 8 ft.
Given,
The area of the room is 192 feet^2, by using the formula of area of a rectangle we get,
A = l × w
192 = (2w - 8) × w
Now,
192 = 2w^2 - 8w ( By expanding)
200 = 2w^2 (By adding 8w to both sides)
100 = w^2 (Dividing both sides by 2)
If we take square root on both sides,
w = 10
So,
The width of the living room is 10 feet.
PLEASE HELP!!! VERY URGENT
A person walks due south from point A for 500 yards and then due west for 300 yards, arriving at point B. Answer the following questions using complete sentences. 2 points for each correct answer and 2 points for each correct explanation.
i. What is the person's displacement from the starting point? How did you calculate this? Be sure to round to the nearest hundredth.
ii. From point B, in what direction would the person have to look in order to be looking back at point A (the starting point)? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
iii. A friend is standing at point A looking at point B. In what direction would that friend be looking? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
Answers
The answers are mentioned below.
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).
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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.
Therefore, the displacement can be calculated as the
√(500² + 300²)
= 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.
Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be
360 - 31.39
= 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.
However, the true bearing is measured from the north and therefore, the true bearing would be
90 + 59.04
= 149.04 degrees (rounded to the nearest hundredth).
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Bodmas sums
2.4of4.5-5.6/1.4+3.8*2
Answers
On solving the provided question, we can say that By BODMAS, 2.4of4.5-5.6/1.4+3.8*2 => 10.8-5.6/1.4+3.8*2 => 10.8-4+3.8*2 = > 14.4
what is BODMAS ?The abbreviation BODMAS aids kids in recalling the hierarchy of mathematical operations (the correct order for solving math problems). The acronym BODMAS is made up of the following terms: B Bracket, O Degree (Power/Exponent or Root), D Division, M Multiplication, A Addition, and S Subtraction. BODMAS is also referred to as PEDMAS in some locales. This symbolizes exponents, division, multiplication, addition, and subtraction. It also represents parentheses. The BODMAS rule states that parentheses must be handled first, followed by powers or roots (i.e., of), divisions, multiplications, additions, and lastly subtractions. While he is known as BODMAS in India and the UK, PEMDAS is primarily utilized in the US. However, they are identical to one another. The parentheses, order, and order of the operations of addition, subtraction, multiplication, and division are the same for the two rules.
By BODMAS
2.4of4.5-5.6/1.4+3.8*2
10.8-5.6/1.4+3.8*2
10.8-4+3.8*2
10.8-4+7.6
14.4
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A train travelling at 105km/hr goes through a tunnel 1575m long. Calculate in seconds,the time a passenger on the train spends in the tunnel
Answers
Correct me if im wrong :)
-2√x+5 +1
End behavior
Answers
Answer: The end behavior of a function is the behavior of the function as x approaches positive infinity or negative infinity.
For the function f(x) = -2√x + 5 + 1, as x approaches positive infinity, the square root of x approaches positive infinity as well. So, the function approaches negative infinity as x approaches positive infinity:
lim x → ∞ f(x) = lim x → ∞ -2√x + 5 + 1 = -∞
As x approaches negative infinity, the square root of x approaches 0, so the function approaches:
lim x → -∞ f(x) = lim x → -∞ -2√x + 5 + 1 = 7
Therefore, the end behavior of the function is that it approaches negative infinity as x approaches positive infinity, and it approaches 7 as x approaches negative infinity.
Step-by-step explanation:
Distance formula is D=~^ (X2-X1)*2 + (Y2- Y1)*2
pls help!
Answers
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})\qquad P2(\stackrel{x_2}{-3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{(~~-3 - 6~~)^2 + (~~5 - 3~~)^2} \implies P1P2=\sqrt{( -9 )^2 + ( 2 )^2} \\\\\\ P1P2=\sqrt{ 81 + 4 } \implies P1P2=\sqrt{ 85 }[/tex]
Q.Find the mistake made in the steps and justifications for solving the equation below.
Picture attached?
A. The justification for step 1 is incorrect and should be the multiplication property of equality.
B. The justification for step 3 is incorrect and should be the addition property of equality.
C. Step 5 is incorrect and should show be x=10/16.
D. Step 4 is incorrect and should be 10x = 24.
Answers
Answer:
The correct answer is D. Step 4 is incorrect and should be 10x = 24.
(1) Find the temperature at 8:00 pm and midnight in your town. Then find the find the Difference between the two Temperatures.
(2) Clear Parenthesis and combine like terms, 12-3(x+2y-5).
Answers
1. The difference between the temperature is 14°C.
2. The value of the expression will be -3x - 6y + 27.
How to calculate the valueThe difference between the temperature will be:
= -10 + 24
= 14°C.
For the second part of your question, to clear the parenthesis in the expression "12 - 3(x + 2y - 5)", you can first simplify the expression inside the parenthesis:
x + 2y - 5
Next, multiply this expression by 3:
3(x + 2y - 5) = 3x + 6y - 15
Finally, substitute this back into the original expression:
12 - 3(x + 2y - 5) = 12 - (3x + 6y - 15) = 12 - 3x - 6y + 15 = -3x - 6y + 27
So, the final expression after clearing the parenthesis and combining like terms is -3x - 6y + 27.
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Convert 40 fluid ounces to pints.
Answers
Answer:The answer is 2.5 pints.
Graph the function y=x/4
Answers
Answer:
Step-by-step explanation:
Suppose that the world's current oil reserves is R = 2090 billion barrels. If, on average, the total reserves is decreasing by 18 billion barrels of oil each year, answer the following: A.) Give a linear equation for the total remaining oil reserves, R , in terms of t , the number of years since now. (Be sure to use the correct variable and Preview before you submit.) R = B.) 15 years from now, the total oil reserves will be billions of barrels. C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately years from now. (Round your answer to two decimal places.)
Answers
a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.
b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.
c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.
What is a linear equation?A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.
A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.
The current total world oil reserves, R = 2,090 billion barrels
Average decrease per year = 18 billion barrels
a) Linear equation for R is 2,090 - 18t
b) In 15 years, the total oil reserves = 2,090 - 18(15)
= 2,090 - 270
= 1,820
c) The constant rate of decrease = 18 billion barrels per year
The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).
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Isosceles trapezoid KRWT is shown
Given KRWT is an isosceles trapezoid with KR and TW
Prove: WK = TR
An incomplete two-column proof is shown
Answer Choices:
-
-
-
-
What is the missing statement in step 3
More info is in the picture
Thank you for any help!
Answers
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In isosceles trapezoid KRWT, the trianngles are ΔKTW and ΔRWT are formed.
In trianngles ΔKTW and ΔRWT, then we have
KW = TR {Given}
∠W = ∠T {Isosceles angles}
WT = WT {Common side}
Then the trianngles ΔKTW and ΔRWT are congruent to each other.
The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.
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Annie made 4 glasses of juice,her 5 friends drank 1/2 glass each.what fraction of juice was left? how to solve it
Answers
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank [tex]\frac{1}{2}[/tex] glass each.
Meaning of fraction = An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
Annie made 4 glasses of juice
To find = fraction of juice that was left
Total glasses of juice = 4
Her 5 friends drank 1/2 glass each
= 5 × [tex]\frac{1}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
Fraction of juice that left,
5 - [tex]\frac{5}{2}[/tex]
Subtracting by taking LCM,
= [tex]\frac{10 - 5}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank 1/2 glass each.
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Fill in the table for y = 3x - 1
Answers
Answer:
1. -7
2. -1
3. 5
Step-by-step explanation:
Substitute the value given into the equation
Complete this sentence: The longest side of a triangle is always opposite the
• A. angle with the greatest measure
• B. second-longest side
• C. shortest side
• D. angle with the smallest measure
Answers
The longest side of a triangle is always opposite the,
A. angle with the greatest measure.
What is the way of classifying a triangle?If a² + b² < c² then it is an acute angle triangle.
If a² + b² = c² then it is a right-angle triangle.
If a² + b² ≥ c² then it is an obtuse angle triangle.
We know, The length of the largest side in a triangle is opposite to the largest angle.
The statement, The longest side of a triangle is always opposite the
angle with the greatest measure.
Because A longer angle will be more spread out and hence the opposite side will be longer too.
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Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales orice Zion Sun
Chairs must sell each chair for to earn a monthly profit of $65,000, if of the total monthly fixed costs are $17,363.50
and the variable cost per chair is $52.17.
• $71.49
• $75.21
O $23.04
O $25.67
Answers
Zion Sun Chairs must sell each chair for at least $75.21 to earn a monthly profit of $65,000.
To determine the minimum sales priceTo determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $65,000, we can use the following formula:
Total Profit = Total Revenue - Total Cost
We know that the monthly fixed costs are $17,363.50, and the variable cost per chair is $52.17. Therefore, the total cost to produce 3,575 beach chairs each month can be calculated as follows:
Total Cost = Fixed Cost + (Variable Cost per Chair x Number of Chairs)
Total Cost = $17,363.50 + ($52.17 x 3,575)
Total Cost = $203,871.25
To earn a monthly profit of $65,000, we can set up the equation as follows:
$65,000 = Total Revenue - $203,871.25
Total Revenue =$268,871.25
To find the minimum sales price per chair, we can divide the total revenue by the number of chairs:
Minimum Sales Price per Chair = Total Revenue / Number of Chairs
Minimum Sales Price per Chair = $268,871.25 / 3,575
Minimum Sales Price per Chair ≈ $75.208
Therefore, Zion Sun Chairs must sell each chair for at least$75.21 to earn a monthly profit of $65,000, given the monthly fixed costs, variable cost per chair, and production quantity.
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y=-2x-5 solve algebraically
Answers
The graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y=2x-5.
Substitute x=0, 1, 2, 3, 4, ..... in the equation y=2x-5, we get
When x=0,
y=-5
When x=1,
y=-3
When x=2,
y=-1
When x=3
y=1
So, the ordered pair is (0, -5), (1, -3), (2, -1), (3, 1) and so on.
Therefore, the graph of ordered pairs (0, -5), (1, -3), (2, -1), (3, 1) is given below.
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Suppose a biologist tagged 53 penguins in antarctica during mating season. The next year, they caught 82 and found that 11 of them had tags. Estimate the total number penguins in the area.
Answers
It can be estimated that there are 395 penguins in the area.
What is Proportion ?Proportion is a mathematical comparison between two numbers. According to proportion, two sets of specified numbers are said to be directly proportional to each other if they increase or decrease in the same ratio. Symbols of proportions include "::" and "=".
We approach this problem by doing a simple proportion.We can presume that the same proportion of penguins were tagged during mating season if the biologists discovered 11 tagged individuals out of 82 penguins.
The proportion should therefore be [tex]x:53=82:11[/tex] where x represents the total number of penguins. By solving this proportion, we may determine what x is worth:
[tex]11x=53*82\\\\11x=4346\\\\x=395.0909[/tex]
Since there is no such thing as half a penguin, we can round off the answer to the nearest unit.
395 penguins are in the area according to our estimation.
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PLEASE HELP ME ASAP
5. The first row of a stem-and-leaf chart appears as follows: 62 | 1 3 3 7 9. Assume whole
number values.
a. What is the "possible range" of the values in this row?
b. How many data values are in this row?
c. List the actual values in this row of data.
Answers
b. There are 5 data values in this row.
c. The actual values in this row of data are 621, 623, 623, 627, and 629.
5.3A Find Two Numbers Whose Product and Sum is as Indicated
Answers
Due to length restrictions, we kindly invite to read the explanation of this question for further details about two numbers related to a given sum and a given product.
How to find a set of two real numbers
In this problem we find 48 case of two numbers that must be found and whose sum and product are given. Mathematically speaking, the expressions describing the problem:
x₁ + x₂ = b
x₁ · x₂ = c
Whose solution can be found by numerical methods.
Now we proceed to determine the values for each cases:
(x₁, x₂) = (6, 1)(x₁, x₂) = (4, 9)(x₁, x₂) = (3, - 2)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (- 8, 2)(x₁, x₂) = (2, - 2)(x₁, x₂) = (4, - 2)(x₁, x₂) = (- 4, 3)(x₁, x₂) = (- 5, - 4)(x₁, x₂) = (5, - 3)(x₁, x₂) = (6, 2)(x₁, x₂) = (- 2, - 3)(x₁, x₂) = (- 2, - 7)(x₁, x₂) = (2, 8)(x₁, x₂) = (11, - 2)(x₁, x₂) = (5, - 4)(x₁, x₂) = (- 8, 1)(x₁, x₂) = (8, - 3)(x₁, x₂) = (7, 8)(x₁, x₂) = (8, 8)(x₁, x₂) = (6, 4)(x₁, x₂) = (6, 9)(x₁, x₂) = (3 - 2√2, 3 + 2√2)(x₁, x₂) = (9, - 4)(x₁, x₂) = (8, - 7)(x₁, x₂) = (- 4, - 9)(x₁, x₂) = (8, - 2)(x₁, x₂) = (- 9, - 9)(x₁, x₂) = (- 15, 3)(x₁, x₂) = (7, - 6)(x₁, x₂) = (- 7, - 7)(x₁, x₂) = (- 8, - 8)(x₁, x₂) = (12, - 3)(x₁, x₂) = (- 3, - 8)(x₁, x₂) = (4, - 3)(x₁, x₂) = (- 12 - √119, - 12 + √119)(x₁, x₂) = (7, - 4)(x₁, x₂) = (- 6, - 9)(x₁, x₂) = (5, 7)(x₁, x₂) = (- 8, 4)(x₁, x₂) = (- 7, 6)(x₁, x₂) = (5 / 2 + √73 / 2, 5 / 2 - √73 / 2)(x₁, x₂) = (5, 6)(x₁, x₂) = (- 10, 4)(x₁, x₂) = (- 9, 4)(x₁, x₂) = (- 9, 7)(x₁, x₂) = (6, 8)(x₁, x₂) = (- 7, 3)To learn more on real numbers: https://brainly.com/question/24908711
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Consider a lease for 120,000 square feet of space and specifies base rent of $5 psf. In addition, the lease provides for percentage rent of 3% of sales in excess of the natural breakpoint. a) Calculate the natural breakpoint for this lease.
Answers
Answer:
$20M
Step-by-step explanation:
You want the "natural breakpoint" for a lease that specifies rent is the maximum of $5 per square foot for 120,000 square feet, or 3% of sales.
Minimum rentThe minimum rent is ($5/ft²)×(120000 ft²) = $600,000.
BreakpointThe amount of sales that makes $600,000 equal to 3% of sales is ...
$600000 = 0.03s
s = $600000/0.03 = $20,000,000
The "natural breakpoint" is $20M in sales.
__
Additional comment
When sales exceeds $20M, 3% of sales is more than $5/ft², so the rent will be based on sales.
Help me with this question…..
Answers
The volume of the cone shown can be described to be A. 513 π cubic units
How to find the volume of a cone ?The volume of a cone can be found by the formula :
= π x radius ² x height / 3
The radius of this cone is 9 units and the height is 19 units.
The volume of this cone then is :
= π x radius ² x height / 3
= π x 9 ² x 19/ 3
= π x 81 x 19/ 3
= π x 513
= 513 π cubic units
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Solve the question with Steps
Answers
The solution of the question sin(50)sin(80)cos(50)cos(80) is cos^2(80o), the correct option is D.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot. Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).
Given;
sin(50)sin(80)cos(50)cos(80)
Now,
=sin(20°)cos(80°) – cos(20°)sin(80°)
=sin(A-B) = sinA.cosB – cosA.sinB
=sin(20°-80°)
=sin(-60°)
=cos^2(80o)
Therefore, by trigonometry the answer will be cos^2(80o).
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Find dy/dx by implicit different iation xy^2= 4.
Answers
The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).
What is differentiation by parts?By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.
Given function is xy²= 4. The given expression will be different as below,
dy / dx ( xy² ) - 4 = 0
2xy( dy / dx) + y² = 0
dy / dx = -y / 2x
Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).
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Need help on algebra please
Answers
Answer:
Step-by-step explanation:
PLS help fast this is the last day for my test solve the system of linear equations. check your solution. 3y+4y=-10 y=-3/4x - 5/2
Answers
This equation has infinitely many solutions.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here, we have
Given: 3x+4y = -10...(1),
y = -3/4x - 5/2....(2)
We solve this linear equation and we get
We multiply equation (2) by 4 and we get
4y + 3x = -5(2)
4y + 3x = -10
Hence, this equation has infinitely many solutions.
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If it takes 6 people 8 hours to finish the job, how long would it take 4 people?
Answers
12 hours
If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours
Answer:
5.333 hours.
Step-by-step explanation:
Put this on a chart:
6 people = 8 hours
4 people = ? hours
To find ? Use crisscross multiplication and solve:
? = (4 * 8) / 6
? = 32 / 6
? = 5.333
Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.
