To find f(-1), we can use the fact that the derivative of a function f(x) gives us the slope of the tangent line to the graph of f(x) at any point x. We can use this information along with the given value of f(1) to find the equation of the tangent line at x=1, and then use that equation to find the value of f(-1).
First, we find the equation of the tangent line at x=1:
- The slope of the tangent line at x=1 is f'(1) = 833 + 12(1) + 2 = 847
- The point (1, f(1)) lies on the tangent line, so we can use the point-slope form of the equation of a line to write the equation of the tangent line:
y - (-4) = 847(x - 1)
y + 4 = 847x - 847
y = 847x - 851
Now we can use this equation to find f(-1):
- The point (-1, f(-1)) also lies on the tangent line, so we can substitute x=-1 and solve for y:
f(-1) + 4 = 847(-1) - 851
f(-1) + 4 = -1698
f(-1) = -1702
Therefore, f(-1) = -1702.
To find f(-1), we first need to determine the function f(x). We know f'(x) = 833 + 12x + 2. To find f(x), we need to integrate f'(x) with respect to x:
∫(833 + 12x + 2) dx = 833x + 6x^2 + 2x + C
Now, we use the given condition f(1) = -4 to find the constant C:
-4 = 833(1) + 6(1)^2 + 2(1) + C
Solve for C:
C = -4 - 833 - 6 - 2 = -845
Now we have the function f(x) = 833x + 6x^2 + 2x - 845. To find f(-1), plug in x = -1:
f(-1) = 833(-1) + 6(-1)^2 + 2(-1) - 845
f(-1) = -833 + 6 - 2 - 845
f(-1) = -1674
So, f(-1) equals -1674.
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How much must be deposited today into the following account in order to have a $110,000 college fund in 17 years? Assume no additional deposits are made.
An account with quarterly compounding and an APR of 4.9%
Therefore, an initial deposit of $37,728.66 is required to have a college fund of $110,000 in 17 years with quarterly compounding and an APR of 4.9%.
What is a deposit used for?An amount held in an account is referred to as a deposit. It might be put up in a bank as collateral for goods that are being rented out or bought. A deposit is used in many different sorts of economic transactions.
Compound interest can be calculated using the following formula to determine the required down payment:
A = P(1 + r/n)(nt)
where:
A = the future value of the account (in this case, $110,000)
P = the principal or initial deposit
r = the annual interest rate (4.9%)
n = the number of times the interest is compounded per year (4 for quarterly compounding)
t = the number of years (17)
When we enter the specified numbers into the formula, we obtain:
$110,000 = P(1 + 0.049/4)(4*17)
$110,000 = P(1.01225)⁶⁸
$110,000 = P * 2.9126
Dividing both sides by 2.9126, we get:
P = $37,728.66
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What is the volume of this shape? help me please i really need help
The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.
A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.
Volume of cube = length × breadth × height
length = 5 unit
breadth = 5 unit
height = 5 unit
Volume = 5 × 5 × 5
= 125 unit³
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Mrs. Ramirez worked on her personal trainer to help develop a nutrition plan. The circle graph shows the recommended percentages for her daily intake. If she will be eating 1800 cal, then how many calories should be from proteins?
630 calories of total calory intake of Mrs. Ramirez should be from proteins.
From the circle graph we can see that,
percentage of calories from fruits is = 15%
percentage of calories from grains is = 15%
percentage of calories from vegetables is = 25%
percentage of calories from proteins is = 35%
percentage of calories from Dairy is = 10%
Here it is also given that Mrs. Ramirez need to eat 1800 calories.
So the calories should be from proteins
= 35% of 1800 calories
= (35/100)*1800 calories
= 35*18 calories
= 630 calories.
Hence, 630 calories should be from proteins.
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The question is incomplete. The complete question will be -
QuestionThe mean monthly salary of the 12 employees of a firm is Rs. 1450. If one more person joins the firm who gets Rs. 1645 per month, what will be the mean monthly salary of 13 employees?ARs. 1465BRs. 1954CRs. 2175DRs. 2569Medium
1465 will be the mean monthly salary .The answer is (A) Rs. 1465.
Let the sum of the 12 employees' salaries be S.
Then, the mean monthly salary of the 12 employees is given by:
S/12 = 1450
S = 12 * 1450
S = 17400
If one more person joins with a salary of Rs. 1645, the new sum of the 13 employees' salaries is:
S' = S + 1645
S' = 17400 + 1645
S' = 19045
The new mean monthly salary of the 13 employees is:
S'/13 = 19045/13
S'/13 = 1465
Therefore, the answer is (A) Rs. 1465.
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3 For y=f(x) = 9x, x= 3, and Ax = 0.03 find a) y for the given x and Ax values, b) dy = f'(x)dx, to) dy for the given x and Ax values.
a) To find y for the given x and Δx values, first calculate x + Δx:
x + Δx = 3 + 0.03 = 3.03
Now, use the function y = f(x) = 9x to find the y values:
y = 9(3) = 27 (for x = 3)
y = 9(3.03) = 27.27 (for x = 3.03)
b) To find dy, we first need to find the derivative of the function (f'(x)). The function is y = f(x) = 9x, and its derivative (using differentiation) is:
f'(x) = 9
c) To find dy for the given x and Δx values, we can now use the formula dy = f'(x)dx:
dy = f'(x)dx = 9(0.03) = 0.27
So, for the given x and Δx values, a) y is 27 and 27.27, b) dy is equal to 9, and c) dy for the given x and Δx values is 0.27.
What 2 number multiple to make -14 and add to make -3?
By using factoring and the zero product property the two numbers that multiply to make -14 and add to make -3 are -7 and 4.
What is zero product property?The zero product property is a fundamental property of algebra that states that if the product of two or more factors is zero, then at least one of the factors must be zero. In other words, if a × b = 0, then either a = 0 or b = 0 or both a and b are zero. This property is often used to solve equations and factor polynomials. For example, if we have the equation (x - 3)(x + 5) = 0, we know that the only way the product can be zero is if one of the factors is zero, so we set each factor equal to zero and solve for x:
(x - 3)(x + 5) = 0
x - 3 = 0 or x + 5 = 0
x = 3 or x = -5
Thus, the solutions to the equation are x = 3 and x = -5.
According to the given informationWe can solve this problem by using factoring and the zero product property.
First, we need to find two numbers that multiply to make -14. The factors of -14 are (-1, 14) and (1, -14), so the two numbers could be -1 and 14, or 1 and -14.
Next, we need to find which pair of numbers adds up to -3. The only pair of numbers that works is -7 and 4 because (-7) + 4 = -3.
Therefore, the two numbers that multiply to make -14 and add to make -3 are -7 and 4.
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A coin (H: heads; T: tails) is flipped and a number cube (1, 2, 3, 4, 5, 6) is rolled. What is the sample space for this experiment?
The sample space for this experiment contains a total of 12 possible outcomes.
How to find the probability and determine the sample space?The sample space for this experiment is the set of all possible outcomes. In this case, we have two independent events: flipping a coin and rolling a number cube.
The possible outcomes for flipping a coin are H (heads) and T (tails).
The possible outcomes for rolling a number cube are 1, 2, 3, 4, 5, and 6.
To determine the sample space for the experiment, we need to consider all possible combinations of these outcomes. Therefore, the sample space consists of all possible pairs of outcomes:
Sample space = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
So the sample space for this experiment contains a total of 12 possible outcomes.
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Help with this please
Answer:
sin(θ) = (2/9)√14; csc(θ) = (9√14)/28cos(θ) = 5/9; sec(θ) = 9/5tan(θ) = (2/5)√14; cot(θ) = (5√14)/28Step-by-step explanation:
Given cos(θ) = 5/9, you want the six trig functions of θ.
IdentitiesThe relevant identities are ...
sin(θ) = ±√(1 -cos(θ)²)tan(θ) = sin(θ)/cos(θ)csc(θ) = 1/sin(θ)sec(θ) = 1/cos(θ)cot(θ) = 1/tan(θ)SineThe sine of θ is ...
sin(θ) = √(1 -(5/9)²) = √(81 -25)/9 = (√56)/9
sin(θ) = (2/9)√14
Then the cosecant is ...
csc(θ) = 1/sin(θ) = (9/2)/√14
csc(θ) = (9√14)/28
TangentThe tangent of θ is ...
tan(θ) = sin(θ)/cos(θ) = ((2/9)√14)/(5/9)
tan(θ) = (2/5)√14
Then the cotangent is ...
cot(θ) = 1/tan(θ) = (5/2)/√14
cot(θ) = (5√14)/28
SecantThe secant of θ is ...
sec(θ) = 1/cos(θ) = 1/(5/9)
sec(θ) = 9/5
The cosine is given in the problem statement.
Find the perimeter of a square that has a side length of 4.3x + 2 inches.
The calculated perimeter of the square from the side length is 17.2x + 8
Finding the perimeter of a square from the side lengthFrom the question, we have the following parameters that can be used in our computation:
A square that has a side length of 4.3x + 2 inches.
Using the above as a guide, we have the following:
Perimeter = 4 * side length
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 4 * (4.3x + 2)
When teh brackets are opened, we have
Perimeter = 17.2x + 8
Hence, the perimeter is 17.2x + 8
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Helppp translation and reflection
The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.
How to compute the image of a point by translation
In this problem we find must determine the image of two points by translation, whose formula is introduced below:
T(x, y) = P'(x, y) - P(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.First, determine the translation vector:
T(x, y) = (1, 4) - (0, 0)
T(x, y) = (1, 4)
Second, determine the images of points B and C:
B'(x, y) = (- 3, 2) + (1, 4)
B'(x, y) = (- 2, 6)
C'(x, y) = (- 2, 3) + (1, 4)
C'(x, y) = (- 1, 7)
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If donuts are 12 cents a dozen how much does 100 donuts cost.
The cost of 100 donuts is $ 1 if a dozen of donuts cost 12 cents.
This question is solved using the unitary method. The unitary method is a method in which you find the value of a unit and then the value of the required number of units.
1 dozen refers to a group of 12.
Cost of 1 dozen donuts or 12 donuts = 12 cents
Cost of 1 donut = [tex]\frac{12}{12}[/tex] = 1 cent
Cost of 100 donuts = 1 * 100 = 100 cents
100 cents = 1 dollar.
Thus, the cost of 100 donuts is 100 cents or 1 dollar.
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ANSWER THE QUESTIONS A AND B ! 1ST ONE WHO ANSWERS WITH A CORRECT ANSWER WILL BE MARkED BRAINLIEST!
Answer:
A is -4.5,2 and B is 0,-3.5
Step-by-step explanation:
Answer:
Coordinates of A: (-4.5, 2), Coordinates of B: (0, -3.5)
5) Write the rule for the reflection shown below.
Answer: 2,2
Step-by-step explanation: if you have the 2,-2 then that would be your answer because the reflection is the same as the 2,-2 but on a different thing
How much would you have to deposit in
an account with a 4.75% interest rate,
compounded continuously, to have
$20,000 in your account 20 years later?
Answer:
Pe^(.0475 × 20) = $20,000
P = $7,734.82
6. (07.06 LC)
Given a polynomial f(x), if (x-4) is a factor, what else must be true? (3 points)
Of(0) = 4
Of(0) = -4
Of(4) = 0
Of(-4)=0
None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0
What is a statement?
A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.
What is meant by factor?
A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.
According to the given information
If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.
Therefore, the correct statement is: f(4) = 0
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A smart phone screen measures 5 inches by 7 inches. It is surrounded by a frame of width w. Write an expression in standard form for the total area of the screen and frame
Answer:
4x² + 24x + 35
Step-by-step explanation:
Total area = (7 + 2x)(5 + 2x)
= 35 + 10x + 14x + 4x²
= 4x² + 24x + 35
Consider triangle ABC with vertices A(0,0), B (0,6), and C (4,0). The image of triangle ABC after a dilation has vertices A'(0,0), B' (0,21), and C' (14,0).
What is the scale factor of the dilation?
k = ?
Answer:
k=0.3
Step-by-step explanation:
Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get 2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get 16 = 2x Dividing both sides by 2, we get x=8
Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation.
f(x) = 4 tan x- 6x, Xo = 1,4
After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.
To compute the first 10 iterations of Newton's method for the given function and initial approximation, follow these steps:
1. Write down the function and its derivative:
[tex]f(x) = 4 * tan(x) - 6 * x
f'(x) = 4 * sec^2(x) - 6[/tex]
2. Define the initial approximation, X₀ = 1.4.
3. Apply Newton's method formula to find the next approximation, X₁:
X₁ = X₀ - f(X₀) / f'(X₀)
4. Repeat steps 3-4 for a total of 10 iterations (X₁ to X₁₀).
Note that I'm unable to perform calculations on this platform, but I'll provide a general outline for performing the iterations:
Iteration 1 (X₁):
[tex]X₁ = 1.4 - (4 * tan(1.4) - 6 * 1.4) / (4 * sec^2(1.4) - 6)[/tex]
Iteration 2 (X₂):
[tex]X₂ = X₁ - (4 * tan(X₁) - 6 * X₁) / (4 * sec^2(X₁) - 6)[/tex]
Repeat these steps up to the 10th iteration (X₁₀).
After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.
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Jessica's cookie recipe calls for 1 1/2
cups of flour. She only has enough
flour to make 1/3 of a batch. How much
flour does she have?
A 1/3 cup
B 1/2 cup
C 1 cup
D 2 cups
Answer:
B
Step-by-step explanation:
1 1/2 x 1/3
=1/2
So therefore the answer is B (1/2 cup)
Answer:
The answer is B ( 1/2 cup)
The null and alternate hypotheses are:
H0 : μd ≤ 0
H1 : μd > 0
The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of 4 days last month.
Day: 1, 2, 3, 4
Day Shift: 12, 16, 20, 24
Afternoon Shift: 12, 10, 16, 18
At the 0. 05 significance level, is there a difference in the mean number of citations given by the two shifts?
a. What is the p-value?
Note that where the above statistics are give, the p-value is 0.04.
What is the explanation for the above ?1st , we calculate the differences between the number of citations given in the day shift and afternoon shift for each day
Differences - 0, 6, 4, 6
The mean difference is (m) = (0 + 6 + 4 + 6) / 4 = 4
The sample standard deviation of the differences is s = √ ([((0-4)² + (6-4)² + (4-4)² + (6-4)²)/3]) = 2.31
The standard error of the mean difference is SE(m) = s / √(n) = 2.31 / √(4) = 1.155
The t-statistic is t = (m - 0) / SE(m) = 4 / 1.155 = 3.4632034632
The paired t-test has n-1=3 degrees of freedom. We calcu0late the p-value associated with a t-statistic of 3.46 using a t-table or a t-distribution calculator with three degrees of freedom.
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G
Given: ABCD is a trapezoid.
BA CD
CA
Prove: BD
Proving Trapezoid Theorems
C
Pretests
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Angles Segments Triangles Statements Reasons
ZBAD
Statements
ZCDA
Reasons
BD = CA is proved using the Pythagorean theorem.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as 1/2 x the sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
From the trapezium ABCD,
BA = CD ______(A)
Now,
We can have two triangles:
ΔABD and ΔACD
Using the Pythagorean theorem.
BD² = AB² + AD² _____(1)
And,
CA² = CD² + AD² ______(2)
From (1), (2), and (A).
BD² = BA² + AD²
CA² = BA² + AD²
This means,
BD² = CA²
BD = CA
Proved
Thus,
BD = CA can be Proven as above.
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Answer:
Step-by-step explanation:
Given y = 4x² + 3x, find dy/dt when x= -1 and dx/dt = 3(Simplify your answer.)
Given the function y = 4x² + 3x, we will find dy/dt by differentiating y with respect to t. Therefore, the value of dy/dt is -15.
Using the chain rule, we have:
dy/dt = (dy/dx)(dx/dt)
Differentiating y with respect to x, we get:
dy/dx = 8x + 3
Now, we are given that x = -1 and dx/dt = 3. We can substitute these values into our equation:
dy/dt = (8(-1) + 3)(3)
dy/dt = (-5)(3)
dy/dt = -15
So, when x = -1 and dx/dt = 3, the value of dy/dt is -15.
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Hey, I'm struggling with this lately, please help!
The measure of the exterior angle of the triangle is 128°.
How to find the measure of the exterior angle?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Trigonometric functions are the functions that denote the relationship between angle and sides of a right-angled triangle.
Sin θ = Opposite Side/Hypotenuse
Cos θ = Adjacent Side/Hypotenuse
Tan θ = Opposite Side/Adjacent
Recall that the measure of the exterior angle of a triangle is the sum of the opposite interior angles. That is:
x = 38 + 90
x = 128°
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When Nabhitha goes bowling, her scores are normally distributed with a mean of 115
and a standard deviation of 11. What percentage of the games that Nabhitha bowls
does she score between 93 and 142, to the nearest tenth?
The percentage of the games that Natasha scores between 93 and 142 is given as follows:
96.9%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation are given as follows:
[tex]\mu = 115, \sigma = 11[/tex]
The proportion of games with scores between 93 and 142 is the p-value of Z when X = 142 subtracted by the p-value of Z when X = 93, hence:
Z = (142 - 115)/11
Z = 2.45
Z = 2.45 has a p-value of 0.992.
Z = (93 - 115)/11
Z = -2
Z = -2 has a p-value of 0.023.
0.992 - 0.023 = 0.969, hence the percentage is of 96.9%.
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Select the correct answer from each drop-down menu. José and Manuel are soccer players who both play center forward for their respective teams. The table shows the total number of goals they each scored in each of the past 10 seasons. Season José Manuel 1 7 17 2 12 23 3 17 21 4 4 31 5 18 30 6 25 5 7 38 26 8 32 37 9 37 19 10 11 9 The measure of center that best represents the data is mean , and its values for José and Manuel are and , respectively. Comparing this measure of center for José’s and Manuel's data sets shows that generally scores more goals in a game
The measure of center that best represents the data is mean and its values for José and Manuel are 20.1 and 21.8, respectively. Comparing the mean values, José generally scores less goals in a game than Manuel.
What is the measure of center for the number of goals scored?To find the measure of center that best represents the data, we will use the mean.
The measure is calculated by adding up all the values and dividing by the total number of values.
The mean number of goals for José is:
= (7+12+17+4+18+25+38+32+37+11)/10
= 20.1
The mean number of goals for Manuel is:
= (17+23+21+31+30+5+26+37+19+9)/10
= 21.8.
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Use the scatter plot to fill in the missing coordinate of the ordered pair.(,12)
Answer: Pairs (0, 14) and (10, 0
Step-by-step explanation:
Traffic Jam
There are 8 cans of strawberry jam, 7 raspberry jam,
and 5 cherry jam in the cellar. You're trying to sneak
some out, but don't want to attract attention or take
too many. It's dark, so you can't tell what kind of jam
you're taking.
How many cans can you sneak out of the
cellar in the dark with the certainty that there
will still be at least 4 cans of one kind of jam
and 3 cans of another left over?
Answer:
Hey!
You could obviously count how many you're taking, so that's 7 left behind. My guess is that you could taste the jam... but that's the best I've got.
The requreid we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.
What is arithmetic?It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Let's first find the minimum number of cans that need to be left in the cellar to meet the given criteria. We want at least 4 cans of one kind of jam and 3 cans of another leftover. This means we can take a maximum of:
8 - 4 = 4 cans of strawberry jam
7 - 3 = 4 cans of raspberry jam
5 - 3 = 2 cans of cherry jam
So, we can take a maximum of 4 + 4 + 2 = 10 cans in total.
To have certainty that we meet the criteria, we need to take one less than the maximum number of cans, which is 9 cans. So, we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.
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In the expression πr² + πrℓ, what
part of the expression is π?
a constant
a coefficient
a variable
a term
In the expression πr² + πrℓ, the part of the expression that is π is a constant.
A constant is a value that does not change in an expression, and in this case π represents a fixed value of approximately 3.14159. It is not a coefficient, which is a numerical factor that multiplies a variable, nor a variable or term, which represent varying quantities in an expression.
Liquid a has a density of 1. 2 g/cm'
150 cm of liquid a is mixed with some of liquid b to make liquid c.
liquid c has a mass of 220 g and a density of 1. 1 g/cm
find the density of liquid b.
If Liquid a has a density of 1. 2 g/cm³, 150 cm of Liquid a is mixed with some of Liquid b to make Liquid c whose mass is 220 g and has a density of 1.1 g/cm³, then the density of liquid B is 0.8 g/cm³.
To find the density of liquid B, you can follow these steps:
1. Calculate the mass of liquid A using its density and volume:
Liquid A has a density of 1.2 g/cm³ and a volume of 150 cm³.
Mass of A = Density of A × Volume of A = 1.2 g/cm³ × 150 cm³ = 180 g
2. Calculate the mass of liquid B using the mass of liquid C and mass of liquid A:
Liquid C has a mass of 220 g.
Mass of B = Mass of C - Mass of A = 220 g - 180 g = 40 g
3. Calculate the volume of liquid C using its mass and density:
Liquid C has a density of 1.1 g/cm³.
Volume of C = Mass of C ÷ Density of C = 220 g ÷ 1.1 g/cm³ = 200 cm³
4. Calculate the volume of liquid B using the volume of liquid C and the volume of liquid A:
Volume of B = Volume of C - Volume of A = 200 cm³ - 150 cm³ = 50 cm³
5. Calculate the density of liquid B using it's mass and volume:
Density of B = Mass of B ÷ Volume of B = 40 g ÷ 50 cm³ = 0.8 g/cm³
So, the density of liquid B is 0.8 g/cm³.
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67. 8 x 9. 7 pls someone answer within the next 20 Minutes with work I'm in school lol