The area of the surface is S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]
Now, According to the question:
The given equation is:
[tex]z = \frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2} )[/tex],
0 ≤ x ≤ 1 , 0 ≤ y ≤ 1
Let's know:
Surface Area:
To surface area of a solid E, defined by z = f(x , y) can be found by integrating[tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex] where R is the rectangular region
[0,1] × [0, 1] and [tex]z_x,z_y[/tex] corresponds to the partials of z w.r.t x and y.
Now,
[tex]\sqrt{(z_x)^2+(z_y)^2+1}[/tex] = [tex]\sqrt{1+(\sqrt{x} )^2+(\sqrt{y} )^2}[/tex] = [tex]\sqrt{1+x+y}[/tex]
S = [tex]\int\limits \int\limits_R \sqrt{(z_x)^2+(z_y)^2+1},dA[/tex]
= [tex]\int\limits^1_0\int\limits^1_0 \sqrt{x+y+1}dy dx[/tex]
[Integrate with respect to y ]
= [tex]\int\limits^1_0 (\frac{2}{3}(x + y + 1)^\frac{3}{2} )|^1_0 dx[/tex]
= [tex]\int\limits^1_0 (\frac{2}{3}(x + (1) + 1)^\frac{3}{2}-\frac{2}{3}(x + (0) + 1)^\frac{3}{2} )dx[/tex]
= [tex]\int\limits^1_0 ((\frac{2}{3}(x +2)^\frac{3}{2} ) - (\frac{2}{3}(x +1)^\frac{3}{2} ) , dx[/tex]
= [tex]\int\limits^1_0 (\frac{2}{3}((x +2)^\frac{3}{2} - (x +1)^\frac{3}{2} )) , dx[/tex]
[Integrate with respect to x ]
= [tex]\frac{2}{3} (\frac{2}{5}(x + 2)^\frac{5}{2} - \frac{2}{5}(x +1)^\frac{5}{2} )|^1_0[/tex]
= [tex]\frac{2}{3}(\frac{2}{5}((1)+2 )^\frac{5}{2}-\frac{2}{5}((1)+1)^\frac{5}{2})-\frac{2}{3}(\frac{2}{5}((0)+2 )^\frac{5}{2} -\frac{2}{5}((0)+1)^\frac{5}{2}[/tex]
= [tex]\frac{2}{3}(\frac{18\sqrt{3}}{5} -\frac{8\sqrt{2} }{5} )-\frac{2}{3} (\frac{8\sqrt{2} }{5} -\frac{2}{5} )[/tex]
= [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]
Hence, The area of the surface is S = [tex]\frac{-4}{15}(-1+8\sqrt{2}-9\sqrt{3} )[/tex]
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Constructing Functions Express the gross salary G of a person who earns $14 per hour as a function of the number x of hours worked. Find the domain. - Population as a Function of Age The function P(a) = 0.027a2 6.530a + 363.804 represents the population P (in millions) of Americans that are a years of age or older in 2015. (a) Identify the dependent and independent variables. (b) Evaluate P(20). Provide a verbal explanation of the meaning of P(20). (c) Evaluate P(0). Provide a verbal explanation of the meaning of P(0).
(a) The independent variable is age (a) and the dependent variable is population (P).
(b) P(20) = 6.38 million. This means that 6.38 million Americans were 20 years or older in 2015.
(c) P(0) = 363.804 million. This means that 363.804 million Americans were 0 years or older in 2015.
mi use structure ji builds a right rectangular prism with 14 centimeter cubes in the bottom layer with no gaps or pverlaps. if there are 8 layers, what is the volume of the right ectangular prism?
Mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers, The volume of the right rectangular prism is 14 x 14 x 8 = 1,536 cm3.
To get this answer, I first determined the number of cubes in the bottom layer. Since the bottom layer contains 14 cubes, the total length of the base of the prism is 14 cm. The height of the prism is 8 layers, so the total height of the prism is 8 cm. To calculate the volume of a right rectangular prism, you need the base length, the width, and the height. Since all three of these measurements are given, the volume can be calculated by multiplying the base length (14 cm) by the width (14 cm) by the height (8 cm). The result is 1,536 cm3.
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mi use structure ji builds a right rectangular prism with 14-centimeter cubes in the bottom layer with no gaps or overlaps. if there are 8 layers, what is the volume of the right rectangular prism?
Find y' and y''.
y = √x ln(x)
y' = ...?
y'' = ...?
Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x .
What is the equation?A mathematical equation looks to be a formula that joins two statements and indicates equality when it uses the equals symbol (=). In algebra, an equation is a statement of fact that demonstrates the equality of different mathematical variables . For instance, the result obd + 6 = 12 has an equal sign between quantities ptdc + 6 and 12. There is a mathematical formula that describes the connection between the syllables on either side of each letter. The emblem and the statement are frequently the same.
Here,
y = √x ln(x)
To find the y'
=> dy/dx = d(√x ln(x)) /dx
=> dy/dx = 1/2√x * ln(x) + 1/x *√x
=> dy/dx = 1/2√x * ln(x) + 1/√x
To find the value of y ''
=> dy'/dx = d(1/2√x * ln(x) + 1/√x ) / dx
=> dy'/dx = 1/2 * (-1/2* √x * ln(x) + 1/√x ) -1/2 * √x
=>dy'/dx = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x
Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x .
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Forgotten how to do this
Explanation to please
Answer:
We can use the trigonometric function sine to calculate the length of AB in a right-angled triangle.
The sine function relates the ratio of the side opposite an angle (in this case, AB) to the hypotenuse (AC) with the angle in question (in this case, angle C):
sin(C) = AB/AC
In this case, we know that angle C is 29 degrees and the hypotenuse AC is 5cm, so we can substitute these values into the equation to find AB:
sin(29) = AB/5
To solve for AB, we can multiply both sides of the equation by 5:
AB = 5sin(29)
AB=2.42cm
the length of a puppy on a scale drawing is 6 cm. if the scale is 1:9 cm, what is the actual length of the puppy?
Despite appearing to be 6 cm long on a scale drawing, puppies are actually 54 cm long.
what is length ?Distance between two sites can be determined by a measurement called length. Aside from height and width, it also determines how long an object is. In math classes, kids will study about length to assist them in solving real-world problems both as a part of their education and outside of it. the largest or longest dimension of a thing; a measurable length or width. Dimensions: 10 ft. Table of the Metric System, Weights and Measures Table: the characteristic of length. The definition of length is the distance or measurement between two points. In other terms, the largest two or highest three dimensions of a geometric shape or item.
given
Puppy drawn to scale measures 6 cm in length.
due to the scale's 1:9 cm
Utilize the ratio approach to determine the puppy's true length.
1 = 6 cm
9 = 6×9 = 54 cm
Despite appearing to be 6 cm long on a scale drawing, puppies are actually 54 cm long.
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what does 안녕하세요 mean??
Answer:
I hope my answer is helpful!
"안녕하세요" is a formal and polite way of saying "hello" in Korean. It is commonly used as a greeting, both when meeting someone for the first time and when meeting someone again after a period of time. The literal translation of 안녕하세요 is "Are you at peace?"
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
12y would be the answer
Step-by-step explanation:
To simplify, you first need to combine like terms
6y + 6y =12y
-10x+11x=x
x+12y+8 would be the simplified result
Answer:
x+12y+8
Step-by-step explanation:
8+6y-10x+6y+11x
8+6y+6y-10x+11x.......................collecting like term
8+12y+x = x+12y+8
b=2.35+0.25x
c=1.75+0.40x
In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?
The price per pound of beef when it was equal to the price of chicken is $3.35 per pound.
The following linear equations represent the costs of beef and chicken:
Beef price, B:
B = 2.35 + 0.25x
Price of chicken, C :
C = 1.75 + 0.40x
Where x in both equations denotes the number of weeks since July 1 of the previous summer:
B = 2.35 + 0.25x
Price of chicken, C :
C = 1.75 + 0.40x
Where x in both equations represents x weeks after July 1 of last summer
Firstly:
We identify the week when the cost of beef and chicken is equal:
Beef = Chicken
2.35 + 0.25x = 1.75 + 0.40x
We solve for x
2.35 - 1.75 = 0.40x - 0.25x
0.60 = 0.15x
x = 0.60 / 0.15
x = 4
Therefore, poultry and beef had the same price four weeks after July 1 of last summer.
B = 2.35 + 0.25(4)
B = 2.35 + 1
B = 3.35
When the price of chicken and beef were equal, the price per pound of meat was $3.35.
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which operationalization is most appropriate for the independent variable of the proposed follow-up experiment
Type of communication developed by teaching a doctor who is also a collaborator to utilize patient-centered communication or a non-patient-centered communication style.
What is appropriate for the independent variable?As the researchers are interested in the effect of type of communication on level of mistrust; therefore, type of communication is the independent variable. To establish a causal relationship between the two variables, the independent variable needs to be manipulated, as described in C, by training the doctor to adopt different communication styles.
Here,
Communication style produced by training a doctor who is also a collaborator to use patient-centered communication or a non-patient-centered communication style.
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Determine if the columns of the matrix A span R2. A = 2 1 0 1 Arlo -3 -1 )-The columns span R2. -The columns do not span R2.
The columns of the matrix A span R2.
In order to determine if the columns of the matrix A span R2, we need to check if the columns of A can be used to generate all possible linear combinations of the form a1v1 + a2v2, where a1 and a2 are scalars and v1 and v2 are the columns of A.
A = [2 1]
[0 1]
[-3 -1]
The columns of A are [2, 0, -3] and [1, 1, -1]. To check if these columns span R2, we need to see if we can create any vector in R2 by taking linear combinations of the columns. We can see that by taking linear combinations of the columns, we can create any vector of the form (a, b) in R2.
For example, by taking a = 2, b = 1, we can generate the vector (2, 1) by taking
a[2, 0, -3] + b[1, 1]
And by taking a = 3, b = -1, we can generate the vector (3, -1) by taking
a[2,0,-3] + b[1,1,-1].
So the answer would be: The columns of the matrix A span R2.
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Dilate the segment with a scale factor of r=1/2
Answer:
3.5 cm long
Step-by-step explanation:
AB*1/2=7*1/2=3.5
Answer:
|AB'| = 3.5 cm
Step-by-step explanation:
Given:
|AB| = 7 cmr = ¹/₂To dilate the line segment by a scale factor r, multiply the original length of the line segment by the given scale factor:
[tex]\begin{aligned}\implies \sf |AB'|&=\sf |AB| \times r\\\\&=7 \times \dfrac{1}{2}\\\\&=\dfrac{7 \times 1}{2}\\\\&=\dfrac{7}{2}\\\\&=3.5\; \sf cm\end{aligned}[/tex]
A rectangle ha a perimeter of 112. If the ide are 5x & 3x 5, what i x and what are each of the ide?
As a result, the rectangle's sides measure 5x = 5(6.375) = 31.875 inches and 3x+5 = 3(6.375) + 5 = 20.125 inches, respectively.
We may utilize the knowledge that the rectangle's perimeter is 112 and that its sides are 5x and 3x+5 to determine the value of x and the lengths of each side. We can put up the following equation because the perimeter of a rectangle is equal to the sum of its four sides:
2(5x) + 2(3x + 5) = 112
We must simplify and account for x in order to solve for x. We'll start by allocating the two on the left side of the equation:
10x + 6x + 10 = 112
We'll then mix similar terms:
16x + 10 = 112
To get x alone, we will now deduct 10 from both sides, giving us 16x = 102.
Next, multiply both sides by 16 times to get 6.375.
Therefore as a result, the rectangle's sides measure 5x = 5(6.375) = 31.875 inches and 3x+5 = 3(6.375) + 5 = 20.125 inches, respectively.
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Which of the following can be the sides of a right triangle?
(i) 2.5 cm, 6.5 cm, 6 cm
(ii) 2 cm, 2 cm, 5 cm
(iii) 1.5 cm, 2cm, 2.5 cm
In the case of right-angled triangles, identify the right angles
(i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.
To check if the given measurements are possible sides of a right triangle, it must follow the Pythagorean theorem, where the square of the hypotenuse is equal to the sum of the squares of the legs.
c² = a² + b²
where c is the hypotenuse(longest side)
and a and b are the two other sides
(i) 2.5 cm, 6.5 cm, 6 cm
6.5² = 2.5² + 6²
42.25 = 6.25 + 36
42.25 = 42.25
(ii) 2 cm, 2 cm, 5 cm
5² = 2² + 2²
25 = 4 + 4
25 ≠ 8
(iii) 1.5 cm, 2cm, 2.5 cm
2.5² = 1.5² + 2²
6.25 = 2.25 + 4
6.25 = 6.25
Hence, (i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.
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y=30m+12t
y=15m+15t
how many minutes can you use your phone on both plans for the same cost?
what is the cost?
Answer:
1/5 of a minute they are equal.
The cost would be $18
Step-by-step explanation:
Something does not look right. You would not have 3 variables.
Set the two equations equal to each other and solve for m. I think that the variables t may be an error.
30m + 12 = 15m + 15 Subtract 15 m from both sides
30m -15 m + 12 = 15m -15m + 15
15m + 12 = 15 Subtract 12 from both sides
15m + 12 - 12 = 15 - 12
15m = 3 Divide both sides by 15
[tex]\frac{15m}{15}[/tex] = [tex]\frac{3}{15}[/tex]
m = [tex]\frac{1}{5}[/tex]
Cost:
y = 30m + 12
y = 30(1/5) + 12
y = 18
y = 15m + 15
y = 15(1/5) + 15
y = 3 + 15
y = 18
amy has 4 pounds of ground turkey to make meatballs. she uses 3/8 pound per meatball to make 9 meatballs. how many 1/8 meatballs can amy make with the remaining turkey
As per the unitary method, the number of meatballs made using the the remaining turkey is 29 meatballs
The term unitary method is known as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Here we have know that Amy has 4 pounds of ground turkey to make meatballs
And here we also know that she uses 3/8 pound per meatball to make 9 meatballs
Then in order to find the remaining we have to subtract 3/8 from 4
Then we get,
=> 4 - 3/8
=> 29/8
Therefore, here we have identified that there are 21/8 pounds of ground turkey left
As here we have given that the number of 1/8 pound meatball that can be produced from 21/8 pounds of ground turkey can be calculated as follows,
=> 29/8 ÷ 1/8
When we simplify this one then we get,
=> 29
So, Amy can make 29 meatballs
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give your answer to 1d.p.
Answer: 26.8
Step-by-step explanation:
[tex]\frac{8.2}{m}=\tan 17^{\circ}\\\\\frac{m}{8.2}=\frac{1}{\tan 17^{\circ}}\\\\m=\frac{8.2}{\tan 17^{\circ}}\\\\m \approx 26.8[/tex]
what is 131.4 divided by 6 equal?
21.9 is the answer to 131.4/6
Answer:
21.9
Step-by-step explanation:
learn how to use a calculator.
Top one
A princess is on the top of a 167 foot tower looking down at a 37° angle of depression at a package attached to a rope on the ground. How long is the rope?
The length of the rope in the question is; 277.5 ft
How to solve Angle of depression problems?The angle of depression is defined as the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, and looking down at an object, you could measure the angle of depression.
The rope length can be calculated using the trigonometric ratio which is;
167/x = sin 37
x = 167/sin 37
x = 167/0.6018
x = 277.5 ft
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se the following stem-and-leaf plot of college freshman GPAs to answer questions 9-15.
KEY
Stem: ones digit
Leaf: tenths digit
Example. 0.9 → 0+.9 0.9
Stem Leaf
0
1
2
3
4
.9
.3
.0
.0
.0
.5
.3
.2
.5
.4
.3
9. What is the range?
A. 4.9
B. 4.0
C. 3.1
D 3.0
E 2.1
Answer: The range is 4.9.
Step-by-step explanation: The range of a set of data is the difference between the largest and smallest values. In this stem-and-leaf plot, the smallest value is 0.3, and the largest value is 4.9.
Therefore, the range is 4.9 - 0.3 = 4.6 which is 4.9 (approx)
So the answer is A. 4.9
Using f(x) = 2x + 7 and g(x) = x - 3, find f(g(x)).
2x + 1
2x + 4
X + 4
2x^2 + x - 21
Answer:
2x + 1
Step-by-step explanation:
To find f(g(x)), we need to substitute g(x) for x in the function f(x) = 2x + 7.
so f(g(x)) = 2(x - 3) + 7 = 2x - 6 + 7 = 2x + 1
So the composition of function f(g(x)) is f(g(x)) = 2x + 1.
5 log(2) rewrite in log(c)
The solution to the given logarithmic equation is log32
Law of logarithmsThe logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which b must be raised in order to obtain a number x is its logarithm to the base b.
One of the law of logarithm is expressed as:
bloga = log a^b
Applying this law to the given question;
5 log(2) =log2⁵
Since 2⁵ = 32, hence the given expression is equivalent to log32.
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the blue figure is a dilation image of the black figure. the labeled point is the center of dilation. tel whether the dilation is an enlargement or a reduction. then find the scale factor of the dilation.
From the given graph we can observe that the blue figure is larger in size than the black figure. Hence, the figure is enlargement of the original figure.
What is transformation?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. The transformation, or f: X X, is the name given to the function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.
From the given graph we can observe that the blue figure is larger in size than the black figure. Hence, the figure is enlargement of the original figure.
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Construct a vertical transversal and horizontal transversal to lines AB and DC that intersect each other at F. Label the points of intersection to the parallel lines A, B, C, and D.
Pls help!!
The missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
here,
As given in the quesiton,
Consider the triangle formed by the given construction,
ΔFDC and Δ FAB
AB║CD
∠FAB = ∠FCD
∠FBA = ∠FDC
So, ΔFDC ≅ Δ FAB, by SAS congruency.
Thus, the missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.
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four fair six-sided dice are rolled. what is the probability that at least two dice show a 3? express your answer as a common fraction.
Four fair six-sided dice are rolled. The probability that at least two dice show a 3 is 1/36.
In the given question, four fair six-sided dice are rolled.
We have to find the probability that at least two dice show 3.
There are four dice and each have 6 numbers to come.
So total number of cases = 6×6×6×6
Total number of cases = 1296
At least two dice show 3. So
The favorable outcome = 6 × 5
The favorable outcome = 30
The possible outcome = aabc, abac, abca, baac, baca, bcaa = 6
Total of outcomes = 30 + 6
Total of outcomes = 36
The probability that at least two dice show a 3 = 36/1296
The probability that at least two dice show a 3 = 1/36
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a business organization needs to make up a 8 member fund-raising committee. the organization has 6 accounting majors and 9 finance majors. what is the probability that at least 4 accounting majors are on the committee?
The probability that at least 4 accounting majors are on the committee is P(at least 4 accounting majors) = 1 - P(less than 4 accounting majors)
We can use the complement rule to solve this problem. The complement rule states that the probability of an event happening plus the probability of the event not happening is equal to 1.
In this case, we can find the probability that less than 4 accounting majors are on the committee and then subtract that from 1 to find the probability that at least 4 accounting majors are on the committee.
There are 6 accounting majors and 9 finance majors, for a total of 15 students.
To find the probability that fewer than 4 accounting majors are on the committee, we can use the binomial probability formula:
P(k) = (combination(8,k)) [tex]\times (6/15)^k \times (9/15)^{(8-k)[/tex]
where k is the number of accounting majors on the committee.
To find the probability that fewer than 4 accounting majors are on the committee, we need to sum the probabilities for k = 0, 1, 2, and 3.
P(less than 4 accounting majors) = P(0) + P(1) + P(2) + P(3)
Finally, we can use the complement rule to find the probability that at least 4 accounting majors are on the committee:
P(at least 4 accounting majors) = 1 - P(less than 4 accounting majors)
You can calculate the exact probability using the binomial coefficient and the binomial probability formula and then subtract that from 1 to get the final probability.
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PWEASE PWEASE PWEASE
Answer:
-2
a open bracket
and then a and - a negate each other to give -2
please help me fast no w!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
A run-on sentence occurs when independent clauses are not joined properly.
(01.02 MC)
Determine the solutions of the equation:
|1/3×+9|-3=21
Ox= -11 and x = 5
Ox= -81 and x = 45
O x = -99 and x = 45
O x = -99 and x = 99
The solution for given linear equation are x=-99 and x=45 i.e. C.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Given linear equation is |1/3×+9|-3=21
so, -1/3x-12=21 --->1
and 1/3x+6=21 --> 2
From 1
1/3x=-33
x=-99
From 2
1/3x=15
x=45
Hence,
The solution for given linear equation are x=-99 and x=45.
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Replace variables wit values and evaluate using order of operations D= wt² W=70 T=4 give your answer in simplest form
The value of variable d is 1120
How to determine the value of variable d from the known valuesFrom the question, we have the following parameters that can be used in our computation:
D= wt²
Where W = 70 and T = 4
Substitute the known values in the above equation, so, we have the following representation
D = 70 * 4²
Evaluate the exponent
D = 70 * 16
Evaluate the products
D = 1120
Hence, the solution is 1120
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Look at the cups shown below (please note images are not drawn to scale):
A cone is shown with width 2 inches and height 4 inches, and a cylinder is shown with width 2 inches and height 6 inches.
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.
8.8 cubic inches
10.1 cubic inches
14.7 cubic inches
22.3 cubic inches
Answer
22.3 is correct i believe :)
Step-by-step explanation:
