WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
Answers
The missing parts of the proof are: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
What is a Square?A square is a special type of rectangle whose consecutive sides are congruent. All four sides of a square are congruent.
In the proof given, the distance formula [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] was used to find ST = a units in step 2.
By the definition of congruence, RS = ST in step 4.
Finally, RSTU is stated to be a square because if two consecutive sides of a rectangle are congruent, then it is a square.
The option that completes the proof in the right order is: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
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Answer:
distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square
Step-by-step explanation:
so its c for me
Related Questions
find the equation of the tangent line at the given point on the following curve.
x^2+y^2=8, (-2,-2)
Answers
Using derivatives, the equation of the tangent line is: y + 2= -(x + 2)
What is the equation to the tangent line of a function f(x) at point (x0, y0)?The equation is:
[tex]y - y_0 = m(x - x_0)[/tex]
In which m is the derivative at point [tex](x_0, y_0)[/tex].
The function is:
[tex]x^2 + y^2 = 8[/tex].
Applying implicit differentiation, the derivative is:
[tex]2x\frac{dx}{dx} + 2y\frac{dy}{dx} = 0[/tex]
[tex]2ym = -2x[/tex]
[tex]m = -\frac{x}{y}[/tex]
We have that x = y = -2, hence m = -1 and the equation is:
y + 2= -(x + 2)
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two sides of a triangle are 5 and 55 cm complete the inequality to show the possible lengths of the third side _ < x < _
Answers
Answer:
50<x<60
Step-by-step explanation:
The triangle can only be formed with these two side lengths if the third side is bigger than (Subtract them)
55 - 5
...and smaller than (Add them)
55 + 5
55-5 < x < 55+5
50 < x < 60
Complete the table by finding the missing equivalent form for each row. a = b = c =
Answers
Answer:
a=10%, b=25/100, c=1/2
Step-by-step explanation:
a: If the denominator is exactly 100, then the numerator represents a percentage.
b: when you change a fraction to have a greater denominator, an easy way to figure out how to change the numerator to match it and make the value of the rewritten fraction equal to the old version, is to divide the new value of the denominator by the old value (in this case being 100/4=25), and put the answer where the numerator goes.
c: When simplifying a fraction with a lesser numerator than denominator, find the greatest common factor (a factor is a whole number a number can be divided by without resulting in a negative or a decimal number) and divide both the numerator and denominator by it.
La siguiente figura 1, ilustra el salto de una rana sobrepuesto en un plano cartesiano. La longitud del salto es de 9 ft y la altura máxima con respecto al suelo es 3 ft. Encuentra la ecuación estándar a fin de calcular la trayectoria de la rana.
3. La salinidad de los océanos se refiere a la cantidad de material disuelto que se encuentra en una muestra de agua marina. La salinidad S se puede calcular a partir de la cantidad C de cloro en agua de mar con la ecuación S = 0.03 + 1.805 C, donde S y C se miden por peso en partes por millar. Calcula la C si S es 0.35.
4. El arco de un puente es semielíptico, con eje mayor horizontal. La base del arco mide 50 ft de un lado al otro y la parte más alta del arco mide 15 ft arriba de la calzada horizontal. Encuentre la altura del arco a 12 ft del centro de la base.
Investiga la hipérbola con centro en el origen y fuera del origen. Eje focal en x y en y.
2. De las expresiones que se indican a continuación, Identifica si es una recta o ecuación lineal,
una ecuación cuadrática o de segundo grado, una ecuación de tercer grado, una
circunferencia, una hipérbola, justifica tu respuesta y elabora su respectiva gráfica.
3x – 2y + 4= 0
4x + y2 -7 = 0
x2 + y2 = 16
y = x3 - 3x +1
x2 + 4y2 = 4
3. A partir de tu investigación resuelve los siguientes ejercicios:
a) Traza la gráfica
9x2 – 4 y2 = 36
Encuentra los focos y ecuaciones de las asíntotas.
b) Traza la gráfica
4y2 – 2 x2 = 1
Encuentra los focos y ecuaciones de las asíntotas.
c) Dadas las siguientes ecuaciones, decir qué cónica representan:
9 x2 - 4 y2 - 54 x - 16 y + 29 = 0
4 x2 + 2 y2 - 7 x + y - 5 = 0
x2 - 6 x + 5 y - 11 = 0
Answers
Debido a restricciones de longitud invitamos cordialmente a leer la explicación de esta pregunta para aprender sobre las cuestiones de las ecuaciones cónicas.
¿Cómo analizar y aplicar las ecuaciones cónicas?
Según la geometría analítica, existen cinco tipos de secciones cónicas: recta, circunferencia, elipse, parábola e hipérbola. Aquí se presentan problemas que emplean este tipo de ecuaciones.
1) La trayectoria de la rana describe la forma de una parábola. Asumimos que el punto máximo de la trayectoria de la rana es de la forma (h, k) = (0, k), entonces tenemos que la ecuación de la parábola es:
y - k = C · x² (1)
Donde C es la constante del vértice.
Si sabemos que (h, k) = (0, 3) y (x, y) = (9, 0), entonces la ecuación de la parábola es:
C = (0 - 3) / 9²
C = - 1 / 27
La ecuación de la parábola es y - 3 = (- 1 / 27) · x².
2) Se determina el tipo de categoría de cada ecuación:
a) 3 · x - 2 · y + 4 = 0: Recta (a · x + b · y + c = 0)
b) 4 · x + y² - 7 = 0: Parábola ((y² - k) = 4 · p · (x - h))
c) x² + y² = 16: Circunferencia ((x - h)² + (y - k)² = r²)
d) y = x³ - 3 · x + 1: Ecuación cúbica
e) x² + 4 · y² = 4: Elipse (b² · (x - h)² + a² · (y - k)² = a² · b²)
3) Se debe hallar el valor C de la función lineal tal que S = 0.35 por medios algebraicos:
0.35 = 0.03 + 1.805 · C
0.32 = 1.805 · C
C = 0.32 / 1.805
C = 0.177
4) El arco semielíptico tiene una longitud de semieje mayor de 25 pies (paralelo al eje x) y una longitud de semieje menor de 15 pies (paralelo al eje y). Si consideramos que el centro de la elipse está en el origen, entonces tenemos que la ecuación es:
x² / 25² + y² / 15² = 1
y = 15 · √(1 - x² / 25²)
y = 15 · √(1 - 12² / 25²)
y = 13.159 pies
5) a) y b) Ahora graficamos la hipérbola y presentamos las ubicaciones de los focos y las asíntotas correspondientes. a) Las ecuaciones de las asíntotas son y = ± (3 / 2) · x, b) Las ecuaciones de las asíntotas son y = ± (√ 2 / 2) · x.
c) Se puede determinar la naturaleza de cada ecuación por métodos algebraicos:
9 · x² - 4 · y² - 54 · x - 16 · y + 29 = 0
[9 · x² - 2 · 9 · (3 · x) + 81] - [4 · y² - 2 · 8 · (2 · y) + 64] = 116
(3 · x - 9)² - (2 · y - 8)² = 116
9 · (x - 9)² - 4 · (y - 4)² = 116
(x - 9)² /12.889 - (y - 4)² / 29 = 1 - Hipérbola
4 · x² + 2 · y² - 7 · x + y - 5 = 0
[4 · x² - 2 · (7 / 4) · (2 · x) + 49 / 16] + [2 · y² + 2 · (√2 / 2) · (√2 · y) + 1 / 2] = 5
(2 · x - 7 / 4)² + (√2 · y + √2 / 2)² = 5
4 · (x - 7 / 8)² + 2 · (y + 1 / 2)² = 5
(x - 7 / 8)² / 1.25 + (y + 1 / 2)² / 2.5 = 1 - Elipse
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Suppose a set of scores in College Mathematics are 5, 15, 25, 30, 3. Which of the following is true?
a.
the mean is equal to the median
b.
the mean is less than the median
c.
the mean is greater than the median
d.
the mode is 15
Answers
Answer: c. the mean is greater than the median
Explanation:
To find out the correct answer, we first must know the true meanings and the method of calculation of the terms, "mean", "mode" and "median".
Mean: The mean is a type of average. It is the sum of all the values in a set of data, such as numbers of measurements, divided by the numbers of values on the list.
Formula for finding mean-[tex]\bar{x} = \dfrac{\sum x}{n}[/tex] where, [tex]\bar{x}=[/tex] sample mean
[tex]\sum x =[/tex] sum of each value in sample
[tex]n =[/tex] number of values in the sample
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the mean is 5.875 (6+3+9+6+6+5+9+3/8).
Mode: The mode is the number which appears most often in a set of numbers.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.
Median: The median is the "middle" of a sorted list of numbers in ascending order (small to big). To find the Median, place the numbers in value order and find the middle.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the median is 6. (in 3,3,5,6,6,9,9, the middle number is 6 )
with an even amount of numbers things are slightly different.
In that case we find the middle pair of numbers, and then find the value that is half way between them. This is easily done by adding them together and dividing by two. (basically averaging the middle two numbers incase there is an even set of numbers)
Example: 3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers.
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
In this example the middle numbers are 21 and 23.
To find the value halfway between them, add them together and divide by 2: 21 + 23 = 44, then 44 ÷ 2 = 22
So the Median in this example is 22.
(Note that 22 was not in the list of numbers ... but that is OK because half the numbers in the list are less, and half the numbers are greater.)
Now that you understand the terms clearly, let's find out the mean, mode and median from your given set of numbers.
5, 15, 25, 30, 3
Mean: (5+15+25+30+3)/5 is, 15.6
Mode: None since none of the numbers repeated more than once.
Median: 3,5,15,25,30 , so the middle number is 15 .
Since there is no mode, option d. can never be the answer. And clearly, 15.6 is greater than 15 so the answer should be c. the mean is greater than the median.
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hope it helped
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Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
(–∞, –3)
(–∞, 3)
(–3, ∞)
(3, ∞)
Answers
Using translation concepts, it is found that g(x) is positive on the following interval:
(3, ∞)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Function [tex]g(x) = \sqrt[3]{x - 3}[/tex] is a shift right of 3 units of [tex]f(x) = \sqrt[3]{x}[/tex], which is positive on the interval (0, ∞), hence g(x) is positive on the interval (3, ∞).
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PLSS HELPPPPP ASAPP
Answers
Answer:
Step-by-step explanation:
area=length×width
=(2x+3)(3x-5)
Area=6x²-10x+9x-15
=6x²-x-15
Find the missing side of the triangle.
pythagorean 4
A. 337‾‾‾‾√ km
B. 5‾√ km
C. 193‾‾‾‾√ km
D. 112‾√ km
Answers
Applying the Pythagorean theorem, the missing side of the triangle is: C. √193 km.
How to Apply the Pythagorean Theorem?To find the missing side (x) in the right triangle, based on the Pythagorean theorem, we would have the following equation:
x = √(12² + 7²)
x = √(144 + 49)
x = √193
The missing side of the triangle is: C. √193 km
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Answer:
C.) 193√ km
Step-by-step explanation:
I got it right on founders edtell
30 POINTS!,!!!!!!!!!!!!
A packaging factory is open from Monday to Saturday. In a particular week, 15,000 packets were packed on Monday and the factory was also closed on Tuesday. If no less than 100,000 packets should be packed in that week, what is the minimum equal number of packets that must be packed per day for the remaining days?
Answers
Answer:
A minimum of 21250 packets per day.
Step-by-step explanation:
If Monday produced 15,000 packets, and Tuesday was closed they produced 15,000 packets in 2 days.
The factory is open 6 days a week.
They need 100,000 packets.
They have 15,000 packets.
6 subtract 2 is 4.
100,000 subtract 15,000 is 85,000.
They need 85,000 packets in 4 days.
That is a minimum of 21250 packets per day.
Add these fraction
1) 2/3 + 6/3
2) 4/6+9/6
3) 6/6+6/6
Answers
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
What is the value of the addition operation?Given that;
1) 2/3 + 6/3
We combine the numerators over the common denominators
= ( 2 + 6 ) / 3
= 8/3
2) 4/6 + 9/6
We combine the numerators over the common denominators
= ( 4 + 9 ) / 6
= 13/6
3) 6/6 + 6/6
We combine the numerators over the common denominators
= ( 6 + 6 ) / 6
= 12/6
= 2
The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.
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Use the following triangle to find Sec theta.
Note: enter the exact, fully simplified and rationalized answer
Answers
Answer:
[tex]\frac{\sqrt{41}}{4}[/tex]
Step-by-step explanation:
sec(theta) is defined as: [tex]sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}[/tex]
In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
So this gives us the equation where a=adjacent side:
[tex]a^2+5^2=\sqrt{41}^2[/tex]
[tex]a^2+25=41[/tex]
Subtract 25 from both sides
[tex]a^2=16[/tex]
Take the square root of both sides
[tex]a=4[/tex]
So now plug this into the definition of sec(theta) and you get: [tex]\frac{\sqrt{41}}{4}[/tex]. This is in most simplified form since 41, has no factors besides 41 and 1.
what is 73 division 84,649
Answers
73 division 84, 649 would give 8. 64 × 10^-4
How to determine the valueIn order to determine the value of the division, we have
= [tex]\frac{73}{84649}[/tex]
Using the calculator, put the values in
We would have
= 8. 64 × 10^-4
Thus, 73 division 84, 649 would give 8. 64 × 10^-4
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What is the radian measure of central angle AOB in the circles? Write down the answer in the lowest terms
Answers
5pi/12 radians
The arc measure is 75, so theta must also be the same. if theta is 75, and 75 in radians is 5pi/12 radians, then the answer is that.
HELP !!show the work tooo
Answers
the probability of getting heads on a two-face coin is simply 1/2.
now, what is the probability of getting 1/2 AND 1/2 AND 1/2 AND 1/2 AND 1/2? well, AND means "times", namely
[tex]\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\implies \cfrac{1}{32}[/tex]
well, and since it's a two-face coin, the probability for each face is equal, 1/2, so Heads has a chance of 1/2 each time, or we can also say that Tails has a chance of 1/2 each time, so if Tails has the same probability over 5 times as Head does.
Explain the difference between using the trigonometric ratios (sin, cos, tan) to solve for a
missing angle in a right triangle versus using the reciprocal ratios (sec, csc, cot). You must
use complete sentences and any evidence needed (such as an example) to prove your
point of view. (10 points)
Answers
Answer:
ok
this called f to do
Step-by-step explanation:
1. take a _____
To fight a fire breathing dragon, a knight needs a sword made of Dragon Alloy #13, which contains 7% gold, 3% silver, and 90% magic steel. The dwarves promised to forge such a sword for the knight. At the moment, they have an alloy that contains magic steel, 21% gold, and 9% silver. How much of that alloy and how much magic steel do the dwarves have to combine to get 2.7 kg of Dragon Alloy #13?
Answers
Let [tex]x[/tex] and [tex]y[/tex] be the amounts of available alloy (AA) and pure magic steel that are used, so we also have
[tex]x + y = 2.7[/tex]
DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of
[tex]0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}[/tex]
[tex]0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}[/tex]
[tex]0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}[/tex]
For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; [tex]x[/tex] kg of it will contain [tex]0.21x[/tex] kg of gold, [tex]0.09x[/tex] kg of silver, and [tex]0.70x[/tex] kg of steel. Each kg of magic steel of course contributes 1 kg of steel; [tex]y[/tex] kg of it will contribute [tex]y[/tex] kg of steel.
Then the dwarves need
• total gold: [tex]0.21x = 0.189[/tex]
• total silver: [tex]0.09x = 0.081[/tex]
• total steel: [tex]0.70x + y = 2.43[/tex]
Solve for [tex]x[/tex] and [tex]y[/tex]. The first two equations are consistent and give [tex]x = 0.90[/tex], and substituting this into the third we find [tex]y = 1.80[/tex]. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.
what would be your return on the investment if you bought when rates were 7% and sold when rates were 10%
Answers
The return on the investment is 3%
How to determine the return on investment?The given parameters are:
Buying rate = 7%
Selling rate = 10%
The return on the investment is
ROI = Selling - Buying
So, we have:
ROI = 10% - 7%
Evaluate
ROI = 3%
Hence, the return on the investment is 3%
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On a number line, suppose point E has a coordinate of 4, and EG = 11. What are the possible coordinates of point G?
The possible coordinates for G are
(Type integers or decimals. Use
comma to separate answers as needed.)
Answers
Answer:
-7, 15
Step-by-step explanation:
The positive difference between E and G is 11.
SolutionG - E = 11
G = 11 + E = 11 + 4
G = 15 . . . . . . . . . . . . . when G is right of E
__
E - G = 11
E - 11 = G = 4 - 11
G = -7 . . . . . . . . . . . . when G is left of E
Possible coordinates for G are -7 and 15.
please answer this i have tried lots of answers but they are all wrong urgent
Answers
(b). Kite and irregular trapezium.
(c). Isosceles Triangles.
(a). All four sides are equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is focused on spatial characteristics that relate to the proximity, size, shape, and relative placement of objects.
(a). Two features that make the shape square are all four sides equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
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3. Luke, the furniture maker, knows that he has 54 stools in stock. Some of these stools have three legs and some have four legs. Luke, however, does not know how many of each type of stool he has in stock. Since the stools are stored upside down, he only counts the number of legs to find out how many of of stool he has in stock. He counts 200 legs. each type 3.1 If the number of four-legged stools is x, write an algebraic expression for the number of three-legged stools. 3.2 Now write algebraic expressions for the number of legs that the three- legged stools have altogether as well as the number of legs that the four- legged stools have altogether. 3.3 Use your answers to Question 3.2 to write an equation in x and then determine the number of four-legged and three-legged stools in stock.
Answers
The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.
Simultaneous equationlet
number of four-legged stools = xnumber of three-legged stools = yx + y = 54
4x + 3y = 200
From equation (1)
x = 54 - y
Substitute x = 54 - y into4x + 3y = 200
4(54 - y) + 3y = 200
216 - 4y + 3y = 200
216 - y = 200
- y = 200 - 216
-y = -16
y = 16
substitute y = 16 intox + y = 54
x + 16 = 54
x = 54 - 16
x = 38
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need help on this problem
Answers
Using an exponential function, it is found that:
For Country A, the doubling time is of 43 years.For Country B, the growth rate is of 1.9% per year.What is the exponential function for population growth?The exponential function for population growth is given as follows:
[tex]P(t) = P(0)e^{kt}[/tex]
In which:
P(t) is the population after t years.P(0) is the initial population.k is the exponential growth rate, as a decimal.t is the time in years.For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{0.016t}[/tex]
[tex]e^{0.016t} = 2[/tex]
[tex]\ln{e^{0.016t}} = \ln{2}[/tex]
[tex]0.016t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.016}[/tex]
t = 43 years.
For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{36k}[/tex]
[tex]e^{36k} = 2[/tex]
[tex]\ln{e^{36k}} = \ln{2}[/tex]
[tex]36k = \ln{2}[/tex]
[tex]k = \frac{\ln{2}}{36}[/tex]
k = 0.019.
For Country B, the growth rate is of 1.9% per year.
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a square foot has 16 tiles each tile is 1 square ft what is the length of one side of the square floor
Answers
Answer:
4 ft
Step-by-step explanation:
The area of each tile is tile is 1 square ft, so the total area of the floor is 16 square ft.
Therefore, the side length is 4 ft.
Someone please help!
Answers
Answer:
obtuse
Step-by-step explanation:
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
In the above problem, it's given that one of the angles of the triangle exceeds 90° [ that is : 97° ]
[tex] \qquad \large \sf {Conclusion} : [/tex]
hence, it's an obtuse angled triangle
a company has six employees.The salary of five of the employees are P2200,P1300,P800,P940 and P560.When the sixth employee is included,the total monthly salaries of the employees becomes P7000.
Calculate the salary of the sixth employees
The company is joined by two more employees whose salaries are of equal amounts.The mean salary of all 8 employees is P1100
Calculate the monthly salary of each of the new employees
Answers
Answer:
First answer is 1200
Second answer is 900 for each new employee
Step-by-step explanation:
First answer:
2200+1300+800+940+560+x = 7000
5800+x = 7000 subtract 5800 from both sides and you get your answer
x = 1200
Second answer:
x = 900. Each of the two employees made 900 a month or 1800 a month for both of them.
To find the average we take the total salaries and divide by the number of people to find the average salary. In this case, we know the average and we know all of the salaries, but two. We can figure this out.
(7000 + 2x)/8 = 1100 multiple both sides by 8 to clear the fraction/
7000 +2x = 8800 Subtract both sides by 7000
2x = 1800 Divide both sides by 2
x = 900
he cone below has a radius of 3 inches, a height of 4 inches, and a slant height of 5 inches.
What is the approximate lateral area of the cone? Use 3.14 for π and round to the nearest whole number.
38 in.2
47 in.2
75 in.2
94 in.2
Answers
The lateral area of the cone is calculated as: B. 47 in.².
How to Find the Lateral Area of a Cone?Lateral area = πrl
Given the following:
Slant height (l) = 5 inches
Radius (r) = 3 inches.
π = 3.14
Plug in the values
Lateral area = (3.14)(3)(5)
Lateral area ≈ 47 in.²
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What are the coordinates of the point p if the coordinates of the other three vertices of the rectangle in the figure shown to the right are (3,7),(3,9) and (6,9)
Answers
Considering the given rectangle, the coordinates of p are (6,7).
What are the coordinates of p?For x, there are two vertices at x = 3 and one at x = 6, hence the x-coordinate of p is x = 6.
For y, there are two vertices at y = 9 and one at y = 7, hence the y-coordinate of p is y = 7.
Then, the coordinates of p are (6,7).
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Evaluate the limit, lim x -> 0 (x * cos theta - theta * cos x)/(x - theta)
Answers
The limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex].
What are limits?In Mathematics, a limit exists described as a value that a function approaches the output for the provided input values. Limits exist necessary in calculus and mathematical analysis and exist utilized to determine integrals, derivatives, and continuity.
Given:
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)$$[/tex]
Substitute the value x = 0, then we get
[tex]$=\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}$$[/tex]
Simplify the above equation, we get
[tex]$\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}= 1$[/tex]
Therefore, the limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex]
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An employee at a fireworks company is designing a rocket. The rocket will consist of a cardboard circular cylinder with a height that is seven times as large as the radius. On top of the cylinder will be a cone with a height of 5 in. and a radius equal to the radius of the base as shown in the figure. If the company wants to fill the cone and the cylinder with a total of 204 in.^3 of powder, then what should be the radius of the cylinder? Note that the volume of a right circular cylinder with radius r and height h is and the volume of a cone with a base of radius r and height h is .
Answers
The radius of the cylinder should be approximately 2.040 inches long.
How to calculate the radius of a rocket to contain a required quantity of powder
The volume required to store the powder is the sum of the volumes of the cylinder and the cone, whose expression is in this case:
204 in³ = (π/3) · r² · (4 in) + π · r² · h
204 in³ = (4/3 + h) · π · r²
204 in³ = (4/3 + 7 · r) · π · r²
204 = (4π/3) · r² + 7π · r³
7π · r³ + (4π/3) · r² - 204 = 0
The positive roots of the cubic equation are:
r ≈ 2.040 in
The radius of the cylinder should be approximately 2.040 inches long.
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Please help!!!! all qustions please
Answers
See below for the missing terms of the sequences
The first term of the sequenceThe given parameters are:
T4 = 30
T5 = 49
Calculate the third term as follows:
T3 = T5 - T4
T3 = 49 - 30
T3 = 19
Calculate the second term as follows:
T2 = T4 - T3
T2 = 30 - 19
T2 = 11
Calculate the first term as follows:
T1 = T3 - T2
T1 = 19 - 11
T1 = 8
Hence, the first term of the sequence is 8
The first term and the other terms of the sequenceThe given parameters are:
T2 = x
T3 = y
Calculate the first term as follows:
T1 = T3 - T2
T1 = y - x
Calculate the fourth term as follows:
T4 = T2 + T3
T4 = x + y
Calculate the fifth term as follows:
T5 = T3 + T4
T5 = y + x + y
T5 = x + 2y
Hence, the missing terms of the sequence are y - x, x + y and x + 2y
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za = a + b/m, solve for a
Answers
Answer: [tex]a=\frac{b}{zm-1}[/tex]
Step-by-step explanation:
Let's first multiply both sides by m to get rid of the denominator.
[tex]za=\frac{a+b}{m}\\zam=a+b[/tex]
Now, we have an a on both sides of the equation. It will be easier to solve if there is only one, so let's divide both sides by a.
[tex]\frac{zam}{a}=\frac{a+b}{a}\\zm=\frac{a}{a}+\frac{b}{a}\\zm=1+\frac{b}{a}[/tex]
The 1 on the right can be moved to the left to isolate the fraction.
[tex]zm-1=\frac{b}{a}[/tex]
We want to get a by itself, so let's multiply it on both sides to remove it from the denominator.
[tex]a(zm-1)=b[/tex]
Finally, we can divide zm-1 from both sides to get a by itself.
[tex]a=\frac{b}{zm-1}[/tex]