Answer:
Step-by-step explanation:
tanα=height/distance
tanα=h/d
d=h/tanα so
d1=h/tanα and d2=h/tanß
Then the distance between them is:
d=h/tanß-h/tanα, we know that h=1300, α=(90°-71.9°=18,1°), and ß=90°-27.1°=62.9°) so
d=(3100*tan62.9)-(3100*tan18.1) meters
d≈2116 (to nearest meter)
Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).
Answer:
5 cubic units.
Step-by-step explanation:
We have been given that a can soda can has a volume of 15 cubic units and a diameter of 2.
First of all let us find the height of cylinder using volume of cylinder formula.
[tex]\text{Volume of cylinder}=\pi r^2 h[/tex], where,
r = radius of cylinder,
h = Height of cylinder.
Now let us divide our diameter by 2 to get the radius of cylinder.
[tex]\text{radius of cylinder}=\frac{2}{2}=1[/tex]
Let us substitute our given values in volume of cylinder formula to get the height of cylinder.
[tex]15=\pi*1^2*h[/tex]
[tex]15=\pi*h[/tex]
[tex]\frac{15}{\pi}=\frac{\pi*h}{\pi}[/tex]
[tex]\frac{15}{\pi}=h[/tex]
Now we will use volume of cone formula to find the volume of our given cone inscribed inside cylinder.
[tex]\text{Volume of cone}=\frac{1}{3}\pi*r^2h[/tex]
Since the height and radius of the largest cone that can fit inside the can will be equal to height and radius of can, so we will substitute [tex]\frac{15}{\pi}=h[/tex] and [tex]r=1[/tex] in the volume formula of cone.
[tex]\text{Volume of cone}=\frac{1}{3}\pi*1^2*\frac{15}{\pi}[/tex]
[tex]\text{Volume of cone}=\frac{1}{3}*1*15[/tex]
[tex]\text{Volume of cone}=5[/tex]
Therefore, volume of our given cone will be 5 cubic units.
Solve using perfect square factoring patterns. x2 – 8x + 16 = 25
Suppose a youth organization wants to choose a president, vice-president and secretary for the upcoming year from its 35 person membership. In complete sentences, explain why this is a permutation. Determine how many different ways the youth board can be chosen.
A video game is on sale for 30% off the regular price of 50$. What is the sale price of the game?
Find the indicated terms of the sequence defined by each of the following recursive formulas:
a3 = −11 and an = 2an − 1 − 1
a2 =
a4 =
a4 = −36 and an = 2 an − 1 − 4
a3 =
a2 =
Answer:
1.
Given the recursive formula:
[tex]a_3 = -11[/tex] and
[tex]a_n = 2a_{n-1} -1[/tex]
For n = 3:
[tex]a_3=2a_2 -1[/tex]
Substitute [tex]a_3 = -11[/tex] we have;
[tex]-11=2a_2 -1[/tex]
Add 1 to both sides we have;
[tex]-10 = 2a_2[/tex]
Divide both sides by 2 we have;
[tex]-5 = a_2[/tex]
or
[tex]a_2 = -5[/tex]
For n = 4, we have;
[tex]a_4=2a_3 -1[/tex]
Substitute [tex]a_3 = -11[/tex] we have;
[tex]a_4 = 2 \cdot -11 -1 = -22-1 = -23[/tex]
⇒[tex]a_4 = -23[/tex]
2.
Given:
[tex]a_4 = -36[/tex] and [tex]a_n = 2a_{n-1} -4[/tex]
For n = 4, we have;
[tex]a_4=2a_3 -4[/tex]
Substitute [tex]a_4 = -36[/tex] we have;
[tex]-36 = 2a_3 -4[/tex]
Add 4 to both sides we have;
[tex]-32 = 2a_3[/tex]
Divide both sides by 2 we have;
⇒[tex]a_3 =-16[/tex]
For n = 3:
[tex]a_3=2a_2 -4[/tex]
Substitute [tex]a_3 = -16[/tex] we have;
[tex]-16=2a_2 -4[/tex]
Add 4 to both sides we have;
[tex]-12 = 2a_2[/tex]
Divide both sides by 2 we have;
[tex]-6 =a_2[/tex]
or
⇒[tex]a_2 = -6[/tex]
The indicated terms of the sequence defined by each of the following recursive formulas are as follows:
[tex]\mathbf{a_{2} = -5}[/tex][tex]\mathbf{a_4 = -23}[/tex][tex]\mathbf{{a_3}=-16}[/tex][tex]\mathbf{{a_2}=-6}[/tex]What are recursive formulas?A recursive formula is one that describes each term in a series in terms of the term before it. The general term for an arithmetic sequence by using a recursive formula is [tex]\mathbf{a_n = a_{n-1} + d}[/tex]
From the given information:
[tex]\mathbf{a_3 = -11}[/tex] [tex]\mathbf{a_n = -2a_{n-1} -1}[/tex]Now, when n = 3
[tex]\mathbf{a_3 = -2a_{3-1} -1}[/tex]
[tex]\mathbf{-11= -2a_{2} -1}[/tex]
[tex]\mathbf{2a_{2} = -10}[/tex]
[tex]\mathbf{a_{2} = -5}[/tex]
When n = 4
[tex]\mathbf{a_4= -2a_{4-1} -1}[/tex]
[tex]\mathbf{a_4 = 2(-11) -1}[/tex]
[tex]\mathbf{a_4 = -23}[/tex]
Second Part:
[tex]\mathbf{a_4 = -36}[/tex][tex]\mathbf{a_n = 2_{an-1}-4}[/tex]When n = 4
[tex]\mathbf{a_4 = 2_{a4-1}-4}[/tex]
[tex]\mathbf{a_4= 2_{a3}-4}[/tex]
[tex]\mathbf{-36+4= 2_{a_3}}[/tex]
[tex]\mathbf{2_{a_3}=-32}[/tex]
[tex]\mathbf{{a_3}=-16}[/tex]
When n = 3
[tex]\mathbf{a_3= 2_{a3-1}-4}[/tex]
[tex]\mathbf{a_3= 2_{a2}-4}[/tex]
[tex]\mathbf{-16= 2_{a_2}-4}[/tex]
[tex]\mathbf{2_{a_2}=-12}[/tex]
[tex]\mathbf{{a_2}=-6}[/tex]
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Find the value of each variable.
A. a = 15, b = 5, c = 8, d = 4
B. a = 15, b = 4, c = 8, d = 5
C. a = 14.5, b = 5, c = 6, d = 4
D. a = 14.5, b = 4, c = 6, d = 5
Answer:
(A)
Step-by-step explanation:
From the figure, since RT is parallel to QU, therefore ΔSQU is similar to ΔSRT, thus using the basic proportionality theorem, we get
[tex]\frac{SR}{SQ}=\frac{ST}{SU}[/tex]
[tex]\frac{c}{12+c}=\frac{10}{25}[/tex]
[tex]25c=120+10c[/tex]
[tex]15c=120[/tex]
[tex]c=8[/tex]
Also, QU is parallel to PV, therefore from ΔPVS and ΔSRT, we have
[tex]\frac{SR}{SP}=\frac{ST}{SV}[/tex]
[tex]\frac{c}{c+12+d}=\frac{10}{30}[/tex]
[tex]\frac{8}{20+d}=\frac{1}{3}[/tex]
[tex]24=20+d[/tex]
[tex]d=4[/tex]
Now, from ΔSRT and SQU, we have
[tex]\frac{RT}{QU}=\frac{ST}{SU}[/tex]
[tex]b=\frac{10{\times}12.5}{25}[/tex]
[tex]b=5[/tex]
Also, from ΔSQU and SPV,
[tex]\frac{12.5}{a}=\frac{25}{30}[/tex]
[tex]a=15[/tex]
Thus, value of a,b,c and d are 15,5,8 and 4 respectively.
What is the data path width for a dimm that supports ecc?
Normally, the data path width for DIMMs is 64 bits but for the DIMMs that support ECC, the data path is 72 bits.
To add, error checking uses the extra 8 bits. ECC memory is more reliable than non-ECC memory but it costs more than a non-ECC memory. Comprising the DIMMS are a series of dynamic random-access memory integrated circuits. Mounted on a printed circuit board, these modules are designed for use in personal computers, workstations and servers.
The most common kinds of internal data corruption are detected and corrected by a type of computer data storage called error-correcting code memory.
The variable Z is directly proportional to X. When X is 3, Z has the value 54. Wha is the value of Z when X= 12
now find new Z
Z = 18X
Z = 18(12)
Z = 216
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x= 5 + y
28x – 9y= -12
A student took a test which had 6 questions. He would score 8 points on the test if all his answers are correct. If y represents the student's score when he got x questions incorrect, which graph best represents this situation?
Which is the slope of the line that connects points (3,17) and (7,25) ?
HELP If f(x)=1/7x-9,then f^-1(x)=?
Answer:
Plato/Edementum
Step-by-step explanation:
this is the correct answer if you are taking Inverse of a Function: Mastery Test just type in 7x+63 type it in like that and it will be correct
Find the fifth roots of 243(cos 240° + i sin 240°)
A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4). What are the new coordinates if the triangle is dilated with a scale factor of 1/5?
What value should go in the empty box to complete the calculation for finding the product of 62.834 × 0.45?
What is the correct name for this circle?
the circled is named for the letter in the center
so this one is named circle C
Mike and adam left a bus terminal at the same time and traveled in opposite directions. mike’s bus was in heavy traffic and had to travel 20 mi/h slower than adam’s bus. after 3 hours, their buses were 270 miles apart. how fast was each bus going?
What time is 5 3/4 hours after 9:22 PM?
On a blueprint, the scale indicates that 7 cm represent 16 ft. What is the length of a room that is 9.8 cm long and 5 cm wide on the blueprint?
7/16 =9.8/ x =156.8/7 = 22.4 feet long
7/16 = 5/x = 80/7 = 11.428 feet wide round to 11.43 or 11.4 feet
Given the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2
Please Help! Given that line s is perpendicular to line t, which statements must be true of the two lines? Check all that apply.
a.Lines s and t have slopes that are opposite reciprocals.
b.Lines s and t have the same slope.
c.The product of the slopes of s and t is equal to -1
d.The lines have the same steepness.
e.The lines have different y intercepts.
f.The lines never intersect.
g.The intersection of s and t forms right angle.
h.If the slope of s is 6, the slope of t is -6
Remember, it is check all that apply, so there will be multiple answers.
In geometry, when line s is perpendicular to line t, statements a, c, and g are true: Lines s and t have slopes that are opposite reciprocals, the product of the slopes of s and t equal -1, and the intersection of s and t forms a right angle.
Explanation:In geometry, if line s is perpendicular to line t, several facts about these two lines can be stated:
a. Lines s and t have slopes that are opposite reciprocals. This is true. If the slope of one line is m, the slope of the line perpendicular to it is -1/m.b. Lines s and t have the same slope. This is false as orthogonal lines have slopes that are negative reciprocals of each other.c. The product of the slopes of s and t is equal to -1. This is true. When two lines are perpendicular, the product of their slopes is -1.d. The lines have the same steepness. This is false because perpendicular lines have different slopes.e. The lines have different y intercepts. This assertion is not necessarily true. Perpendicular lines may or may not have different y-intercepts.f. The lines never intersect. This is false. Perpendicular lines intersect once, forming a 90 degrees angle.g. The intersection of s and t forms a right angle. This is true. The definition of perpendicular lines states that they intersect at a right angle.h. If the slope of s is 6, the slope of t is -6. This is false. If the slope of s is 6, the slope of t, being a negative reciprocal, would be -1/6, not -6.Learn more about Perpendicular Lines here:https://brainly.com/question/18271653
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Solve the inequality. 8x-5>_27. A.x>_4. B.x>_11/4. C.x<_4. D.x<_11/4
The solution for the inequality 8x - 5 ≥ 27 can be written as x [4, ∞) or x ≥ 4, so option A is correct.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
8x - 5 ≥ 27
Solve the above inequality as shown below,
Add 5 to both sides of an inequality,
8x - 5 + 5 ≥ 27 + 5
8x ≥ 32
Divide both sides by 8,
8x / 8 ≥ 32 / 8
x ≥ 4
x [4, ∞)
Thus, x can be any real number greater than 4 or equal to four.
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Suppose that 66% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?
The probability of two people owning a dog when 66% of people own dogs is found by squaring the probability (0.66), giving us a result of 0.4356 or 43.56%.
Explanation:The question asks to calculate the probability that both people picked at random own a dog when it is known that 66% of people own dogs. To find this probability, we can simply multiply the probability of the first person owning a dog by the probability of the second person owning a dog, assuming that these events are independent.
The probability that one person owns a dog is given as 66%, which is 0.66 in decimal form. Thus, the probability that both people own a dog is 0.66 × 0.66 (or 0.66 squared). Calculation yields:
0.66 × 0.66 = 0.4356
Therefore, the probability that both people own a dog is 0.4356, or 43.56%.
A small school has 110 students who occupy three classrooms: a, b, and
c. after the first period of the school day, half the students in room a move to room b, one-fifth of the students in room b move to room c, and one-third of the students in room c move to room
a. nevertheless, the total number of students in each room is the same for both periods. how many students occupy each room?
There are 20, 50 and 30 in each room respectively.
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, there are 110 students in total in all the class.
According to question,
a+b+c = 110
After the room changes, we have
a/2 + c/3 = a
4b/5 + a/2 = b
2c/3 + b/5 = c
or,
a/2 = c/3
a/2 = b/5
b/5 = c/3 = a/2
so, substituting in,
a + 5a/2 + 3a/2 = 110
2a + 5a + 3a = 220
a = 22
b = 55
c = 35
Hence, there are 20, 50 and 30 in each room respectively.
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Find the sum of the arithmetic sequence. 15, 17, 19, 21, ..., 33
Answer:
240
Step-by-step explanation:
Hope this helps! :)
Let g(x) = 2x and h(x) = x2 + 4. Evaluate (g ∘ h)(3).
What is the y intercept of Y = 3x - 4?
Which of the following graphs represents the function f(x) = −2x3 − x2 + 3x + 1?
graph with 3 real zeros, down on left, up on right
graph with 3 real zeros, up on left, down on right
graph with 2 real zeros, down on left, down on right
graph with 2 real zeros, up on left, up on right
The function f(x) = −2x3 − x2 + 3x + 1 is represented by the graph with 3 real zeros, down on the left and up on the right, due to the negative leading coefficient and odd degree.
Explanation:The function you're looking at is f(x) = −2x3 − x2 + 3x + 1. To determine the correct graph, we consider the leading term, −2x3. Since the coefficient of the highest-degree term (which is -2) is negative, the graph will start down on the left and go up on the right. The degree of the function is the highest power of x, which is 3, a odd number. For polynomials, if the degree is odd and the leading coefficient is negative, the end behavior will be down on the left and up on the right. Therefore, the correct graph will have the description: Graph with 3 real zeros, down on the left, up on the right.
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Table that organizes two categorical variables is called?
It says it has 13 letters
What is the problem to this