Answers
Because you are collecting like terms with -5z and +5z and it will give you 10z and 30 will be by it’s self because it has nothing to add or subtract with .
Related Questions
The minimum diameter for a hyperbolic cooling tower is 57 feet...
Answers
Answer:
Can give you the example then you have to figure out.
Step-by-step explanation:
We are assuming the center of the tower is at the origin, so we can use the standard form of a horizontal hyperbola centered at the origin: \displaystyle \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1
a
2
x
2
−
b
2
y
2
=1, where the branches of the hyperbola form the sides of the cooling tower. We must find the values of \displaystyle {a}^{2}a
2
and \displaystyle {b}^{2}b
2
to complete the model.
First, we find \displaystyle {a}^{2}a
2
. Recall that the length of the transverse axis of a hyperbola is \displaystyle 2a2a. This length is represented by the distance where the sides are closest, which is given as \displaystyle \text{ }65.3\text{ } 65.3 meters. So, \displaystyle 2a=602a=60. Therefore, \displaystyle a=30a=30 and \displaystyle {a}^{2}=900a
2
=900.
To solve for \displaystyle {b}^{2}b
2
, we need to substitute for \displaystyle xx and \displaystyle yy in our equation using a known point. To do this, we can use the dimensions of the tower to find some point \displaystyle \left(x,y\right)(x,y) that lies on the hyperbola. We will use the top right corner of the tower to represent that point. Since the y-axis bisects the tower, our x-value can be represented by the radius of the top, or 36 meters. The y-value is represented by the distance from the origin to the top, which is given as 79.6 meters. Therefore,
x
2
a
2
−
y
2
b
2
=
1
Standard form of horizontal hyperbola
.
b
2
=
y
2
x
2
a
2
−
1
Isolate
b
2
=
(
79.6
)
2
(
36
)
2
900
−
1
Substitute for
a
2
,
x
,
and
y
≈
14400.3636
Round to four decimal places
The sides of the tower can be modeled by the hyperbolic equation
\displaystyle \frac{{x}^{2}}{900}-\frac{{y}^{2}}{14400.3636 }=1,\text{or}\frac{{x}^{2}}{{30}^{2}}-\frac{{y}^{2}}{{120.0015}^{2} }=1
900
x
2
−
14400.3636
y
2
=1,or
30
2
x
2
−
120.0015
2
y
2
=1
The shape of hyperbolic cooling tower is a conic section that can be described with a formula equation.
a = 28.5, b ≈ 52.65
[tex]Equation \ of \ hyperbola;\ \dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
Reasons:
The parameters of the hyperbolic cooling tower are;
Minimum diameter = 57 feet
The height at which the diameter occurs = 155 ft.
The diameter of the tower = 175 feet
Total height of the tower = 200 feet
Height at which the center of the hyperbola occurs = 155 feet
Solution:
The equation of a hyperbola is; [tex]\dfrac{(x - h)^2}{a^2} - \dfrac{(y- k)^2}{b^2} = 1[/tex]
The center of the hyperbola = (0, 155)
[tex]a = \dfrac{57}{2} = 28.5[/tex]
At y = 155,
Therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y -155)^2}{b^2} = 1[/tex]
At y = 200 feet [tex]x = \dfrac{75 \ feet}{2} = 37.5 \ feet[/tex]
Therefore;
[tex]\dfrac{37.5^2}{28.5^2} - \dfrac{(200 -155)^2}{b^2} = 1[/tex]
b² = 2769.0340909
b ≈ 52.62
The equation of the hyperbola is therefore;
[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]
Learn more here:
https://brainly.com/question/3351710
Calculating Percent Change
Determine the Percent Change for each of the following.
Express each answer as a percent, rounded to the nearest tenth.
A quantity decreases from 20 to 15-% decreased
A quantity increases from 15 to 20-% increase
The price of a Latte dropped from $3.12 to $2.9-% decrease
The cost of Gasoline rose from $2.9 to $3.12-% increase
Answers
Answer:
the last one is an increase of $.22
Step-by-step explanation:
the last one is an increase of $.22
Help me out in this question please
Answers
20
Step-by-step explanation:There are two ways to solve this (both will end up with the same answer):
1st way:
You can find 4/9 of 36 to find how many displays the class explored so far. You can write it as 4/9 x 36, which is equal to 16. So, the class explored 16 displays so far. All you need to do is subtract 16 from 36 to find how many displays the class needs to explore, which can be written as 36-16, and is equal to 20.
Final answer: 20
2nd way:
You can do 1 minus 4/9 to find the left over fraction of the displays that the class needs to explore, which is equal to 5/9. Then, you need to find 5/9 of 36 to find how many displays are left for the class to explore. You can write it as 5/9 x 36, which is equal to 20.
Final answer: 20
Hope you understand and that this helps with your question :)
PLEASE HELP ME WITH THIS ALGEBRA QUESTION!! THANK YOU!!
Answers
Answer:
The first four terms of the sequence are: {-10,-23,-62,-179}
Step-by-step explanation:
Given recursive formula is:
[tex]a_n = 3a_{n-1}+7[/tex]
First term = a1 = -10
The first term is already known. In order to find the next terms, we will put n=2,3,4 in the recursive formula.
Putting n=2
[tex]a_2 = 3a_{2-1}+7\\a_2 = 3a_1+7\\a_2 = 3(-10)+7\\a_2 = -30+7\\a_2 = -23[/tex]
Putting n=3
[tex]a_3 = 3a_{3-1}+7\\a_3 = 3a_2+7\\a_3 = 3(-23)+7\\a_3 = -69+7\\a_3 = -62[/tex]
Putting n=4
[tex]a_4 = 3a_{4-1}+7\\a_4 = 3a_3+7\\a_4 = 3(-62)+7\\a_4 = -186+7\\a_4 = -179[/tex]
Hence,
The first four terms of the sequence are: {-10,-23,-62,-179}
5+1000000000000000000
Answers
Answer:
1000000000000000005
Answer:
1000000000000005
Step-by-step explanation:
A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room
Answers
_____________________
good luck on your assignment!! <3
1/4 divided 3 please help me
Answers
Answer: 1/12
Step-by-step explanation:
PLEAS HURRY I HAVE NO TIME LEFT
PLEASE HELP ME WITH THIS QUESTION
Question: Name each polygon by its number of sides and then classify it as CONVEX or CONCAVE and REGULAR or IRREGULAR
Answers
Answer:
no you scam me if I see what is promises I will help you
A ceramics teacher orders 5 blocks of gray clay for every 3 blocks of red clay.
How many blocks of gray clay will the teacher order if she orders 15 blocks of red
clay? *
17
20
25
28 ( plz help if you can)
Answers
Answer:
25
Step-by-step explanation:
trust me it's right it might be easier if you use paoer
10 kg of potatoes cost $4.50. How much will 50 kg of potatoes cost at this rate?
Answers
Answer:
$22.5
Step-by-step explanation:
10 kg=$4.50
50kg = x
(do cross multiplication)
10x =225
x=$22.5
i give up on math. help.
Answers
Answer:
try b
Step-by-step explanation:
Answer:
The answer is A. g(x) = f(x) + 4
If a cross section of the paperweight is cut parallel to the base, which shape describes the cross section?
Answers
Answer:
Yes, that's right: the cross section will be a rectangle (but also a parallelogram).
Step-by-step explanation:
Help Please!! I WILL give brainliest and thanks!!
Which of these inequalities are equivalent to r > -11?
Check all that apply.
-r -33
-3r 33
Random answers get reported
Answers
Answer:
ez pts tysm
Step-by-step explanation:
The third and the sixth term of a geometric progression are 24 and 64/9 respectively. Find
a) the first term and common ratio
b) the sum of the first five terms
Answers
Answer:
Ai. Common ratio = 2/3
Aii. First term = 54
B. Sum of the first five terms = 422/3
Step-by-step explanation:
From the question given above, the following data were obtained:
3rd term (T3) = 24
6Th term (T6) = 64/9
First term (a) =?
Common ratio (r) =?
Sum of the first five terms (S5) =?
Ai. Determination of the common ratio (r).
T3 = ar²
T3 = 24
24 = ar²....... (1)
T6 = ar⁵
T6 = 64/9
64/9 = ar⁵......... (2)
The equation are:
24 = ar²....... (1)
64/9 = ar⁵......... (2)
Divide equation 2 by equation 1.
64/9 ÷ 24 = ar⁵ / ar²
64/9 × 1/24 = r³
8/27 = r³
Take the cube root of both side
r = 3√(8/27)
r = 2/3
Thus, the common ratio is 2/3
Aii. Determination of the first term (a).
T3 = ar²
3rd term (T3) = 24
Common ratio (r) = 2/3
First term (a) =?
24 = a(2/3)²
24 = 4a/9
Cross multiply
24 × 9 = 4a
216 = 4a
Divide both side by 4
a = 216/4
a = 54
Thus, the first term (a) is 54
B. Determination of the sum of the first five terms.
Common ratio (r) = 2/3
First term (a) = 54
Number of term (n) = 5
Sum of first five terms (S5) =?
Sn = a[1 –rⁿ] / 1 – r
S5 = 54[1 – (⅔)⁵] / 1 – ⅔
S5 = 54 [1 – 32/243] / ⅓
S5 = 54 (211/243) × 3
S5 = 54 × 211/81
S5 = 6 × 211/9
S5 = 2 × 211/3
S5 = 422/3
Thus, the sum of the first five terms is 422/3
what apple group is the correct one
Answers
Answer:
i don`t understand you
Step-by-step explanation:
but i think i phone...?
Answer:
ummm there is no other context did you mean to post a picture? All I could find was this
The Apple User Group Connection (AUGC) was established in 1985 by Apple and led by Apple employee Ellen Petry Leanse.
how many 2/3 size pieces are in 4 wholes
Answers
Divide 4 wholes by 2/3 pieces to fnd number of pieces.
4 / 2/3
When you divide by a fraction, flip the fraction over then multiply:
4 x 3/2 = (4 x 3)/2 = 12/2 = 6
There are 6 pieces.
Answer:
6
Step-by-step explanation:
lets put this in terms of 3, because of 2/3. the number above the three will be divided by three to get to four. So if we multiply three by four to get twelve, we can put that over 3, and then find our answer. 12/3=4, so we know that is correct. and since we need to find how many 2/3 pieces we need, we divide 12/3 by 2/3 to get 6. so you need 6 2/3 pieces to get four wholes.
Write an equation in point-slope form of the line that passes through (-4,1) and (4.3).
Answers
Answer:
a
Step-by-step explanation:
:P
Combine 2x^2+5x-6+8x
Answers
x^2-x-12 factor completely
Answers
2
−
−
1
2
x
2
−
x
−
12
x2−x−12
2
+
3
−
4
−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12
2
Common factor from the two pairs
2
+
3
−
4
−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12
(
+
3
)
−
4
(
+
3
)
x
(
x
+
3
)
−
4
(
x
+
3
)
x(x+3)−4(x+3)
3
Rewrite in factored form
(
+
3
)
−
4(+3)x
(x+3)−4(x+3)
x(x+3)−4(x+3)
(−4)(+3)
(x−4)(x+3)
(x−4)(x+3)
how many hectares of land are there in a field that is 450 m long and 1200 dm wide.
Answers
Answer:
Step-by-step explanation:
Given
[tex]Length = 450\ m[/tex]
[tex]Width = 1200\ m[/tex]
Required
Determine the number of hectares in this dimension
First, we need to calculate the area of the land
[tex]Area = Length * Width[/tex]
[tex]Area = 450m * 1200dm[/tex]
Convert dm to m
[tex]Area = 450m * 120m[/tex]
[tex]Area = 54 000 m^2[/tex]
[tex]1 hectare = 0.0001m^2[/tex]
So, we have:
[tex]1\ hectare = 0.0001m^2[/tex]
Multiply by 54000
[tex]Hectare = 0.0001 * 54000[/tex]
[tex]Hectare = 5.4[/tex]
Hence, there are 5.4 hectares
Please help.
Will rate Brainliest!
Thanks in advance!
Answers
Answer:
y = 8x + 13
Step-by-step explanation:
slope-intercept form: y = mx + b
Given equation: [tex]y = -\frac{1}{8}x -2[/tex]
Second equation: unknown
Slope: unknown
Given point: (-2, -3)
When two lines are perpendicular, their slopes are negative reciprocals. So, since the slope(m) of the given line is [tex]-\frac{1}{8}[/tex], the slope of the line perpendicular to it is 8.
Now we know the slope of the line. To find the y-intercept, input the values of the slope and the given point into the equation format and solve for b:
y = mx + b
-3 = 8(-2) + b
-3 = -16 + b
13 = b
The y-intercept is 13.
Now that we know the slope and the y-intercept, we can write the equation:
y = 8x + 13
Hope this helps :)
What is the probability that a randomly selected camper likes swimming or having a cookout, but not both?
A.
B.
C.
D
Answers
The probability that a randomly selected camper likes to have a cookout or swimming, but not both, is 0.10.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
The Venn diagram displays the campers’ preferences.
One circle is labeled S, 0.06,
the other circle is labeled C, 0.04,
the shared area is labeled 0.89,
and the outside area is labeled 0.01.
The probability that a randomly selected camper likes to have a cookout or swimming, but not both,
= 0.06 + 0.04
= 0.10
Therefore, 0.10 is the required probability.
To learn more about the probability;
brainly.com/question/11234923
#SPJ5
37/6 divided by 1/2.
Answers
Answer: 12 1/3
hope this helps.. stay safe and have a great day
Step-by-step explanation:
Explation: I hope this help
If y= 6x + 8 what is y when x= -3
Answers
Answer:
y=2
Step-by-step explanation:
y = 26
If you substitute x for -3 in the equation y = 6x + 8, your equation becomes:
y = 6(-3) + 8 now you can simplify it and solve for y
6 x -3 = -18
18 + 8 = 26
y = 26
What is the value of 5x when x=3.2
Answers
Answer: 16
Step-by-step explanation:
All you have to do is plug 3.2 into the expression. So 5 * 3.2 is 16.
00
3-2 Checking Accounts
12. Justin Nucci listed these items on his deposit slip: (bills) 8 one-hundreds,
27 fifties, 83 fives, 141 ones; (coins) 13 quarters, 117 nickels; (checks) $317.94,
$57.89, $527.24 and $77.49. He received cash back of 30 twenties and 11 tens.
What total deposit did he make?
603
120] Chapter 3 Banking
Answers
Answer: 4,405.66
Step-by-step explanation:
Add all the amounts together.
This is my study island math and I need all the questions to be done so I’m doing them in order.
Answers
Answer:
A
Step-by-step explanation:
Hope I helped
Answer:
The answer is A, $11.60
Step-by-step explanation:
0.66=spent 9 minutes
0.66x9=5.94
5.94+5.66=$11.60
Btw, luv ur profile pic uwu!
Use trigonometric identities to transform the left side of the equation into the right side (0 < < /2).
Answers
Sin^2
Cos^2
This is the answer
Which of the following shows the correct sums that would be found when clustering is used to find the answer to the problem 34 x 12?
340 + 68 = 408
340 + 34 = 374
340 + 68 = 398
300 + 8 = 308
Answers
The first option is correct.
The calculation is as follows:if we multiply the 34 and 12 so it comes 408
And according to first option, it we add 340 and 68 so it comes 408.
Learn more: brainly.com/question/16911495
Please help I’m stuck on this question
Answers
Answer:
C. Supplementary angles
Step-by-step explanation:
Supplementary angles always equal 180 degrees.
The answer is (C) because, the sum of both the angle is equals to 180° i.e they are pair of supplementary angles.