9514 1404 393
Answer:
√6 -1 ≈ 1.44949√6 +1 ≈ 3.44949Step-by-step explanation:
Let x represent the smaller number. Then the sum of squares is ...
x² +(x+2)² = 14
2x² +4x +4 = 14 . . . eliminate parentheses
2x² +4x -10 = 0 . . . put in standard form
x² +2x -5 = 0 . . . . . divide by 2 (because we can)
(x +1)² -6 = 0 . . . . . complete the square
x +1 = √6 . . . we want the positive root
x = -1 +√6
x+2 = 1 +√6
The numbers are √6±1.
2〖sen〗^2 x+3 senx+1=0
2cotxsecx+ 2secx+cotx+1=0
senx〖cos〗^2 x=senx
2〖cos〗^2 x+2senx-12=0
2〖csc〗^2 x+〖cot〗^2 x-3=0
2 sin²(x) + 3 sin(x) + 1 = 0
(2 sin(x) + 1) (sin(x) + 1) = 0
2 sin(x) + 1 = 0 OR sin(x) + 1 = 0
sin(x) = -1/2 OR sin(x) = -1
The first equation gives two solution sets,
x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ
x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ
(where n is any integer), while the second equation gives
x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ
2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0
2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0
(2 sec(x) + 1) (cot(x) + 1) = 0
2 sec(x) + 1 = 0 OR cot(x) + 1 = 0
sec(x) = -1/2 OR cot(x) = -1
cos(x) = -2 OR tan(x) = -1
The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives
x = tan⁻¹(-1) + nπ = -π/4 + nπ
sin(x) cos²(x) = sin(x)
sin(x) cos²(x) - sin(x) = 0
sin(x) (cos²(x) - 1) = 0
sin(x) (-sin²(x)) = 0
sin³(x) = 0
sin(x) = 0
x = sin⁻¹(0) + 2nπ = 2nπ
2 cos²(x) + 2 sin(x) - 12 = 0
2 (1 - sin²(x)) + 2 sin(x) - 12 = 0
-2 sin²(x) + 2 sin(x) - 10 = 0
sin²(x) - sin(x) + 5 = 0
Using the quadratic formula, we get
sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2
but the square root contains a negative number, which means there is no real solution.
2 csc²(x) + cot²(x) - 3 = 0
2 (cot²(x) + 1) + cot²(x) - 3 = 0
3 cot²(x) - 1 = 0
cot²(x) = 1/3
tan²(x) = 3
tan(x) = ± √3
x = tan⁻¹(√3) + nπ OR x = tan⁻¹(-√3) + nπ
x = π/3 + nπ OR x = -π/3 + nπ
Question 8
A log with diameter 60 cm is 3 m in length its hollow centre is 20 cm in diameter.
Find the surface area of the log in cm', including the ends and the inside, correct to one decimal place.
Answer:
The surface area of the log including the ends and the inside is 80424.8 cm²
Step-by-step explanation:
To determine the surface area of the log with hollow center including the ends and the inside, we will find the surface area of the outer part of the log, surface area of the inner part of the log and the surface area of the two ends; and then sum everything up.
From the question,
Diameter of log = 60 cm
Length of log = 3 m = 300 cm
Diameter of hollow center = 20 cm
For the surface area of the outer part,
Area of the outer part = Circumference of the outer part × length
Circumference = 2πr = πd
∴ Area of the outer part = πd × l
(NOTE: d here is the diameter of the log)
d = 60 cm and l = 300 cm
Area of the outer part = 60π × 300 = 18000π cm²
For the surface area of the inner part,
Area of the inner part = Circumference of the inner part × length = πd × l
(NOTE: d here is the diameter of the hollow center)
d = 20 cm and l = 300 cm
Area of the inner part = 20π × 300 = 6000π cm²
For the surface area of one end
This is the difference between the area of the outer end and the area of the inner end
Here, we can determine the area by using
Area = πr², where r is the radius
Radius = Diameter / 2
Radius of outer end (R) = Diameter of log / 2 = 60cm / 2 = 30cm
Radius of inner end (r) = Diameter of hollow center / 2 = 20cm / 2 = 10 cm
∴ Surface area of one end = πR² - πr² = π(R²-r²)
= π (30²-10²)
= π (900 - 100)
= 800π cm²
This is the area of one end
For the two ends,
Area of the two ends = 2 × 800π cm² = 1600π cm²
Hence, the surface area of the log is 18000π cm² + 6000π cm² + 1600π cm²
Surface area of the log = 25600π cm²
Putting the value of π (π = 3.141592654)
Surface area of the log = 25600 × 3.141592654 cm²
Surface area of the log = 80424.77193 cm²
Surface area of the log = 80424.8 cm²
Hence, the surface area of the log including the ends and the inside is 80424.8 cm² (to one decimal place)
Please help will MARK BRANLIEST!!
As part of a landscaping project, put in a flower bed measuring 10 feet by 20 feet. Surround the bed with a uniform border of low-growing plants.
a. Write a polynomial that describes the area of the uniform border that surrounds the flower bed.
b. The low growing plants surrounding the flower bed require 1 square foot each when mature. If there are 216 of these plants, how wide a strip around the flower bed should be prepared for the border?
Answer:
took me time to try and answer your question hope it proves helpful
Question 3: Determine the missing base in the equation problem below. 75eight = 23 base
Answer:
29
Step-by-step explanation:
Given the expression [tex]75_8 = 23_x[/tex] where x is the unknown base:
[tex]75_8 = 23_x\\7\times8^1 +5\times8^0 = 2\times x^1+3 \times x^0\\56+5 = 2x+3\\61 = 2x+3\\2x = 61-3\\2x = 58\\x = 58/2\\x = 29[/tex]
Hence the missing base is 29
Use the number line below, where RS=9y+2, ST=2y+6, and RT= 52
Answer:
Step-by-step explanation:
Given
RS=9y+2, ST=2y+6, and RT= 52
The addition postulate is true for the number line.
RS+ST = RT
Substitute
9y+2+(2y+6) = 52
9y+2y+8 = 52
11y = 52-8
11y = 44
y = 44/11
y = 4
Find RS
RS = 9y+2
RS = 9(4)+2
RS = 36+2
RS = 38
Find ST:
ST = 2y+6
ST = 2(4)+6
ST = 8+6
ST = 14
Hence y = 4, RS = 38 and ST = 14
List and describe the characteristics of a wave
Answer:
Crest = Highest point of the wave.
Trough = Lowest point of the wave.
Wavelength = Distance from one crest/trough to the next (m)
Wave Height = Height from trough to crest (m)
Wave steepness = ratio of wave height to wavelength.
Amplitude = distance from the centre of wave to the bottom of the trough (m)
Step-by-step explanation:
Is 1.994 greater or lesser than 1.493
Answer:
greater than
Step-by-step explanation:
1.994 is closer to 2 than 1.493 so it is greater!
The average of the first 3 weights was 14 pounds. The average of the next 7 was 4 pounds. What was the overall average of the weights?
Answer:
[tex]Average = 10[/tex]
Step-by-step explanation:
Given
[tex]First\ Three = 14[/tex] --- Average
[tex]Next\ Seven= 4[/tex] --- Average
Required
Determine the overall average
Represent the sum of the first three with x.
So:
[tex]\frac{x}{3} = 14[/tex]
Solve for x
[tex]x = 14 * 3[/tex]
[tex]x = 42[/tex]
Represent the sum of the next seven with y.
So:
[tex]\frac{y}{7} = 4[/tex]
Solve for y
[tex]y = 4 * 7[/tex]
[tex]y = 28[/tex]
The overall average is calculated as thus:
[tex]Average = \frac{x + y}{7}[/tex]
[tex]Average = \frac{42 + 28}{7}[/tex]
[tex]Average = \frac{70}{7}[/tex]
[tex]Average = 10[/tex]
Which expression is equivalent to 27 + 15?
1) 3(24 + 12)
2) 319 + 5)
3) 9(3 + 15)
4) 9(18+ 6)
convert 2 3/7 to an improper fraction
Answer:The mixed number 2 3/7 can be converted to the improper fraction 17/7. The easiest way to do this is to multiply the denominator of the fraction (7 in...
Step-by-step explanation:
what are the steps we should follow to solve and equation
Please help me out! Help me please! This is so important!
The ratio of girls to boys in a primary school is 4:5. If there are 24 girls, how many boys are there? Help!
Answer:
there are 30 boys
Step-by-step explanation:
If there is 24 girls you divide that by 4 and you get six so that means you multiply with six and you get 30.
A ratio of 4:5 means that for every 4 girls, there are 5 boys.
24 girls / 4 girls = 6
5 * 6 = 30 boys
There are 30 boys if there are 24 girls
The Complex Conjugate of 2 + 5i is equal to: _______+_________i
Answer:
2 - 5i
Step-by-step explanation:
For any complex number like say "z" written in rectangular form as;
z = a + ib, then from definitions the complex conjugate is given by the relation:
z* = a − ib
Now, from our question, we want to find the complex conjugate of 2 + 5i.
From the relationship above, it's clear that the complex conjugate here is;
2 - 5i
Unpredictable numbers that are distributed over a certain range are ____.
A. Random numbers
B. Random equations
C. Random formulas
D. Tables of formulas
Answer:
random numbers
Step-by-step explanation:
because they are randomly picked
Unpredictable numbers that are distributed over a certain range are _Random numbers_.
What is random experiment?Random experiments are repeated multiple times to determine its likelihood.
The number of times an experiment is repeated is better described as number of trials.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
Now, Unpredictable numbers that are distributed over a certain range are random numbers because they are randomly picked.
Unpredictable numbers that are distributed over a certain range are _Random numbers_.
To Learn more about Random numbers, click here;
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Which of the following is equal to the opposite of −45?
−|45|
−|−45|
−(−45)
−45
Which of the following statements does not represent the same value as the others?
the absolute value of 9
the absolute value of negative 9
the opposite of 9
the distance between 0 and −9
All of the following are true statements except _____.
|−93| = −93
|−93| = 93
−|93| = −93
|93| = 93
If you move from zero to 15 on the number line, you are representing all of the following except _____.
the absolute value of 15
the distance between zero and 15
the opposite of −15
the opposite of 15
All of the following expressions are equal to N except _____.
−(− N )
− N
| N |
|− N |
Answer:
The first one
Step-by-step explanation:
Find the value of x.
(A) 16 (B) 41 (C) 5 (D) 25 (E) 66
Answer:
D. 25Step-by-step explanation:
D. 25 is the correct answer....Hopes it helps you....Hopes to get BRAINLIEST.. .Thank you ☺️☺️☺️
a pizzeria had 4 cans of tomato sauce how many pizzas could they make with the cans if each pizza took one fourth of a can
Answer:
16 pizzas.
Step-by-step explanation:
That is 4 divided by 1/4
= 4 * 4/1
= 16.
Answer:
16
Step-by-step explanation:
There are 4 pizzas per can and you have 4 cans.
4 x 4 = 16
can you write an equivalent fraction for 9/11 and 6/7 using the least common denominator ?
Answer:
The least common denominator is 77 so the fractions would become 63/77 and 66/77.
Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select the true statement.
Answer:
segment EF is twice as long as segment AB
Step-by-step explanation:
Quadrilateral EFGH and quadrilateral ABCD are similar polygons. We can say that two polygons are similar if their corresponding angles are equal to each other and their corresponding sides are proportional to each other.
From the image attached, we can see that side CD and side GH are corresponding sides. The ratio of their sides are to be proportional.
GH / CD = 12 / 6 = 2
Therefore Quadrilateral EFGH is twice the size of Quadrilateral ABCD. Since side EF and side AB are proportional, therefore segment EF is twice as long as segment AB
Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 2525 dollars and a standard deviation of 88 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 2828 dollars in interest
Complete Question
Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 25 dollars and a standard deviation of 8 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 28 dollars in interest
Answer:
0.354
Step-by-step explanation:
We solve for z score in this question.
The formula is given as:
z = (x-μ)/σ, where
x is the raw score = $28
μ is the population mean = $25
σ is the population standard deviation = $8
z= 28 - 25/8
z = 0.375
P-value from Z-Table:
P(x<28) = 0.64617
P(x>28) = 1 - P(x<28)
= 1 - 0.64617
= 0.35383
Approximately to 3 decimal places = 0.354
The proportion of the bank's Visa cardholders pay more than 28 dollars in interest is 0.354.
Which of the following are like terms
Answer:
i would say a but i could be wrong
Step-by-step explanation:
A car wash detailed 132 cars in 4 hours. How many cars did they detail per hour?
Answer:
33 CarsStep-by-step explanation:
132 / 4 = 33
Therefore,
The answer is,
33 CarsCharlene and Gary want to make confetti. In order to get the right balance of ingredients for their tastes they bought 3 pounds of paper hearts at $2.46 per pound, 5 pounds of sparkling stars for $3.05 per pound, and 3 pounds of shiny coils for $2.33 per pound. Determine the cost per pound of the coffeti.
Answer:
0.712 cents per pound
Step-by-step explanation:
Since we are given the exact amount of each ingredient as well as the price for that amount then we simply need to calculate how much each pound of the confetti actually costs. We do this by adding together all of the pound of all of the ingredients and then adding together all of the costs. Lastly, we divide the cost by the total amount of pounds to find the cost per pound of the confetti like so...
3lbs. + 5lbs. + 3lbs. = 11 lbs.
$2.46 + $3.05 + $2.33 = $7.84
$7.84 / 11 lbs. = 0.712 cents per pound
Therefore, the cost per pound of the confetti is 0.712 cents per pound
Select all the possible (x,y) coordinates for the following linear equation y=3x+2
Answer:
x = 2/3
Step-by-step explanation:
To find x-intercept/zero, subtract y = 0
0 = 3x + 2
Move variable to the left-hand side and change its sign
-3 = 2
Divide both ides of the equation by - 3
x = - 2/3
Solution
x = - 2/3
Alternate form
x = - 0.6
Bryce orders the following items from a catalog. What is the total price he charges to his credit card if the sales tax is 6 percent and nontaxable shipping costs $5 for the order? Round to the nearest cent if necessary.
Answer:
The answer is C : $115.54
Step-by-step explanation:
If you add every single items cost together, the total is $109.00
60 + 14 = 74
10 + 25 = 35
74 + 35 = $109
You then caculate what 6% percent of 109 is = $6.54
After that, you add the total and percent together
$6.54 + $109.00 = $115.54
Answer:answer is c
Step-by-step explanation:I took edge 2022
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Answer:
Ooooook?
Step-by-step explanation:
Fine
How do I write Domain and Range in inequality notation?
Answer:
Step-by-step explanation:To combine two intervals using inequality notation or set-builder notation, we use the word “or.” As we saw in earlier examples, we use the union symbol, \displaystyle \cup∪, to combine two unconnected intervals. For example, the union of the sets \displaystyle \left\{2,3,5\right\}{2,3,5} and \displaystyle \left\{4,6\right\}{4,6} is the set \displaystyle \left\{2,3,4,5,6\right\}{2,3,4,5,6}. It is the set of all elements that belong to one or the other (or both) of the original two sets. For sets with a finite number of elements like these, the elements do not have to be listed in ascending order of numerical value. If the original two sets have some elements in common, those elements should be listed only once in the union set. For sets of real numbers on intervals, another example of a union is
Describe the similarities and differences between a bar graph and a histogram.
Answer:
Bar graphs are used with nominal or ordinal scores; histograms are used with interval or ratio scores.
Step-by-step explanation:
PLEASE HELP
Select the correct answer from each drop-down menu. Options are (equal to, not equal to)
Answer:
Not equal to.
Step-by-step explanation:
Help please for brainliest