Solution:
Given:
Volume of tank = Length x Breadth x HeightLength = 6mBreadth = 5mHeight = 3mLet's substitute the values of Length, Breadth, and Height to obtain the volume of the tank.
Volume of tank = Length x Breadth x Height=> Volume of tank = 6 x 5 x 3=> Volume of tank = 90 m³Now, let's convert meters into liters.
1 cubic meter = 1000 liters=> 90 m³ = 1000 x 90=> 90 m³ = 90000 litersHoped this helped!
Determine all solutions to the equation 1 over sine theta equals 2 times sine theta on the interval [0, 2π).
The solution to the trigonometric equation in the interval is given by:
[tex]x = \frac{\pi}{4}[/tex]
What is the trigonometric equation?In this problem, the equation is given by:
[tex]\frac{1}{\sin{\theta}} = 2\cos{\theta}[/tex]
Applying cross multiplication, we have that:
[tex]2\sin{\theta}\cos{\theta} = 1[/tex]
Applying a trigonometric identity, we have that:
[tex]\sin{2x} = 1[/tex]
We have that on the interval [0, 2π), [tex]\sin{\left(\frac{\pi}{2}\right)} = 1[/tex]
Hence:
[tex]\sin{2x} = 1[/tex]
[tex]\sin{2x} = \sin{\left(\frac{\pi}{2}\right)}[/tex]
[tex]2x = \frac{\pi}{2}[/tex]
[tex]x = \frac{\pi}{4}[/tex]
For [tex]\frac{3\pi}{4}[/tex], we have that:
[tex]\sin{2x} = \sin{\left(\frac{3\pi}{2}\right)} = -1[/tex]
Hence only the first solution is correct.
More can be learned about trigonometric equations at https://brainly.com/question/24680641
A farmer's truck is carrying 42/3 tons of hay and straw. If 325 tons of the load is
hay, how much straw is the truck carrying??
Answer:
1[tex]\frac{4}{15}[/tex] of straw
Step-by-step explanation:
The total amount of straw and hay together is, [tex]4 \frac{2}{3}[/tex].
and the total amount of hay alone is, [tex]3\frac{2}{5}[/tex]
All you need to do is subtract the hay from the total, which gives you, the answer above.
Verify trigonometric identiy
Answer:
see explanation
Step-by-step explanation:
Using the identity
cos²Θ = 1 - sin²Θ
Consider the left side
sin²Θ - cos²Θ
= sin²Θ - (1 - sin²Θ ) ← distribute parenthesis by - 1
= sin²Θ - 1 + sin²Θ
= 2sin²Θ - 1
= right side , thus verified
What is an equation of the line that passes through the points (-4, -2) and (-8, 3)?
Answer:
[tex]y = -\frac54x -7[/tex]
Step-by-step explanation:
Slope:
[tex]\frac{3 - (-2)}{-8 - (-4)}[/tex][tex]-\frac{5}{4}[/tex]Y-intercept:
[tex]y = -\frac54x + b\\[/tex][tex]-2 = -\frac54(-4) + b[/tex][tex]-2 = 5 + b[/tex][tex]b=-7[/tex]y = -5/4x -7
-Chetan K
The water pipe of a house was leaking gallons of water per minute. What is the constant rate of water that is lost per minute according to the graph?
A triangle has a perimeter of 66 feet. If the three sides of the triangle are n, 3n+3, and 4n - 9, what is the length of each side?
Separate multiple entries with a comma.
Answer:
9, 30, 27
Step-by-step explanation:
To find the perimeter, you must add up each side. In this scenario, we know that the perimeter is 66 feet. We also know the sides, which are n, 3n+3 and 4n-9.
So, we must add the sides to get 66 feet.
n+3n+3+4n-9=66
Combine like terms, and solve:
(n+3n+4n)+(3+-9)=66
8n+-6=66
8n-6=66
n=9
So if n=9, we can easily find the value of the other sides.
3(9)+3=30 feet.
4(9)-9=27 feet
So, the sides are 9, 30, and 27 feet (in order).
Find the value of x.
R
(2x + 3)^
25°
Q
S
(3x – 17) 10
(
O
Answer:
10
Step-by-step explantion
Simplifying
2x + 3 + 25 = 3x + -17
Reorder the terms:
3 + 25 + 2x = 3x + -17
Combine like terms: 3 + 25 = 28
28 + 2x = 3x + -17
Reorder the terms:
28 + 2x = -17 + 3x
Solving
28 + 2x = -17 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
28 + 2x + -3x = -17 + 3x + -3x
Combine like terms: 2x + -3x = -1x
28 + -1x = -17 + 3x + -3x
Combine like terms: 3x + -3x = 0
28 + -1x = -17 + 0
28 + -1x = -17
Add '-28' to each side of the equation.
28 + -28 + -1x = -17 + -28
Combine like terms: 28 + -28 = 0
0 + -1x = -17 + -28
-1x = -17 + -28
Combine like terms: -17 + -28 = -45
-1x = -45
Divide each side by '-1'.
x = 45
Simplifying
x = 45
Answer:
x = 45Step-by-step explanation:
Exterior angle is same as sum of two remote interior angles:
2x + 3 + 25 = 3x - 172x + 28 = 3x - 173x - 2x = 28 + 17x = 45Choose the equation of the line in slope-intercept form.
Parallel to y = 3x - 1 and has the point (-2,-1).
A. y = -1/3x + 2
B. y = -1/3x + 5
C. y = 3x + 5
D. y = 3x + 2
answer:
y = 3x + 5
steps-explanation:
given sample equation:
y = 3x - 1comparing to the formula of slope intercept form: y = mx + b
[ where m is the slope and b is the y-intercept ]
we can determine here that the slope is 3 and -1 is the y-intercept.
but here we need only the slope.
in parallel, the slope is same: 3
formula:
y - y1 = m(x - x1)using the formula: [ here known that y1 is -1 and x1 is -2 ]
y - -1 = 3(x - -2)y + 1 = 3x + 6y = 3x + 5Please solve for brainliest.
Answer: The first four terms are 33/4, 63/8, 15/2, and 57/8.
Step-by-step explanation: To make it easier, turn 8 1/4 into an improper fraction: 33/4. 33/4=66/8. Because the denominator is the same, it’s easier to subtract.
66/8 - 3/8 = 63/8
63/8 - 3/8 = 60/8
60/8 - 3/8 = 57/8
The first 4 terms in the sequence are 66/8, 63/8, 60/8, and 57/8. But we’re not done b/c we need to simplify. That means the first four terms are 33/4, 63/8, 15/2, and 57/8.
E Homework: 2.3 Linear Inequalities
Question 14, 2.3.101
Part 1 of 2
Assume that in 2005 consumers used credit and debit cards to pay for 43% of all purchases. This percentage is projected to be 58% in 2011.
(a) Find a linear function that models the data, where x is the year and P(x) is the percentage.
(b) Estimate when this percentage was between 48% and 53%.
(a) P(x) =
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Linear functions are functions that change at a constant rate
The linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]
The equation of the linear functionFrom the question, we have the following ordered pairs
(x,P(x)) = (2005,43%) and (2011,58%)
Start by calculating the slope (m)
[tex]m = \frac{P(x2) - P(x1)}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{58\% - 43\%}{2011 - 2005}[/tex]
Evaluate the differences
[tex]m = \frac{15\%}{6}[/tex]
Evaluate the quotient
[tex]m = 2.5\%[/tex]
The linear function is then calculated as:
[tex]P(x) = m(x - x_1)+ P(x_1)[/tex]
So, we have:
[tex]P(x) = 2.5\%(x - 2005) + 43\%[/tex]
Rewrite as:
[tex]P(x) = 0.025(x - 2005) + 0.43[/tex]
This gives
[tex]P(x) = 0.025x -50.125 + 0.43[/tex]
[tex]P(x) = 0.025x -49.695[/tex]
Hence, the linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]
Read more about linear functions at:
https://brainly.com/question/15602982
Ted is installing lighting in a new block of 12 apartments . He will need 60 metres of cable for each apartment. Each mew spool holds 100 metres of cable . What is smallest number of new spools that Ted will need for his job
Answer: 8 spools
Step-by-step explanation:
There are 12 apartments, and each apartment will need 60 meters of cable, so 12×60= 720 meters of cable needed.
If each spool only has 100 meters and he needs 720 meters, then 720÷100= 7.2. So he would need to purchase at least 8 spools, and will have 80 meters left over.
Translate and solve: 3884.4 is what percent of 46.8?
Answer:
3884.4 is what percent of 46.8 is 8300
NEED HELP ASAP!
Of the rocks in a box, 1/3 are igneous, 60 are
metamorphic, and the remaining 40% are sedimentary.
How many rocks are in the box?
1= 160
2= 180
3= 200
4= 225
2) What is the most precise name for a quadrilateral ABCD with vertices A(-2,4), B(5,6), C(12,4), D(5,2)?
parallelogram
rhombus
quadrilateral
rectangle
3) What is the most precise name for a quadrilateral ABCD with vertices A(4,4), B(5,8), C(8,8), D(8,5)?
square
rhombus
kite
parallelogram
Answer:
2 rhombus
3 parallelogram
Express alphabetically: Double the sum of p and q
Answer:
that would be:::
2(p+q)
What is the slope of the line in the graph?
Answer:
[tex] \frac{ - 2 - 1}{4 - 0} \\ \\ \frac{ - 3}{4} \\ \\ \frac{3}{ - 4} [/tex]
A fishing supply store buys fishing rods for $11 and sells them at a markup of 220% One day, they decide to put the rods on sale and
mark them down by 20%
What is the sale price of a fishing rod?
$35.20
$28.16
$19.36
$7,04
Answer:28.16
Step-by-step explanation:
A markup of 220% would bring 11 to 35.20, and a mark down of 20% would bring 35.20 to 28.16.
Your'e Welcome (ФДФ) .
You have $50 in savings. Two months later, you have $80. After the third month, you have $95. You plan to continue to save the same amount each month. What will be in saving after 12 months?
Answer:
230
Step-by-step explanation:
multiply 12 by 15 and add it onto the 50 to get your answer!
Have a good day!
53 fl oz = c
A. 6
B. 6 5/8
C. 13 1/4
D. 424
Answer:
Option B
Step-by-step explanation:
Given the following question:
53 oz = c?
[tex]1c=8oz[/tex]
[tex]53\div8=6.625[/tex]
[tex]6.625=\frac{6625}{1000}\div125=\frac{53}{8}[/tex]
[tex]\frac{53}{8} =53\div8=6\frac{5}{8}[/tex]
[tex]=6\frac{5}{8}[/tex]
Your answer is option B or "6 5/8 cups."
Hope this helps
2.2,
Write the ratio 1 2/3: 2 2/3 in the simplest form.
,
Answer:
1:2
Step-by-step explanation:
this would be the answer as 1 2/3: 2 2/3 are the same as 1:2 if you cancel out the 2/3 from both sides.
Answer:
5 : 8
Step-by-step explanation:
1 [tex]\frac{2}{3}[/tex] : 2 [tex]\frac{2}{3}[/tex] ( change both mixed numbers to improper fractions )
= [tex]\frac{5}{3}[/tex] : [tex]\frac{8}{3}[/tex] ( multiply both parts by 3 to eliminate the fractions )
= 5 : 8
Chad used a number line to show the distance from the library to his house and the distance from the library to Kelli's house. How much farther is Chad's house than Kelli's house from the library? A number line from 0 to 1 is divided into 8 equal parts. Library is at 0, Kelli's House is at four-eighths, and Chad's House is at seven-eighths on the number line.
Chad's house is 3/8 units farther away than Kelly's house.
How to use the number line?By reading the number line, we can see that:
Library = 0Kelli's House = 4/8Chad's House = 7/8.These fractions are the positions of each location. We want to find how much farther is Chad's house than Kelli's house from the library, this is given by:
(Chad's house position - library position) - (Kelli's house position - library position)
Writting the fractions, we get:
(7/8 - 0) - (4/8 - 0) = 3/8
So Chad's house is 3/8 units farther away than Kelly's house.
If you want to learn more about fractions, you can read:
https://brainly.com/question/11562149
Answer: 3/8
Step-by-step explanation: 7/8 -4/8 equals 3/8
What is the difference between-4 and 62
-10
-2
2
10
Answer:
-10
Step-by-step explanation:
if negative meets a negative its gone come out as a positive
the Sims family drove 5 miles to the store and 3 miles to their grandparent's house. How
many yards did they drive in all?
Answer:
yards: 14080
miles: 8
that's basically it
Answer:
14080 yards
Step-by-step explanation:
A yard is 1/1760 mile, meaning 1 mile = 1760 yards.
5 miles + 3 miles = 8 miles
8 miles to yards = ?
8 x 1760 = 14080.
The Sims family drove 14.08k yds or 14080 yards.
Please please help f(x)7x1/5+6
Answer:
third answer
Step-by-step explanation:
solve for and isolate x by moving over all other numbers to the left and then take the fifth power to make x^1/5 = to x
What is the total amount that Matthew’s bank will receive after lending him$8,000 for four years at an interest rate of 6 percent, compounded annually?
Which measurement is a reasonable length for 3 new pencils laid end-to-end?
A) 3 inches
B) 18 inches
C) 13 feet
D) 8 feet
help geometry test is coming up and teacher hasn’t taught anything yet,(80% of grade)
Answer: I think it’s 647.96
Step-by-step explanation:
warning: this is not the exact value (it’s rounded)
First you find the height of the traingle
To do that, do pythagoras theorem
square root 36 squared minus 25.5 squared
then use formula for area of a triangle
nee answer asap plz im stuck
Which point represents the least value on the number line?
help me with this pleasee
Need help with homework
Answer:
5. the other angle has to be 2x because of the other lines being equals so
2x+2x+x-15=180
5x-15=180
5x=195
x=19
6. the other two angle is ajacent to the other two so
3x+17+3x+17+x-9+x-9=360
8x+16=360
8x=344
x=43
7. this ones pretty simple
2x-4+3x+5+2x+11=180
7x+12=180
7x=168
x=24
8. this one to
x+x+4+3x-9=90
5x+5=90
5x=85
x=17
Hope This Helps!!!