Answers
Answer:
y = 7Step-by-step explanation:
We know that the sum of the measures of angles on one side of the parallelogram is 180°.
We have the equation:
(6x - 12) + (132 - x) = 180
6x - 12 + 132 - x = 180 combine like terms
(6x - x) + (-12 + 132) = 180
5x + 120 = 180 subtract 120 from both sides
5x = 60 divide both sides by 5
x = 12
Opposite angles in the parallelogram are congruent.
Therefore:
6y + 18 = 6x - 12
Put the value of x to the equation and solve it for y:
6y + 18 = 6(12) - 12
6y + 18 = 72 - 12
6y + 18 = 60 subtract 18 from both sides
6y = 42 divide both sides by 6
y = 7
Related Questions
What scale factor is shown by this graph?
1/2
2
4
1
SEE ATTACHED image!
Answers
the scale factor is 2.
because
if you look at the length AL in the smaller shape, it is 2 squares.
now if you look at the length AL in the enlarged shape, it is 4 squares.
to find the scale factor, do 4 ÷ 2 which is 2.
therefore the scale factor is 2
Answer:
The correct option is 2. The scale factor is 2.
Step-by-step explanation:
The coordinates of preimage are A(1,2), T(0,0), K(4,1) and L(3,2).
The coordinates of image are A'(2,4), T'(0,0), K'(8,2) and L'(6,4).
If a figure dilated by scale factor k with center at origin then the rule of dilation is
[tex](x,y)\rightarrow (kx,ky)[/tex]
[tex]A(1,2)\rightarrow A'(2,4)[/tex]
[tex]k=\frac{\text{x coordinate of image}}{\text{x coordinate of preimage}}[/tex]
[tex]k=\frac{2}{1}[/tex]
[tex]k=2[/tex]
Therefore the scale factor is 2 and the correct option is 2.
Please answer this question, will give brainliest!
Answers
Answer:
I dont really know the answer.. but ill try; if its wrong I am so sorry;
Step-by-step explanation:
First you must get the area of a circle, which is; A= pi r squared
and all you have to do is fill it in like this;
A= 3.14 x 2.0
^
A= 6.28
Use the stem-and-leaf plot below to match the terms with the correct value. Round to the nearest whole number.
Mean
Median
Mode
Answers
Answer:
The mean is 5
the median is also 5
and the mode is 1
Step-by-step explanation:
Answer:60,61,73,75,79,81,81,81,92,96,98
Step-by-step explanation: Mean:80
Median:81
Mode:81
The ratio of a model car to a regular car is 1:16. The model is 6.25 inches long. What is the length of the actual car in feet and inches?
Answers
What is the length of the actual car in feet and inches? 4/5 ft 48/72in
2+(x+y)=(2+x)+y is and example of which algebraic property?
A)Distributive property
B)Associative property of addition
C)Commutative property of addition
D)Symmetric property
Answers
distributive property because u need to mulptiply the number outside with the parentheses
Answer:
A)Distributive property
Step-by-step explanation:
This is because you need to multiply
Find linearly independent functions that are annihilated by the given differential operator. (give as many functions as possible. use x as the independent variable. enter your answers as a comma-separated list.) d2 − 12d − 45
Answers
We want to find all [tex]f(x)[/tex] such that
[tex](D^2-12D-45)[f(x)]=0[/tex]
We have
[tex](D^2-12D-45)[f]=(D-15)(D+3)[f]=0[/tex]
so that either
[tex](D-15)[f]=0\implies f'-15f=0\implies f(x)=e^{15x}[/tex]
or
[tex](D+3)[f]=0\implies f'+3f=0\implies f(x)=e^{-3x}[/tex]
These solutions are linearly independent; we confirm this by computing the Wronskian:
[tex]W=\begin{vmatrix}e^{15x}&e^{-3x}\\15e^{15x}&-3e^{-3x}\end{vmatrix}=-3e^{12x}-15e^{12x}=-18e^{12x}\neq0[/tex]
We can also confirm that these solutions are correct by substituting the solutions for [tex]f(x)[/tex] in the differential equation:
[tex](D^2-12D-45)[e^{15x}]=225e^{15x}-12(15e^{15x})-45e^{15x}=0[/tex]
[tex](D^2-12D-45)[e^{-3x}]=9e^{-3x}-12(-3e^{-3x})-45e^{-3x}=0[/tex]
The linearly independent functions that are annihilated by the differential operator d2 − 12d - 45 are e^{15x} and e^{-3x}, found by solving the quadratic equation associated with the differential equation.
Explanation:The differential operator given is d2 − 12d - 45. To find out the linearly independent functions that are annihilated by this operator, we have to solve the homogeneous differential equation d2 − 12d - 45 = 0. This is a second order equation, so we expect two linearly independent solutions.
To find the solutions, we seek the roots of the associated quadratic equation m^2 - 12m -45 = 0. This can be factored into (m-15)(m+3), thus giving roots m = 15 and m = -3.
The general forms of the solutions for these roots are e^{15x} and e^{-3x} respectively. Therefore, the functions e^{15x} and e^{-3x} are linearly independent functions that are annihilated by the given differential operator d2 − 12d - 45.
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How many terms are in the following sequence?
14348907, ..., 9, 3, 1
17
15
16
18
Answers
Answer:
There are 16 terms in the sequence.
Step-by-step explanation:
The given sequence is
14348907, ..., 9, 3, 1
The first term of the sequence is
[tex]a_1=14348907[/tex]
The last term of the sequence is [tex]l=1[/tex]
The common ratio is [tex]r=\frac{1}{3}[/tex]
The nth term of this sequence is;
[tex]a_n=a_1(r)^{n-1}[/tex]
We plug in the common ratio and the first term to get;
[tex]a_n=14348907(\frac{1}{3})^{n-1}[/tex]
The find the number of terms in the sequence , we plug in the last term of the sequence.
This implies that;
[tex]1=14348907(\frac{1}{3})^{n-1}[/tex]
[tex]\frac{1}{14348907}=(\frac{1}{3})^{n-1}[/tex]
[tex]\Rightarrow 3^{-15}=3^{-(n-1)}[/tex]
Since the bases are the same, we equate the exponents;
[tex]-15=-(n-1)[/tex]
[tex]15=n-1[/tex]
[tex]15+1=n[/tex]
[tex]n=16[/tex]
Justin had to pay 4.5% simple interest on the $5000 loan for five years at the end of the five years, how much did Justin have to pay?
Answers
I am thinking the answer is 225. Sorry if I'm wrong!
if the probability of p(m and n) =0.2 p(m)=0.4 and m and independent events, what is p(n)?
Answers
Answer:
P(n) = 0.5
Step-by-step explanation:
For two events which are independent, we use the multiplication rule which states P (A and B) = P(A) * P(B). Substitute P(m) = 0.4 and P(m and n) = 0.2 into this formula.
P (m and n) = P(m) * P(n)
0.2 = 0.4*P(n)
Divide by 0.4 on both sides.
0.2 / 0.4 = P(n)
0.5 = P(n)
The points R(3,−3), S(8,0), and T(4,1) are connected to form △RST.
What is the most appropriate classification of △RST?
right isosceles
isosceles
scalene
equilateral
Answers
right isosceles
rs:34&rs=rt+st
rt:17
st:17
ab=[(x(a)-x(b))+(y(a)+y(b))]
Answer:
Isosceles.
Step-by-step explanation:
We are going to check it with the distance formula
d(R,T) = [tex]\sqrt[2]{(3-4)^{2}+(-3-1)^{2}}[/tex]
= [tex]\sqrt[2]{(-1)^{2}+(-4)^{2}}[/tex]
= [tex]\sqrt[2]{1+16}[/tex]
= [tex]\sqrt[2]{17}[/tex].
d(T,S) = [tex]\sqrt[2]{(4-8)^{2}+(1-0)^{2}}[/tex]
= [tex]\sqrt[2]{(-4)^{2}+(1)^{2}}[/tex]
= [tex]\sqrt[2]{16+1}[/tex]
= [tex]\sqrt[2]{17}[/tex].
d(S,R) = [tex]\sqrt[2]{(8-3)^{2}+(0-(-3))^{2}}[/tex]
= [tex]\sqrt[2]{(5)^{2}+(3)^{2}}[/tex]
= [tex]\sqrt[2]{25+9}[/tex]
= [tex]\sqrt[2]{34}[/tex].
Then, as the triangle has two sides with the same length, the triangle is isosceles.
(2Q) Simply the expression.
Answers
Answer:
no simplify. answer is:
b. log(1/7)
ANSWER
d.
[tex] \frac{1}{7} [/tex]
EXPLANATION
We want to simplify
[tex] {10}^{ log( \frac{1}{7} ) } [/tex]
Recall that the common logarithm has a base of 10.
This implies that,
[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } [/tex]
Recall again that:
[tex] {p}^{ log_{p}(q) } = q[/tex]
Therefore,
[tex] {10}^{ log( \frac{1}{7} ) } = {10}^{ log_{10}( \frac{1}{7} ) } = \frac{1}{7} [/tex]
To get to your school, 25 of the students walk, 13 of the students ride the bus, and the rest come in cars. How many students come to school in cars?
Answers
Answer:
12
Step-by-step explanation:
subtract 25 minus 13 and you get 12 which means 12 students come in cars
Enter an inequality that represents the phrase the sum of 1 and y is greater than or equal to 6.
Answers
1+y (greater than or equal to symbol) 6
Complete the table to represent how much each individual monthly deposit of $50 will be worth at the end of 12 months. Enter your answers as an expression in the form
a(1 + r)n, as shown for the first month.
Answers
The first month has the equation raised to 11 which is the number of months left in the period.
So each month the equation would be the same except it would be raised to 1 less than the previous month.
Month 2 = 50(1.003)^10
Month 3 = 50(1.003)^9
Month 4 = 50(1.003)^8
Month 5 = 50(1.003)^7
Month 6 = 50(1.003)^6
Month 7 = 50(1.003)^5
Month 8 = 50(1.003)^4
Month 9 = 50(1.003)^3
Month 10 = 50(1.003)^2
Month 11 = 50(1.003)^1
Month 12 = 50(1.003) ( the last month would not be raised to anything)
Answer:
600
Step-by-step explanation:
its 50 X 12
thats how you would solve that
3 quarters of the batch of 20 cookies burned when you forgot to take them out of the oven how many cookies burned
Answers
Answer:
15 cookies
Step-by-step explanation:
We have 20 cookies and we know that three quarters of them were burned. To find the number of cookies burned, divide the 20 cookies into 4 equal parts.
This will give you 4 parts of 5 cookies.
[5] + [5] + [5] + [5]
Then they tell us that 3 quarters were burned. This means that of these 4 parts [5] + [5] + [5] + [5], 3 were burned. Then take 3 of these parts and add them.
[5] + [5] + [5] = 15 cookies.
This is the same as multiplying:
[tex]20 * \frac{3}{4} = 15[/tex]
Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18–31) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determine that 43% of them live at home with their parents. With this data, they test the following hypotheses. H0: Of Millennial students at their campus, 36% live at home with their parents. Ha: More than 36% of Millennial students at their campus live at home with their parents. In order to assess the evidence, which question best describes what we need to determine? If we examine a sample of students at their campus and determine the proportion who still live at home with their parents, how likely is that proportion to be 36%? If we examine a sample of students at their campus and determine the proportion who still live at home with their parents, how likely is that proportion to be 43% or more? If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be 36%? If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%? If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be 43%?
Answers
To assess the evidence of Hypothesis testing, the students need to determine the likelihood of the proportion of Millennial students at their campus that live at home with their parents being 36% or higher.
Explanation:The question here is regarding the testing of a population proportion using statistical hypothesis testing, specifically a one-sample z-test. The null hypothesis (H0) is that the population proportion is equal to a specified value, in this case, 36%). The alternative hypothesis (Ha) is that the population proportion is greater than the specified value (more than 36%).
The question we need to answer is 'If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?'
The scenario suggests an indication towards a right-tailed z-test as we're looking to see if the data indicates a proportion >36%. However, as with all statistical tests, one should be cautious about drawing definitive conclusions without additional context and understanding the potential for sampling variability and error.
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What is the measure of each interior angle in heptagon ABCDEFG
Answers
Answer:
Step-by-step explanation:
First att all, let's take angle B... It's bigger than 180° and smaller than 360. Then: 180 < 6x < 360. So 6x = 288°. The only alternative what's correct is the first one.
I hope I helped you
A Ferris wheel has a radius of 30 feet. Two particular cars are located such that the central angle between them is 140°. To the nearest tenth, what is the length of the intercepted arc between those two cars on the Ferris wheel?
Answers
Answer:
230.4
feet
Explanation:
arc length
=
circumference
×
fraction of circle
×
×
×
×
=
2
π
r
×
165
360
×
×
×
×
=
2
×
π
×
80
×
165
360
×
×
×
×
=
230.4
feet to nearest tenth
Step-by-step explanation:
The length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft
Since the distance between the two cars is the length of an arc, we need to know what the length of an arc is.
What is the length of an arc?The length of an arc is given by L = Ф/360 × 2πr where
Ф = angle of arc and r = radius of circleGiven that for the ferris wheel
Ф = 140° and r = 30 ftSubstituting the values of the variables into the equation, we have
L = Ф/360 × 2πr
L = 140°/360 × 2π × 30 ft
L = 14/36 × 60π ft
L = 14/3 × 5π ft
L = 70π/3 ft
L = 219.91 ft/3
L = 73.3 ft
So, length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft
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How do you write an equation for.... what number a is 25% of 64? An equation is =0.25?
Answers
a=0.25•64
a=16
If 9 out of 10 doctors in a small city recommend afternoon naps, and there are 8 doctors in the city who don’t recommend naps, how many doctors in the city do recommend afternoon naps?
Answers
Answer:
72
Step-by-step explanation:
1 out of 10 do not recommend naps, so 9 times as many do recommend naps.
9 × (8 doctors) = 72 doctors . . . . . recommend naps
25 points!! Probability question.
This is from Math-a-thon, pls solve this problem to help me help children with cancer...
Destructimous has 7 sonic blasts and 13 heat rays. It also has a 2/7 chance of using its ultra power blast. Luckily, Octagon’s sheild reflected that blast and stopped all the robots. How many ultra power bots did Destructimous have? Pls show/ explain your work. (i know the answer i just dont know how to find it).
Answers
Destructimous had 6 ultra power blasts.
The total number of blasts Destructimous has is:
Total blasts = Sonic blasts + Heat rays
Total blasts = 7 + 13
Total blasts = 20
Now, we know that Destructimous has a 2/7 chance of using its ultra power blast. To find out how many ultra power blasts it fires, we calculate 2/7 of the total blasts:
Ultra power blasts = (2/7) * Total blasts
Ultra power blasts = (2/7) * 20
Ultra power blasts = 40/7
Now, since we can't have a fraction of a blast, we need to round this number to the nearest whole number. In this case, 40/7 is approximately 5.71, so when rounded, it's 6.
So, Destructimous had 6 ultra power blasts.
-------------------------------------
116. use what you know about the area and circumference of circles to answer the questions below. show all work. leave answers in terms of π. homework help ✎ if the radius of a circle is 14 units, what is its circumference? what is its area? if a circle has diameter 10 units, what is its circumference? what is its area? if a circle has circumference 100π units, what is its area? if a circle has circumference c, what is its area in terms of c?
Answers
Answer:
28π and 196π
10π and 25π
2500π
A = C/4π
Step-by-step explanation:
The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and area.
if the radius of a circle is 14 units, what is its circumference? what is its area?
Substitute r = 14.
C = 2πr = 2π(14) = 28π
A = πr² = π(14)² = 196π
if a circle has diameter 10 units, what is its circumference? what is its area?
Substitute r = 5.
C = 2πr = 2π(5) = 10π
A = πr² = π(5)² = 25π
if a circle has circumference 100π units, what is its area?
Substitute C = 100π to find the radius. Then substitute the radius into the are formula.
C = 2πr
100π=2πr
100 = 2r
50 = r
A = πr² = π(50)² = 2500π
if a circle has circumference c, what is its area in terms of c?
Cole the circumference formula for r. Then substitute the expression into the area formula.
C = 2πr
r = C / 2π
A = πr² = π(C/2π)² = πC/4π² = C/4π
1. Circumference: [tex]\(28\pi\)[/tex]units, Area: [tex]\(196\pi\)[/tex] square units.
2. Circumference: [tex]\(10\pi\)[/tex]units, Area: [tex]\(25\pi\)[/tex]square units.
3. Area: [tex]\(2500\pi\)[/tex]square units.
4. Area: [tex]\(\frac{C^2}{4\pi}\)[/tex] square units.
Let's go through each question one by one, using the formulas for the circumference and area of a circle.
1. If the radius of a circle is 14 units, what is its circumference? What is its area?
- The circumference [tex]\( C \)[/tex] of a circle is given by the formula:
[tex]\[ C = 2\pi r \][/tex]
where [tex]\( r \)[/tex] is the radius.
Given [tex]\( r = 14 \)[/tex] units, we have:
[tex]\[ C = 2\pi \times 14 = 28\pi \text{ units} \][/tex]
- The area [tex]\( A \)[/tex]of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Given [tex]\( r = 14 \)[/tex] units, we have:
[tex]\[ A = \pi \times 14^2 = \pi \times 196 = 196\pi \text{ square units} \][/tex]
2. If a circle has diameter 10 units, what is its circumference? What is its area?
- The diameter [tex]\( d \)[/tex] is related to the radius by [tex]\( d = 2r \)[/tex]. Therefore, the radius [tex]\( r \)[/tex] is:
[tex]\[ r = \frac{d}{2} = \frac{10}{2} = 5 \text{ units} \][/tex]
- Using the circumference formula [tex]\( C = 2\pi r \):[/tex]
[tex]\[ C = 2\pi \times 5 = 10\pi \text{ units} \][/tex]
- Using the area formula [tex]\( A = \pi r^2 \):[/tex]
[tex]\[ A = \pi \times 5^2 = \pi \times 25 = 25\pi \text{ square units} \][/tex]
3. If a circle has circumference [tex]\( 100\pi \)[/tex] units, what is its area?
- Given the circumference [tex]\( C = 100\pi \),[/tex] we can find the radius [tex]\( r \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]
[tex]\[ 100\pi = 2\pi r \][/tex]
Dividing both sides by [tex]\( 2\pi \):[/tex]
[tex]\[ r = \frac{100\pi}{2\pi} = 50 \text{ units} \][/tex]
- Using the area formula [tex]\( A = \pi r^2 \):[/tex]
[tex]\[ A = \pi \times 50^2 = \pi \times 2500 = 2500\pi \text{ square units} \][/tex]
4. If a circle has circumference [tex]\( C \),[/tex] what is its area in terms of [tex]\( C \)[/tex]
- Given the circumference [tex]\( C \),[/tex] we can express the radius [tex]\( r \)[/tex] in terms of [tex]\( C \)[/tex] using the formula [tex]\( C = 2\pi r \):[/tex]
[tex]\[ r = \frac{C}{2\pi} \][/tex]
- Using the area formula [tex]\( A = \pi r^2 \)[/tex] and substituting [tex]\( r = \frac{C}{2\pi} \):[/tex]
[tex]\[ A = \pi \left( \frac{C}{2\pi} \right)^2 = \pi \left( \frac{C^2}{4\pi^2} \right) = \frac{\pi C^2}{4\pi^2} = \frac{C^2}{4\pi} \][/tex]
How many faces does a pyramid with a square base have? A. Five B. Eight C. Six D. Seven
Answers
Answer:
The answer is five.
Step-by-step explanation:
A pyramid with a square base has one square face and there are four triangle faces, so there are five in total.
I hope this helped! :-)
Number of faces of pyramid with a square base is 5.
Hence option A is correct.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Since we know that
A pyramid having square base have,
Number of square face = 1
Number of triangular face = 4
Hence total face in this triangle is,
= 1+4
= 5
Hence total faces = 5.
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There are 21 luxury vehicles in 3 shipments sent to a dealership . Which of the following expresses the ratio of shipments to luxury vehicles?
A. 21/3
B. 21 to 3
C. 21:3
D. 3:21
Answers
Answer:
There are 21 luxury vehicles in 3 shipments sent to a dealership . Which of the following expresses the ratio of shipments to luxury vehicles?
A. 21/3
B. 21 to 3
C. 21:3
D. 3:21
Step-by-step explanation:
Answer:
The answer is D. 3:21 Hope this helps!
An online music club has a one-time registration fee of $20 and charges $0.50 for each song download. If Ella has $50.00 to join the club and buy songs, which inequality gives the maximum number of songs, s, she can buy?
Answers
Answer:
D.
Step-by-step explanation:
50-20=30 (because of the initial cost)
Then multiply 30*0.5=60
so she can buy less than or equal to 60
Answer:
D. S ≤ 60
Step-by-step explanation:
Ella has $50.00 and the registration fee is $20. This means that she would have $30.00 to buy songs and each song costs $0.50, so:
$30.00/$0.50= 60
The number of songs that she would be able to buy is 60.
According to this, the inequality that gives the maximum number of songs that she can buy is S ≤ 60 as it indicates that the maximum number of songs (s) that she can buy is less than or equal to 60.
Work out the area of a semicircle with radius 3cm. give your answer in terms of 3.142
Answers
1.5 • 3.142= 4.713 should be the answer
Answer: 4.5π ≈ 14.14 cm²
Step-by-step explanation:
[tex]Area_{\ circle}=\pi \cdot r^2\\\\Area_{\ semicircle}=Area_{\ circle}\div 2\\\\\\A=\dfrac{\pi \cdot 3^2}{2}\\\\\\.\quad =\dfrac{9}{2}\pi\\\\\\.\quad =4.5\pi\\\\\\.\quad =14.14[/tex]
Compute all values of x such that x-1 is the reciprocal of x+1. Express your answer in simplified radical form.
Answers
Answer:
x = ±√2
Step-by-step explanation:
x - 1 = 1/(x + 1)
(x -1)(x + 1) = 1 Multiplied each side by x + 1
x² - 1 = 1 Difference of two squares
x² = 2 Add 1 to each side
x = ±√2
x-1 is the reciprocal of x+1 when x = -√2 or x = √2.
Check:
(a) x = -√2
-√2 - 1 = 1/(-√2 + 1)
-(√2 + 1) = (√2 +1)/[(-√2 +1)(√2 + 1)]
-(√2 + 1) = (√2 +1)/(-2 +1)
-(√2 + 1) = (√2 +1)/(-1)
-(√2 + 1) = -(√2 +1)
(b) x = √2
√2 - 1 = 1/(√2 + 1
√2 - 1 = (√2 - 1)/[(√2 + 1)(√2 - 1) ]
√2 - 1 = (√2 - 1)/(2 - 1)
√2 - 1 = (√2 - 1)/1
√2 - 1 = √2 - 1
OK.
Answer:x = ±√2
Step-by-step explanation: this is because reciprocal means the numerator and denominator switches
So the equation is x-1=1/(x+1)
And you solve for it thats how u get the answer
The sea turtle habitat at the zoo is made by connecting two large aquariums. The first aquarium is 6 m6\text { m}6 m6, space, m long, 4 m4\text { m}4 m4, space, m wide, and 2 m2\text { m}2 m2, space, m high. The second aquarium is 8 m8\text { m}8 m8, space, m long, 9 m9\text { m}9 m9, space, m wide, and 3 m3\text { m}3 m3, space, m high.
Answers
Answer:
264 cubic meters
Step-by-step explanation:
The sea turtle habitat at the zoo has a total volume of 264 cubic meters.
To find the total volume of the sea turtle habitat, which consists of two connected aquariums, you can calculate the volume of each aquarium separately and then add them together.
For the first aquarium:
- Length = 6 meters
- Width = 4 meters
- Height = 2 meters
The volume of the first aquarium is calculated as:
Volume_1 = Length * Width * Height
Volume_1 = 6 m * 4 m * 2 m
Volume_1 = 48 cubic meters
For the second aquarium:
- Length = 8 meters
- Width = 9 meters
- Height = 3 meters
The volume of the second aquarium is calculated as:
Volume_2 = Length * Width * Height
Volume_2 = 8 m * 9 m * 3 m
Volume_2 = 216 cubic meters
Now, to find the total volume of the sea turtle habitat, you add the volumes of the two aquariums together:
Total Volume = Volume_1 + Volume_2
Total Volume = 48 cubic meters + 216 cubic meters
Total Volume = 264 cubic meters
So, the total volume of the sea turtle habitat at the zoo is indeed 264 cubic meters, as provided.
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Convert the angle 0=14pi/9 radians to degree
Answers
Answer:
280 degrees.
Step-by-step explanation:
To convert radians to degrees we multiply by 180/pi:
angle O = 14pi/ 9 * 180 / pi
= 14*180 / 9
= 280 degrees.
The angle 0=14pi/9 radians can be converted to degrees by using the conversion factor 1 radian = 57.3°. Multiplying the given angle in radians by the conversion factor results in an equivalent angle of 280° in degrees.
Explanation:To convert the angle from radians to degrees, we use the conversion factor 1 rad = 57.3°. The problem provides the angle 0 = 14pi/9 radians. By using the conversion factor, the process of conversion would be as follows:
Multiply the value in radians by the conversion factor. So, 0 in degrees = 14pi/9 * 180°/pi = 280°
Therefore, the angle 0=14pi/9 radians is equal to 280° in degrees.
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Experimenting, you have found that 12 ounces of 180°F coffee in your favorite cup will take 20 minutes to cool to a drinking temperature of 110°F in a 70°F room. Assume that when you add cream to the coffee, the two liquids are mixed instantly, and the temperature of the mixture instantly becomes the weighted average of the temperature of the coffee and of the cream (weighted by the number of ounces of each fluid). Also assume that the cooling constant of the liquid (the constant k in the equations on p. 237 in section 3.8 for Newton's Law of Cooling) does not change when you add the cream. (a) If you add 2 ounces of 40°F cream to the 180°F coffee in the cup, how long will it take for the mixture to reach drinking temperature? Give your answer (in minutes) in decimal form with at least 3 decimal digits (for example, 12.345 minutes).
Answers
Answer:
16.033 min
Step-by-step explanation:
We can write Newton's Law of Cooling as
T = Tₐ + (T₀ - Tₐ)e^(-kt), where
Tₐ = ambient temperature of the surroundings
T₀ = initial temperature of the object
k = the cooling constant
t = the time
(1) Calculate the cooling constant
Data:
T = 110 °F
T₀ = 180 °F
Tₐ = 70 °F
t = 20 min
Calculation:
110 = 70 + (180 - 70)e^(-k×20)
40 = 110e^(-20k)
0.363 64 = e^(-20k)
-1.0116 = -20k
k = 0.050 580 min⁻¹
(2)After adding cream
(a) Calculate T₀
2 oz × 40 °F + 12 oz × 180 °F = 14 oz × T₀
80 °F + 2160°F = 14T₀
2240 °F = 14T₀
T₀ = 160 °F
(b) Calculate the time to cool to drinking temperature
110 = 70 + (160 - 70)e^(-0.050 580t)
40 = 90e^(-0.050 580t)
0.444 44 = e^(-0.050 580t)
-0.810 93 = -0.050580t
t = 16.033 min
It will take 16.033 min for the mixture to reach drinking temperature
To determine the time it takes for the mixture to reach drinking temperature, we first calculate the initial temperature of the mixture after adding 2 ounces of 40°F cream to the 180°F coffee, which turns out to be 165°F. Then, according to Newton's Law of Cooling, the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F would be the same as the time it took for the original coffee to cool from 235°F to 180°F, given the cooling constant doesn't change when we add the cream. Therefore, the mixture will take approximately 20 minutes to reach drinking temperature.
Explanation:To determine the time it takes for the mixture to reach drinking temperature, we first need to calculate the initial temperature of the mixture. When you add 2 ounces of 40°F cream to the 180°F coffee, the temperature of the mixture instantly becomes the weighted average of the temperature of the coffee and of the cream. Thus, we have:
(12 * 180 + 2 * 40) / (12 + 2) = 165°F.
Now we need to calculate the time it takes for the mixture to decrease from 165°F to the drinking temperature of 110°F. According to Newton's Law of Cooling, the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature. If we assume that the proportionality constant (or the cooling constant) doesn't change when we add the cream, then the time it takes for the mixture to cool from 165°F to 110°F will be the same as the time it took for the original coffee to cool from 235°F (165 + 70) to 180°F (110 + 70), which is 20 minutes. We can conclude that the mixture will take approximately 20 minutes to reach drinking temperature.
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