Answer:
(x + 5.66, y + 5.66) where (x, y) is the location of the crater
Step-by-step explanation:
Locating volcano's crater at (0, 0), the new vent is at angle equal to 45° respect x-axis, and at distance of 8 km from the crater. In polar coordinates that is radius (r) = 8, angle (α) = 45°. We are asked to transform these polar coordinates into rectangular coordinates. To do it, we have to use the following formulas:
x = r*cos α = x = 8*cos 45 = 5.66
y = r*sin α = 8*sin 45 = 5.66
If the crater is at position (x, y) then the vent would be translated at position (x + 5.66, y + 5.66)
Final answer:
The new vent's position relative to the crater, with the helicopter circling at an 8 km radius, is described by polar coordinates as (8 km, 45°) east of due north. This grants a clear visualization of the vent's specific location in relation to the volcano's crater, emphasizing its displacement and direction.
Explanation:
The position of the new vent relative to the crater, given that the helicopter is circling at an 8 km radius around the volcano's crater and that the new vent is located 45° east of due north from the crater, can be described using polar coordinates (r, θ) where r is the radius and θ is the angle from a reference direction. In this case, the reference direction is due north, and the angle is measured towards the east, meaning that the position of the new vent can be represented as (8 km, 45°). This means the vent is 8 km away from the crater at an angle of 45° east of due north. To visualize this, imagine the crater at the center of a circle, with the helicopter moving along the boundary of this circle. The new vent is located on the circumference of this circle, such that if you draw a line from the center (crater) to the vent, this line makes a 45° angle with the northward direction.
Jim Tree bought a home with a 10% adjustable rate mortgage for 20 years. He paid $9.66 monthly per thousand on his original loan. At the end of 2 years he owes the bank $55,000. Since interest rates have risen to 12%, the bank will not renew the mortgage at this rate, or Jim can pay the bank $55,000. He decides to renew and will now pay $11.02 monthly per thousand on his loan. For comparison purposes the small amount of principal that has been paid during the 2 years can be ignored.
Old monthly payment =_______
New monthly payment =_______
Percent increase in monthly payment (to nearest tenth) =______
Old monthly payment = $966
New monthly payment = $605.10
Percent increase (to nearest tenth) = -37.3%
Given that,
Jim Tree bought a home with a 10% adjustable rate mortgage for 20 years.
He paid $9.66 monthly per thousand on his original loan.
At the end of 2 years, he owes the bank $55,000.
Interest rates have risen to 12%, and the bank will not renew the mortgage at this rate.
Jim can either pay the bank $55,000 or renew the mortgage at the higher interest rate.
Jim decides to renew and will now pay $11.02 monthly per thousand on his loan.
For comparison purposes, the small amount of principal that has been paid during the 2 years can be ignored.
Based on the information provided, Jim's old monthly payment can be calculated as follows:
Calculate Jim's original loan amount. We know that he paid $9.66 monthly per thousand on his original loan,
So if we divide his monthly payment by 1000,
We get his monthly interest rate:
$9.66 ÷ 1000 = 0.00966
Use the loan formula to calculate Jim's original loan amount:
Loan amount = Payment amount ÷ (Interest rate x (1 + Interest rate[tex])^N[/tex]- 1)
Where N is the number of payment.
Using this formula, and plugging in Jim's numbers, we get:
Loan amount = $9.66 ÷ (0.00966 x [tex](1 + 0.00966)^{240}[/tex] - 1)
= $100,000
Now that we know Jim's original loan amount, we can calculate his old monthly payment:
Old monthly payment = Loan amount x Payment amount per thousand
= $100,000 x $9.66
= $966
Therefore, Jim's old monthly payment was $966.
To calculate the new monthly payment and the percent increase,
We can follow these steps:
First, we need to calculate Jim's new loan amount.
We know that he owes the bank $55,000 after 2 years,
So we can use this amount as his new loan amount:
New loan amount = $55,000
Calculate Jim's new monthly interest rate.
We know that the interest rate has increased from 10% to 12%,
So we can calculate the new monthly interest rate as follows:
New monthly interest rate = 12% ÷ 12
= 0.01
Use the loan formula again to calculate Jim's new monthly payment:
New monthly payment = Loan amount x Payment amount per thousand
= $55,000 x $11.02
= $605.10
Therefore, Jim's new monthly payment is $605.10.
To calculate the percent increase,
we can use the following formula:
Percent increase = ((New value - Old value) ÷ Old value) x 100%
Plugging in Jim's numbers, we get:
Percent increase = ((605.10 - 966) ÷ 966) x 100% = -37.3%
Therefore, the percent increase (to the nearest tenth) is -37.3%.
However, note that this is a negative value, which means that Jim's new monthly payment is actually lower than his old monthly payment.
This is likely due to the fact that the loan amount has decreased significantly since Jim has already paid off a portion of the loan during the first 2 years.
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Final Answer:
Old monthly payment = $531.30
New monthly payment = $605.10
Percent increase in monthly payment (to the nearest tenth) = 13.9%
Explanation:
Let's calculate each part step by step.
Firstly, we will calculate the old monthly payment. Jim was paying at a rate of $9.66 monthly per thousand dollars of the original loan. We'll first determine how many thousands of dollars Jim owed at the beginning:
1. Old Monthly Payment:
Since he owes $55,000 at the end of 2 years and hasn't paid much towards the principal, we assume that the original loan amount was approximately $55,000.
Now, if he paid $9.66 per thousand dollars of the loan, we will calculate the monthly payment with the following steps:
- Divide the loan amount by 1,000 to find out how many "units" of $9.66 he would have to pay.
- Multiply the number of units by $9.66 to find the monthly payment.
Doing the calculations:
[tex]\( \frac{55,000}{1,000} = 55 \) units. \\\\\( 55 \text{ units} \times $9.66 = 55 \times 9.66 = $531.30 \).[/tex]
So, the old monthly payment was $531.30.
2. New Monthly Payment:
Now that the interest rate has increased to 12%, Jim will be paying at a rate of $11.02 monthly per thousand dollars.
Using the same method as above:
- Divide the loan amount by 1,000 to get the number of units.
- Multiply the number of units by $11.02 to find the new monthly payment.
Calculations:
[tex]\( \frac{55,000}{1,000} = 55 \) units.\\\\\( 55 \text{ units} \times $11.02 = 55 \times 11.02 = $605.10 \).[/tex]
So, the new monthly payment is $605.10.
3. Percent Increase in Monthly Payment:
To find the percent increase, we'll use the formula:
[tex]\[ \text{Percent Increase} = \left( \frac{\text{New Payment} - \text{Old Payment}}{\text{Old Payment}} \right) \times 100 \][/tex]
Performing the calculation:
[tex]\[ \text{Percent Increase} = \left( \frac{605.10 - 531.30}{531.30} \right) \times 100 \\\\\[ \text{Percent Increase} = \left( \frac{73.80}{531.30} \right) \times 100 \\\\\[ \text{Percent Increase} = 0.1388 \times 100 \\\\\[ \text{Percent Increase} = 13.88\% \][/tex]
To find the nearest tenth, we'll round the percent increase to one decimal place:
13.88% rounded to the nearest tenth is 13.9%.
Now, we can write down the final answers:
Old monthly payment = $531.30
New monthly payment = $605.10
Percent increase in monthly payment (to the nearest tenth) = 13.9%
What is 351.68 rounded to the nearest tenth?
Answer:
351.7
Step-by-step explanation:
The first number after the decimal is the tenth. Round up if the second number is 5 or above, round down if the second number is below 5.
Answer:
351.7
Step-by-step explanation:
Look at the tenths space which is one place to the right of the decimal. It is a 6.
Then look at the number behind it: if the number behind is is 4 or less the number in front stays the same, if the number behind it is 5 or more the number in front goes up one more
so there is an 8 behind the 6, so you round the 6 to a 7
400 ml squash is made by mixing 50 ml of cordial with water. what fraction of the drink is water?give your answer in its simplest form.
squash = cordial + water
400 ml = 50 ml + x ml
350 ml = x ml
Therefore, 350 ml are water.
350 ml / 400 ml = 0.875 = [tex]\frac{350}{400} = \frac{35}{40} = \frac{7}{8}[/tex]
So the answer is 7 / 8
Tessa bought stock in a restaurant for $238.00. Her stock is now worth $330.82. What is the percentage increase of the value of Tessa's stock?
Answer:
39%
Step-by-step explanation:
Old value = $238.00
New value = $330.82
Change in value = New value - old value
= $330.82 - $238.00
= $92.82
percentage increase = Change in value/ old value * 100
= 92.82 / 238 * 100
= 0.39 * 100
= 39%
Factor each trinomial completely.
4x^2 - 25b^2 and x^2 - 81
Step-by-step explanation:
4x2 - 25b2
We can solve it by the squares so
(2x - 5b) (2x + 5b)
2) x2 - 81
The same case is here so
(x - 9) (x + 9)
The factorization of the trinomial are;
a. 4x² - 25b² = (2x + 5b)(2x - 5b)
b. x² - 81 = (x + 9)(x - 9)
What is the factorization of the trinomial?To factor the trinomial 4x² - 25b², we can use the difference of squares formula, which states that a² - b² can be factored as (a + b)(a - b).
Applying this formula to 4x² - 25b², we have:
4x² - 25b² = (2x)² - (5b)²
Now, we can rewrite the trinomial as a difference of squares:
4x² - 25b² = (2x + 5b)(2x - 5b)
Therefore, the trinomial 4x² - 25b² can be factored as (2x + 5b)(2x - 5b).
To factor the trinomial x^2 - 81, we can use the difference of squares formula once again:
x² - 81 = x² - 9²
This can be written as a difference of squares:
x² - 81 = (x + 9)(x - 9)
Thus, the trinomial x² - 81 can be factored as (x + 9)(x - 9).
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I will give you a Brainly crown if it is right. Will you help me
Answer: 811.2
Step-by-step explanation:
The time it takes for a canoe to go 3 miles upstream and back 3 miles downstream is 4 hours. The current in the lake is 1 mile per hour. Find the average speed of the canoe.
Final answer:
The average speed of the canoe is 1.5 mph.
Explanation:
To find the average speed of the canoe, we need to calculate the time it takes for the canoe to go both upstream and downstream. Let's start with the time it takes to go upstream:
Distance = 3 miles
Speed of canoe = Speed in still water - Speed of current = 8 mph - 1 mph = 7 mph
Time = Distance / Speed = 3 miles / 7 mph = 0.429 hours
Now, let's calculate the time it takes to go downstream:
Distance = 3 miles
Speed of canoe = Speed in still water + Speed of current = 8 mph + 1 mph = 9 mph
Time = Distance / Speed = 3 miles / 9 mph = 0.333 hours
Finally, we can find the average speed of the canoe by dividing the total distance traveled (6 miles) by the total time taken (4 hours): average speed = total distance / total time = 6 miles / 4 hours = 1.5 mph.
factor polynomial 4a^2-4a+1
Answer:
(2a−1)(2a−1)
Step-by-step explanation:
Factor 4a2−4a+1
4a2−4a+1
=(2a−1)(2a−1)
Answer:(2a-1)(2a-1)
Step-by-step explanation:
4a2-4a+1
Factorise
Factors of -4 is -2&-2
Substitute
4a2-2a-2a+1
2a(2a-1)-1(2a-1)
(2a-1)(2a-1)
Or we say
(2a-1) twice
Consider triangle ABC and triangle ACD in the diagram below. Which of the following complete the proof above?
Options
- AB =AD
- AC=AC
- AC=BD
- BC=DC
Given:
AC is perpendicular bisector of BD
AB ≅ AD
To prove:
ΔABC ≅ ΔACD
Solution:
In triangle ABC and triangle ACD,
Step 1: Given
AC is perpendicular bisector of BD and
AB ≅ AD (Side)
Step 2: By perpendicular bisector definition,
BC ≅ CD (Side)
Step 3: By reflexive property,
AC ≅ AC (Side)
Step 4: By SSS congruence criterion,
ΔABC ≅ ΔACD
Hence proved.
Answer:
BC=DC
Step-by-step explanation:
I did the test yourself and got it right :)
What is the slope of y = -4?
Answer:
Slope is 0
y-intercept:-4
Step-by-step explanation:
Answer:-4
Step-by-step explanation:
Because the slope is 0 so substitute
Find the tangent of theta
Given:
Right triangle.
Base = 10
Hypotenuse = 26
To find:
The missing side length
Solution:
Let the missing side length be x.
Using Pythagoras theorem:
In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.
[tex]10^2+x^2=26^2[/tex]
[tex]100+x^2=676[/tex]
Subtract 100 from both sides.
[tex]100+x^2-100=676-100[/tex]
[tex]x^2=576[/tex]
Taking square root on both sides.
[tex]x=24[/tex]
The missing side length of the right triangle is 24.
Does someone knows the correct answer?? I think is d but I don’t know
Answer:
I think you are right
Step-by-step explanation:
Answer:
YES I AM PRETTY SURE ITs :D GOOD LUCK HAVE A GREAT DAY
Step-by-step explanation:
You need $40 to buy a new pair of shoes. You have saved $15. Which inequality
models how much more you must save?
Answer:
40<or= 15+ x
Step-by-step explanation:
Plz plz plz this is due today and I really need help
Answer:
The y-intercept is (0, 34).
I used Demos graphing calculator and included an image of what values I put in.
What is the measure of ?
Angles are not necessarily drawn to scale.
149
Answer:
60
Step-by-step explanation:
The base diameter and the height of a cone are both equal
to x units
Which expression represents the volume of the cone, in
cubic units?
Pix^2
Answer:
1/3 times x squared divided by 4 times pi times x.
Step-by-step explanation:
Hope this helps!
Calculate the Rate of Return on an initial investment of $6,000 valued at $6,500.
Answer:
8.3%
Step-by-step explanation:
The rate of return on initial investment is 8.34%.
What is the percentage?
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the investment is $6,000 and valued at $6,500. The rate of the return will be calculated as,
Rate of return = ( 6500 - 6000) / 6000
Rate of return = 800 / 6000
Rate of return = 8.34%
Therefore, the rate of return on initial investment is 8.34%.
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A pot of piping hot stew has been removed from the stove and left to cool.
The relationship between the elapsed time, m, in minutes, since the stew was removed from the stove, and the
temperature of the stew. T(m), measured in C is modeled by the following function.
T(m) = 20 + 50 - 10-0.0477
How many minutes will it take for the stew to cool to a temperature of 30°C?
Round your answer, if necessary to the nearest hundredth.
minutes
Answer: 17.47 minutes
Step-by-step explanation:
To find the number of minutes it will take for the stew to cool to a temperature of 30°C, solve the given nonlinear equation or graph it to find the intersection point.
Explanation:The given function that models the relationship between the elapsed time, m, in minutes, and the temperature of the stew, T(m), is:
T(m) = 20 + 50 - 10^(-0.0477m)
To find the number of minutes it will take for the stew to cool to a temperature of 30°C, we need to solve the equation:
30 = 20 + 50 - 10^(-0.0477m)
By isolating the unknown variable, m, we can solve for it using logarithms or graphing. However, since the equation is nonlinear, graphing is a more intuitive approach. Graph the equation and find the x-coordinate at which the graph intersects with the y-coordinate 30. This value of m will give you the number of minutes it will take for the stew to cool to 30°C.
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Find the value of x
Options being
A) 27
B) 4
C) 2
D) 8
Answer:
B
Step-by-step explanation:
81 = 9 × 9 = 3 × 3 × 3 × 3 = [tex]3^{4}[/tex]
Thus the [tex]\sqrt[4]{81}[/tex] = [tex]\sqrt[4]{3^{4} }[/tex] = 3
Hence x = 4 → B
PLS HELP ME IF YOU WANT A BRAINLIEST IM DOING THIS NOW and IDU, Students from Williams Middle School are also recycling aluminum cans. The data for the numbers of cans brought in each school day for a month were divided by quartiles and summarized in the box plot. Use the drop-down menus to choose the median, interquartile range, and range.
>Median:
>Interquartile range:
>Range:
Answer: Median: 18
Interquartile range: 4
Range: 18
Step-by-step explanation: The median line is at 18, the interquartile range is the difference between the ends of the box, 20 - 16 = 4. The range is the difference between the ends of the line, 28 - 10 = 18. Let's take a look at how the data can be compared, from the two schools using the box plot.
From the information provided, it is clear that the
Median = 18Interquartile range = 4Range = 18How do we arrive at the following above?By observation, the median line is at 18. Note that the median of a distribution is the quantity that lies at the midpoint of a frequency distribution.
The interquartile range is the variance between the quantity at the end of the box, 20 - 16 = 4. The interquartile range (IQR)is defined as the mid 50% of the values in distribution when arranged from the lowest to the highest.
The range is defined as the difference between the quantities at the terminal points of the line. Hence, 28 - 10 = 18.
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At 6: 00 a.m., Buffalo, NY had a temperature of 10℉. At noon, the temperature was −10℉, and at midnight it was −20℉.
write a statement comparing -10 and -20
Answer:
It got colder Because some nights it gets colder?
PLEASE HELP ME OUT I NEED HELP ASAP!!!!!!!
Answer:
c
Step-by-step explanation:
when you add the same number to the previous number it forms a straight line
given the sequence 3, 6... what would the 10th term be?
Answer:
30
It is the multiple of 3.
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
That are counting by 3’s so the 10th term would be 30 because 3×10 =30
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Larry is building a frame around a rectangular picture. He will need 46 inches of wood to do the entire frame. If the frame is 13
inches long, how wide is the frame?
A. 10 inches
B. 23 inches
C. 8 inches
D. 20 inches
Answer:
Step-by-step explanation:
How many centimeters is Campsite 3 from the canoe rental office?
Answer:
hi
Step-by-step explanation:
u need to give more information plz thanks
Answer:5 centimeterts
Step-by-step explanation:it right
Which complex number is equivalent to (5 + 12i) − (9i2 − 6i), where i =
−1
?
Answer:
14 + 18i
Step-by-step explanation:
[tex](5 + 12i) - (9 {i}^{2} - 6i) \\ = (5 + 12i) - (9 \times (- 1) - 6i) \\ = (5 + 12i) - ( - 9 - 6i) \\ = (5 + 12i) + ( 9 + 6i) \\ = 5 + 12i + 9 + 6i \\ \red { \bold{ = 14 + 18i}}[/tex]
Answer: It's 14+18i I got a correct
Genevieve works on her scrapbook from 11:27 am to 11:58 am. How many minutes does she work on her scrapbook
Answer:
31
Step-by-step explanation:
time is tricky due to the 60 minute interface. In those questions add to the lower number until you hit a rounded number.
Fortunately you don't need to use this in this problem, and can just subtract 58-27 to get 31
shape 2
shape 1
8
10
12
14
16
Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true?
A.
Shape 1 is congruent to shape 2, which can be shown using a sequence of dilations and translations.
B.
Shape 1 is not congruent to shape 2 because the shapes do not have the same absolute coordinates.
C.
Shape 1 is congruent to shape 2, which can be shown using a translation
D.
Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 ontos
Answer:
a)shape 1 is congruent to shape 2 which can be shown using a sequence of dilutions and translations
Evan's science class planted sunflower seeds as part of a research project. A student was sent out each week to measure the height of a flower of their choice. The data in the scatter plot shows their findings from week 2 to week 12.
Which function, h(w), approximates the height of the sunflowers after w weeks?
A) h(w) = 0.30x - 1.09
B) h(w) = 0.30x + 1.52
C) h(w) = 3.18x + 3.78
D) h(w) = 3.23x - 4.14
Answer:
D
Step-by-step explanation:
If you graph equation D you get the following graph, which is closest to the plots
It's impossible to determine the accurate function h(w) that approximates the height of the sunflowers after w weeks from the question alone. This would typically involve evaluating a scatter plot and applying linear regression to find the best fitting function. The approximating function would be understood as the one that best matches the given options, minimizing the distance between the data points and the line.
Explanation:The function that approximates the height of the sunflowers after w weeks (h(w)) cannot be determined directly from the question as it depends on the data present in the scatter plot that was mentioned. Given a scatter plot, we would aim to find a function that best approximates the trend or pattern seen in the plot.
It's an instance of linear regression, a statistical method used to model the relationship between a dependent variable (in this case, height of the sunflowers) and one or more independent variables (in this case, number of weeks). Assuming a linear relationship between weeks and the height of the sunflowers, we want to fit a linear equation (like the given options) that represents this correlation, minimizing the distance between the data points and the line.
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The polynomial p(x) = x^3 - 21x - 20 has a known factor of (x-5). Rewrite p(x) as a product of linear factors.
Answer:
p(x) = (x - 5)(x + 1)(x + 4)
Step-by-step explanation:
Using Synthetic division to find the quotient on dividing p(x) by (x - 5)
5 | 1 0 - 21 - 20 ← 0 to represent the coefficient of x² term
5 25 20
-----------------------
1 5 4 0 ← remainder is zero
quotient = x² + 5x + 4 = (x + 1)(x + 4)
p(x) = (x - 5)(x + 1)(x + 4)
The polynomial p(x) = x^3 - 21x - 20 can be written as a product of linear factors as follows;
(x-5) (x+4) (x+1).
According to the question, the polynomial, p(x) = x^3 - 21x - 20 has a known factor of (x- 5).
To further factorise this polynomial such that it becomes a product of linear factors, we must first, perform the long division of x³ - 21x - 20 divided by (x-5).The polynomial long division is as in the image attached;
The result of the division of x³ - 21x - 20 by (x-5) yields;
x² + 5x + 4.The expression, x² + 5x + 4 can however be further factorised so that we have;
x² + 5x + 4 = (x+4) (x-1)Ultimately, the polynomial p(x) = x^3 - 21x - 20 can be written as a product of linear factors as follows;
(x-5) (x+4) (x+1).
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