Answer:
25 and 18
Step-by-step explanation:
Let's say that the first number is x and the second one is y.
First, the difference between them is 7, so x-y=7
Next, the sum of their squares is 949, so x²+y² = 949
We have
x-y=7
x²+y²=949
One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there
Adding y to both sides in the first equation, we have
x = 7 + y
Plugging that into the second equation for x, we have
(7+y)²+ y² = 949
expand
(7+y)(7+y) + y² = 949
49 + y² + 7y + 7y + y² = 949
combine like terms
2y² +14y + 49 = 949
subtract 949 from both sides to put this in the form of a quadratic equation
2y² + 14y - 900 = 0
divide both sides by 2
y² + 7y - 450 = 0
To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.
The factors of 450 are as follows:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have
y² + 25y - 18y - 450 = 0
y(y+25) - 18(y+25) = 0
(y-18)(y+25) = 0
Solving for 0,
y-18 = 0
add 18 to both sides
y=18
y+25 = 0
subtract 25 from both sides
y= -25
As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so
x-18 = 7
add 18 to both sides to isolate x
x = 25
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F. (Let y be measured in degrees Fahrenheit, and t be measured in seconds.) (a) Determine the cooling constant k. k = s−1 (b) What is the differential equation satisfied by the temperature y(t)? (Use y for y(t).) y'(t) = (c) What is the formula for y(t)? y(t) = (d) Determine the temperature of the bar at the moment it is submerged. (Round your answer to one decimal place.)
Answer:
a. k = -0.01014 s⁻¹
b. [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
c. [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
d. y(t) = 130.485°F
Step-by-step explanation:
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.
(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)
We are to determine :
a. Determine the cooling constant k. k = s−1
By applying the new law of cooling
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]
[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]
Taking the integral.
[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]
㏑ (T -60) = kt + C
T - 60 = [tex]e^{kt+C}[/tex]
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
After 20 seconds, the temperature of the bar submersion is 120°F
T(20) = 120
From equation (1) ,replace t = 20s and T = 120
[tex]120 = 60 + C_1 e^{20 \ k}[/tex]
[tex]120 - 60 = C_1 e^{20 \ k}[/tex]
[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]
After 1 min i.e 60 sec , the temperature = 100
T(60) = 100
From equation (1) ; replace t = 60 s and T = 100
[tex]100 = 60 + c_1 e^{60 \ t}[/tex]
[tex]100 - 60 =c_1 e^{60 \ t}[/tex]
[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]
Dividing equation (2) by (3) , we have:
[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]
[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]
[tex]-40 \ k = In (\dfrac{3}{2})[/tex]
- 40 k = 0.4054651
[tex]k = - \dfrac{0.4054651}{ 40}[/tex]
k = -0.01014 s⁻¹
b. What is the differential equation satisfied by the temperature y(t)?
Recall that :
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]
Since y is the temperature of the body , then :
[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
(c) What is the formula for y(t)?
From equation (1) ;
where;
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
Let y be measured in degrees Fahrenheit
[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]
From equation (2)
[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]
[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]
[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]
[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]
[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
(d) Determine the temperature of the bar at the moment it is submerged.
At the moment it is submerged t = 0
[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]
y(t) = 60 + 70.485
y(t) = 130.485°F
Consider these five values a population: 7, 4, 6, 4, and 7. Determine the mean of the population. (Round your answer to 1 decimal place.)
Answer:
[tex]Mean = 5.6[/tex]
Step-by-step explanation:
Given
[tex]7,4,6,4,7[/tex]
Required
Determine the mean
Mean is calculated as thus;
[tex]Mean = \frac{\sum x}{n}[/tex]
Where n is the number of observation;
In this case;
[tex]n = 5[/tex]
and [tex]\sum x[/tex] is the sum of the observations
The expression becomes
[tex]Mean = \frac{7+4+6+4+7}{5}[/tex]
[tex]Mean = \frac{28}{5}[/tex]
[tex]Mean = 5.6[/tex]
Hence, the mean of the population is 5.6
Based on a poll, 40% of adults believe in reincarnation. Assume that 4 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below.Required:a. The probability that exactly 3 of the 4 adults believe in reincarnation is? b. The probability that all of the selected adults believe in reincarnation is? c. The probability that at least 3 of the selected adults believe in reincarnation is? d. If 4 adults are randomlyselected, is 3 a significantly high number who believe inreincarnation?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(3) = 0.154[/tex]
b
[tex]P(4) = 0.026[/tex]
c
[tex]P( X \ge 3 ) = 0.18[/tex]
d
option C is correct
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.4
The sample size is n= 4
This adults believe follow a binomial distribution is because there are only two outcome one is an adult believes in reincarnation and the second an adult does not believe in reincarnation
The probability of failure is mathematically evaluated as
[tex]q = 1 - p[/tex]
substituting values
[tex]q = 1 - 0.4[/tex]
[tex]q = 0.6[/tex]
Considering a
The probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as
[tex]P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}[/tex]
substituting values
[tex]P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}[/tex]
Here [tex]\left 4} \atop {}} \right.C_3[/tex] means 4 combination 3 . i have calculated this using a calculator and the value is
[tex]\left 4} \atop {}} \right.C_3 = 4[/tex]
So
[tex]P(3) = 4* (0.4)^3 * (0.6)[/tex]
[tex]P(3) = 0.154[/tex]
Considering b
The probability that all of the selected adults believe in reincarnation is mathematically represented as
[tex]P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}[/tex]
substituting values
[tex]P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}[/tex]
Here [tex]\left 4} \atop {}} \right.C_3[/tex] means 4 combination . i have calculated this using a calculator and the value is [tex]\left 4} \atop {}} \right.C_4 = 1[/tex]
so
[tex]P(4) = 1* (0.4)^4 * 1[/tex]
=> [tex]P(4) = 0.026[/tex]
Considering c
the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as
[tex]P( X \ge 3 ) = P(3 ) + P(n )[/tex]
substituting values
[tex]P( X \ge 3 ) = 0.154 + 0.026[/tex]
[tex]P( X \ge 3 ) = 0.18[/tex]
From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is [tex]p(4) = 0.026 < 0.05[/tex]
But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is [tex]P(3) = 0.154 \ which \ is \ > 0.05[/tex]
Hence 3 is not a significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.
Which shapes are quadrilaterals?
1. Scalene right triangle
2. Obtuse scalene triangle
3. Isosceles right triangle
4. Hexagon
5. Pentagon
6. Right trapezoid
7. Venn diagram
Hey there! I'm happy to help!
A quadrilateral is any polygon (enclosed shape) with four sides. Let's see what each of these shapes are.
Scalene right triangle - the prefix tri- means three (tricycle, tripod, triple, etc.), and all triangles have three sides, so this is not a quadrilateral.Obtuse scalene triangle - once again a triangle, so not a quadrilateral.Isosceles right triangle - would you look at that, another triangle! Not a quadrilateral.Hexagon - a hexagon is a six-sided polygon (hex=six), so this is not a quadrilateral.Pentagon - a pentagon is a five-sided polygon (pent=five, like Pentatonix!). Not a quadrilateralRight trapezoid - a trapezoid is a quadrilateral with at least one pair of parallel sides!Venn diagram - a Venn diagram is a compare and contrast chart made of two overlapping circles (ZERO sides), so this is not a quadrilateral.So, the only shape on your list that is a quadrilateral is 6. right trapezoid.
Have a wonderful day! :D
A lottery exists where balls numbered 1 to "20" are placed in an urn. To win, you must match the balls chosen in the correct order. How many possible outcomes are there for this game?
Answer: 1860480
Step-by-step explanation:
Initially, there are 20 balls where 5 must be chosen in order.
The number of possible outcomes may be calculated using the concept of permutations.
The formula for permutations is:
nPr =n!/(n−r)!
where n represents the number of items and r represents the number of items to be selected.
The number of ways of selecting 5 balls in order out of 20 is:
20P5 = 20!/15!
= 1860480
To conclude, there are 1860480 possible outcomes.
An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answer:
(a) After t years, the height is
18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Step-by-step explanation:
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
[tex] \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = what[/tex]
Answer I'll make and mark as brainlist.
Answer Fast.
Post on - 2 Aug 2021
Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α= 0.01.
Internet Users 80.3 78.2 56.4 67.6 77.7 38.6
Award Winners 5.6 9.3 3.2 1.6 10.9 0.1
Required:
a. Construct a scatterplot.
b. Determine the null and alternative hypotheses.
c. The test statistic is:_________
d. The P-value is:_________
Answer:
There is not sufficient evidence to support a claim of linear correlation between the two variables.
Step-by-step explanation:
(a)
The scatter plot for the provided data is attached below.
(b)
The hypothesis to test significance of linear correlation between the two variables is:
H₀: There is no linear correlation between the two variables, i.e. ρ = 0.
Hₐ: There is a significant linear correlation between the two variables, i.e. ρ ≠ 0.
(c)
Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.
The correlation coefficient between the number of internet users and the award winners is,
r = 0.786.
The test statistic value is:
[tex]t=r\sqrt{\frac{n-2}{1-r^{2}}}[/tex]
[tex]=0.786\times\sqrt{\frac{6-2}{1-(0.786)^{2}}}\\\\=2.5427\\\\\approx 2.54[/tex]
Thus, the test statistic is 2.54.
(d)
The degrees of freedom is,
df = n - 2
= 6 - 2
= 4
Compute the p-value as follows:
[tex]p-value=2\cdot P(t_{n-2}<2.54)=2\times 0.032=0.064[/tex]
*Use a t-table.
p-value = 0.064 > α = 0.05
The null hypothesis will not be rejected.
Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.
How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10-feet wall?
Answer:
√69 or 8.3 feets
Step-by-step explanation:
Hypotenuse=13
Therefore
13²=x²+10²
x²=169-100
x²=69
x=√69 feets
The distance from the base of the house is 8.3 feet.
What is the pythagoras theorem?The pythagoras theorem is used to obtain the sides of a right angled triangle.
Given that;
The hypotenues of the triangle is 13-foot
The length of the opposite side is 10 feet
Thus;
13^2 = 10^2 + a^2
a^2 = 13^2 - 10^2
a = √13^2 - 10^2
a = 8.3 feet
Learn more about pythagoras theorem:https://brainly.com/question/343682
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The distance between two cities on a map is 4 centimeters. If the scale is 0.5 cm:1 km, how many kilometers apart are the actual cities?
Answer:
8 km
Step-by-step explanation:
1 km
4 cm x -------- = 8 km
0.5 cm
The actual cities are 8 km apart from each other at the scale 0.5 cm = 1 km.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The distance between two cities on a map = 4 centimeters.
Also, the scale
0.5 cm = 1 km
To find actual distance between cities, use ratio properly,
0.5 cm = 1 km
1 cm = 2 km
4 cm = 8 km
The distance between the actual cities is 8 km.
To learn more about Ratio on :
https://brainly.com/question/13419413
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Determine the value of x in the figure. Question 1 options: A) x = 90 B) x = 85 C) x = 45 D) x = 135
Answer:
A.) x=90°
Step-by-step explanation:
Note:
The triangle shown is an isosceles triangle, which means that it has 2 congruent sides (as shown by the small intersecting lines), and this also means that it has two congruent angles.
We are given an angle measure adjacent to one of the missing angles. These two form supplementary angles, which means that they're sum is equal to 180°, or a straight line. So, to find:
[tex]180=135+y[/tex]
y is the unknown angle. Solve for y:
[tex]180-135=y\\\\y=45[/tex]
y is 45°. Since this and the other angle are congruent, add:
[tex]45+45=90[/tex]
Note:
Triangles angles will always add up to a total of 180°.
To find the missing angle x°, use:
[tex]180=a+b+c[/tex]
These are the angles in a triangle. Substitute any known values and solve:
[tex]180=45+45+x\\\\180=90+x\\\\180-90=x\\\\x=90[/tex]
The missing angle x° is 90°.
:Done
Which is the zero of the function f(x)=(x+3) (2x-1)(x+2) ?
Answer:
x= -3 x = 1/2 x=-2
Step-by-step explanation:
f(x)=(x+3) (2x-1)(x+2)
Set equal to zero
0 =(x+3) (2x-1)(x+2)
Using the zero product property
x+3 =0 2x-1 =0 x+2 =0
x= -3 2x =1 x = -2
x= -3 x = 1/2 x=-2
A new fast-food firm predicts that the number of franchises for its products will grow at the rate dn dt = 6 t + 1 where t is the number of years, 0 ≤ t ≤ 15.
Answer:
The answer is "253"
Step-by-step explanation:
In the given- equation there is mistype error so, the correct equation and its solution can be defined as follows:
Given:
[tex]\bold{\frac{dn}{dt} = 6\sqrt{t+1}}\\[/tex]
[tex]\to dn= 6\sqrt{t+1} \ \ dt.....(a)\\\\[/tex]
integrate the above value:
[tex]\to \int dn= \int 6\sqrt{t+1} \ \ dt \\\\\to n= \frac{(6\sqrt{t+1} )^{\frac{3}{2}}}{\frac{3}{2}}+c\\\\\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}+c\\\\[/tex]
When the value of n=1 then t=0
[tex]\to 1= \frac{12(0+1)^{\frac{3}{2}}}{3}+c\\\\ \to 1= \frac{12(1)^{\frac{3}{2}}}{3}+c\\\\\to 1-\frac{12}{3}=c\\\\\to \frac{3-12}{3}=c\\\\\to \frac{-9}{3}=c\\\\\to c=-3\\[/tex]
so the value of n is:
[tex]\to n= \frac{(12\sqrt{t+1} )^{\frac{3}{2}}}{3}-3\\\\[/tex]
when we put the value t= 15 then,
[tex]\to n= \frac{(12\sqrt{15+1} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\sqrt{16} )^{\frac{3}{2}}}{3}-3\\\\\to n= \frac{(12\times 64)}{3}-3\\\\\to n= (4\times 64)-3\\\\\to n= 256-3\\\\\to n= 253[/tex]
A middle school has 470 students. Regina surveys a random sample of 40 students and finds that 28 have cell phones. How many students at the school are likely to have cell phones? A. 132 students B. 188 students C. 329 students D. 338 students Please include ALL work! <3
Answer:
C. 329
Step-by-step explanation:
So 28 is 70% of 40
so we know that 70% percent of students have phones
70% of 470
329
Thats how I solved it have a great day :)
Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. What would be the present value of this loan if it carried a 10% interest rate?
Answer:
The present value is [tex]PV = \$ 396,987[/tex]
Step-by-step explanation:
From the question we are told that
The interest payment per year is [tex]C = \$ 85[/tex]
The principal payment is [tex]P = \$ 1000[/tex]
The duration is n = 8 years
The interest rate is [tex]r = 10\% = 0.10[/tex]
The present value is mathematically represented as
[tex]PV = [ \frac{C}{r} * [1 - \frac{1 }{ (1 +r)^n} ] + \frac{P}{(1 + r)^n} ][/tex]
substituting values
[tex]PV = [ \frac{85}{0.10} * [1 - \frac{1 }{ (1 +0.10)^8} ] + \frac{1000}{(1 + 0.10)^ 8} ][/tex]
[tex]PV = \$ 396,987[/tex]
A store has clearance items that have been marked down about 30%. They are having a sale, advertising an additional 55% off clearance items. What percent of the original price do you end up paying
Answer:
60% discount given in total, so only 40% is paid.
Step-by-step explanation:
can you please help ?
Answer:
69
Step-by-step explanation:
The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.
We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.
[tex]\frac{5(x)}{2} -6[/tex]
[tex]\frac{5(30)}{2}-6[/tex]
[tex]\frac{150}{2}-6[/tex]
[tex]75-6[/tex]
[tex]69[/tex]
Solve the equation using square roots x^2+20=4
Answer:
Step-by-step explanation:
x^2+20=4 first isolate the variable by subtracting 20 on both sides.
x^2=-16 again isolate the variable but this time you square root both sides.
[tex]\sqrt{x}^2[/tex]=[tex]\sqrt{-16[/tex] then simplify
x= ±4
Simplify using calculator.. I'm not sure if i am putting it in the calculator right
You would type in
32^(6/5)
Or you could type in
32^(1.2)
since 6/5 = 1.2
Either way, the final result is 64
Look at the chore chart--write a notice and a wonder about the chart. Click on the image to see the chart. Enter ur answer
Answer:
I noticed that to babysit my cousin was the chore that doled out the most, and I wonder why pet my dog is even a chore. Do they not love their pets?
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were:
1. y=a+bx
2. b=-0.669
3. a=27.41
4. r2=0.760384
5. r=-0.872
Use this to predict the number of situps a person who watches 3.5 hours of TV can do. Round to one decimal place.
Answer: The correct answer is 19 sit ups.
Step-by-step explanation: Given that the regression equation to find a a relationship between hours of TV watched per day (x) and number of situps a person can do (y) was done.
The result was
y = ax+b
Correlation coefficient = 0.865
To predict the number of situps a person who watches 3 hours of TV
y = -1.23(3)+22.738
= 19.048
Approximately 19 situps.
please Factor 12n - 18.
Answer:
[tex]\large \boxed{6(2n-3)}[/tex]
Step-by-step explanation:
[tex]12n-18[/tex]
Factor out 6 from each term.
[tex]6(2n)+6(-3)[/tex]
Take 6 as a common factor.
[tex]6(2n-3)[/tex]
Answer:
[tex] \boxed{3(4n - 6)}[/tex]Step-by-step explanation:
[tex] \mathsf{12n - 18}[/tex]
In such expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor
Factor out 3 from the expression
[tex] \mathsf{ = 3(4n - 6)}[/tex]
Hope I helped!
Best regards!
Find the measure of ZJ, the smallest angle in a triangle
with sides measuring 11, 13, and 19. Round to the
nearest whole degree.
O 30°
O 34°
o 42°
O 47°
Solve the system of equations.
6x−y=−14
2x−3y=6
whats the answer please C:
Answer:
Step-by-step explanation:
14. Find the distance between (7,217pi/180 ) and (5,-23pi/36 ) on the polar plane.
Answer: the distance is 3.49 units
Step-by-step explanation:
There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.
When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:
x = R*cos(θ)
y = R*sin(θ)
Then we have:
(7,217pi/180 )
R = 7
θ = (217/180)*pi
x = 7*cos( (217/180)*pi) = -5.59
y = 7*sin( (217/180)*pi) = -4.21
So this point is (-5.59, -4.21) in rectangular coordinates.
And the other point is (5,-23pi/36 )
R = 5
θ = -(23/36)*pi
x = 5*cos( -(23/36)*pi ) = -2.11
y = 5*sin( -(23/36)*pi ) = -4.53
So this point is (-2.11, - 4.53)
Then the point distance between those points is:
D = I (-2.11, -4.53) - (-5.59, -4.21) I
D = I (-2.11 + 5.59, -4.53 + 4.21) I
D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) = 3.49
what is 5(2x - 2y) - (4x + 3y)
Answer:
6x - 13y
Step-by-step explanation:
5(2x - 2y) - (4x + 3y)
10x - 10y - 4x - 3y
10x - 4x - 10y - 3y
6x - 13y
Need to be in order Smallest to biggest question.
Want to check if my answers are right.
Answer:
a49%, 1/2,0.55,3/5
b)0.2,1/4,27%,3/10
c)9/10,95%,0.99,97/100
d)30%,1/3,0.6,2/3
e)0.09,10%,11/100,0.125
Maite has money in an interest-bearing account. The table shows how much money is in the account at the end of each year.
N
Year Amount
1 $1,000.00
$1,030.00
3 $1,060.90
4 $1,092.73
5 $1,125.51
This situation represents
sequence.
The common
is
At the end of the seventh year, Maite will have $
in the account
Determining how much money will be in the account of Maite at the end of each year, we use an exponential growth factor, since this is a geometric sequence.
1. This situation represents a geometric sequence.
A geometric sequence increases by a common exponential growth factor.
2. The common exponential factor is 1.03 (which gives a growth rate of 3% annually). See how this factor is determined below.
3. At the end of the seventh year, Maite will have $1,194.05 in the account. See the calculation below.
Data and Calculations:
Year Amount
1 $1,000.00
2 $1,030.00
3 $1,060.90
4 $1,092.73
5 $1,125.51
6 $1,159.27 ($1,125.51 * 1.03)
7 $1,194.05 ($1,159.27 * 1.03)
The common exponential factor = 1.03 (1 + 0.03)
To obtain the common exponential factor, subtract Year 2 account balance from Year 1 account balance. Divide the result by Year 1 account balance. This operation can also be carried out with Year 2 and Year 3 balances or Year 4 and Year 5 balances.
To determine how much money will be in the account of Maite at the end of Year 6, using Year 5 as a base = (Year 5 account balance * Exponential Factor)
= $1,159.27 ($1,125.51 * 1.03)
To determine Year 7 account balance, we use Year 6 above as the base
= $1.194.05 ($1,159.27 * 1.03)
Learn more about geometric sequence and exponential growth here: https://brainly.com/question/7154553
Answer:
This situation represents a geometric sequence.
The common ratio is 1.03
At the end of the seventh year, Maite will have $1,194.06 in the account.
Step-by-step explanation:
Plato
Calculate the surface area of this composite shape.
Answer:
1284 m^2
Step-by-step explanation:
Front face and back face:
2 * [28 m * 5 m + (22 m - 5 m) * 6 m] = 484 m^2
Left face and right face:
2 * 22 m * 8 m = 352 m^2
Bottom face and top face:
2 * 28 m * 8 m = 448 m^2
total surface area = 484 m^2 + 352 m^2 + 448 m^2 = 1284 m^2
HELP ASAP ROCKY!!! will get branliest.
Answer:
y = 8x + 70
Step-by-step explanation:
Start with the third line.
x = 3, y = 94
Subtract 1 from x and 8 from y:
x = 2, y = 86; this is the second line
Subtract 1 from x and 8 from y:
x = 1, y = 78; this is the first line
Subtract 1 from x and 8 from y:
x = 0; y = 70
For selling 0 games, she earns $70.
y = mx + b
y = mx + 70
For each game she sells, her commission is $8.
y = 8x + 70