Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of T and the temperature of the region, TR or dT over dt equals k times the quantity T minus T sub R end quantity. An object with core temperature of 1200°F is removed from a fire and placed in a region with a constant temperature of 80°F. After 1 hour, its core temperature is 830°F. What is the object's core temperature 4 hours after it is taken off the fire? (1 point)
Answers
Answer:
305 °F
Step-by-step explanation:
The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.
Cooling ModelThe solution to the differential equation described by Newton's law of cooling is the exponential equation ...
y = ab^t +c
where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.
For this problem, the ambient temperature is c=80, and the differences of interest are ...
a = 1200 -80 = 1120
b = (830 -80)/1120 = 75/112
Using these values in the model gives ...
y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t
Note that units of time are hours.
ApplicationWe want y when t=4.
y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212
The core temperature after 4 hours is about 305 °F.
__
Additional comment
The differential equation will have a solution of the form ...
[tex]T-T_R=(T_0-T_R)e^{kt}[/tex]
where k = ln(75/112) ≈ -0.40101
In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.
Related Questions
Which equation has no solution?
4(x + 3) + 2x = 6(x + 2)
5 + 2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 6(2 + x) = 2(3x + 8)
Answers
Answer:
equation 1 has no solution
Step-by-step explanation:
when you compare each of the equations, all the equations gives a correct answer with the exception of equation 1
Determine the domain:
[tex]f(x) = \frac{ln(ln(x + 1))}{e {}^{x} - 9 } [/tex]
Answers
The denominator cannot be zero, so
[tex]e^x - 9 = 0 \implies e^x = 9 \implies x = \ln(9)[/tex]
is not in the domain of [tex]f(x)[/tex].
[tex]\ln(x)[/tex] is defined only for [tex]x>0[/tex], and we have
[tex]\ln(x+1) > 0 \implies e^{\ln(x+1)} > e^0 \implies x+1 > 1 \implies x>0[/tex]
so there is no issue here.
By the same token, we need to have
[tex]x+1 > 0 \implies x > -1[/tex]
Taking all the exclusions together, we find the domain of [tex]f(x)[/tex] is the set
[tex]\left\{ x \in \Bbb R \mid x > 0 \text{ and } x \neq \ln(9)\right\}[/tex]
or equivalently, the interval [tex](0,\ln(9))\cup(\ln(9),\infty)[/tex].
△ABC has vertices A(-2, 0), B(0,8), and C(4,2) Find the equations of the three altitudes of △ABC
Answers
The equations of the three altitudes of triangle ABC include the following:
3y - 2y - 4 = 0.y + 3x - 8 = 0.4y + x - 6 = 0.What is a triangle?A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Also, the point-slope form of a straight line is given by this equation:
y - y₁ = m(x - x₁)
Assuming the following parameters for triangle ABC:
Let AM be the altitudes on BC.Let BN be the altitudes on CA.Let CL be the altitudes on AB.For the equation of altitude AM, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2
Slope of AM = -1/slope of BC
Slope of AM = -1/(-3/2)
Slope of AM = 2/3.
The equation of altitude AM is given by:
y - y₁ = m(x - x₁)
y - 0 = 2/3(x - (-2))
3y = 2(x + 2)
3y = 2x + 4
3y - 2y - 4 = 0.
For the equation of altitude BN, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3
Slope of BN = -1/slope of CA
Slope of BN = -1/(1/3)
Slope of BN = -3.
The equation of altitude BN is given by:
y - y₁ = m(x - x₁)
y - 8 = -3(x - 0)
y - 8 = -3x
y + 3x - 8 = 0.
For the equation of altitude CL, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4
Slope of CL = -1/slope of AB
Slope of CL = -1/4
The equation of altitude CL is given by:
y - y₁ = m(x - x₁)
y - 2 = -1/4(x - 4)
4y - 2= -(x - 4)
4y - 2= -x + 4
4y + x - 2 - 4 = 0.
4y + x - 6 = 0.
In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:
3y - 2y - 4 = 0.y + 3x - 8 = 0.4y + x - 6 = 0.Read more on point-slope form here: brainly.com/question/24907633
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1-cos(6x)=___?
A. 3sin(2x)
B. 2sin^2(3x)
C. 3cos(2x)
D. 2cos^2(3x)
Answers
The solution to 1 - cos(6x) is 2sin²(x).
Hence, option B) 2sin²(x) is the correct answer.
What is solution to 1 - cos(6x)?Given that; 1 - cos(6x) = ?
First, we rewrite using trig identity
1 - cos(2 × 3x)
Using the double angle identity, { cos2(x) = 1 - 2sin²(x) }
1 - ( 1 - 2sin²(x) )
Eliminate the parentheses
1 - 1 + 2sin²(x)
2sin²(x)
The solution to 1 - cos(6x) is 2sin²(x).
Hence, option B) 2sin²(x) is the correct answer.
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Find the maximum value of s = xy + yz + xz where x+y+z=9.
Answers
From the constraint, we have
[tex]x+y+z=9 \implies z = 9-x-y[/tex]
so that [tex]s[/tex] depends only on [tex]x,y[/tex].
[tex]s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy[/tex]
Find the critical points of [tex]g[/tex].
[tex]\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9[/tex]
[tex]\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0[/tex]
Using the given constraint again, we have the condition
[tex]x+y+z = 2x+y \implies x=z[/tex]
so that
[tex]x = 9 - x - y \implies y = 9 - 2x[/tex]
and [tex]s[/tex] depends only on [tex]x[/tex].
[tex]s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2[/tex]
Find the critical points of [tex]h[/tex].
[tex]\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3[/tex]
It follows that [tex]y = 9-2\cdot3 = 3[/tex] and [tex]z=3[/tex], so the only critical point of [tex]s[/tex] is at (3, 3, 3).
Differentiate [tex]h[/tex] again and check the sign of the second derivative at the critical point.
[tex]\dfrac{d^2h}{dx^2} = -6 < 0[/tex]
for all [tex]x[/tex], which indicates a maximum.
We find that
[tex]\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)[/tex]
The second derivative at the critical point exists
[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex] for all x, which suggests a maximum.
How to find the maximum value?Given, the constraint, we have
x + y + z = 9
⇒ z = 9 - x - y
Let s depend only on x, y.
s = g(x, y)
= xy + y(9 - x - y) + x(9 - x - y)
= 9y - y² + 9x - x² - xy
To estimate the critical points of g.
[tex]$&\frac{\partial g}{\partial x}[/tex] = 9 - 2x - y = 0
[tex]$&\frac{\partial g}{\partial y}[/tex] = 9 - 2y - x = 0
Utilizing the given constraint again,
x + y + z = 2x + y
⇒ x = z
x = 9 - x - y
⇒ y = 9 - 2x, and s depends only on x.
s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²
To estimate the critical points of h.
[tex]$\frac{d h}{d x}=18-6 x=0[/tex]
⇒ x = 3
It pursues that y = 9 - 2 [tex]*[/tex] 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).
Differentiate h again and review the sign of the second derivative at the critical point.
[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex]
for all x, which suggests a maximum.
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For the rhombus, what are the slopes of the two diagonals? DO NOT introduce any new variables.
Answers
The slopes of the two diagonals of the rhombus are: A. b - f/a - e and -a + e/b - f.
What is the Slope of a Line Segment?To find the slope, the formula used is: change in y/change in x.
If two lines are perpendicular to each other, their slope values will be negative reciprocals.
What is the Diagonals of a Rhombus?In a rhombus, the two diagonals in the rhombus bisects each other at angle 90 degrees. This means that the two diagonals of a rhombus are perpendicular to each other. Therefore, the slope of the diagonals of any rhombus would be negative reciprocals.
The slope of the diagonals of the rhombus given would therefore be negative reciprocals to each other.
Given two endpoints of one of the diagonals as:
(a, b) = (x1, y1)
(e, f) = (x2, y2)
Slope (m) = change in y / change in x = b - f/a - e
The negative reciprocal of b - f/a - e is -a + e/b - f.
Therefore, the slopes of the two diagonals are: A. b - f/a - e and -a + e/b - f.
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Distance between two points
What is the length of the line?
Answers
Answer: B
Step-by-step explanation:
The horizontal change is 6.
The vertical change is 5.
So, the distance is [tex]\sqrt{6^2 + 5^2}=\sqrt{61}[/tex]
A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was 15.1 eggs. Let μ = the true mean number of eggs the chickens lay each day. Under the assumption that the true mean number of eggs is 16, 100 simulated means for samples of size 10 are shown in the dotplot. A dotplot titled mean number of eggs. A number line labeled simulated means of samples, n = 10, goes from 15.0 to 17.2. A sample mean of eggs of 15.1 or less only occurred twice. Using the dotplot, is there evidence that the chickens are laying fewer than 16 eggs? Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16. Yes, since a sample mean number of eggs of 15.1 is less than the mean number of eggs of 16, there is evidence to prove that the true mean number of eggs is less than 16. No, since a sample mean number of eggs of 15.1 is only 0.9 eggs less than a mean number of eggs of 16, there is insufficient evidence that the true mean number of eggs is less than 16. No, since a sample mean number of eggs of 15.1 never occurred in the dotplot, it is not possible that a random sample of 10 eggs will have a mean number of eggs of 15.1. Therefore, there is insufficient evidence that the true mean number of eggs is less than 16.
Answers
Given the above information, it is correct to say Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16. (Option A)
What is the explanation for the above?
Recall that the mean (statistically speaking) is a measure of central tendency of a probability distribution along median and mode.
You could also state that it is an expected value. Given that samples of actual value taken from the
Hence, since from 100 samples taken, the number of eggs of 15.1 or less occurred, then the true mean or actual mean is less than 16.
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Tami earned $20.64 in simple interest by investing a principal of $400 in a Treasury bill.
If the interest rate was 1.72%/a, for how many years did she have her investment?
Answers
The number of years she had her investment is after 3 years
How to determine the years of investment?From the question, the given parameters are:
Principal Amount, P = $400Interest Rate, r = 1.72%Simple Interest, I = $20.64The number of years (T) is calculated from the following simple interest formula
I = PRT
Substitute the given parameters in the above equation
20.64 = 400 * 1.72% * t
Express 1.72% as decimal without percentage
20.64 = 400 * 0.0172 * t
Evaluate the product
20.64 = 6.88 * t
Divide both sides by 6.88
20.64/6.88 = 6.88/6.88 * t
Evaluate the quotient
3 = t
Rewrite the equation as
t = 3
This means that she had her investment after 3 years
Hence, the number of years she had her investment is after 3 years
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Anthony travels from Newcastle to Manchester at an average speed of 65 miles per hour.
The journey takes him 2 hours and 15 minutes.
Declan makes the same journey in 2 hours and 35 minutes.
(a) Work out Declan's average speed for the journey.
Answers
Answer:
See below
Step-by-step explanation:
Distance = rate * time
= 65 m/hr * 2 1/4 hr = 146.25 miles
rate = distance / time
for Declan : rate = 146.25 miles / (2 hrs + 35/60 min) = 56.61 mph
when a fraction of 17 is taken away from 17 what remains exceeds one third of seventeen by six Using symbolic language
Answers
Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. So that the required symbolic language required in the question is: 17 - [tex]\frac{x}{17}[/tex] = [tex]\frac{17}{3}[/tex] + 6
Thus the value of x is 90[tex]\frac{2}{3}[/tex].
Fraction is a topic that deals with expressing the relationship between two numbers or terms in the form of a ratio. Some types of fractions are mixed fractions, proper fractions, and improper fractions.
Thus to express the given question in a symbolic language, let the fraction of 17 taken away be represented by x.
So that;
i. a fraction of 17 is taken away from 17 can be expressed as 17 - [tex]\frac{x}{17}[/tex].
ii. remains exceeds one-third of seventeen by six can be expressed as [tex]\frac{17}{3}[/tex] + 6
Therefore the required symbolic language to the question is:
17 - [tex]\frac{x}{17}[/tex] = [tex]\frac{17}{3}[/tex] + 6
So that,
[tex]\frac{289 - x}{17}[/tex] = [tex]\frac{17 + 18}{3}[/tex]
cross multiply to have
3(289 - x) = 17(17 + 180)
867 - 3x = 595
3x = 867 - 595
=272
x = [tex]\frac{272}{3}[/tex]
= 90[tex]\frac{2}{3}[/tex]
x = 90[tex]\frac{2}{3}[/tex]
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an angle exceeds three times its complement by 10 find it. please explain properly i will mark as brilliant
Answers
Answer:
It's supplementary angle I think
Answer:
one angle is 20° and the other is 70°
Step-by-step explanation:
Complementary angles add up to 90°.
Here it is given that an angle exceeds 3 times its complement by 10. So, we are taking the complement as x. Since it exceeds its complement 3 times, we are multiplying the complement 3 times. so we get [tex]3x[/tex].
Now we also need to add 10, so we get the final equation [tex]3x+10[/tex], which is the second angle.
As of now, first angle = x and second angle = 3x+10.
Since they are complementary angles, both angles add up to 90°
⇒ 1st angle + 2nd angle = 90°
∴ [tex]x+3x+10 = 90[/tex] [since 3x and x are like expressions, we should add 3x + x = 4x]
⇒ [tex]4x = 90 - 10[/tex] [by transposing 10 from LHS to RHS]
⇒ [tex]4x = 80[/tex]
⇒ [tex]x = \frac{80}{4}[/tex] [by transposing 4 from LHS to RHS]
⇒ [tex]x = 20[/tex]
∴The complementary angle is 20° and the given angle is [(3 × 20) + 10)] = 70°
Complete the table of inputs and outputs for the function.
f(x) = -5(x + 7)
X
-9
01
0
f(x)
0
-60
Answers
Answer:
10, -7, -35, 5
Step-by-step explanation:
f(9) = -5(-9 + 7) = 10
0 = -5(x + 7)
0 = x + 7
x = -7
f(0) = -5(0 + 7) = -35
-60 = -5(x + 7)
12 = x + 7
x = 5
What is the difference? \frac{x+5}{x+2}-\frac{x+1}{x^{2}+2x}
Answers
Answer:
Step-by-step explanation:
x² + 2x = x(x + 2)
[tex]\sf \dfrac{x +5}{x + 2}-\dfrac{x+1}{x^2+2x}=\dfrac{x + 5}{x +2}-\dfrac{x+1}{x(x+2)}[/tex]
LCM = x(x+2)
[tex]\sf =\dfrac{(x+5)*x}{(x+2)*x}-\dfrac{x+1}{x(x+2)}\\\\=\dfrac{x*x + 5*x}{x^2+2x}-\dfrac{x+1}{x^2+2x}\\\\=\dfrac{x^2+5x - (x+1)}{x^2+2}\\\\=\dfrac{x^2+5x -x - 1}{x^2+2x)}\\\\=\dfrac{x^2+4x-1}{x^2+2x}[/tex]
(06.04 MC)
If [tex]\int\limits^3_ {-2} \, [2f(x)+2]dx=18[/tex] and [tex]\int\limits^1_ {-2} \, f(x)dx =8[/tex], then [tex]\int\limits^3_ {1} \, f(x)dx[/tex] is equal to which of the following?
4
0
−2
−4
Answers
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex]\large\bm{ -4}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Before performing any calculation it's good to recall a few properties of integrals:
[tex]\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}[/tex]
[tex]\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }[/tex]
So we apply the first property in the first expression given by the question:
[tex]\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}[/tex]
And we solve the second integral:
[tex]\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }[/tex]
Then we take the last equation and we subtract 10 from both sides:
[tex]\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}[/tex]
And we divide both sides by 2:
[tex]\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}[/tex]
Then we apply the second property to this integral:
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
Then we use the other equality in the question and we get:
[tex]\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}[/tex]
We substract 8 from both sides:
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}[/tex]
• [tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}[/tex]
A two-digit number has two less units than tens. The difference
between twice the number and the number reversed is 93. Find
the number.
Answers
The required two-digit number is 75.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
let the number in tenth place be x.
And has two fewer units than tens.
= x - 2
The two-digit number can be given as
= 10x + (x - 2)
= (11x - 2)
Reversing the digits
= (x - 2)10 + x
= 11x -20
The difference between twice the number and the number reversed is 93.
[tex]2(11x - 2) - (11x - 20) = 93\\22x-4-11x+20 = 93\\11x+16 = 93\\11x = 93-16\\11x = 77\\x = 7[/tex]
Now the required two-digit number is,
= 11x -2
= 11*7 - 2
= 77 -2
= 75
Thus the required two-digit number is 75.
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Help I can’t figure out anything with this question
Answers
Answer: Look in step-by-step explanation
Step-by-step explanation:
Area has a unit of cm^2 or m^2, whilst Volume has a unit of cm^3 or m^3
Using this information, we can see that we have to square both sides of the similarity ratio for the area ratio and cube both sides of the similarity ratio for the volume ratio
For example, question 2 states that the similarity ratio is 3:6, so the area ratio is 3^2:6^2 or 9:36 and the volume ratio is 3^3:6^3 = 27:216
You can do the rest from here
What is the total number of common tangents that can be drawn to the circles?
Answers
The total number of common tangents that can be drawn to the circles is 1
What are the tangent lines?The tangent lines of a circle are the lines drawn, that touch the circle at only one point
How to determine the total number of common tangents that can be drawn to the circles?The complete question is added as an attachment
From the attached figure, we have the following highlights:
The circles have different radiiThe smaller circle is completely inside the bigger circleBoth circles have one point of intersectionThe one point of intersection is the only point where both circles can have common tangents
Since there is only one point of intersection, then the number of common tangents on the circles is 1
Hence, the total number of common tangents that can be drawn to the circles is 1
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Simplify: 9x + 2(x - 3) - 2x + 10
Answers
Answer: 9x+4
Step-by-step explanation: We take out the parentheses by multiplying both values by 2 (2 times x and 2 times 3) to get 2x-6. Now our equation is 9x+2x-6-2x+10. We can see that there is a +2x and a -2x so we just take both of them out as they cancel out each other. Now our equation is 9x -6+10. we add 10 to -6 to get +4. The result is 9x+4.
Answer:
9x + 4
Step-by-step explanation:
9x + 2x - 6 - 2x + 10
Rearranging,
=> 9x + 2x - 2x + 10 - 6
=> 9x + 4
8 -2 5\8 how do I solve this. Can u show me the steps
Answers
Answer:
= 5.375
Step-by-step explanation:
Use the algorithm method.
7 9 9 10
8 . 0 0 0
- 2 . 6 2 5
5 . 3 7 5
= 5.375
Answer:
5 3/8
Step-by-step explanation:
change it so that every number is a improper fraction and same denominator
64/8 - 21/8 = 43/8 = 5 3/8
12.Find the range, the standard deviation, and the variance for the given samples.
13. A data set has a mean of x=3905 and a standard deviation of 110.Find the z-score for each of the following
Answers
Answer:
12. standard deviation =6.22972...
. variance = 38.80952...
Draw a line between the points representing wicket 3 and wicket 9 on the diagram. Then, find the
area of the rectangle. Show your work and round your answer to the nearest hundredth.
Answers
Based on the calculations, the area of a rectangle to the nearest hundredth is equal to 1143.92 ft².
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b represents the base area.h represents the height.By drawing a line between the points representing wicket 3 and wicket 9, we can logically deduce that wicket 2 forms a perpendicular bisector. Thus, the distance between the points representing wicket 3 and wicket 9 is given by:
Distance = 1/2 × 36.77
Distance = 36.77/2
Distance = 18.39 ft.
For the height of this triangle, we would apply Pythagorean's theorem:
h² = 25.02² - 18.39²
h² = 626.0004 - 338.1921
h² = 287.8083
h = √287.8083
h = 16.97 ft.
Area of triangle = 1/2 × b × h
Area of triangle = 1/2 × 36.77 × 16.97
Area of triangle = 311.99 ft².
For area of the rectangle, we have:
Mathematically, the area of a rectangle can be calculated by using this formula;
Area = LW
Area = 36.77 × 31.11
Area = 1143.92 ft².
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A new baby grew 3/4 of an inch in June and 7/16? 4- in July. How many total inches did the baby grow during these two months?
Answers
Answer:
The baby grew 1 3/16 inches
Step-by-step explanation:
A new baby grew:
3/4 of an inch in June,7/16 of an inch in July.Total inches during two months:
3/4 + 7/16 = Fractions with different denominators3*4/(4*4) + 7/16 = Multiply the first fraction by 4 12/16 + 7/16 = Add numerators19/16 = Numerator is greater than denominator(16 + 3)/16 = Convert to mixed fraction16/16 + 3/16 = 1 + 3/16 = 1 3/16 Answer13
Company A has 800 employees, and it decides to grant each of the employees 50 share options as
part of its new rewards plan. The options are exercisable over 5 years and subject to a 3-year
service condition. The fair value of each option at the grant date is $16. The company estimates
that 80% of its employees will meet the service condition required for receiving the options.
Calculate the total share-based payment expense for Company A assuming that 80% of the
employees actually meet the service condition.
$512,000
$853,333
$341,333
$170,667
Answers
Option A. The total share expense that the company would share would be given as 512,000
What is meant by share expense?These are the necessary expenses that are needed for the smooth functioning of a particular business that are not within the confinement of the O and M agreement. It has to do with shared facilities.
How to solve for the share expenseThe total number of the employees that are knwon to satistfy condition are given as
800 * 0.8
= 640
The options that are estmated that would be exercised
This is given as the employees * share option
= 640×50
=32000.
The total shae for the company would be gotten as
= 32000× $16
This gives us $512,000.
Hence it can be concluded that the total share of the company if they have 80 percent meeting the condition is $512000.
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4. Find the number of paths between c and d in the graph of length
Answers
The number paths between c and d of length 2.
What are the number paths?A counting model is a number path. Rectangles symbolize numbers, and it is possible to count each rectangle. Like a ruler, a number line is a model of length. The length starting at zero is used to represent each integer.A number path offers a more reassuring representation of numbers, which is crucial since we want representations that constantly assist pupils in gaining confidence and correctly resolving issues.Start adding the first number in the number sentence and work your way to the right after that. Starting with the largest number in the number sentence, go to the left on the number line to subtract. Skip counting by the number you are multiplying by when you multiply.Find the number of paths between c and d in the graph of length:
The number of paths between c and d is 0.
There is the number of paths between c and d of length 2.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.
Quadratic equation8x² + 16x + 3 = 0
8x² + 16x = -3
8(x² + 2x) = -3
Using completing the square8(x² + 2x + 1) = -3 + 8
factorization8(x² + 1) = 5
(x² + 1) = 5/8
Taking the square root of both sides(x + 1) = ± √5/8
x = -1 ± √5/8
Therefore,
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
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WHEN LOIS MARTIN WAS BORN, HER FATHER DEPOSITED $2000 IN A SAVINGS
ACCOUNT IN HER NAME AT A SAVINGS AND LOAN ASSOCIATION (S&L). AT THE TIME,
THE S&L PAID 6% INTEREST COMPOUNDED SEMI-ANNUALLY. AFTER 10 YEARS, THE
S&L CHANGED TO A RATE OF 6% COMPOUNDED QUARTERLY. WHAT WAS THE
VALUE OF THE ACCOUNT AFTER 18 YEARS WHEN THE MONEY WAS WITHDRAWN TO
HELP PAY FOR HER COLLEGE EXPENSES
Answers
The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.
How are the future values determined?The future values of the savings account are calculated in two installments.
The first installment is for 10 years when the account earns 6% compounded semiannually.
Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.
Future values can be determined using the future value formula or an online finance calculator, as follows:
Data and Calculations:Investment of $2,000 for 10 years:N (# of periods) = 20 (10 years x 2)
I/Y (Interest per year) = 6%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
FV = $3,612.22
Total Interest $1,612.22
Investment of $3,612.22 for 8 years:N (# of periods) = 32 (8 years x 4)
I/Y (Interest per year) = 6%
PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)
PMT (Periodic Payment) = $0
Results:
FV = $5,816.85
Total Interest $2,204.63
Thus, the value of the account after 18 years was $5,816.85.
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(x+ 3/8 ) 2 + y 2 =1
what is the radius & units?
Answers
The radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
How to determine the radius of the circle?The circle equation of the graph is given as:
(x + 3/8)^2 + y^2 = 1
The general equation of a circle is represented using the following formula
(x - a)^2 + (y - b)^2 = r^2
Where the center of the circle is represented by the vertex (a, b) and the radius of the circle is represented by r
By comparing the equations (x - a)^2 + (y - b)^2 = r^2 and (x + 3/8)^2 + y^2 = 1, we have the following comparison
(x - a)^2 = (x + 3/8)^2
(y - b)^2 = y^2
1 = r^2
Rewrite the last equation as follows:
r^2= 1
Take the square root of both sides of the equation
√r^2 = √1
Evaluate the square root of 1
√r^2 = 1
Evaluate the square root of r^2
r = 1
Hence, the radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
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1.
Berkley is flying a kite. The string is all the way out, which means it is 425 meters away. Berkley is looking up at the kite at an angle of 42°. Berkley's dog is watching the kite too and the angle from Berkley to the dog to the kite is 87°. How would you find the distance between the kite and the dog? Is it possible? Explain your answer using the law of sines.
Answers
Using the law of sines, it is found that the distance between the kite and the dog is of 284.77 meters.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
For the situation described, we have that:
The height is opposite to the angle of 42º.The 425 meters are opposite to the angle of 87º.Hence:
[tex]\frac{\sin{42^\circ}}{h} = \frac{\sin{87^\circ}}{425}[/tex]
Applying cross multiplication:
[tex]h = 425\frac{\sin{42^\circ}}{\sin{87^\circ}}[/tex]
h = 284.77 meters.
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What is the value of 2 + (- 2/3)^2 ÷ 1/3 ?
16
3
-2
0
Answers
Answer:
3
Step-by-step explanation:
2+ (-2/3)^2 ÷ 1/3
make -2/3 postive because its being raised by an even exponent
you never divide by fractors so make 1/3 into 3 and make it multiplication
2+ (2/3)^2 × 3
raise the fraction to the power of 2
2+ (4/9)× 3
cancel out the GCF
2+ 4/3
add
10/3
simplify
3.3 ≅ 3