Answer:
soln
6+r =2r+3
6-3=2r-r
3=r
ans r=3A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,
6.7 km apart, to be 38° and 41°, as shown in the figure.
A
NOTE: The picture is NOT drawn to scale.
38°
6.7 km
41°
B
What is the elevation of the plane in meters? Give your answer to the nearest whole number.
height=
meters
Answer:
a) 4.46 miles
b) 3 miles
Step-by-step explanation:
Law of Sines:
[tex]\dfrac{\text{a}}{\text{sin(A)}} =\dfrac{\text{b}}{\text{sin(B)}}[/tex]
a) The distance of the plane from point A
The angle of depression corresponds to the congruent angle of elevation therefore, 180 - 28 - 52 = 100°
[tex]\dfrac{\text{6.7}}{\text{sin(100)}} =\dfrac{\text{b}}{\text{sin(41)}}[/tex]
[tex]\text{b}=\dfrac{6.7\text{sin}(41)}{\text{sin}(100)}[/tex]
[tex]\text{b}=4.46 \ \text{miles}[/tex]
b) Elevation of the plane
[tex]\text{sin}=\dfrac{\text{opposite}}{\text{hypotenuse}}[/tex]
hypotenuse is 4.46 and opposite is the elevation(h) to be found
[tex]\text{sin}(38)=\dfrac{\text{h}}{4.46}[/tex]
[tex]\text{h}=\text{sin}(38)4.46[/tex]
[tex]\text{h}=3[/tex]
Considering only the values of α and β for which cos(α−β)cosαcosβ is defined, which of the following expressions is equivalent to cos(α−β)cosαcosβ?
Select the correct answer below:
tanα−tanβ
1+tanαtanβ
cotαcotβ−1
cotα+cotβ
According to the given condition, the correct expressions is:
cotαcotβ−1
What is trigonometric equations?Trigonometric equations are mathematical equations that involve trigonometric functions, such as sine, cosine, tangent, cotangent, secant, or cosecant, and their variables. Trigonometric equations typically involve finding the values of the unknowns that satisfy the given equation, subject to certain restrictions or conditions on the domain of the trigonometric functions.
According to the given information:
Using trigonometric identities, we can simplify the expression cos(α−β)cosαcosβ:
cos(α−β)cosαcosβ = cos(α−β) * (cosα * cosβ)
Next, we can use the identity cos(α−β) = cosαcosβ + sinαsinβ to substitute into the expression:
cos(α−β)cosαcosβ = (cosαcosβ + sinαsinβ) * (cosα * cosβ)
Now, we can distribute and simplify:
cos(α−β)cosαcosβ = cosα² * cosβ² + sinαsinβ * cosα * cosβ
Finally, using the identity cotα = 1/tanα, we can rewrite the expression as:
cos(α−β)cosαcosβ = cotαcotβ - 1
So, the equivalent expression is cotαcotβ - 1.
Therefore, according to the given condition. The correct answer is:
cotαcotβ−1
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Helen pulls one marble out of the box at random, records its color, replaces it, and mixes up the marbles again. If she does this 200 times, how many blue marbles should she excpect to pull out?
1/2 of the marbles are yellow
1/8 of the marbles are red
The rest of the marbles are blue
Answer:
The answer to your problem is, 75
Step-by-step explanation:
Yellow = [tex]\frac{1}{2}[/tex] of the marbles
Red = [tex]\frac{1}{8}[/tex] of the marbles
Blue = [tex]1 - \frac{1}{2} - \frac{1}{8} = \frac{1}{2} - \frac{1}{8}[/tex]
= [tex]\frac{1*4}{2*4} - \frac{1}{8}[/tex]
= [tex]\frac{1}{2} or \frac{4}{8} - \frac{1}{8}[/tex]
= [tex]\frac{3}{8}[/tex]
[tex]\frac{3}{8}[/tex] of the marbles are represented as blue.
200 x [tex]\frac{3}{8}[/tex] = 25 x 3 = 75
Thus the answer to your problem is, 75
What is the slope of a line that passes through the points (-2,4) and (-6,12)
In golf, scores that are under par for the entire round are shown as negative scores; positive scores are shown for scores that are over par, and 0 is par. Player A was the winner of the 2014 golf tournament. Her scores were -4 ,-4 ,-4 , and -3 . What was her overall score?
the overall score of Player A in the 2014 golf tournament was -15.
In golf, scores that are below par are represented with negative numbers. Therefore, to calculate the overall score, we need to add up all the scores.
Let's call the scores for each round A1, A2, A3, and A4, respectively. We can write the given scores as:
A1 = -4
A2 = -4
A3 = -4
A4 = -3
To find the overall score, we add up all the scores:
Overall score = A1 + A2 + A3 + A4
Overall score = (-4) + (-4) + (-4) + (-3)
Overall score = -15
Therefore, the overall score of Player A in the 2014 golf tournament was -15.
It's worth noting that in golf, the winner is the player who has the lowest score or the most negative score. So, in this case, Player A had the lowest score, making her the winner of the tournament.
In general, the overall score in golf can be calculated by adding up the scores for each hole or round. The player with the lowest score at the end of the tournament is declared the winner. Scores can be compared between different golfers or rounds, regardless of the difficulty of the course or weather conditions, by using the number of strokes above or below par.
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can you solve this question?
y'=?
The solution of given derivative of y = √(arctan(x)) is:
Y' = 1 / (2√arctan(x)(1 + x²))
What do you mean by Differentiate ?In general, the term "differentiate" means to distinguish or recognize the differences between two or more things or concepts.
In mathematics, differentiation refers to the process of finding the rate at which a function changes with respect to one of its variables. It is a fundamental concept in calculus and involves calculating the derivative of a function. The derivative gives us the slope of a tangent line to the curve of the function at a specific point
To differentiate Y = √arctan(x), we need to use the chain rule and the formula for differentiating the arctan function, which is:
d/dx arctan(x) = 1 / (1 + x²)
Using the chain rule, we have:
Y = √arctan(x)
Y = [tex](arctan(x))^(1/2)[/tex]
Y' =[tex](1/2)(arctan(x))^(-1/2) * d/dx (arctan(x))[/tex]
Y' = [tex](1/2)(arctan(x))^(-1/2) * (1 / (1 + x^{2} ))[/tex]
Putting it all together, we have:
Y' = (1 / 2√arctan(x)) * (1 / (1 + x²))
Simplifying the expression, we get:
Y' = 1 / (2√arctan(x)(1 + x²))
Therefore, the derivative of Y = √arctan(x) is:
Y' = 1 / (2√arctan(x)(1 + x²))
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At the beginning of the school year, Ms. Lopez asks her students to select 4 books to read
from a list of 20 books.
a. How many different groups of 4 books can be selected?
b. How many different ways can 4 books be selected if the books must be listed in order of
preference?
Answer:
Step-by-step explanation:
A] five as 20 divided by four is five
Select the correct answer.
Which statement about the end behavior of the logarithmic function f(x) = log(x + 3) – 2 is true?
A.
As x decreases to the vertical asymptote at x = -3, y decreases to negative infinity.
B.
As x decreases to the vertical asymptote at x = -1, y decreases to negative infinity.
C.
As x decreases to the vertical asymptote at x = -3, y increases to positive infinity.
D.
As x decreases to the vertical asymptote at x = -1, y increases to positive infinity.
the correct answer is A: as x decreases to the vertical asymptote at x = -3, y decreases to negative infinity.
To determine the end behavior of the logarithmic function f(x) = log(x + 3) - 2, we need to look at what happens to the function as x approaches positive and negative infinity.
As x approaches negative infinity, the argument of the logarithm, (x + 3), becomes more and more negative. However, since logarithms are not defined for negative arguments, we need to shift the graph of the function to the left by 3 units to avoid the undefined region. This means that the vertical asymptote of the function is at x = -3. As x approaches -3 from the left, the argument of the logarithm becomes smaller and smaller negative numbers. However, the logarithm of a small negative number is a large negative number. Therefore, as x approaches -3 from the left, the function f(x) = log(x + 3) - 2 decreases to negative infinity. This eliminates options C and D.
As x approaches positive infinity, the argument of the logarithm, (x + 3), becomes more and more positive. Therefore, as x approaches positive infinity, the logarithm of (x + 3) becomes larger and larger. This means that the function f(x) = log(x + 3) - 2 approaches infinity as x approaches positive infinity. However, it approaches infinity from below since we subtract 2 from the logarithmic value.
To summarize, as x approaches -3 from the left, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches infinity from below. Therefore, the correct answer is A: as x decreases to the vertical asymptote at x = -3, y decreases to negative infinity.
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I cant seem to figure out this answer. Can anyone help?
A company makes wax candles in the shape of a solid sphere. Suppose each candle has a diameter of 18 cm. If the company has a total of 152,604 cm³ of w
how many candles can be made?
Use 3.14 for x, and do not round your answer.
Answer:
50 spherical candles can be made with 152,604 cm³ of wax.
Step-by-step explanation:
Since the wax candles are in the shape of a solid sphere, we can calculate the volume of one candle by using the volume of a sphere formula.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
The diameter of a sphere is twice its radius.
Therefore, if the diameter of the spherical candle is 18 cm, its radius is:
[tex]\implies r=\dfrac{d}{2}=\dfrac{18}{2}=9\; \sf cm[/tex]
Substitute r = 9 and π = 3.14 into the formula to calculate the volume of one spherical candle.
[tex]\begin{aligned}\implies \textsf{Volume of one candle}&=\sf \dfrac{4}{3} \cdot 3.14 \cdot (9\;cm)^3\\\\&=\sf \dfrac{4}{3} \cdot 3.14 \cdot 729\;cm^3\\\\&=\sf 3052.08\; \sf cm^3\end{aligned}[/tex]
Given the company has a total of 152,604 cm³ of wax, to calculate how many candles can be made, divide the total amount of available wax by the wax needed to make one candle.
[tex]\begin{aligned}\textsf{Total number of candles}&=\sf \dfrac{152604\; cm^3}{3052.08 \;cm^3}\\\\&=\sf 50\end{aligned}[/tex]
Therefore, 50 spherical candles can be made with 152,604 cm³ of wax.
unfortunately, the set up of these problems is very confusing for me because they keep altering and changing per problem
Answer:
2292.03
Step-by-step explanation:
Start with the formula for continuously compounded interest.
Then substitute all given values in the formula.
Finally, solve for the only variable remaining.
[tex] A = Pe^{rt} [/tex]
A = future value = $5000
P = principal (deposited amount) = unknown
r = 6.5% = 0.065
t = time = 12 years
[tex] 5000 = Pe^{0.065 \times 12} [/tex]
[tex] 5000 = Pe^{0.78} [/tex]
[tex]5000 = P \times 2.18147[/tex]
[tex] P = \dfrac{5000}{2.18147} [/tex]
[tex] P = 2292.03 [/tex]
Answer: $2292.03
Answer:
P = $2366.91
(maybe try answering without a comma)
Step-by-step explanation:
The formula for continuous compounding is:
A = Pe^(rt)
Where:
A = final amount
P = principal amount (initial deposit)
e = Euler's number (approximately 2.71828)
r = annual interest rate (as a decimal)
t = time (in years)
We are given:
r = 6.5% = 0.065 (annual interest rate)
t = 12 years
A = $5000 (final amount)
So we can rearrange the formula to solve for P:
P = A / e^(rt)
Substituting the values:
P = 5000 / e^(0.065*12)
P = $2366.91 (rounded to the nearest cent)
Therefore, you would need to deposit $2366.91 in an account with a 6.5% interest rate, compounded continuously, to have $5000 in your account 12 years later.
Speed limit of 45 mph is equivalent to 72 km an hour. a sign says speed limit is 90 km an hour. what is the speed limit in miles per hour?
The required answer is the speed limit of 90 km/h is equivalent to approximately 56 mph.
To convert the speed limit from kilometers per hour (km/h) to miles per hour (mph), use the conversion factor of 1 km/h = 0.621371 mph. Let's follow these steps:
Step 1: Determine the conversion factor.
Since we know the conversion factor is 1 km/h = 0.621371 mph, use this to convert the speed limit from km/h to mph.
Step 2: Calculate the speed limit in mph.
The given speed limit is 90 km/h. Multiply this value by the conversion factor to obtain the equivalent speed in mph:
90 km/h x 0.621371 mph/km/h = 55.92339 mph
Step 3: Round the result, if necessary.
To provide a practical speed limit, we can round the result to the nearest whole number. Therefore, the speed limit in miles per hour is approximately 56 mph.
Hence, the speed limit of 90 km/h is equivalent to approximately 56 mph.
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Whish of the following are necessary when proving that the angles of a parallelogram are congruent
D. Angle Addition Postulate is necessary when proving that the angles of a parallelogram are congruent.
What is parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.
To prove that opposite angles of a parallelogram are congruent, we need to use the properties of parallelograms, such as opposite sides are parallel and congruent, opposite angles are congruent, consecutive angles are supplementary, and diagonals bisect each other.
We do not need the Segment Addition Postulate, as it is used to find a length of a segment, not to prove the congruence of angles.
We also do not need to use the Opposite sides are perpendicular property, as this is only true for a rectangle or a rhombus, but not necessarily for a parallelogram.
Similarly, the Angle Addition Postulate is used to find the measure of an angle, not to prove that angles are congruent.
Therefore, the only necessary property to prove that opposite angles of a parallelogram are congruent is that opposite angles are congruent, which is a property of parallelograms.
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In a marriage ceremony of Pemba's daughter, he has to make arrangement for accommodation of 150 persons. For this purpose he plans to build a conical tent in such a way that each person has 4 sq.m. of the space on ground and 20 cu.m. of air to breadth. What should be the height of the tent? Find it.
Answer:
This is the answer of that question
Ayudaaaa necesito sacar los límites!!!
Debido a restricciones de longitud, los límites de la función aparecen descritos en la explicación de esta pregunta.
¿Cómo determinar los limites de una función?
En este problema debemos determinar los límites de un punto y los límites laterales de la función. El limite de un punto se determina mediante la evaluación directa de la función, mientras los límites laterales de la función se determinan viendo a que valor tiende la función.
A continuación, determinamos los límites de las funciones:
Caso 1:
Subcaso A (x = 1)
f(x) = - 1
Subcaso B (x = 5)
f(x) = 1
Subcaso C (x = 3⁻)
f(x) → - ∞
Subcaso D (x = 3⁺)
f(x) → + ∞
Subcaso E (x = 3)
No existe
Case 2:
Subcaso A (x = 0)
f(x) = 0
Subcaso B (x = - 2)
f(x) = 0.5
Subcaso C (x = 3⁻)
f(x) → - ∞
Subcaso D (x = - 3⁺)
f(x) → + ∞
Subcaso E (x = - 3)
No existe
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Find areas of the trapezoids.
(I'm giving 100 points to whoever answers.)
Answer:
a) Area of STAR = 48 square units
b) Area of SKCO = 42 square units
Step-by-step explanation:
The formula for the area of a trapezoid is half the sum of the bases multiplied by the height:
[tex]\boxed{\sf Area=\dfrac{a+b}{2} \cdot h}[/tex]
The bases of a trapezoid are the parallel sides.
The height of a trapezoid is the perpendicular distance between the two bases.
a) Trapezoid STARThe bases are parallel sides SR and TA.
The height is the perpendicular distance between SR and TA.
Therefore:
a = SR = 4 unitsb = TA = 8 unitsh = 8 unitsSubstitute these values into the formula and solve for area:
[tex]\begin{aligned}\sf \implies Area\;STAR&=\dfrac{4+8}{2} \cdot 8\\\\&=\dfrac{12}{2} \cdot 8\\\\&=6\cdot 8\\\\&=48\;\sf square\;units\end{aligned}[/tex]
b) Trapezoid SKCOThe bases are parallel sides SK and OC.
The height is the perpendicular distance between SK and OC.
Therefore:
a = SK = 4 unitsb = OC = 10 unitsh = 6 unitsSubstitute these values into the formula and solve for area:
[tex]\begin{aligned}\sf \implies Area\;SKCO&=\dfrac{4+10}{2} \cdot 6\\\\&=\dfrac{14}{2} \cdot 6\\\\&=7 \cdot 6\\\\&=42\;\sf square\;units\end{aligned}[/tex]
Find the lateral surface area of the prism
The lateral surface area of the triangular prism is 275.5 sq. mm.
What is lateral surface area?"Being to the side" is the definition of the term "lateral." A triangular prism's lateral area is equal to the sum of its side faces' areas (which are 3 rectangles). Specifically, it is the total surface area less the surface areas of the two bases. Also called the lateral surface area (LSA). Due to the two dimensions involved in its calculation, we measure it in square units.
The lateral surface area of the triangular prism is given as:
LSA = (a + b + c)h
Here, the value of a = 7.5, b = 10.5, and c = 11mm, and h = 9.5mm.
Substitute the values:
LSA = (7.5 + 10.5 + 11) (9.5)
LSA = 275.5 sq. mm
Hence, the lateral surface area of the triangular prism is 275.5 sq. mm.
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how create the own congruent postulate sss
Step-by-step explanation:
The SSS (Side-Side-Side) Congruence Postulate states that if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.
To create your own SSS Congruence Postulate, you could use the following statement:
"If the corresponding sides of two triangles are congruent, then the triangles are congruent."
This postulate would encompass the SSS Postulate, as well as two other postulates: the SAS (Side-Angle-Side) Postulate and the ASA (Angle-Side-Angle) Postulate.
Using this postulate, you could show that two triangles are congruent if, for example, their corresponding sides are all 5cm long. This would mean that the triangles have the same shape and size, even if they are oriented differently.
Hopes this helps
Which steps can be used to solve for the value of y?
2/3 (y+57)=178
A. Divide both sides by 2/3, then subtract 57 from both sides.
B. Subtract 57 from both sides, then divide both sides by 2/3.
C. Multiply both sides by 2/3, then subtract 57 from both sides.
D. Subtract 2/3 from both sides, then subtract 57 from both sides.
Margo borrows $1400, agreeing to pay it back with 5% annual interest after 17 months. How much interest will she pay? Round your answer to the nearest cent, if necessary.
well, let's keep in mind that since a year has 12 months, then 17 months is really 17/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1400\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &\frac{17}{12} \end{cases} \\\\\\ I = (1400)(0.05)(\frac{17}{12}) \implies I \approx 99.17[/tex]
A volcano on a recently discovered planet rises to a height of 69,657.652 ft.
Use the table of facts to find the height of the volcano in miles.
Round your answer to the nearest tenth.
Answer:
13.2 miles
Step-by-step explanation:
We can use the following conversion factors:
1 mile = 5,280 feet
Using this conversion, we can divide the height of the volcano in feet by 5,280 to get the height in miles:
69,657.652 ft ÷ 5,280 ft/mi ≈ 13.2 mi
Therefore, the height of the volcano on the recently discovered planet is approximately 13.2 miles.
Hopes this helps
need help with this problem
Answer:
area=28cm^2
Step-by-step explanation:
4×5=20
20÷2=10 area of the bigger triangle
4×2=8
8÷2=4 area of the smaller triangle
10+10=20 for area of the the 2 bigger triangles
4+4=8 for the area of the 2 smaller triangles
area of kite= 20+8= 28
I’m terrible with this stuff please help
As, a1/a2 = b1/b2 = c1/c2 = 2 .Thus, the given system of equations forms the identical lines.
Explain about the solution of system of equations:A list of numbers x, y, z, etc. that simultaneously make all of the equations true is the solution of a system of equations. A system of equations' solution set is the whole of all possible answers. Finding all answers using formulas containing a certain number of parameters is known as solving the system.
For the given system of equations:
6x - y - 2 = 0
here, coefficients a1 = 6, b1 = -1 and constant c1 = -2
Now,
3x - 1/2y - 1 = 0
here, coefficients a2 = 3, b2 = -1/2 and constant c2 = -1
taking the ratios:
a1/a2 = 6/3 = 2
b1/b2 = -1/(-1/2) = 2
c1/c2 = -2/(-1) = 2
As, a1/a2 = b1/b2 = c1/c2 = 2 .Thus, the given system of equations forms the identical lines.
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T
√
Guided Instruction: Measures of Arcs and Central Angles
X
A
Undo (Ctrl + Z)
Circle G has radii GH and GK. Find the value of x if
m2KGH = 122° and mKH = (5x + 7)⁰.
3
Submit
15 of 21
On solving the provided question we can say that As a result, the value angles of x is 23.
what are angles?An angle is a shape in Euclidean geometry that is made up of two rays that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are located. When two planes collide, an angle is generated. They are referred to as dihedral angles. An angle in plane geometry is a possible configuration of two radiations or lines that express a termination. The word "angle" comes from the Latin word "angulus," which meaning "horn." The vertex is the place where the two rays, also known as the angle's sides, meet.
m(arc GH) = 122° plus 5x plus 7
5x + 129 = m(arc GH)
When we plug this into the equation we discovered earlier, we get:
5x + 7 = ½
(5x + 129)
10x + 14 = 5x + 129
5x = 115
x = 23
As a result, the value of x is 23.
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3
Select the correct answer.
Which phase of the business cycle would be marked by an increase in productivity while employment and profits also rise?
Answer:
The phase of the business cycle that would be marked by an increase in productivity while employment and profits also rise is known as the Expansion phase.
can you solve this question?
dy/dx=?
The solution of the equation is: dy/dx = -3[tex]e^{3x}[/tex]/ √(1-[tex]e^{6x}[/tex])
What is the solution?
Let's start by using the chain rule to find dy/dx:
dy/dx = dy/du * du/dx
where u = [tex]e^{3x}[/tex]
We can find du/dx using the power rule:
du/dx = 3[tex]e^{3x}[/tex]
Now we need to find dy/du. We can use the derivative of arccos function:
dy/du = -1/√(1-u²)
Substituting u = [tex]e^{3x}[/tex], we get:
dy/dx = dy/du * du/dx
dy/dx = -1/√(1-[tex]e^{6x}[/tex]) * 3[tex]e^{3x}[/tex]
So the final answer is:
dy/dx = -3[tex]e^{3x}[/tex] / √(1-[tex]e^{6x}[/tex])
what is chain rule?
The chain rule is a fundamental rule of calculus that allows you to find the derivative of a composite function. A composite function is a function that is formed by taking one function and plugging it into another function.
For example, if we have two functions f(x) and g(x), the composite function is defined as:
h(x) = f(g(x))
To find the derivative of the composite function h(x), we use the chain rule, which states that:
h'(x) = f'(g(x)) * g'(x)
In words, this means that to find the derivative of the composite function, we first take the derivative of the outer function f(x) with respect to its input, evaluated at the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to its input.
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Complete question is: dy/dx = -3[tex]e^{3x}[/tex]/ √(1-[tex]e^{6x}[/tex])
Find a5 and a-n for the geometric sequence with a1=7, r= -3
Answer:
an = 7·(-3)^(n -1)a5 = 567Step-by-step explanation:
You want the 5th term and the general term of an geometric sequence with a1 = 7 and r = -3.
General termThe general term of an arithmetic sequence is ...
an = a1·r^(n-1)
For a1=7 and r=-3, the general term is ...
an = 7·(-3)^(n-1)
Fifth termUsing n=5, the above equation evaluates to ...
a5 = 7·(-3)^(5 -1)
a5 = 7·(-3)^4 = 7·81
a5 = 567
identify the two forms of the simplified expression: x^5/x^10
Use the words exponent, numerator (top) and denominator (bottom) in your description
Please help.
The expression [tex]x^{5}[/tex]/[tex]x^{10}[/tex] can be written in two forms: Exponent form, which is simplified and has a base of x, and Fraction form, which has a numerator and denominator separated by a horizontal line.
What is an exponent form?Exponents are a shortened notation for repeated multiplication of a number, and exponent form is a means of formulating a mathematical equation using exponents. A superscript (a little raised number) is written to the right of a number or variable that has been raised to a power in exponent form.
There are two distinct but equal ways to write the expression "[tex]x^{5}[/tex]/[tex]x^{10}[/tex]":
Exponent form: In this format, the exponents of the equation are consolidated and made simpler. We may subtract the exponents in the denominator from the exponents in the numerator since the bases of the numerator and denominator are both x:
[tex]x^5/x^10 = x^(5-10) = x^(-5)[/tex]
Fraction form: In this format, the equation is expressed as a fraction with a horizontal line between the numerator and denominator. X is increased to the fifth power in the denominator and to the tenth power in the numerator:
[tex]x^5/x^10[/tex]
X is increased to the fifth power, or x, in the numerator. X is multiplied by 10 to create the denominator, or [tex]x^{10}[/tex].
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The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 117 and standard deviation of 22 .
Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.
a. Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer rounded to two decimal places.
b.
b. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue!
C. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places.
According to the question we can say that the area to the right of z = 2.00 is 0.0228 or 2.28%.
a. To find the percentage of adults in the USA with stage 2 high blood pressure, we need to find the area under the normal distribution curve to the right of 160.
Using a standard normal distribution table or a statistical software, we can find that the z-score corresponding to 160 systolic blood pressure is:
z = (160 - 117) / 22 = 2.00
The area to the right of z = 2.00 is 0.0228 or 2.28%. Therefore, around 2.28% of adults in the USA have stage 2 high blood pressure.
b. To find how many people out of a sample of 2000 would be expected to have systolic blood pressure greater than 160, we can use the same z-score from part (a) and the standard normal distribution formula:
z = (x - μ) / σ
Rearranging the formula to solve for x, we get:
x = z * σ + μ
Substituting the values, we get:
x = 2.00 * 22 + 117 = 161.4
So the expected number of people with systolic blood pressure greater than 160 out of a sample of 2000 is:
2000 * (1 - P(Z < 2.00)) = 2000 * (1 - 0.9772) = 45.6
Rounding up, we can expect about 46 people to have systolic blood pressure greater than 160 out of a sample of 2000.
c. To find the percentage of adults in the USA who qualify for stage 1 high blood pressure, we need to find the area under the normal distribution curve between 140 and 160.
Using the standard normal distribution formula and z-scores, we get:
z1 = (140 - 117) / 22 = 1.05
z2 = (160 - 117) / 22 = 1.95
Using a standard normal distribution table or a statistical software, we can find the area to the left of z1 and z2, and then subtract the two areas to get the area between z1 and z2:
P(z1 < Z < z2) = P(Z < z2) - P(Z < z1) = 0.9744 - 0.8531 = 0.1213
Therefore, approximately 12.13% of adults in the USA qualify for stage 1 high blood pressure.
d. To find the systolic blood pressure corresponding to the 30th percentile, we need to find the z-score that has an area of 0.30 to its left.
Using a standard normal distribution table or a statistical software, we can find the z-score that corresponds to the area 0.30:
z = -0.52
Using the standard normal distribution formula and the given mean and standard deviation, we can solve for the systolic blood pressure:
x = z * σ + μ = -0.52 * 22 + 117 = 105.16
Therefore, if you are in the 30th percentile for blood pressure among US adults, your systolic blood pressure is approximately 105.16.
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Write the following as an algebraic expression in u, u > 0. sin (artan u/ square root 3)
Answer: Let's start by using the identity:
tan(arctan(x)) = x
to simplify the expression inside the sine function. So, we have:
arctan(u) / sqrt(3) = tan(arctan(u) / sqrt(3))
Now, using the trigonometric identity:
tan(x/y) = sin(x) / (cos(y) + sin(y))
with x = arctan(u) and y = sqrt(3), we get:
tan(arctan(u) / sqrt(3)) = sin(arctan(u)) / (cos(sqrt(3)) + sin(sqrt(3)))
Simplifying further, we know that:
sin(arctan(u)) = u / sqrt(1 + u^2)
and
cos(sqrt(3)) + sin(sqrt(3)) = 2cos(sqrt(3) - pi/4)
So, the expression becomes:
sin(arctan(u) / sqrt(3)) = u / sqrt(1 + u^2) / [2cos(sqrt(3) - pi/4)]
Simplifying the denominator, we have:
sin(arctan(u) / sqrt(3)) = u / sqrt(1 + u^2) / (2(cos(sqrt(3))cos(pi/4) + sin(sqrt(3))sin(pi/4)))
Using the values for cosine and sine of pi/4, we get:
cos(pi/4) = sin(pi/4) = 1/sqrt(2)
So, we have:
sin(arctan(u) / sqrt(3)) = u / sqrt(1 + u^2) / [2(sqrt(3)/2 + 1/2)]
Simplifying further:
sin(arctan(u) / sqrt(3)) = u / (sqrt(1 + u^2) * (sqrt(3) + 1))
Therefore, the algebraic expression for sin(arctan(u) / sqrt(3)) is:
u / (sqrt(1 + u^2) * (sqrt(3) + 1))
Step-by-step explanation:
A ship is 115 miles from one radio transmitter and 140 miles from another transmitter. If the angle between the signals is 132°, how far apart are the transmitters? Round to the nearest tenth.
The transmitters are approximately 115.1 miles apart.
How to find how far apart are the transmittersThis is a trigonometry problem that can be solved using the Law of Cosines.
We can use the law of cosines to solve this problem. Let's call the distance between the transmitters "d". Then we have:
d^2 = 115^2 + 140^2 - 2(115)(140)cos(132°)
d^2 = 13212.4
d ≈ 115.1 miles (rounded to the nearest tenth)
Therefore, the transmitters are approximately 115.1 miles apart
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