Tthe range of the function \( y=\sec (\pi x-4 \pi)-3 \) is \((- \infty, -4] \cup [-2, \infty)\) in interval notation.
To determine the range of the function \( y=\sec (\pi x-4 \pi)-3 \), we need to find the values of \(y\) that the function can take.
First, let's consider the range of the function \(y=\sec(\theta)\). The secant function is the reciprocal of the cosine function, so the range of \(y=\sec(\theta)\) is the set of all real numbers except the values for which \(\cos(\theta)=0\). The cosine function is equal to zero at \(\theta=\frac{\pi}{2}+n\pi\), where \(n\) is an integer. Therefore, the range of \(y=\sec(\theta)\) is \((- \infty, -1] \cup [1, \infty)\).
Now, let's consider the transformation of the function. The function \( y=\sec (\pi x-4 \pi)-3 \) is a transformation of the function \(y=\sec(\theta)\) with a horizontal shift of \(4\) units to the right and a vertical shift of \(3\) units down. The horizontal shift does not affect the range of the function, but the vertical shift does. The range of the function \( y=\sec (\pi x-4 \pi)-3 \) is \((- \infty, -4] \cup [-2, \infty)\).
Therefore, the range of the function \( y=\sec (\pi x-4 \pi)-3 \) is \((- \infty, -4] \cup [-2, \infty)\) in interval notation.
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What is the solution of the inequality: b+1>-8
Answer: The answer would be b<-9 for the nonsimplified version though.
Step-by-step explanation:
b+1>-8
first, -1 from each side.
then you will have -9>b
But you are going to divide by a negative number, so you are going to flip the inequality.
( b>-9 )
I remember learning this is like 7th grade haha. Let me know if you have any questions
Darrell measured a city and made a scale drawing. The scale of the drawing was 1 inch : 4 yards. The actual width of a neighborhood park is 60 yards. How wide is the park in the drawing?
This question does not require a diagram to be drawn, so based on the scale factor or ratio of 1 inch : 4 yards and since the actual width of the neighborhood park is 60 yards, the width of the drawing is 15 inches.
What is the scale factor?The scale factor is the ratio of a scale drawing or model to the actual dimension of the object.
The scale factor is also measured as the dimension of the new shape ÷ dimension of the original shape.
The Ratio of the scale drawing = 1 inch : 4 yards
The actual width of the park = 60 yards
The scaled-down width of the drawing = 15 inches (60/4).
Thus, we can conclude that the scale drawing's width that Darrell made was 15 inches.
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A
As the side length increases by 1, the area does not increase or decrease by an equal amount.
B
As the side length increases by 1, the area increases and then decreases by an equal amount. The area increases and then decreases by an equal factor.
C
As the side length increases by 1, the area does not change.
D
As the side length increases by 1, the area increases and then decreases by an equal factor
The sοlutiοn οf the given prοblem οf area cοmes οut tο be the side length rises by 1, the area grοws and then shrinks by an equal factοr.
What precisely is an area?Calculating hοw much space wοuld be needed tο fully cοver the οutside will reveal its οverall size. When determining the surface οf such a trapezοidal fοrm, the surrοundings are additiοnally taken intο accοunt. The surface area οf sοmething determines its οverall dimensiοns. The number οf edges here between cubοid's fοur trapezοidal extremities determines hοw much water it can hοld inside.
Here,
Optiοn B
The area grοws initially and then decreases by an amοunt equivalent tο the side length multiplied by 1. The area grοws befοre decreasing by an equivalent amοunt.
This is the case because a square's surface and side length are inversely prοpοrtiοnal. Where r is the οriginal side length, the area grοws by a factοr οf (1 + 2r + r2) as the side length rises by 1.
When r is big, hοwever, the term r2 dοminates and the area increase is less nοticeable.
Eventually, as r gets clοser tο infinite, the area increases οnly marginally and eventually reaches a limit.
As a result, as the side length rises by 1, the area grοws and then shrinks by an equal factοr.
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Complete question:
Assume that y = f(x) is a rational function satisfying the following constraints: i. There is a x-intercept at x = 0, and the local approximation here is given by y = ii. There is a vertical asymptote at x = 3, with associated local approximation y 568-332 5(x-3) ili. There is a vertical asymptote at x = -2, with associated local approximation y - 2 5(x+2) iv. There is a horizontal asymptote at y = 2 Sketch and appropriately label the graph of a rational function y = f(x), that displays these four constraints.
The graph of the rational function y = f(x) is represented by the blue line on the graph above. The x-intercept is the point at which the function crosses the x-axis and is labeled (0, 0).
The vertical asymptote at x = 3 is the red line. The local approximation for the vertical asymptote at x = 3 is represented by the black line and is given by y = 568 - 332(x - 3). Similarly, the vertical asymptote at x = -2 is the purple line and the associated local approximation is given by y = -2(x + 2). Finally, the horizontal asymptote at y = 2 is the orange line.
To illustrate the graph, assume the function f(x) is the following: f(x) = (x + 2)(x - 3) / (x + 5). This function is a rational function, as it is the ratio of two polynomials, and it has the given constraints.
To graph the rational function, we begin by finding the x-intercept, which is (0, 0). Then, we look at the vertical asymptote. At x = 3, the local approximation is given by y = 568 - 332(x - 3). We solve the equation y = 568 - 332(x - 3) for x, and get x = 3, thus we mark this point on the graph as the vertical asymptote. We do the same for the vertical asymptote at x = -2 and mark this point on the graph. Finally, we draw the line for the horizontal asymptote at y = 2. This gives us the complete graph of the rational function y = f(x).
In conclusion, the graph of the rational function y = f(x) that displays the four constraints can be sketched and labeled as shown in the figure above.
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A remote controlled car travels 8 feet in 2 seconds Label the other tick marks on the double number line with equivalent rates for the constant speed of the car
The car travels 4 feet in 1 second, 16 feet in 4 seconds, 24 feet in 6 seconds, 32 feet in 8 seconds.
Describe Distance?Distance is a measure of the amount of space between two objects or points. It is the length of the shortest path between the two points, and it is typically measured in units such as meters, kilometers, miles, or feet.
In mathematics, distance is often calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The car travels 4 feet in 1 second, which is equivalent to a rate of 4 feet per second.
The car also travels 16 feet in 4 seconds, which is also equivalent to a rate of 4 feet per second.
Similarly, the car travels 24 feet in 6 seconds, 32 feet in 8 seconds, and so on, all at a constant rate of 4 feet per second.
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\( \left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right),\left(\begin{array}{l}5 \\ 0 \\ 4\end{array}\right),\left(\begin{array}{l}0 \\ 0 \\ 4\end{array}\right) \)
The cross product of the first two vectors is -60.
The given vectors are: \( \left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right),\left(\begin{array}{l}5 \\ 0 \\ 4\end{array}\right),\left(\begin{array}{l}0 \\ 0 \\ 4\end{array}\right) \).
To find the cross product of the first two vectors, we use the formula:
\(\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right) \times \left(\begin{array}{l}b_1 \\ b_2 \\ b_3\end{array}\right) = \left(\begin{array}{l}a_2b_3-a_3b_2 \\ a_3b_1-a_1b_3 \\ a_1b_2-a_2b_1\end{array}\right) \)
Plugging in the values from the given vectors, we get:
\(\left(\begin{array}{l}1 \\ 3 \\ 4\end{array}\right) \times \left(\begin{array}{l}5 \\ 0 \\ 4\end{array}\right) = \left(\begin{array}{l}(3)(4)-(4)(0) \\ (4)(5)-(1)(4) \\ (1)(0)-(3)(5)\end{array}\right) = \left(\begin{array}{l}12 \\ 16 \\ -15\end{array}\right) \)
Now, to find the dot product of this vector with the third given vector, we use the formula:
\(\left(\begin{array}{l}a_1 \\ a_2 \\ a_3\end{array}\right) \cdot \left(\begin{array}{l}b_1 \\ b_2 \\ b_3\end{array}\right) = a_1b_1 + a_2b_2 + a_3b_3 \)
Plugging in the values from the vectors, we get:
\(\left(\begin{array}{l}12 \\ 16 \\ -15\end{array}\right) \cdot \left(\begin{array}{l}0 \\ 0 \\ 4\end{array}\right) = (12)(0) + (16)(0) + (-15)(4) = -60 \)
Therefore, the final answer is -60.
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give the new coordinates of the ordered pair(7,-4) after a reflection across the x-axis?
Answer:
(7,4)
Step-by-step explanation:
Reflection across x-axis is making the y value the opposite of what it was prior. (x, y)→(x,-y)
That is the formula.
(Pls mark me brainiest if it's correct :)
find the length of wire required to fence a circular park of diameter 280m with 3 rounds
Step-by-step explanation:
To fence a circular park with 3 rounds, we need to find the total length of wire required to go around the park 3 times.
The circumference of a circle is given by the formula:
C = πd
where C is the circumference, π is the constant pi, and d is the diameter.
Substituting the given diameter of the park (280 m) into the formula, we get:
C = π * 280 m
≈ 879.65 m
So the length of wire required to fence the park once is approximately 879.65 m.
To fence the park three times, we need to multiply this length by 3:
3 rounds of wire = 3 * 879.65 m
= 2638.95 m
Therefore, the length of wire required to fence a circular park of diameter 280 m with 3 rounds is approximately 2638.95 m.
use the rule “add 8” to find the cost of 6 T-shirts. Explain how you found your answer.
Use the rule, “add 8” to find the cost of 6 T-shirts. The cost of the T-shirt is $48.
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.
We see that the price of headbands changes abruptly, going from 0 to 2, then to 4, then to 6, etc., always increasing by 2 units.
The “add 8” rule applies to the price of T-shirts because each one costs $8.
In order to determine the cost of six headbands, we then perform the following calculations:
8 + 8 + 8 + 8 + 8 + 8 = 6 x 8 = $48
We see that we can easily multiply the required quantity of T-shirts by the cost per unit of T-shirts.
Therefore, the cost of the T-shirt is $48.
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The question is incomplete, the complete question is given below:
The school store sells headbands for $2 each and T-shirts for$8 each. Write ordered pairs to compare the cost of headbands to T-shirts for 0,1,2,3,4, and 5 of each item.
Cost of Headbands ($)
0
2
4
6
8
10
Cost of T-shirts ($)
8
16
24
32
40
Ordered Pairs
(0, 0)
(2, 8)
(4, 16)
(6, 24)
(8, 32)
(10, 40)
Fill in the missing value. Input fractions as( a)/(b). (n^(2))^(2)=n Answer Check
The missing value in this equation is 4, or (4)/(1) in fraction form.
The missing value in this equation is the exponent of n in the final expression. To find this value, we can use the rule of exponents that states that when raising a power to another power, we multiply the exponents. In this case, we have (n^(2))^(2), so we multiply the exponents 2 and 2 to get a final exponent of 4. Therefore, the missing value is 4 and the equation can be written as (n^(2))^(2)=n^(4).
In fraction form, the missing value would be (4)/(1), since any whole number can be written as a fraction with a denominator of 1. So, the equation can also be written as (n^(2))^(2)=n^((4)/(1)).
Overall, the missing value in this equation is 4, or (4)/(1) in fraction form.
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Please Help! I don't understand.
Answer:
36πmm^2
Step-by-step explanation:
6mm^2=36mm
36mm×π=36πmm^2
What is the shortest network (of straight lines) connecting a given set of three points? If the three points are collinear, the answer is obvious. If not, then the answer has two parts: Let A,B and C be the three points. Then
(I) If some angle of the triangle ABC is greater than or equal to120 , the shortest network is the path along the two shortest sides of the triangle.
(II) If all angles of triangle ABC are less than 120 degrees, then construct the point S such that the three angles at S made by the lines AS ,BS and CS are equal to one another. The shortest network is the "Y-shaped" structure made up of the segments AS ,BS and CS .
Where is the point S(in relation to the vertices A ,B and C ) in the case where ABC is an equilateral triangle. What is the total length of the network in this case? How much shorter is it (percentage-wise) than the path made up of the shortest two sides?
This is shorter than the path made up of the two shortest sides by 33%.
In the case where ABC is an equilateral triangle, the point S is the center of the triangle. The total length of the network in this case is the sum of the lengths of the three sides (AS, BS, and CS) of the triangle, which is 3 times the length of a single side.
This is shorter than the path made up of the two shortest sides by 33%,
since the total length of the path made up of the two shortest sides is the sum of the lengths of the two sides, which is 2 times the length of a single side.
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if a delivery truck contains 1500 cans of soda, how many cans will contain between 11.95 and 11.98 ounces of drink?
There will be 40 cans that contain between 11.95 and 11.98 ounces of drink.
To calculate this, the total number of cans in the delivery truck must first be divided by the total range of ounces in the cans (12.00-11.95 = 0.05). 1500/0.05 = 30000.
This number is then multiplied by the range of ounces being searched for (11.98-11.95 = 0.03). 30000*0.03 = 900.
Finally, the total number of cans is divided by the total range of ounces again (12.00-11.95 = 0.05). 900/0.05 = 40 cans.
Therefore, 40 cans contain between 11.95 and 11.98 ounces of drink.
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In a Poisson distribution with µ = 7
a. What is the probability that x = 10?
b. What is the probability that x > 5?
a. The probability that x=10 in a Poisson distribution with µ = 7 is 0.0942.
b. The probability that x > 5 in a Poisson distribution with µ = 7 is 0.4790.
A discontinuous probability distribution is a Poisson distribution. It provides the likelihood that an occurrence will occur a specific number of times (k) over a predetermined period of time or place. The mean number of occurrences, denoted by the letter "lambda," is the only component of the Poisson distribution.
When a discontinuous count variable is the subject of concern, poisson distributions are used. Many financial and economic data are count variables, such as how frequently someone is laid off in a given year, which makes them amenable to study using a Poisson distribution.
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Determine if the expression -a^(2)+b^(4)-7a^(3) is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The expression -a^(2)+b^(4)-7a^(3) is a polynomial.
A polynomial is a mathematical expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The given expression satisfies all these conditions, and therefore, it is a polynomial.
The type of the polynomial is determined by the number of terms it has. In this case, the polynomial has 3 terms, so it is a trinomial.The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent is 4 (in the term b^(4)), so the degree of the polynomial is 4. Therefore, the expression -a^(2)+b^(4)-7a^(3) is a trinomial of degree 4.
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What is the current through a 2.5 ohm resistor that is connected across a 6.0 V potential difference?
The current thrοugh the 2.5 οhm resistοr is 2.4 A.
What is current?Electric current is defined as the rate οf flοw οf electric charge thrοugh any crοss-sectiοn οf a cοnductοr.
Tο calculate the current thrοugh a 2.5 οhm resistοr cοnnected acrοss a 6.0 V pοtential difference, we can use Ohm's law, which states that the current thrοugh a cοnductοr between twο pοints is directly prοpοrtiοnal tο the vοltage acrοss the twο pοints, and inversely prοpοrtiοnal tο the resistance between them. The mathematical expressiοn fοr Ohm's law is:
V = I x R
where V is the vοltage, I is the current, and R is the resistance.
We can rearrange this fοrmula tο sοlve fοr the current I:
I = V / R
Substituting the given values, we get:
I = 6.0 V / 2.5 οhm
I = 2.4 A
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Find the area of each shaded region.
The area of the shaded region which is a triangle will be 32 square inches.
What is the area?Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
From the graph, the height of the triangle is given as,
2h = L
2h = 16 inches
h = 8 inches
And the base of the triangle is half of the base of the rectangle. Then we have
b = L / 2
b = 16 / 2
b = 8 inches
Then the area of the shaded region is given as,
A = 1/2 x 8 x 8
A = 32 square inches
The area of the shaded region which is a triangle will be 32 square inches.
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cups pineapple juice 24 cups orange juice 46 cups seltzer 72 How many servings can be made from 108 cups of punch?
Answer:
First, find the total number of cups of liquid in the punch:
24 cups pineapple juice + 46 cups orange juice + 72 cups seltzer = 142 cups
Then, divide the total cups of liquid by the amount of liquid in each serving:
108 cups / 142 cups per serving = 0.76 servings
Therefore, approximately 0.76 servings can be made from 108 cups of punch.
-Three independent fair coins have been tossed. For i = 1, 2, 3 let
Xi = 1 if the ith coin landed heads and Xi = 0 otherwise. Let Y = X1 + X2 and
Z = X2 + X3.
a. Give Y and Z as functions on the sample space Ω. Determine the joint
probability mass function of (Y, Z).
b. Are Y and Z independent? Why (not)?
Answer:
a. Y = X1 + X2 = 1(Heads) + 1(Heads) = 2
Z = X2 + X3 = 1(Heads) + 1(Heads) = 2
The joint probability mass function of (Y, Z) can be determined by multiplying the individual probabilities:
P(Y, Z) = P(Y) * P(Z)
P(Y, Z) = (2/8) * (2/8) = 1/16
b. Y and Z are not independent because they both include the result of the second coin toss (X2). If X2 is heads, both Y and Z will be affected, and if X2 is tails, both Y and Z will be affected. Therefore, the outcome of one variable affects the outcome of the other, meaning they are not independent.
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A florist sells bouquets containing different flowers.
The ratio of lilies to daffodils to marigolds in a bouquet is 7f:6:2f.
What fraction of the flowers in the bouquet are daffodils?
Give your answer in its simplest form.
The fraction of the flowers in the bouquet are daffodils is 6/ 9f + 6
What is a fraction?A fraction can be defined as the part of a whole number or variable.
The different types of fractions in mathematics are;
Proper fractionsImproper fractionsMixed fractionsSimple fractionsComplex fractionsWhat is ratio?Ratio is defined as a comparison of two or more numbers indicating their sizes in relation to each other.
It shows the number of times one number contains another.
From the information given, we have that;
The ratio of lilies to daffodils to marigolds in a bouquet is 7f:6:2f.
Then, thte number of daffodils would be;
= 6/7f + f+ 2f
= 6/ 9f + 6
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you buy an nft hoping it will increase in value at a compounded rate of 8% each year. if you pay $500 for the nft now. how much do you expect it to be worth in 20 years?
Using cοmpοund interest , the tοtal wοrth after 20 years is $2,330.48.
What is cοmpοund interest?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.
Here the principal P= $500
Rate οf interest r = 8%
Number οf years = 20 years,
Nοw using cοmpοund interest fοrmula then,
=> Total amount = [tex]P(1+\frac{r}{100})^t[/tex]
=> A = [tex]500(1+\frac{8}{100})^{20}[/tex]
=> A = [tex]500(1+0.08)^{20}[/tex]
=> A = [tex]500(1.08)^{20}[/tex]
=>A = $2,330.48
Hence after 20 years , nft's total worth is $2,330.48.
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What is the Area of the triangle?
Add steps Please
0.2083335 is the Area of the triangle.
How do triangles work?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.
180 degrees is the sum of the triangle's three angles. riangle derives from the Roman word triangulus, which means "three-cornered" or "having three angles," from the roots tri-, "three," and angulus, "angle or corner."
1 ft 1 in = 12 + 1 = 13 in
the Area of the triangle = 1/2 * b * h
= 1/2 * 1 * 0.416667
= 0.416667/2
= 0.2083335
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Please help!! I'll give 20 points!
[tex]\stackrel{a}{-117}+\stackrel{b}{44}i \\\\[-0.35em] ~\dotfill\\\\ \theta =\tan^{-1}\left( \cfrac{44}{-117} \right)\implies \theta \approx 339.39^o~\hfill r=\sqrt{(-117)^2 + 44^2}\implies r=125 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o }{3} \right) +i \sin\left( \cfrac{ 339.39^o }{3} \right)\right][/tex]
[tex]5[ \cos(113.13^o) +i \sin(113.13^o)]\approx \boxed{-1.96~~ + ~~4.60i} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 699.39^o }{3} \right) +i \sin\left( \cfrac{ 699.39^o }{3} \right)\right] \\\\\\ 5[\cos(233.13^o)+i\sin(233.13^o)]\approx \boxed{-3.00~~ - ~~4.00i} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\boxed{k=2}\hspace{3em} \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 339.39^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{125} \left[ \cos\left( \cfrac{ 1059.39^o }{3} \right) +i \sin\left( \cfrac{ 1059.39^o }{3} \right)\right] \\\\\\ 5[\cos(353.13^o)+i\sin(353.13^o)]\approx \boxed{4.96~~ - ~~0.60i}[/tex]
Cube roots of complex number - 117 + 14i are,
- 1.96 + 4.60i
- 3.00 - 4.00i
4.96 - 0.60i
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Complex number is,
⇒ - 117 + 14i
Let a = - 117
b = 44
Then, tan ⁻¹ (44/117) = 339.39°
⇒ θ = 339.39°
And, r = √117² + 44² = 125
Hence, We have;
[tex]\sqrt[n]{z} = \sqrt[n]{r} [cos (x + 2\pi k/n) + i sin (x + 2\pi k/n)][/tex]
Where, k = 0,1,2, 3, ..
Now, At k = 0
[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 0/3) + i sin (339.39 + 0/n)][/tex]
= - 1.96 + 4.60i
At k = 1;
[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360/3) + i sin (339.39 + 360/n)][/tex]
= - 3.00 - 4.00i
At k = 2;
[tex]\sqrt[3]{z} = \sqrt[3]{125} [cos (339.39 + 360*2/3) + i sin (339.39 + 360*2/3)][/tex]
= 4.96 - 0.60i
Thus, All Cube roots of complex number - 117 + 14i are,
- 1.96 + 4.60i
- 3.00 - 4.00i
4.96 - 0.60i
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The relative frequency of a 6 on a biased dice is 0.25. The dice land on 6 150 times. How many times was the dice thrown?
Answer: 600
Step-by-step explanation:150=.25*X Divide both sides by .25 to get rid of it on the right and move it to the left so now 150/.25=X 600=X
When 1,250 Superscript three-fourths is written in its simplest radical form, which value remains under the radical?
2
5
6
8
We can represent 1,250 raised to the power of three-fourths as the sum of its prime factors in order to write it in the simplest radical form:
1,250 = 2 × 5 × 5 × 5 × 5
How is radical form determined?Next, we can formulate the statement as follows by using the fact that (a b)c = ac bc:
[tex](2\times5^3)^3/4 = 2^{(3/4)} \times(5^3)^{(3/4)[/tex]
Now, by using the fourth root of 53, we can simplify the statement underneath the radical:
[tex](2\times5^3)^3/4 = 2^{(3/4)} \times5^{(9/4)[/tex]
As a result, the value under the radical is 5(9/4), or the fifth root of five multiplied by nine. 5 being a prime integer prevents any further simplification of this phrase.
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Answer:
5
Step-by-step explanation:
The answer above is correct.
Solve this system of equations using the substitution method.
y = 2x+17
y = 6x - 3
Answer:
this is awnser
Step-by-step explanation:
Answer:
X=5 y=27
Step-by-step explanation:
2x+17=6x-3
Take away 2x both sides
17=4x-3
Add 3 to get x on one side
20=4x
20/4 =5
x=5
Subsitute 5 in, 6 x 5 = 30 30-3=27
Karina is making a large table in the shape of a trapezoid, as shown. She needs to calculate the area of the table. She is making the longest side of the table twice as long as the table's width. Complete parts a and b below.
The number in the bottom box is 9 yd. The number in the top is 9 yd. The area of the table is 90 yd².
Describe Trapezoid?A trapezoid is a four-sided polygon that has at least one pair of parallel sides. The legs of a trapezoid can be of different lengths, and the angles between the legs and the bases can also vary.
The formula for finding the area of a trapezoid is:
Area = ((Base 1 + Base 2) x Height) / 2
where Base 1 and Base 2 are the lengths of the parallel sides of the trapezoid, and Height is the distance between the parallel sides.
There are several types of trapezoids, including:
Isosceles Trapezoid: An isosceles trapezoid has two parallel sides of equal length and two non-parallel sides of equal length. The angles between the legs and the bases are also equal.
Right Trapezoid: A right trapezoid has one right angle between the leg and the base.
Scalene Trapezoid: A scalene trapezoid has two non-parallel sides of different lengths, and the angles between the legs and the bases are also different.
Let the number in the bottom box=
7.5*2=15 yd
Because the longest side of the table is twice as long as the table's width.
So the number in top box is :
15-3-3=9 yd
Area=( 15 + 9 )* 7.5/2 = 12* 7.5 = 90 yd²
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The complete question is:
The table gives the height $ in kilometres of a rocket t seconds after take off: 25 50 75 100 150 15 28 60 130 Remembering ut + gat? a. Find Pearson's correlation coefficient for an appropriate graph b. Find the rocket's acceleration in mls
To find Pearson's correlation coefficient, we need to first calculate the means, standard deviations, and covariance of the given data. Let's first convert the heights in km to m for ease of calculation.
t (s) h (m)
0 25,000
5 28,000
10 30,000
15 31,000
25 33,000
30 34,000
(a) Pearson's correlation coefficient:
We can use the formula
r = (nΣxy - ΣxΣy) / sqrt[(nΣx² - (Σx)²)(nΣy² - (Σy)²)]
where n is the number of data points, Σ is the sum, and x and y are the variables being compared (time and height, in this case).
Using the given data, we get:
n = 6
Σx = 85
Σy = 181000
Σx² = 1375
Σy² = 503,710,000
Σxy = 2,886,000
Substituting into the formula, we get:
r = (62,886,000 - 85181000) / sqrt[(61375 - 85²)(6503710000 - 181000²)]
r = 0.994
Therefore, Pearson's correlation coefficient is 0.994, indicating a strong positive correlation between time and height.
(b) Rocket's acceleration:
We can use the formula:
h = ut + (1/2)at²
where h is the height, u is the initial velocity (assumed to be 0), t is the time, and a is the acceleration.
Rearranging, we get:
a = 2h/t²
Using the final height of 34,000 m and the time of 30 seconds (when the rocket reaches this height), we get:
a = 2*34000/(30²)
a = 75.6 m/s²
Therefore, the rocket's acceleration is 75.6 m/s².
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The Clearwater Beach Kite Festival opened this weekend. Barbara is selling hand-painted
kites from a booth on the boardwalk. The table below shows the types of kites she has sold
so far today.
Type of kite Number sold
diamond
delta
parafoil
sled
11
9
6
4
Based on the data, what is the probability that the next kite Barbara sells will be a diamond?
Write your answer as a fraction or whole number.
The probability that the next kite Barbara sells will be a diamond is:
11/30How to find the probability that the next kite Barbara sells will be a diamondTo find the probability that the next kite Barbara sells will be a diamond, we need to divide the number of diamond kites sold by the total number of kites sold.
The formula for probability is
= required outcome (number of diamond kites) / possible outcome (total number of kites)
required outcome
The number of diamond kites sold is:
11
possible outcome
The total number of kites sold so far is:
11 + 9 + 6 + 4 = 30
Therefore, the probability that the next kite Barbara sells will be a diamond is 11/30
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The diameter of the human hair is 9x10 to the -5th power. The diameter of a spider silk is 3x10 to the -6th power. Answers in scientific notation