A vector equation of the line through (6,4.2) that is perpendicular to the lines r1(t) = (8-2t, 1+8t, 9-5t) and r2(t) = (-2t, 1, 9) is:
r(t) = <6, 4.2, z> + t<2, -5, 0>
where z is a constant that satisfies the equation:
(8-2t - 6)(2) + (1+8t - 4.2)(-5) + (9-5t - z)(0) = 0
To find the equation of the line through the given point (6,4.2) that is perpendicular to the two given lines, we need to find the direction vector of the new line that is perpendicular to both of the given lines. The direction vector is the cross product of the direction vectors of the two given lines.
After finding the direction vector, we can use it to write the vector equation of the line passing through the given point (6,4.2). The constant z is found by substituting the x and y coordinates of the given point into the equation of the line.
The final equation is a vector equation of the desired line.
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Olivia wants to record her favorite songs to one CD. The function t = 40 - 5n represents the recording time t available after n songs are recorded. Find the zero of this function. Describe what this value means in this context.
The zero of the function is 8. Because songs are countable, there will be no more room for recording after the first eight. Furthermore, there will not be enough space to finish recording the ninth song.
What is the value?The value refers to the worth of each digit in relation to its position in the number. We compute it by multiplying the digit's place and face values. Place Value + Face Value = Value.
The absolute value of 9 is represented by the symbol |9| and is equal to 9. As a result, the absolute value of 9 = |9| = 9. 5 has a place value of 500 and is in the hundreds. 4 is a tens number with a place value of 40. 8 is in the first position and has a place value of 8.
The monetary value of something in the market.A reasonable payment in the form of products, services, or cash for the item exchanged. The value of base stealing in baseball communicates nothing of value.Relative value, utility, or significanceGiven:
c = 40 - 5n
Where
c = recording time available
n = number of songs recorded
When c = 0, the
40 - 5n = 0
n = 40/5 = 8
The zero of the function is 8
Because songs are countable, it means that after 8 songs are recorded, there will be no room to record additional songs. Furthermore, there will not be enough room to finish recording the 9-th song.
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Marcie jogs each morning. The relationship between the total number of miles she jogged this week, m, to the total number of miles she jogged last week, t, is represented by the equation m = 2t . Which description best represents this situation? Marcie jogged 2 less miles last week than she jogged this week. Marcie jogged 2 more miles last week than she jogged this week. Marcie jogged three times as many miles last week as she jogged this week. Marcie jogged twice as many miles this week as she jogged this week.
Answer: Marcie jogged twice as many miles this week as she jogged last week
Step-by-step explanation:
if f(x) + x2[f(x)]5 = 34 and f(1) = 2, find f '(1).
if f(x) +\(x^{2}\) \([ f(x) ]^{5}\) = 34 and f(1) = 2, then f '(1) = - \(\frac{64}{81}\)
f ′(x )'s indicates that it is derived from f (x). The second notation is dydx. The instantaneous rate at which y changes in relation to x is shown by this notation.
f(x) + \(x^{2}\) \([ f(x) ]^{5}\) = 34
differentiate with respect to x :
f' (x) + \(x^{2}\) . 5 \([ f(x) ]^{4}\) f'(x) + \([ f(x) ]^{5}\) 2x = 0
putting x = 1
f' (1) + \(1^{2}\) . 5 \(f(1)^{4}\) f'(1) + \(f(1)^{5}\) 2(1) = 0
f' (1) + 1.5 \((2)^{4}\) f'(1) + \((2)^{5}\) . 2 = 0
f' (1) + 80 f' (1) = - 64
81 f' (1) = - 64
f' (1) = - \(\frac{64}{81}\)
thus , the f ' (1) is found.
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Please help me pretty please
Answer:
28.6
Step-by-step explanation:
Pathagorem therom
Which equation does the graph of the systems of equations solve? 2 linear graphs. They intersect at 1,4
Answer:
See below.
Step-by-step explanation:
There is an infinite n umber of systems of equations that has (1, 4) as its solution. Are you given choices? Try x = 1 and y = 4 in each equation of the choices. The set of two equations that are true when those values of x and y are used is the answer.
I need help on this please n-5>-2
Answer:
I think that it is n<3
Step-by-step explanation:
How do you write 400 in scientific notation?
Answer: 4x10^2
Step-by-step explanation:
Solve 3x – ly= 11 and -2x – 4y=-26 by elimination
If anyone can help me with this it’d be appreciated
Answer:
(5, 4 )
Step-by-step explanation:
Given the 2 equations
3x - y = 11 → (1)
- 2x - 4y = - 26 → (2)
Multiplying (1) by - 4 and adding to (2) will eliminate the y- term
- 12x + 4y = - 44 → (3)
Add (2) and (3) term by term to eliminate y
- 14x + 0 = - 70
- 14x = - 70 ( divide both sides by - 14 )
x = 5
Substitute x = 5 into either of the 2 equations and solve for y
Substituting into (1)
3(5) - y = 11
15 - y = 11 ( subtract 15 from both sides )
- y = - 4 ( multiply both sides by - 1 )
y = 4
solution is (5, 4 )
Please Help ASAP and please show your work
Answer:
C. 5x10^-10
Step-by-step explanation:
That equations answer is 5e-7, or 0.00000005, and C is equal to 0.000000005.
Irving lives in Appletown, and plans to drive along Highway 42, a straight highway that leads to Bananatown, located 143 miles east and 45 miles north. Carol lives in Coconutville, located 98 miles east and 32 miles south of Appletown. Highway 86 runs directly north from Coconutville, and junctions with Highway 42 before heading further north to Durianville. Carol and Irving are planning to meet up at park-and-ride at the junction of the highways and carpool to Bananatown. Irving leaves Appletown at 8am, driving his usual 45 miles per hour. If Carol leaves Coconutville at 9am, how fast will she need to drive to arrive at the park-and-ride the same time as Irving?
Answer:
The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time is approximately 47.188 miles per hour
Step-by-step explanation:
The given information are;
The location of Bananatown from Appletown = 143 miles east and 45 miles north
The location of Coconutville from Appletown = 98 miles east and 32 miles south
Taking Appletown as the origin, we have;
The slope, gradient of highway 42 = 45/143
The equation of a line representing highway 42 is given as follows;
y - 0 = 45/143 × (x - 0)
y = 45/143·x
Therefore, at Coconutville, where x = 98, we have, y = 45/143 × 98 ≈ 30.84 miles north
Total distance north Carol has to drive to get to highway 42 = 32 + 30.84 = 62.84 miles
Total distance along highway 42 Carol will drive to get to Bananatown = √((143 - 98)² + (45 - 30.84)²) ≈ 47.175 miles
Total distance Carol drives to Bananatown = 47.175 miles + 62.84 miles ≈ 110.015 miles
The total distance Irvin needs to drive to arrive at Bananatown = √(143² + 45²) ≈ 149.91
The total distance Irvin needs to drive to arrive at Bananatown ≈ 149.91 miles
The time it takes Irvin to arrive at Bananatown = (149.91 miles)/(45 mph) ≈ 3.33 hours
The time he arrives at Bananatown = 8 a.m. + 3.33 hours ≈ 11.33 a.m.
The time available for Carol to meet Irvin at Bananatown at exactly the same time = 11.33 a.m. - 9 a.m. = 2.33 hours
Therefore, the speed at which Carol needs to drive = (110.015 miles)/2.33 hour ≈ 47.188 miles per hour
The speed at which Carol needs to drive to meet Irvin at Bananatown at exactly the same time ≈ 47.188 miles per hour.
I need help very quickly, please!!
Answer:
32ft
Step-by-step explanation:
Tan = opp/adj
Tan(65) = n / 15
Tan(65) x 15 = n
n = 32.16 = 32ft
Answer:
32 feet
Step-by-step explanation:
Hi there!
We are given a right triangle and the angle of elevation (one of the acute angles in the triangle) as 65°, as well as one of the legs (sides that make up the right triangle) as 15
We need to find the height of the triangle.
Let's make the height of the triangle (the side we need to find) x
Since we need to find the height of the triangle, let's use tangent. As we have the angle of elevation given, we'll use that.
Recall that tangent is \(\frac{opposite}{adjacent}\)
in reference to the angle of elevation, the opposite side is x, and the adjacent side is 15
that means that:
tan(65)=\(\frac{x}{15}\)
plug tan(65) into your calculator (make sure it's on degree mode!)
tan(65)≈2.14
2.14=\(\frac{x}{15}\)
multiply both sides by 15 to clear the fraction
32.1=x
The problem asks us to round to the nearest foot, so the height of the building is 32 feet
Hope this helps! :)
20 is what percent of 52? Solve with an Equation
Answer:
38.46
Step-by-step explanation:
Percentage Calculator: 20 is what percent of 52? = 38.46.
The following data show the frequency of rainy days in a year less than 0.01 inch 165 days 0.01 -1 inch 90 days 1.01 - 5 inches 60 days 5.01 -10 inches 40 days more than 10 inches 10 days Find the mode.
The mode of a dataset is the value that appears most frequently. In this case, we need to find the interval of rainfall that occurs most frequently.
From the given data, we can see that the interval "less than 0.01 inch" has the highest frequency with 165 days. Therefore, the mode of this dataset is "less than 0.01 inch"
Effective communication is crucial in all aspects of life, including personal relationships, business, education, and social interactions. Good communication skills allow individuals to express their thoughts and feelings clearly, listen actively, and respond appropriately. In personal relationships, effective communication fosters mutual understanding, trust, and respect.
In the business world, it is essential for building strong relationships with clients, customers, and colleagues, and for achieving goals and objectives. Good communication also plays a vital role in education, where it facilitates the transfer of knowledge and information from teachers to students.
Moreover, effective communication skills enable individuals to engage in social interactions and build meaningful connections with others. Therefore, it is essential to develop good communication skills to succeed in all aspects of life.
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A retail store sells 500 jackets each month. Each jacket costs the store $99, and for holding cost purposes, the store estimates capital costs of 12%, storage costs of 10%, and risk costs of 3%. Furthermore, the store incurs annual operating expenses for purchasing in the amount of $1080 in addition to $10 for inspecting and receiving each order. If the store currently places a replenishment order of 650 jackets each time, what is the total annual holding and ordering cost? (Round your answer to the nearest integer)
Answer:
1) The total annual holding cost is $144,788
2) The annual ordering cost is $1170
Step-by-step explanation:
The parameters given are;
The number of jackets sold per month = 500 jackets
The cost of each jacket = $99
The capital cost = 12%
The storage cost = 10%
The risk cost = 3%
Annual purchasing expenses = $1080
Cost for inspecting and receiving each order = $10
Number of jackets contained in each order = 650 jackets
1) Therefore, we have;
Number of jackets sold per annum = 500 × 12 = 6,000
Number of times jackets are ordered per year = (Number of jackets sold per annum)/(Number of jackets sold per annum)
Number of times jackets are ordered per year = 6000/650 = 9.23≈9 orders
Total cost of order = 9 × 650 × 99 = $579,150
Given that the total annual holding cost = (12 + 10 + 3)% of ordering cost
Therefore, the total annual holding cost = 25% of ordering cost
the total annual holding cost = 0.25 × 579,150
The total annual holding cost = $144,787.5 ≈ $144,788
2) The annual purchasing operating expense = $1080
The total cost of inspecting the 9 orders = 9 × $10 = $90
The annual ordering cost = $1080 + $90 = $1170
When the scale factor is less than 1 The new image is?
The new image would be smaller in sample size than the original image.
For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be
(200 x 0.5) = 100 x (100 x 0.5)
= 50 pixels.
The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be
(200 x 0.75) = 150 x (100 x 0.75)
= 75 pixels.
In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.
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Suppose that the velocity
v(t)
(in meters per second) of a sky diver falling near the Earth's surface is given by the following exponential function, where time t is the time after diving measured in seconds.
v(t)=71-71e^-0.19t
How many seconds after diving will the sky diver's velocity be 59 meters per second?
Round your answer to the nearest tenth, and do not round any intermediate computations.
Approximately 9.4 seconds after diving, the sky diver's velocity will be 59 meters per second.
What is the velocity function for a sky diver falling near the Earth's surface?The velocity function for a sky diver falling near the Earth's surface is given by the exponential function \(v(t) = 71 - 71e^(-0.19t)\), where t represents the time after diving measured in seconds.
To find the number of seconds after diving when the sky diver's velocity is 59 meters per second, we need to solve the equation:
\(59 = 71 - 71e^{(-0.19t)}\)
Let's solve it step by step:
Subtracting 71 from both sides:
\(-12 = -71e^{(-0.19t)}\)
Dividing both sides by -71:
\(e^{(-0.19t)} = \frac{12}{71}\)
Taking the natural logarithm (ln) of both sides to eliminate the exponential:
\(ln(e^{(-0.19t)}) = ln(\frac{12}{71})\\-0.19t = ln(\frac{12}{71})\)
Now, we can solve for t by dividing both sides by -0.19:
\(t =\frac{ln(\frac{12}{71})}{-0.19}\)
Using a calculator or a software, we find:
t ≈ 9.356 seconds (rounded to three decimal places)
Therefore, approximately 9.4 seconds after diving, the sky diver's velocity will be 59 meters per second.
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What is the volume of this sphere? Use : 3.14 and round your answer to the nearest hundredth. 16 ft cubic feet
According to the given graph, the diameter is 16 feet long, which means the radius is 8 feet.
Let's find the volume of the sphere using the proper formula
\(\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot r^3 \\ V=\frac{4}{3}\cdot3.14\cdot(8ft)^3 \\ V\approx2,143.57ft^3 \end{gathered}\)Hence, the volume is 2,143.57 cubic feet.Solve for the unknown. rp = rq + r; Given r =40, p = 2
We have the equation:
\(rp=rq+r\)We know that r = 40 and p = 2, so we have to calculate the value of q:
First, we replace the known values and then proceed to solve the equation:
\(\begin{gathered} rp=rq+r \\ 40\cdot2=40\cdot q+40 \\ \frac{40\cdot2}{40}=\frac{40\cdot q+40}{40} \\ 2=q+1 \\ q=2-1 \\ q=1 \end{gathered}\)The value of the unknown variable q is q = 1
CRITICAL THINKING For what angle measure(s) is the tangent of an acute angle in a right triangle equal to 17 greater than 1? less than 17The tangent of an acute angle in a right triangle is equal to 1 for angle measures of:The tangent of an acute angle in a right triangle is greater than 1 for angle measures that are:than:The tangent of an acute angle in a right triangle is less than 1 for angle measures that arethan:
1. The tangent of an acute angle in a right triangle equal to 17 greater than 1 that measure angle is 57.29 degrees.
2. The tangent of an acute angle in a right triangle equal to 17 less than 1 that measure angle is 45 degrees.
3. The tangent of an acute angle in a right triangle equal to 17 equal to 1 that measure angle is 45 degrees.
In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite to the angle to the length of the adjacent side. Let us denote the acute angle by θ, the length of the side opposite to the angle by a, and the length of the adjacent side by b. Then we have:
tan(θ) = a/b
Since the angle θ is acute, we have a > 0 and b > 0. We can use the Pythagorean theorem to relate the lengths of the two sides to the length of the hypotenuse c:
a^2 + b^2 = c^2
Solving for b, we get:
\(b = \sqrt{c^2 - a^2}\)
Substituting this into the expression for tangent, we get:
tan(θ) = a/ \(\sqrt{c^2 - a^2}\)
Now, we can use the given conditions to find the possible values of the angle θ.
1. If tan(θ) is 17 greater than 1, we have:
tan(θ) > 1 and tan(θ) = 17 + 1 = 18
Using the expression for tangent above, we get:
a/sqrt(c^2 - a^2) > 1 and a/√(c^2 - a^2) = 18
Squaring both sides of the inequality and simplifying, we get:
a^2 < (c^2 - a^2) and a^2 = 324(c^2 - a^2)
Solving for a/c, we get:
a/c = √(324/325)
Since a/c is the sine of the angle θ, we have:
sin(θ) = a/c = √(324/325)
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.9999 radians or 57.29 degrees satisfies the given condition.
2. If tan(θ) is less than 1, we have:
tan(θ) < 1
Using the expression for tangent above, we get:
a/√(c^2 - a^2) < 1
Squaring both sides and simplifying, we get:
a^2 > (c^2 - a^2)
Solving for a/c, we get:
a/c > √(2)/2
Since a/c is the sine of the angle θ, we have:
sin(θ) > √(2)/2
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition.
3. If tan(θ) is equal to 1, we have:
tan(θ) = 1
Using the expression for tangent above, we get:
a/√(c^2 - a^2) = 1
Squaring both sides and simplifying, we get:
a^2 = c^2 - a^2
Solving for a/c, we get:
a/c = √(2)/2
Since a/c is the sine of the angle θ, we have:
sin(θ) = a/c = √(2)/2
Using a calculator or trigonometric table, we can find that the angle whose sine is approximately 0.7854 radians or 45 degrees satisfies the given condition. Alternatively, we can note that the angle whose tangent is equal to 1 is 45 degrees.
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Find the surface area of the compsite figure
The surface area of the composite figure is 416 in².
We have,
From the figure,
We have 10 surfaces.
Now,
There are 4 pairs of surfaces and 2 different surfaces.
1 pair is in square shape.
3 pairs in a rectangle shape.
Now,
Square shape surface area.
= 3² + 3²
= 9 + 9
= 18 in²
Rectangular surface area.
= (6 x 8) + (6 x 8) + (6 x 11) + (6 x 11) + (3 x 11) + (3 x 11)
= 56 + 56 + 66 + 66 + 33 + 33
= 310 in²
And,
Two different Surfaces area.
Both are in rectangular shape.
= (11 x 3) + (11 x (8 - 3))
= 33 + (11 x 5)
= 33 + 55
= 88 in²
Thus,
The surface area of the composite figure.
= 18 + 310 + 88
= 416 in²
Thus,
The surface area of the composite figure is 416 in².
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`h(t)=-5t^{2}+10t+3`
8w-12=-4 anyone know the answer
Answer:
w=1
Step-by-step explanation:
8w-12=-4
8w =-4+12
8w=8
8w/8=8/8
w=1
Mark as brainliest
Answer:
Well first we have to know what -12 is -4. So I know that 8 subtracting 12 is -4 already but, i am explaining to your knowlege so here I go.
What we can do is add 12 to -4 and it will equal what _-12=-4
So -4+12=8
Since the variable is with 8, we have to find what the variable w is. So 8x_=8?
Thats obvious right? 8x1=8!
So 8w-12=-4 = 8x1=8-12=-4
Hope this helps and if it helps enough pls mark as brainliest!
Step-by-step explanation:
assume a player has come up to bat and gotten two hits in a game. what is the probability that both of those hits will be homers (home runs)?
The probability that both hits in the game will be home runs is 1/100 or 0.01.
How is the probability calculated?To calculate the probability that both hits will be home runs, consider the probability of a home run and the total number of possible outcomes.
Given:
The baseball player hits a home run once in every 10 times at bat; hence, the probability of a home run is 1/10.
The player gets exactly two at-bats in every game.
Probability of a home run in one at-bat = 1/10
Probability of both hits being home runs = (1/10) * (1/10)
Probability of both hits being home runs = 1/100
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On average, suppose a baseball player hits a home run once in every 10 times at bat, and suppose he gets exactly two "at bats" in every game. assume a player has come up to bat and gotten two hits in a game. what is the probability that both of those hits will be homers (home runs)?
Anthony was asked to give the coordinates of a point located in quadrant III. He gave the ordered pair (4, –10). Which statement best describes the error that Anthony made? His coordinates are not multiples of 3. His coordinates are both nonzero. His x-coordinate is the wrong sign. His y-coordinate is the wrong sign.
2. Omar has of a pie left. He wants to share it equally among his 7 friends. How much of the pie will each
friend
friend receive? Justify you answer.
Answer:
See explanation
Step-by-step explanation:
p=1 pie
p divided by 7 is p/7 ==> 1/7
Each friend get 1/7 of the pie.
Since Omar only has half of the pie left and needs to share it equally among his 7 friends, we'll need to divide.
So, a pie has 6 pieces and Omar has only 3 pieces left.
Then, we divide 3 by 7. This gives us a REALLY long decimal so we would have to round.
The rounded answer would be 0.43.
Finally, each friend will get forty-three hundredths of the pie that is left.
The following system answer is no solution. Change one number to make the system an infinite solution and explain why it is now an infinite solution.
12y = 17 - 9x
-4y - 3x = 31
Step-by-step explanation:
The following system answer is no solution. Change one number to make the system an infinite solution and explain why it is now an infinite solution.
12y = 17 - 9x
-4y - 3x = 31
Kevin works as a busboy making $10 per hour and as a theater usher making $7 per hour. Let b be the number of hours he works as a busboy this month, and let u be the number of hours he works as an usher. His goal this month is to earn at least $1400 total. Using the values and variables given, write an inequality describing this.
The inequality for the given situation is 10b+7u≥1400.
Given that, Kevin works as a busboy making $10 per hour and as a theater usher making $7 per hour.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let b be the number of hours he works as a busboy this month, and let u be the number of hours he works as an usher.
His goal this month is to earn at least $1400 total.
So, the given inequality is 10b+7u≥1400
Therefore, the inequality for the given situation is 10b+7u≥1400.
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Anyone know how to do this?
Pls help I'll mark brainliest and it's 20 points, very important!
Melanie wants to rent a bike on her vacation for less than $50. At Mike's Bike Shop, she can rent a bike for $8 per hour plus a $6 flat fee. Any portion of an hour is charged as a full hour.
The inequality that represents this situation is 8h+6<50, where h represents the number of hours Melanie rents the bike.
What does the solution for the inequality mean in relation to the situation
The solution h<5.5 means that Melanie can rent the bike for no more than 5.5 hours.
he solution h<7 means that Melanie can rent the bike for no more than 7 hours.
The solution h<5.5 means that Melanie can rent the bike for no more than 5 hours.
Answer:
The solution h < 5.5 means that Melanie can rent the bike for no more than 5.5 hours.
Hope this helps :)
Explanation and Check part below.
Step-by-step explanation:
1. Isolate the variable by doing the inverse operation which is in this case subtracting 6 on bothsides of the equation.
8h + 6 < 50
- 6 - 6
8h < 44
2. Dive both sides of the equation by 8.
8h < 44
--- ----- <--------- fraction bar, divide
8 8
h < 5.5
i need help no links