Start with
[tex]\vec v=x\,\vec\imath+y\,\vec\jmath[/tex]
as a template for the vector [tex]\vec v[/tex]. Its magnitude is 4, so
[tex]\|\vec v\|=\sqrt{x^2+y^2}=4[/tex]
Its component in the [tex]\vec\imath[/tex] direction is twice the component in the [tex]\vec\jmath[/tex] direction, which means
[tex]x=2y[/tex]
So we have
[tex]\sqrt{(2y)^2+y^2}=\sqrt{5y^2}=4\implies y^2=\dfrac{16}5\implies y=\pm\dfrac4{\sqrt5}[/tex]
and
[tex]x=\pm\dfrac8{\sqrt5}[/tex]
Lastly, rationalize the denominator:
[tex]\dfrac1{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{\sqrt5}5[/tex]
So we end up with two possible answers,
[tex]\vec v=\pm\left(\dfrac{8\sqrt5}5\,\vec\imath+\dfrac{4\sqrt5}5\,\vec\jmath\right)[/tex]
Final answer:
The vector v with a magnitude of 4 and i-component being twice the j-component can be found by solving for y in the equation of magnitude based on the given conditions and then determining the i and j components accordingly. The result is the vector v = (8√5 i + 4√5 j) / 5.
Explanation:
To find a vector v whose magnitude is 4, and whose i-component is twice its j-component, we can let the i-component be 2y and the j-component be y. Using the Pythagorean theorem for two-dimensional vectors, we can write the equation for magnitude as v = √((2y)^2 + y^2). Given that the magnitude is 4, the equation becomes:
4 = √(4y^2 + y^2)
4 = √(5y^2)
16 = 5y^2
y^2 = ⅔
y = √(⅔)
y = √(⅔)
y = √(⅔)
y = √(⅔)
y = √(⅔)
y = √(⅔)
(2.0 s) gives us the direction in unit vector notation. The magnitude of the acceleration is à(2.0 s)| = √√5.0² + 4.0² + (24.0)² = 24.8 m/s².
Using the value of y we calculated, the components of vector v are:
i-component = 2y = 2(⅔) = 8√5 / 5
j-component = y = ⅔ = 4√5 / 5
So the vector v can be expressed as v = (8√5 i + 4√5 j) / 5.
Question 1 Find the maximum value of the function for the polygonal convex set determined by the given system of inequalities
Answer:
The maximum value is 126 occurs at (9 , 9)
Step-by-step explanation:
* Lets remember that a function with 2 variables can written
f(x , y) = ax + by + c
- We can find a maximum or minimum value that a function has for
the points in the polygonal convex set
- Solve the inequalities to find the vertex of the polygon
- Use f(x , y) = ax + by + c to find the maximum value
∵ 8x + 2y = 36 ⇒ (1)
∵ -3x + 6y = 27 ⇒ (2)
- Multiply (1) by -3
∴ -24x - 6y = -108 ⇒ (3)
- Add (2) and (3)
∴ -27x = -81 ⇒ divide both sides by -27
∴ x = 3 ⇒ substitute this value in (1)
∴ 8(3) + 2y = 36
∴ 24 + 2y = 36 ⇒ subtract 24 from both sides
∴ 2y = 12 ⇒ ÷ 2
∴ y = 6
- One vertex is (3 , 6)
∵ 8x + 2y = 36 ⇒ (1)
∵ -7x + 5y = -18 ⇒ (2)
- Multiply (1) by 5 and (2) by -2
∴ 40x + 10y = 180 ⇒ (3)
∴ 14x - 10y = 36 ⇒ (4)
- Add (3) and (4)
∴ 54x = 216 ⇒ ÷ 54
∴ x = 4 ⇒ substitute this value in (1)
∴ 8(4) + 2y = 36
∴ 32 + 2y = 36 ⇒ subtract 32 from both sides
∴ 2y = 4 ⇒ ÷ 2
∴ y = 2
- Another vertex is (4 , 2)
∵ -3x + 6y = 27 ⇒ (1)
∵ -7x + 5y = -18 ⇒ (2)
- Multiply (1) by 7 and (2) by -3
∴ -21x + 42y = 189 ⇒ (3)
∴ 21x - 15y = 54 ⇒ (4)
- Add (3) and (4)
∴ 27y = 243 ⇒ ÷ 27
∴ y = 9 ⇒ substitute this value in (1)
∴ -3x + 6(9) = 27
∴ -3x + 54 = 27 ⇒ subtract 54 from both sides
∴ -3x = -27 ⇒ ÷ -3
∴ x = 9
- Another vertex is (9 , 9)
* Now lets substitute them in f(x , y) to find the maximum value
∵ f(x , y) = 9x + 5y
∴ f(3 , 6) = 9(3) + 5(6) = 27 + 30 = 57
∴ f(4 , 2) = 9(4) + 5(2) = 36 + 10 = 46
∴ f(1 , 5) = 9(9) + 5(9) = 81 + 45 = 126
- The maximum value is 126 occurs at (9 , 9)
The maximum value of the function for the polygonal convex set determined by a system of inequalities can be found using linear programming. The key steps are to plot the inequalities, find the vertices of the feasible region, and substitute these points into the function to find the maximum value.
Explanation:This problem is related to linear programming, which is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. To find the maximum value of the function for the polygonal convex set determined by the given system of inequalities, you essentially need to apply the rules of linear programming.
Firstly, plot the system of inequalities on a coordinate system to determine the feasible region, which is the polygonal convex set. Then, find each vertex of this polygonal convex set. These vertices are points where boundaries of the system of inequalities intersect. Once you have these vertices, substitute each of them into the function you are maximizing. The largest output will be the maximum value of the function within the given polygonal convex set.
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If a computer depreciates at a rate of 20% per year, what is the monthly depreciation rate?
6.67%
1.67%
8.19%
5.00%
Answer:
1.67%
Step-by-step explanation:
With the given information that the computer depreciates 20% a year, we have our basis for making the calculation. What is asked for is how much of a depreciation the computer has monthly. One year has 12 months, so in order to get to the result we just simply need to divided the 20% with the number of months in a year to get the result:
20 / 12 = 1.67
The result is 1.67%, thus the computer depreciates 1.67% on a monthly basis.
Find the missing part. l = 8, w = 4, h = 2 Find the diagonal (d) of the rectangular solid.
The diagonal (d) of the rectangular solid with dimensions l=8, w=4, h=2 is found using the Pythagorean theorem in three dimensions. Plugging in the values, d is approximately 9.17 units.
Explanation:To find the diagonal (d) of a rectangular solid with length (l), width (w), and height (h), you can use the Pythagorean theorem in three dimensions. The formula for the diagonal of a rectangular solid is given by:
d = √(l² + w² + h²)
Given that l = 8, w = 4, and h = 2, we can substitute these values into the formula to find d:
d = √(8² + 4² + 2²) = √(64 + 16 + 4) = √84 ≈ 9.17
So the diagonal of the rectangular solid is approximately 9.17 units.
Please help me out ........
Answer:
13.86 units to the nearest hundredth.
Step-by-step explanation:
By Pythagoras:
16^2 = x^2 + 8^2
x^2 = 16^2 - 8^2
x^2 (16 + 8)(16 - 8) = 192
x = √192
= 13.86 (answer).
Answer:
x = 8[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Since the triangle is right use Pythagoras' theorem to solve for x
The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides, thus
x² + 8² = 16²
x² + 64 = 256 ( subtract 64 from both sides )
x² = 192 ( take the square root of both sides )
x = [tex]\sqrt{192}[/tex] = [tex]\sqrt{64(3)}[/tex] = 8[tex]\sqrt{3}[/tex]
PLEASE HELP ASAP!!
The base of a regular pyramid is a hexagon.
What is the area of the base of the pyramid?
Enter your answer in the box. Express your answer in radical form.
cm²
Answer:
The area of the hexagon is [tex]96\sqrt{3}\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the hexagon is equal to
[tex]A=\frac{1}{2}Pa[/tex]
where
P is the perimeter of the hexagon
a is the apothem
Find the Perimeter P
[tex]P=6(8)=48\ cm[/tex]
Find the apothem a
[tex]a=(8)sin(60\°)[/tex]
[tex]a=8(\frac{\sqrt{3}}{2})=4\sqrt{3}\ cm[/tex]
Find the area of the hexagon
[tex]A=\frac{1}{2}(48)(4\sqrt{3})=96\sqrt{3}\ cm^{2}[/tex]
PLEASE HELP!!!
What is -5/8 times 2/3?
Simplify for -5/8*2/3= -5/12
-0.416 as a mixed number
The height, h, of a plant (in inches) w weeks since it was planted is represented by the equation h=1.2w+3. How many weeks will it take the plant to reach one foot?
Answer:
7.5 weeks
Step-by-step explanation:
If you want to find out how long it take for the plant to reach a foot you set up the equation like so:
12=1.2w+3
and solve from there.
12=1.2w+3 Subrtact 3 from both sides
9=1.2w Divide by 1.2 to isolate w
7.5=w Answer is 7.5 weeks
The [tex]7.5[/tex] weeks it will take the plant to reach one foot.
What is height?
In math, height is the vertical distance from the top to the base of the object and it is measured in cm, inches, meters, etc.
It is given that the height [tex]h[/tex] of the plant (in inches) [tex]w[/tex] weeks.
The equation is,
[tex]h=1.2w+3[/tex]
As we know that,
[tex]$12\,\text{inches}=1\,\text{foot}$[/tex]
The number of weeks that it will take the plant to reach one foot will be:
[tex]h=1.2w+3[/tex]
[tex]12=1.2w+3[/tex]
[tex]1.2w=12-3[/tex]
So,
[tex]w=\frac{9}{1.2}[/tex]
[tex]$\therefore w=7.5$[/tex]
Hence, it will take [tex]7.5[/tex] weeks.
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A sweater was on sale at %40 off the regular price. Ella saved $20 by buying the sweater on sale. What was the regular price of the sweater?
so she saved $20 and that was 40% of the regular price, let's say the regular price is "x".
if 20 is 40%, what is "x" or namely the 100%?
[tex]\bf \begin{array}{ccll} amount0&\%\\ \cline{1-2} 20&40\\ x&100 \end{array}\implies \cfrac{20}{x}=\cfrac{40}{100}\implies \cfrac{20}{x}=\cfrac{2}{5}\implies 100=2x \\\\\\ \cfrac{100}{2}=x\implies 50=x[/tex]
Answer:This is an equation! Solutions: x=1.
Step-by-step
1. True or False: For a trigonometric function, y = f(x), then x = F-1(y). Explain your answer. (1 point)
2. True or False: For a one-to-one function, y = f(x), then x = f-1(y). Explain your answer. (1 point)
9514 1404 393
Answer:
FalseTrueStep-by-step explanation:
If y = f(x) then x = f^-1(y) is true if and only if f(x) is a one-to-one function.
__
1. False. Trig functions are periodic, so are not one-to-one.
2. True. The f(x) is specified as being one-to-one.
Answer:
1. True
2. True
Step-by-step explanation:
1. Since a capital letter (F) is used to show that the inverse equation is indeed a function, the question is true. If the inverse (second equation) was written as x=f-1(y), it would be false.
2. For one-to-one functions, all you need to do to reverse them is switch the x and y variables, and the [tex]f^-1[/tex] signifies that it is an inverse function.
Use the inverse of the function y = x2 − 18x to find the unknown values.
y=+- square root bx + c +d
b=
c=
d=
ANSWER
b=1, c=81, and d=9.
EXPLANATION
The given function is:
[tex]y={x}^{2}-18x[/tex]
This function is the same as:
[tex]y={(x - 9)}^{2}-81[/tex]
To find the inverse of this function, we interchange x and y.
[tex]x={(y-9)}^{2}-81[/tex]
Solve for y:
[tex]x+81={(y- 9)}^{2}[/tex]
Take square root of both sides:
[tex]\pm \sqrt{x + 81}=y-9[/tex]
[tex]y=\pm \sqrt{x + 81}+9[/tex]
Hence,
b=1, c=81, and d=9.
Answer: b=1, c=81, d=9
Step-by-step explanation:
19. The areas of corresponding faces of two similar hexagonal prisms are 25 cm² and 121 cm². What is the ratios of the corresponding sides lengths? of the perimeter? of the volumes?
ANSWER
I) 5:11
ii) 5:11
iii) 125:1331
EXPLANATION
Let the side lengths be in the ratio:
x:y
This implies that the area will be in the ratio:
[tex] \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{121} [/tex]
Take positive square root.
[tex] \frac{x}{y} = \sqrt{ \frac{25}{121} } [/tex]
[tex] \frac{x}{y} = \frac{5}{11} [/tex]
Hence the sides are in the ratio:
x:y=5:11
The perimeter of the smaller hexagon is 6×5=30
The perimeter of the larger hexagon is 6×11=66
The ratio of the perimeter is
30:66=5:11
The volume will be in the ratio
5³:11³
125:1331
Kalaty bought 1/12 pounds of butter.How many ounces are 1/12 pounds of butter? Layla hatched 92 eggs.She used 43 and 1/5 of them how many eggs does she have left?
For this case we have that by definition:
1 pound is equivalent to 16 ounces.
We make a rule of three to determine the ounces of butter:
1lb ------------------------> 16onzas
[tex]\frac {1} {12}[/tex]----------> x
Where "x" represents the ounces of butter
[tex]x = \frac {\frac {1} {12} * 16} {1}\\x = \frac {16} {12}\\x = \frac {8} {6}\\x = \frac {4} {3}[/tex]
Thus, there are [tex]\frac {4} {3}[/tex]ounces of butter.
Now we must find the amount of eggs that remain:
[tex]92- (43+ \frac {1} {5}) =\\92 - (\frac {43 * 5 + 1} {5}) =\\92 - (\frac {215 + 1} {5}) =\\92 - (\frac {216} {5}) =\\92-43.2 =\\48.8[/tex]
Round down. There are 48 eggs left.
Answer:
There are [tex]\frac {4} {3}[/tex] ounces of butter.
48 eggs left
Fifty percent of the gases making up the atmosphere are found below ________. 10 miles (16.2 km) 6 â½ miles (10.4 km) 3 â½ miles (5.6 km) 8 miles (12.8 km)
Answer:
im not sure what this means
Step-by-step explanation:
Answer:
5.6 kilometers gradpoint
Step-by-step explanation:
i took the test
Round 4.432 to the nearest tenth.
Answer:
4.4
Step-by-step explanation:
The tenth place in this number is 4.432, so that should be the last digit.
Now, we need to know wether to round up or down. That is determined by the digit that comes after it. If that digit, here it is the hundredth, is 0-4, it rounds down, if it is 5-9, it rounds up. Our next digit is 3, which goes into the first category, so the number rounds down, so the tenth remains the same. That leaves us with 4.4.
Answer:
4.4
Step-by-step explanation:
The tenth decimal place is one to the left of the decimal. The hundreth decimal places is two digits to the right and so on an so forth. Knowing this, you apply the basic rules of rouding. If the digit to the left of the digit being rounded is greater than five, the digit is rounded up one and the others are discarded. In this case, the digit to the left of the digit in subject is less than five, 3. Therefore, the tenth decimal stays the same and the others are discarded.
⦁ Simplify the expression. Show your work. ⦁
+ (32 – 42)
-5 cause it is 32-42 and the anserw is -5
What is the product?
1st pic is the problem
the rest are the answer choices
For this case we must find the product of the following expression:
[tex](y ^ 2 + 3y + 7) (8y ^ 2 + y + 1)[/tex]
We apply distributive property, which states that:
[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]
So:[tex](y ^ 2 + 3y + 7) (8y ^ 2 + y + 1) =\\(y ^ 2) (8y ^ 2) + (y ^ 2) (y) + (y ^ 2) (1) + (3y) (8y ^ 2) + (3y) (y) + (3y) (1 ) + (7) (8y ^ 2) + (7) (y) + (7) (1) =\\8y ^ 4 + y ^ 3 + y ^ 2 + 24y ^ 3 + 3y ^ 2 + 3y + 56y ^ 2 + 7y + 7 =[/tex]
We add similar terms:
[tex]8y ^ 4 + 25y ^ 3 + 60y ^ 2 + 10y + 7[/tex]
Answer:
Option D
A typical stone on the lowest level of the great pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons.What was the volume of the average stone?How much did one cubic foot of this stone weigh?
To find the volume, you need to do length times width times height
SO you have to do 5 times 5 times 6
The volume is 150 cubic feet
Since 150 cubic feet of this rectangular prism is 15 tons
you can do 15 divided by 150
so one cubic feet of this stone sculpture weight 0.1 tons
Btw, a pyramid is a triangular structure, not rectangular
help pls!! plus 20 points!!!!
Answer:
[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]
Step-by-step explanation:
1. Calculate the slope of Line f
y - 3 = -⁹/₄(x – 6)
The coefficient of x is -⁹/₄, so
The slope m₁ = -⁹/₄.
2. Calculate the slope of the perpendicular line
m₂ = -1/m₁
m₂ = ⁴/₉
3. Calculate the y-intercept of line g
y = mx + b
4 = 6(⁴/₉) + b
4 = ⁸/₃ + b
Subtract ⁸/₃ from each side: b = 4 - ⁸/₃ = ⁴/₃
The y-intercept is b = ⁴/₃.
Step 4. Write the equation for line g
[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]
The Figure below shows the graph of line f in red, and the graph of its perpendicular line g in black.
What is the solution to the equation below?
Answer:
[tex]\frac{38}{7}[/tex]
Step-by-step explanation:
Using the properties of logarithms,
[tex]\log(7)+\log(x-4)=1\\\log(7(x-4))=1\\\log(7x-28)[/tex]
Now think about what this is asking. The log function say 10 to the power of whats on the other side of the equals sign, equals whats in the parenthesis. So, this means whats is the parenthesis is equal to [tex]10^1[/tex] or just 10.
We can now solve to x.
[tex]7x-28 = 10\\7x=38\\x=\frac{38}{7}[/tex]
Answer:
x=38/7
Step-by-step explanation:
Just took the test
A box has the shape of a rectangular prism with height of 28 cm. If the height is increased by 0.2 by how much does the surface area of the box increase?
The overall change in surface area when the height of a rectangular prism is increased by 0.2 cm can be calculated with the formula 0.4w + 0.4l.
Explanation:In this question, we are looking at the surface area of a box that is a rectangular prism and how it will change if the height of the box is increased by 0.2 cm. The surface area of a prism is given by the formula 2lw + 2lh + 2wh, where l, w and h are the length, width and height respectively.
Now, if the height is increased by 0.2 cm, the difference in the surface area will be 2lw (because there are two ends with area lw that do not change) plus the change in the area of the sides. The sides' areas will increase by 2w x 0.2 and 2l x 0.2 respectively (since we have two opposing sides that both increase by 0.2 cm in height).
Therefore, the overall change in surface area when the height is increased by 0.2 cm is simply the sum of these two parts, which is 2w x 0.2 + 2l x 0.2. This can also be simplified to 0.4w + 0.4l.
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Which of these shows the result of using the first equation to substitute for Y in the second equation, then combining like terms?
Y=2x
2x+3y=16
A. 8x=16
B. 4x=16
C. 5y=16
D. 5x=16
ANSWER
A. 8x=16
EXPLANATION
The given equations are:
1st equation: y=2x
2nd equation: 2x+3y=16
We substitute the first equation into the second equation to get:
2x+3(2x)=16
This implies that:
2x+6x=16
We combine like terms to get:
8x=16
The correct choice is A. 8x=16
How many cups are in a 16 lb bag?
How many cups are in a 22 lb bag?
Answer:
16lb=30
22=88
Step-by-step explanation:
Answer:
16 lb = 64 cups
22 lb = 88 cups
The graph of 3x + 4x = -1 is shown on the grid. Which ordered pair is in the solution set of 3x + 4y ≤ -1?
A. (2, 6)
B. (6,2)
C. (2, -6)
D. (-2, 6)
ANSWER
C(2,-6)
EXPLANATION
The solution set to given inequality is the shaded region.
The points are also located in the graph above.
The only point that falls in the solution region is C(2,-6)
The ordered pair that is in the solution set is C(2,-6)
The third option is correct.
in algebra a word that means something has been added
Combined?? The sum of ?
Addends is the word in algebra that means something has been added. Addition is an operation to solve the algebraic problems.
What is algebra?Algebra is a field of mathematics that solves problems by substituting letters for numbers.
Addends refer to the numbers that are being added in an addition issue. An addend is a group of numbers that are added together to generate a sum.
Hence, addends is the word in algebra that means something has been added.
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A traveler comes upon a fork in the road on the path to the travelers right a sign reads Mercer 24 km
Answer:
a=25.km
Step-by-step explanation:
A traveler comes upon a fork in the road on the path to the travelers right a sign reads Mercer 24 km
The concluding part could be the following:
On the path to the traveler's left, a sign reads "Turtle Lake: 17km." The traveler also observes that the angle between the paths is 1.3 radians. Assuming both paths are perfectly straight, what is the distance between Mercer and Turtle Lake? km Round your answer to the nearest kilometer
since the angle between them is actually 1.3 rad
lets convert to degrees
74.48 degrees
using cosine of angle we can find the distance between the two destinations
[tex]a^{2} =b^{2} +c^{2} -2bcCos\alpha[/tex]
[tex]\alpha[/tex]=74.48 deg
a^2=17^2+24^2-(2*17*24)cos74.48
a^2=646.65
find the square root of both sides
a=25.42km
approximately=25Km
You are buying two kinds of coffee.1 pound of premium coffee costs $3.00.1 pound of regular coffee costs $2.00.You have $15.00 to spend and want to buy 1 pound of premium coffee.Use the number line to draw the solution set that shows all possible numbers of pounds of regular coffee that you could buy. Must be answered as an inequality: greater than, less than, greater than or equal to, less than or equal to, equal to.
Answer:
Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
[tex]x\leq 7.5\ pounds[/tex]
Part 2) [tex]m+n=(0.76x-0.28)[/tex]
Step-by-step explanation:
Part 1)
Let
x-----> the number of pounds of regular coffee
we know that
The inequality that represent the situation is
[tex]2x\leq 15[/tex]
Solve for x
Divide by 2 both sides
[tex]x\leq 15/2[/tex]
[tex]x\leq 7.5\ pounds[/tex]
The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
The solution of the inequality is the interval ------> (-∞,7.5]
but the number of pounds cannot be a negative number
therefore
The solution is the interval -----> [0,7.5]
see the attached figure
Part 2) we have
[tex]m=0.56x-0.25[/tex]
[tex]m=0.20x-0.03[/tex]
Adds m and n
[tex]m+n=(0.56x-0.25)+(0.20x-0.03)[/tex]
Group terms that contain the same variable
[tex]m+n=(0.56x+0.20x)+(-0.25-0.03)[/tex]
Combine like terms
[tex]m+n=(0.76x-0.28)[/tex]
Find the partial fraction decomposition of
[tex]\dfrac1{x(x-1)}=\dfrac ax+\dfrac b{x-1}[/tex]
[tex]1=a(x-1)+bx[/tex]
If [tex]x=0[/tex], then
[tex]1=-a\implies a=-1[/tex]
If [tex]x=1[/tex], then
[tex]1=b[/tex]
So we have
[tex]\dfrac1{x(x-1)}=\dfrac1{x-1}-\dfrac1x[/tex]
Im more of a algebra man myself.
Angle A= 60
You add angles A and D together and set them equal to 180 because opposite sides in a parallelagram =180. Then you solve for x and get 30 and you should then plug in 30 to angle A and get 60.
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!
Answer:
D
Step-by-step explanation:
If you made a table and filled in the values, the rate column it would look like this:
d = r t
truck 80
car 90
So far so good. If we want the car to catch up with the truck, that means that in the end they travel the exact same amount of miles. So let's fill in the d:
d = r t
truck d 80
car d 90
Again, not too bad. If the car leaves 20 minutes later than the truck, that means that the time the truck is traveling is 20 minutes more than the car's time. So the car's time is t and the truck's time is t + 20:
d = r t
truck d 80 t+20
car d 90 t
Now because the distances are equal, we can set the rate times time for each vehicle equal to each other:
80(t + 20) = 90t
That is choice D
If B=16°45’ and c=13 then find a (picture provided)
Answer:
A. 12.4
Step-by-step explanation:
To find a, we'll use the Law of Sines that says:
[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]
And we'll isolate a to get:
[tex]a = \frac{sin(A) * c}{sin(C)}[/tex]
We first need to find A, which is easy. The sum of the interior angles of a triangle is 180 degrees... and we already have 2 of them, so:
A = 180 - 90 - 16.75 = 73.25
(converted 16°45' to 16.75)
Then we will plug-in the information we already have
[tex]c = \frac{sin(73.25) * 13}{sin(90)} = 12.45[/tex]
So, let's round it to 12.4 to match the answer A.
Answer:
The length of side marked a is 12.4 units.
Step-by-step explanation:
In ΔABC
∠B = 16°45’ = 16.75°
1 min arc = [tex]\frac{1}{60} degrees [/tex]
c = 13 units
a = ?
[tex]\cos \theta=\frac{Base}{Hypotenuse}[/tex]
[tex]\cos B=\frac{a}{13}[/tex]
[tex]0.95757=\frac{a}{13}[/tex]
[tex]a=0.95757\times 13=12.4484\approx 12.4 units[/tex]
The length of side marked a is 12.4 units.