Calculus HELP PLEASE? A highway runs due north. A car traveling at 50 mph exits the highway at a 30° angle. After driving another 1.5 hours at the same speed and direction, how far away is the car from the highway?
Answers
notice that the car exits the northbound highway, and whilst going at 50mph for 1.5 hours, that simply means going for 75 miles.
make sure your calculator is in Degree mode.
Answer:
37.5 miles is the answer.
Step-by-step explanation:
Since car is travelling with a speed = 50 mph
Angle between the highway and the track on which the car is travelling = 30°
Now we know sin∅ = distance between highway and the car/Distance traveled by the car on the new track
Distance traveled by the car in 1.5 hours = speed × time
= 50 × 1.5 = 75 mi.
Therefore sin 30° = x/75
x = 75×sin30° = 75 × 1/2 = 37.5 mi.
Therefore the answer is 37.5 mi away.
Related Questions
Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? k – 2 = 1/9(t – 18) k – 18 = 1/9(t – 2) k – 2 = 9(t – 18) k – 18 = 9(t – 2)
Answers
Answer:
the answer is C
Step-by-step explanation:
using her first part 2 kilometers in 18 minutes
total kilometers - 2
and total time - 18
so you would get:
k – 2 = (t – 18)
MATH HELP!!!
Dwight's gross semimonthly pay is $1220. To maintain his current lifestyle, how much should he save up by the time he retires?
$292800
$317200
$702720
$761280
Answers
Answer:
292,800
Step-by-step explanation:
1220*24 (24 is semimonthly)=29,280
Then you want to multiply by 10
29280*10=292,800
Dwight's save up by the time he retires will be 292800$
Dwight's gross semimonthly pay is $1220
What is the meaning of semimonthly?
semimonthly means two times per month
Semimonthly for per year is,
12(2)=24
Dwight's gross semimonthly pay is $1220.
1220*24 (24 is semimonthly)=29,280
For one year the amount will be 29280
Then you want to multiply by 10
29280*10=292,800
Therefore Dwight's save up by the time he retires will be 292800$.
To learn more about the saving visit:
https://brainly.com/question/25787382
Factor by grouping m^2 +8mn -3mn-24n^2
20 POINTS
Answers
Then solve for the common factor in each bracket group.
m(m + 8n) - 3n(m + 8n)
(m-3n)(m + 8n) is the answer.
16 POINTS. Find the x and y intercepts of number 8 show work. I think my points are wrong.
Answers
y = 2x^4 + 3x^3 - 16x - 24 into the input line.
According to wolframalpha there are 2 real roots and 2 imaginary ones.
there are places on the internet that will solve quartics for you and likely those solutions will show all 4 roots. You were right to be a little suspicious, but the question is a bit unreasonable.
Note to Moderator. Wolframalpha dot com is just a tool. the work is my own.
The width of a rectangle is 6 less than twice its length. if the area of the rectangle is 110 cm^2, what is the length of the diagonal?
Answers
Step 2. Let 2L-6 be the width since the width of a rectangle is 6 less than twice its length.
Step 3. Area A=113=L*(2L-6)
Step 4. Solving for L yields the following steps
Subtract 113 from both sides of the equation to get a quadratic equation
To solve for L, we can use the quadratic formula given as
where a=2, b=-6 and c=-113
Solved by pluggable solver: SOLVE quadratic equation with variableQuadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=940 is greater than zero. That means that there are two solutions: .
Final answer:
The length of the rectangle is 10 cm and the width is 11 cm. Using the Pythagorean theorem, the length of the diagonal can be calculated to be √221 cm.
Explanation:
The length of the rectangle is 10 cm and the width is 11 cm.
To find the length of the diagonal, we can use the Pythagorean theorem:
Diagonal2 = Length2 + Width2
Diagonal = √(102 + 112) = √(100 + 121) = √221 cm.
The length of the rectangle is 10 cm and the width is 11 cm. Using the Pythagorean theorem, the length of the diagonal can be calculated to be √221 cm.
Too many nutrients is not good for bodies of water. This man-made is called what?
A. Cultural eutrophication
B. Point-source pollution
C. Eutrophication
Answers
I believe the answer is most likely Cultural eutrophication because it's the process that speeds up natural eutrophication because of human activity.
The radius r of a circle can be written as a function of the area A with the following equation:
[tex]r= \frac{A}{ \pi } [/tex]
What is the domain of this function? Explain why it makes sense in this context.
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In this context, it makes sense as the radius cannot have a negative value.
Thus, the domain of the function is [0,∞)
This means that the Area can have any positive value starting from zero.
Triangle ABC is congruent to triangle XYZ. Angle A measures 50 degrees, angle B measure 2x+40 degrees, and angle Z measures 4x+8 degrees. Find the value of x.
20.5
13.67
16
10.5
Answers
the sum of the three angles of a triangle is 180, so
50+2x+40+4x+8=180
6x++98=180
6x=82
x≈13.67
Final answer:
To find the value of x, we use the fact that the angles of a triangle sum up to 180 degrees. By setting an equation with the given angle measurements and solving for x, we find the value of x to be 13.67.
Explanation:
The student asks about determining the value of x in two congruent triangles, ABC and XYZ, given the measurements of the angles. If triangles are congruent, their corresponding angles are equal. Using the fact that the sum of the angles in a triangle is 180 degrees, and given Angle A is 50 degrees, Angle B is 2x+40 degrees, and Angle Z is 4x+8 degrees, we can set up an equation because Angle B corresponds to Angle Z in congruent triangles:
50 + (2x + 40) + (4x + 8) = 180
Combine like terms:
50 + 2x + 40 + 4x + 8 = 180
6x + 98 = 180
Subtract 98 from both sides:
6x = 82
Divide both sides by 6:
x = 13.67
Therefore, the value of x is 13.67.
A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 .
What is the volume of the dilated prism?
Enter your answer, as a decimal, in the box.
Answers
The volume would be:
Volume of the prism(without dilated) = (area of the base) * (height)
Since,
Area of base = 5[tex]ft^{2}[/tex]
Height of the prism = 10f
Volume(without dilated) = 5*10 = 50[tex]ft^{3}[/tex]
Now let us apply the dilated factor! For that you need to multiply for factor with the volume of the prism without dilation.
Volume of the dilated prism = [tex]d^{3}[/tex] * (Volume of the prism without dilation)
Where d = dilated factor. Therefore,
[tex]v = (\frac{6}{5} )^{3} * 50[/tex]
v = 86.4[tex]ft^{3}[/tex]
So the correct answer: 86.4[tex]ft^{3}[/tex]
1. Real numbers that cannot represent as a quotient of two integers are ____ numbers.
2. The sum of a number and it’s ____ equals zero.
3. You can simplify an expression by combining it’s ____.
4. ____ is a numbers distance from zero on a number line.
5. when you make conclusions based on patterns you observe, you use ____.
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2. Additive inverse
3. Like terms
4. Absolute value
5. Inductive reasoning
helppppppppppppppppp
Answers
(5 ^ -1) * (5 ^ -3)
Using properties of exponents we have:
(1/5) * (1 / (5 ^ 3))
Rewriting:
(1/5) * (1 / (125))
1/625
answer:
An equivalent expression is:
1/625
option 1
A mortgage broker charges $4000 plus 1.8% of the mortgage amount. What is the mortgage broker fee for a $309,000 mortgage?
Answers
The answer is 9,562. Thank you very much.
The mortgage broker fee for a $309,000 mortgage is calculated by multiplying the mortgage amount by 1.8% and then adding a fixed charge of $4000, resulting in a total fee of $9,562.
Explanation:The mortgage broker fee for a $309,000 mortgage can be calculated by taking 1.8% of the mortgage amount and adding the fixed charge of $4000. To find 1.8% of $309,000, we multiply 0.018 by 309,000.
0.018 \( \times \) $309,000 = $5,562.
Then we add the fixed charge:
$5,562 + $4,000 = $9,562.
So, the mortgage broker fee for a $309,000 mortgage is $9,562.
PLESSSSSS HELP WILL CROWN BRAINLIEST!!!! 20PTS!!!!!!!!!!!!
Answers
<5, -2> + <0, 0> = ((5+0), (-2+0)> = <5, -2>
Find (fxf)(0)
F(x)+3x-2
Answers
To find (fxf)(0), substitute 0 into the given function f(x) = x + 3x - 2. The resulting value is -2.
Explanation:To find (fxf)(0), we need to substitute 0 into the given function. The function is f(x) = x + 3x - 2. Substituting 0 for x, we get f(0) = 0 + 3(0) - 2 = -2. Therefore, (fxf)(0) = f(f(0)) = f(-2).
What metric unit would be appropriate to measure a length of two cities?
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4/5 are girls. Today 3/5 brought there lunch. What fraction of the students are girls who brought there lunch today?
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Tim answered all the questions on his math test but got 10 answers wrong. He received 4 points for every correct answer, and there was no penalty for wrong answers. His score was 76 points.
Answers
PLEASE HELP, 40 points, absurd answers will be reported, good answers will get brainliest
8.03b
(PART 1)
Find at least three examples of conic sections in the real world (marketing, architecture, nature, etc.). Make sure your collage demonstrates at least two of the conic categories you have learned. You may use circles, ellipses, parabolas, or hyperbolas. Arrange your images on paper or in a document.
(PART 2)
Respond to each of the following prompts in a word processing document.
Write a brief description about one of the conics from your collage.
Write the equation that represents your conic in its standard form. To do this either find the measurements of your conic example to create the equation or guess the measurements of the conic.
Your assignment must include:
Your conics collage.
A description about one conic from your collage.
The standard form equation of one of the conics.
An explanation of how the equation for the conic was found.
Answers
Part 2) The Golden Gate Bridge is a suspension Bridge spanning the Golden Gate, a short strait in San Francisco. It is one of the wonders of the Modern World and it was opened in 1937. It cost around 500 million dollars in today's currency and it is one of the longest suspension bridges in the world and from land to land the distance is 1280 m. The height of the suspensions is 230 m.
Part 3) We can think of a parabola of the form y=ax^2 where we need to substitute the values to find a.
Can someone please help me
Answers
Answer:
Convert to inches to solve and then convert back. The first solution is 1 foot 10 inches.
Step-by-step explanation:
To solve convert feet inches into inches by multiplying the number of feet by 12 and adding it to the inches. Then subtract and convert back.
For example: 5 feet is 5*12=60 inches. So 5 feet 7 inches is 60+7=67.
3 feet is 3*12=36 inches. So 3 feet 9 inches is 36+9=45 inches.
Subtract the two.
67-45= 22 inches.
22 inches is 12+10. 12 inches is 1 foot. This is 1 foot 10 inches.
If two quantities are added and the sum is zero, what do you know about the quantities?
Answers
Which of the following is a polynomial function in factored form with zeros at 0, –3, and 4?
A. f(x) = x^3 + x^2 – 12x
B. f(x) = x(x – 3)(x + 4)
C. f(x) = x^3 – x^2 – 12x
D. f(x) = x(x + 3)(x – 4)
Answers
Explanation:
You can find the zeroes of a polynomial function in factored form by setting each factor equal to zero and solve for [tex]x[/tex].
The polynomial function of answer A is not even factored, so we can rule that one out.
Lets set each one of the factors of answer B equal to zero, solve for [tex]x[/tex] and see what happens:
- [tex]x=0[/tex]
- [tex]x-3=0[/tex]
[tex]x=3[/tex]
- [tex]x+4=0[/tex]
[tex]x=-4[/tex]
As you can see, our zeroes are 0,3, and -4, so this is not the correct answer either.
The polynomial function of answer C is not even factored, so we can rule that one out as well.
Lets apply what we just learned to the factored polynomial of answer D:
- [tex]x=0[/tex]
- [tex]x+3=0[/tex]
[tex]x=-3[/tex]
- [tex]x-4=0[/tex]
[tex]x=4[/tex]
This time our zeroes are, 0, -3, and 4; therefore we can conclude that D is the correct answer.
Ravi is driving 440440 miles to visit his grandma. He drives at a rate of 5555 miles per hour. How many hours will it take him to get 3434 of the way there?
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Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55 miles per hour, how many hours will it take him to get 3/4 of the way there?
we have that
3/4 of the way--------------> (3/4)*440=330 miles
I apply a rule of three
if 55 miles----------------> 1 hour
330 miles--------------> X
X=330/55=6 hour
the answer is 6 hour
Find the lateral area of the square pyramid.
Answers
help me....................
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Solve the system of equations using the substitution method.
{2x+8y=4
x=−3y+5
Enter your answers in the boxes.
x=
y=
Answers
Answer:
Step-by-step explanation:
X=14
y=-3
Answer:
(14,-3)
Step-by-step explanation:
Please help asap! lots of points
Answers
y2: -5
y1: -9
x2: 10
x1: 9
Fill in the numbers for the equation and solve. -5 - (-9) is 4. 10 - 9 is 1. 4/1 is just simply 4. There. The slope is 4, but we're not done. We'll use one of the points as x and y. Point-slope form is in the form of y - y1 = m(x - x1). y1 is -9. Because that is a negative number, we will be adding, so that part is y + 9, which eliminates answer choices A and B. x1 is 9. The other part will be 4(x - 9). That eliminates answer choice C. That leaves D, with the problem in point-slope form being y + 9 = 4(x - 9). When you subtract 4x from both sides, subtract 9 to isolate the y, multiply -10 and 4 together to get -40, and subtract 5 from -40 to get -45, the equation becomes -4x + y = -45. You use the values of the second point to find the value on the x-side. There. The answer is D.
Answer:
The answer is D.
Hope I helped :)
Have a blessed day <3
~Michael~
I need 21 centimeters but i need to translate that into millimeters wht is the answer in milli eters
Answers
21cm = 10 x 21 = 210 mm
a flyer on a reconnaissance flight has 4 hours for a round trip. his blade can fly 200 mph in still air. he flies out from his base against a 20 mph wind and immediately returns to his base, flying with the same wind. how many hours did he take for his fight out?
Answers
When flying against the wind, the effective plane speed is 200 - 10 = 180 mph.
Let d = the distance (miles) from his base to the destination.
The time (hours) to travel with the wind is
t₁ = d/220
The time (hours) to travel against the wind is
t₂ = d/180
The total time taken is 4 hours, therefore
t₁ + t₂ = 4
d/220 + d/180 = 4
d(1/220 + 1/180) = 4
0.010101d = 4
d = 396 miles
Therefore
t₁ = 396/220 = 1.8 hours = 1 hour, 48 minutes (floght in)
t₂ = 396/180 = 2.2 hours = 2 hours, 12 minutes (flight out)
Answer: 2.2 hours
A company need to package hazardous chemicals in special plastic rectangular prism containers that had 80 cubic feet. Find the whole number dimensions of the container that would use the least amount of plastic.
Answers
the cube is a prism rectangular with minimum surface area
then
Volume cube=b³=80-------------> b=4.31 ft
the problem is asking me for a whole number
therefore
b=4 ft------------> I assume a rectangular prism of square base
V=b²*h--------------> h=V/b²=80/4²=5 ft
the answer is 4 ft x 4 ft x 5 ft number dimensions of the container
To package hazardous chemicals in special plastic containers the dimensions of the container should be 4 × 4 × 5 feet.
A rectangular prism with a volume of 80 cubic feet needs to be designed to use the least amount of plastic. To do this, we need to find the dimensions (length, width, height) that, while maintaining the given volume, result in the minimum surface area.
The volume of a rectangular prism is given by:
Volume = length × width × height
For our case: length × width × height = 80 cubic feet
To minimize the surface area, the dimensions should be close to a cube as this shape has the smallest surface area-to-volume ratio. We will seek integer dimensions. The formula for the surface area (SA) of a rectangular prism is:
SA = 2(length × width + width × height + height × length)
We start by considering potential combinations of whole numbers whose product is 80:
1 × 1 × 801 × 2 × 401 × 4 × 201 × 5 × 161 × 8 × 102 × 2 × 202 × 4 × 102 × 5 × 84 × 4 × 5Calculating the surface area for each configuration:
1 × 1 × 80: SA = 2(1×1 + 1×80 + 80×1) = 2(1 + 80 + 80) = 322 sq. feet1 × 2 × 40: SA = 2(1×2 + 2×40 + 40×1) = 2(2 + 80 + 40) = 244 sq. feet1 × 4 × 20: SA = 2(1×4 + 4×20 + 20×1) = 2(4 + 80 + 20) = 208 sq. feet1 × 5 × 16: SA = 2(1×5 + 5×16 + 16×1) = 2(5 + 80 + 16) = 202 sq. feet1 × 8 × 10: SA = 2(1×8 + 8×10 + 10×1) = 2(8 + 80 + 10) = 196 sq. feet2 × 2 × 20: SA = 2(2×2 + 2×20 + 20×2) = 2(4 + 40 + 40) = 168 sq. feet2 × 4 × 10: SA = 2(2×4 + 4×10 + 10×2) = 2(8 + 40 + 20) = 136 sq. feet2 × 5 × 8: SA = 2(2×5 + 5×8 + 8×2) = 2(10 + 40 + 16) = 132 sq. feet4 × 4 × 5: SA = 2(4×4 + 4×5 + 5×4) = 2(16 + 20 + 20) = 112 sq. feetThus, the dimensions 4 × 4 × 5 feet are the ones that use the least amount of plastic, giving a surface area of 112 sq. feet.
Two consecutive integers have a sum of 45 . find the integers.
Answers
one number = x
the other number = x + 1
The sum is 45
x + x + 1 = 45
2x + 1 = 45
2x = 45 - 1
2x = 44
x = 22
x = 22
x + 1 = 22 + 1 = 23
The two numbers are 22 and 23.