The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. This means that the surface area of the balloon is increasing at the rate of 8πr cm^2/sec.
The volume of a sphere is given by the formula 4/3πr^3, where r is the radius of the sphere. If the radius of the balloon is 6 cm, then the volume of the balloon is (4/3)π(6^3) = (4/3)π216 = 288π cm^3.
To find the rate at which the volume of the balloon is increasing, we need to take the derivative of the formula for the volume of a sphere with respect to time. This gives us (4/3)π(3r^2)(dr/dt).
Since the radius of the balloon is 6 cm and the surface area of the balloon is increasing at the rate of 8πr cm^2/sec, the rate at which the radius of the balloon is increasing is (8πr/4πr^2) = 2/r = 2/6 = 1/3 cm/sec.
Plugging this into the formula for the rate of change of the volume of the sphere, we get
(4/3)π(3r^2)(dr/dt) = (4/3)π(36^2)(1/3) = (4/3)π108 = 144π cm^3/sec.Therefore, the volume of the balloon is increasing at a rate of 144π cm^3/sec when the radius of the balloon is 6 cm.
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Complete Question:
The surface area of a spherical balloon is increasing at the rate of 2 cm 2/sec. At what rate is the volume of the balloon is increasing when the radius of the balloon is 6 cm?
According to the United States Census Bureau, the state of Texas had a population of 16,986,510 in 1990. Census data shows that in 2000, the population of Texas was 20,851,820. Find the percent of change.
Answer:
22.7551745473%
Step-by-step explanation:
I could be very wrong but to find the percentage of change you have to divide the increase by the original number, and then multiply it by 100.
20851820-16986510=3865310
3865310/16986510=0.22755174547
0.22755174547*100=22.755174547
This answer can then be rounded up to 23%
PLEASE HELP!!!!! I DONT UNDERSTAND THIS
The simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2, so option A is correct.
What is equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Given equation:
8y = -2x + 4
Divide both sides by 8,
8y / 8 = -2x / 8 + 4 / 8
Simplify the above expression,
y = -1 / 4x + 1 / 2
Therefore, the simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2.
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two planes flying at the same altitude are heading toward jwd airport. the paths of these planes form a right triangle. the jet is flying due east toward jwd at 450 mph. the turboprop is approaching jwd from the south at 275 mph. when each is 100 miles from the airport how fast is the distance between the planes changing?
The speed of the distance between the two planes is increasing at 325 mph as they approach JWD Airport.
The two planes form a right triangle, with the jet flying due east at 450 mph and the turboprop approaching from the south at 275 mph. The hypotenuse of the triangle is the distance between the planes, and the length of the hypotenuse is changing as the planes approach the airport. The rate of change of the length of the hypotenuse is equal to the sum of the rates of change of the two sides of the triangle, which are the speeds of the jet and the turboprop. As they are both 100 miles from the airport, the speed of the distance between the two planes is equal to the sum of the two speeds, or 450 mph + 275 mph = 325 mph. Therefore, the distance between the two planes is changing at a rate of 325 mph.
Rate of change of distance between the planes = Rate of change of jet + Rate of change of turboprop
= 450 mph + 275 mph
= 325 mph.
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you are dealt five cards from a thoroughly shfuffeld standard deck of cards. what is the probability that you get a full hosue.
The probability of drawing 3 aces and 2 kings is 9.23×[tex]10^{-6}[/tex] and the probability of a “full house” is 0.00144.
5 cards are drawn from a standard deck of 52 cards.
a) Probability that we draw 3 aces and 2 kings
Number of cards = 52
No of aces = 4
No of kings = 4
Number of cards drawn = 5
So, the probability becomes,
Text, letter
Description automatically generated with medium confidence
[tex]4C_{3}4C_{2}[/tex]/[tex]52C_{5}[/tex]
On simplification,
= 24 / 2598960
= 9.23×[tex]10^{-6}[/tex]
So the probability of drawing 3 aces and 2 kings is 9.23 × [tex]10^{-6}[/tex]
b) a “full house” (3 cards of one kind and 2 cards of another kind)
Since there are 13 sets of each type, we have to select any 2 kinds of it.
The probability becomes
(2×[tex]13 C_{2}[/tex]×[tex]4C_{3}[/tex][tex]4C_{2}[/tex])/[tex]52C_{5}[/tex]
On simplification,
= 3744 / 2598960
= 0.00144
So, The probability of a “full house” is 0.00144.
Therefore, the probability of drawing 3 aces and 2 kings is
9.23×[tex]10^{-6}[/tex] and the probability of a “full house” is 0.00144.
The possibility is the department of arithmetic concerning numerical descriptions of ways in all likelihood an event is to arise, or how in all likelihood it's miles that a proposition is authentic. The opportunity of an occasion varies between zero and 1, wherein, more, or less speaks to me, 0 suggests the impossibility of the event and 1 shows reality. The better the probability of an event, the much more likely it's far that the event will arise.
An easy example is the tossing of a fair (unbiased) coin. for the reason that coin is fair, the 2 effects ("heads" and "tails") are each equally probable; the opportunity of "heads" equals the possibility of "tails"; and considering no other outcomes are viable, the opportunity of either "heads" or "tails" is half off (which can additionally be written as 0.5 or 50%).
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find the length of the curve. r(t) = 4t i + 8t3/2 j + 9t2 k, 0 ≤ t ≤ 1
The length of the curve [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex] is 13.
The given curve is defined by the parametric equation [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex].
The length of a curve is given by the formula
⇒ [tex]|| r(t) || = \int\limits^a_b {\sqrt{{(x')^{2}} + (y')^{2} + (z')^{2} } } \, dt[/tex]
where the variables x', y', z' are defined as
[tex]x' = \frac{d(4t)}{dt} = 4 \\y' = \frac{d(8t^{3/2})}{dt} = 12t^{1/2} \\x' = \frac{d(9t^{2})}{dt} = 18t\\[/tex]
Hence, substituting the values in the formula for the length
⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{(4)^{2}} + (12t^{1/2})^{2} + (18t)^{2} } } \, dt[/tex]
⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]
The given definite integral is in the form of
[tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \int\limits^a_b {\sqrt{{ax^{2} + bx + c}} } \, dx[/tex]
where P(x) is a polynomial of degree 2.
Writing the polynomial P(x) as
⇒ [tex]\sqrt{P(x)} = \sqrt{a}\sqrt{{(x + b_1)^{2} + c_1}} dx[/tex]
⇒ [tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \sqrt{a}\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx[/tex]
where [tex]b_1, c_1[/tex] are defined as
⇒ [tex]b_1= \frac{a}{2b} \\c1 = \frac{c}{a} - b_1^{2}[/tex]
Therefore, the solution will be
⇒ [tex]\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx = \frac{(b_1 + x)\sqrt{P(x)} + c_1log{(b_1 + x + \sqrt{P(x)}}}{2}[/tex]
Hence, solving the integral
⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]
we get the value as 13.
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mason stands on the 5^\text{th}5 th 5, start superscript, start text, t, h, end text, end superscript step of a vertical ladder. the ladder has 151515 steps, and the height difference between consecutive steps is 0.5\text{ m}0.5 m0, point, 5, start text, space, m, end text. h(n)h(n)h, (, n, )models the height above the ground of mason's feet (in \text{m}mstart text, m, end text) after moving nnn steps (if mason went down the ladder, nnn is negative.) which number type is more appropriate for the domain of hhh?
Since the stages are simply whole values taken one after the other, they should be whole numbers or integers.
What in mathematics is a whole number?
Complete numbers those figures that contain zero and natural integers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number. Whole numbers are made up of all the ordinal numbers and 0.
Natural numbers are the term used to describe counting numbers in mathematics. Therefore, the whole number can be described as a combination of all natural numbers and 0. Along with zero, all positive integers are also considered whole numbers.
He is currently on step 5, there are 15 steps total, therefore he is actually 10 steps away from the top of the ladder. If we walk down the ladder with N being negative, he is -5 steps from the ground.
{ N | N ∈ ℤ , -5 ⩽ N ⩽ 10 }
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Find the coordinates of the zeros and the vertex in order to graph the parabola represented by the
equation y = -(x - 1)(x - 5).
Answer:
Step-by-step explanation:
y = (-x+1)(x-5)
zeroes
(-x+1)(x-5) = 0
-x + 1 = 0
x = 1
(1,0)
x -5 = 0
x = 5
(5,0)
Vertex
y = (-x+1)(x-5)
y = -x²+5x + x - 5
y = -x² + 6x - 5
x coordinate
-6/-2
3
y coordinate
-(3)² + 6(3) - 5
-9 + 18 - 5
- 14 + 18
4
V(3,4)
please help by today
Step-by-step explanation:
the angle south-east of x is hard to read.
I assume this is 86 (but could be also 96).
remember, the sum of all angles in a triangle is always 180°.
and the intersection angles between 2 lines are the same in both sides of the lines. the only difference between above and below angles is that they are left-right mirrored.
so,
180 = x + 22 + 86
x = 180 - 22 - 86 = 72°
x and y are intersection angles of 2 lines and are therefore equal (due to the left-right mirroring).
y = x = 72°
180 = w + 33 + 72
w = 180 - 33 - 72 = 75°
remember also that the sum of all angles around a single point on one side of a line is always 180°, because the line can be seen as diameter of a circle with the point being the circle center. and the degrees of a half-circle are 180°.
180 = angle1 + unnamed angle = angle1 + 85
angle1 = 180 - 85 = 95°
180 = angle2 + angle3 + unnamed angle =
= 42 + angle3 + 85
angle3 = 180 - 42 - 85 = 53°
for the third question we don't see a picture of the situation. I assume this is a circle with O being the center of the circle, and Q, N, P are points on the circle arc.
it is not clear, if the angle QOP is part of the angle QON, or if they are separate segments of the circle.
if the angle QOP is part of the angle QON, then the angle PON = 142 - 46 = 96°
if the angle QOP is separate from the angle QON, then the angle PON = 360 - 142 - 46 = 172°
Select the correct answer from each drop-down menu. which if formulas are valid? and are valid if formulas.
Answer:
Step-by-step explanation:
Given function g on the graph, what is the domain of this function?
A part of linear function g is graphed on the grid
Answer: -7[tex]\leq[/tex]x[tex]\leq[/tex]6
If g (n +1) = g (n) +6 and g (1)=-25 then g (26)=?
(1) 131
(2) 125
(3) 54
(4) -19
Answer:
(2) 125---------------------------
Given is an AP with:
The first term of - 25,Common difference of 6.Use the explicit rule to find the 26th term:
t(n) = t + (n - 1)d, where t- the first term and d - common differenceg(n) = - 25 + 6(n - 1) = - 25 + 6n - 6 = 6n - 31g(26) = 6*26 - 31 = 156 - 31 = 125Correct choice is (2).
Check for Reasonableness What is a good estimate for 380% of 60? Explain.
what two terms are used to refer to a search in which each value in a sequence is examined until a target value is found or the end of the sequence is reached?
This problem can be solved using divide and conquer techniques. An method known as "divide and conquer" works by breaking down a large task into smaller ones.
An algorithmic pattern is known as Divide and Conquer. In algorithmic approaches, the idea is to take a dispute involving a large amount of input, divide the input into smaller pieces, solve the problem on each of the smaller pieces, and then combine the piecewise solutions into a comprehensive solution. The Divide and Conquer is the algorithmic name of the approach that was used to solve the issue.
The three steps below are used in a dispute utilizing the Divide and Conquer method.
Create a group of subproblems from the main issue.
Conquer: Recursively and individually solve each subproblem.
Combine: Combine the solutions to the individual subproblems to arrive at the overall solution.
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Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme out
There is no statistical support in the data for the claim that seeded clouds typically cover more than 300 acres per foot by average acrefeet.
Since the significance level is set at 0.10, the meteorologists can conclude that the data does not provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
This is because the calculated p-value is greater than the significance level. This means that there is not sufficient evidence to reject the null hypothesis, which states that the average acrefeet from seeded clouds is no greater than 300.
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pete runs an ice cream stand that also sells snow cones served in paper cones. the paper cones he usually uses have a diameter of 6 inches and a height of 2 inches, but his supplier is out of them. as a replacement, he purchases paper cones with a diameter of 2 inches and a height of 6 inches. how do the volumes of the original and replacement cones compare?
Answer:
replacement is 1/3 the volume of the original
Step-by-step explanation:
You want to compare the volumes of a cone with diameter 6 in and height 2 in to one with a diameter of 2 in and height of 6 in.
VolumeThe volume of a cone is jointly proportional to the height and the square of the diameter:
V ∝ d²h
RatioThe ratio of the volume of the replacement cone to the original is ...
r = V2/V1 = ((2 in)²(6 in))/((6 in²)(2 in) = 2/6 = 1/3
The replacement cone has 1/3 the volume of the original.
Inez heard that a a general rule, he hould pend no more than 30% of her take-home pay on rent. If Inez' take-home pay i $46. 800 per year, what i the maximum amount per month that he hould pent or rent?
The maximum amount per month that Inez would spent on rent is $1170 knowing that he could spend no more than 30% of the take home pay.
Here Inez heard that a a general rule, he should pend no more than 30% of her take-home pay on rent. If Inez' take-home pay i $46. 800 per year.
The term Take-home pay is the net amount of income received after the deduction of taxes, benefits, and voluntary contributions from a paycheck. It is the difference resulting from the subtraction of all deductions from gross income.
Pay = $46,800
Total allowed = 46,800 x 0.30
Total allowed = $14,040
Now since we know that there are 12 months in a year, we need to divide the Total allowed by 12 to find how much Inez can pay in rent per month.
14,040 / 12 = $1,170
Following the rule that he could not spend more than certain of the take home pay he should rent $1170.
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What number must multiply each side of the equation to produce the equivalent equation
x = -80
The number must multiply each side of the equation to produce the equivalent equation is -5/3.
What is an equivalent equation?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
The given equation is -3/5 x= 48
Multiply each side of the equation by -5/3, we get
[tex]\frac{-3x}{5} \times\frac{-5}{3} =48\times(\frac{-5}{3} )[/tex]
x=-80
Therefore, the number must multiply each side of the equation to produce the equivalent equation is -5/3.
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"Your question is incomplete, probably the complete question/missing part is:"
What number must multiply each side of the equation -3/5 x= 48 to produce the equivalent equation x= -80?
32 minutes and 2 seconds - 12 minutes and 15 seconds
32 minutes and 2 seconds - 12 minutes and 15 seconds
0 days 0 hours 32 minutes 2 seconds
- 0 days 0 hours 12 minutes 15 seconds
_________________________________
= 0 days 0 hours 19 minutes 47 seconds
[tex]=\fbox{19 minutes and 47 seconds or 19.783333 minutes}[/tex]
Many businesses and organizations insist that official communications use professional-looking fonts, such as times new roman. fonts characterized as less professional, such as comic sans, should be avoided. a student would like to determine if font choice makes a difference in the average grade on a typed response in english classes. there are currently four english classes available from which the student can collect data, and each class has a similar writing assignment. at the start of the assignment, students are randomly assigned a font, either times new roman or comic sans, and then complete the assignment. the teachers grade the assignments, and the mean grade for each font is found.Method A: At the start of the assignment, students choose a font, either Times New Roman or Comic Sans, and then complete the assignment.Method B: At the start of the assignment, students are randomly assigned one of two fonts, either Times New Roman or Comic Sans, and then complete the assignment.In both methods, the teachers grade the papers received, and the mean grade for each font is determined.Which method describes an experiment?a. Method A is an experiment because the students choose their own font.b. Method B is an experiment because the students are randomly assigned a font.c. Both methods describe experiments because both fonts are used on the assignment.d. Neither method describes an experiment because a third font should be included for comparison.
5 3/5÷2 2/3 in its simpilest form
Answer: 2.1
Step-by-step explanation:
Calculator
In a series of transformations, which transformation would make two figures similar as opposed to congruent?a. dilationb. reflectionc. rotationd. translation
In a series of transformations, dilation would make two figures similar as opposed to congruent.
Rotation, reflection and translation are known as rigid transformations.
This means they do not change the size or shape of a figure, they simply move it.
These rigid transformations preserve congruence.
Dilation, however, are not rigid transformation, since they change the size of a shape.
Dilation would not change the shape, just the size: the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation.
This would give us a similar, but not congruent.
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Write an equation of the line that passes through P(3,3) and Q(1,-1).Write the equation in slope intercept form
Answer:
y = 2x-3
Step-by-step explanation:
Find slope from the two points (which is 2)
and then plug in one of the points (either (3,3) or (1,-1)) to find b in y=mx+b.
Combine everything, and there's your equation
An isosceles triangle has a base that is 3 times the length of its legs. The perimeter of the triangle is 45 cm. What is the length of the base?
Answer:
27cm
Step-by-step explanation:
[tex]s + s + s = p \\3x + x + x = 45 \\ 5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]
That's the length of one of its legs
The length of the base = 3x
= 3 x 9
= 45cm
2. Which of the following best represents the
range of the function?
a. All real numbers.
b. y ≤ 3
c. y = 3
d. x ≤ 3
There are no results for an airplane can carry a maximum of 36600 pound of cargo,passenger and luggage.On on the plane's next flight,it will carry 7,320 pounds of cargo.If each passenger with luggage weighs 220 pounds,what is the greatest number of passengers the plane can carry on its next fligh a 33 passenger b 133passenger c 166 passengers d 199 passengers
Answer:
b. 133 passengers
Step-by-step explanation:
The anount of weight taken by the passengers can be up to [tex]36600-7320=29280[/tex] lbs.
Dividing this by [tex]220[/tex] lb per passenger, we get there can be up to [tex]\lfloor 29280/220 \rfloor=133[/tex]
Show your work below in solving the equation
3^x-7=4
give the exact answer do not approximate
Answer:
x= 2.18265833
Step-by-step explanation:
is this for solve for x, because i got decimal if it was solve for x
3^x=4+7
3^x=11
In (3^x)=In (11)
xIn(3)=In (11)
x= In (11)/ In (3) Divide
X= 2.18265833
Shota built a time travel machine, but he can't control the duration of his trip. Each time he uses the machine he has a 0. 80. 80, point, 8 probability of staying in the alternative time for more than an hour. During the first year of testing, shota uses his machine 202020 times. Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour? round your answer to the nearest hundredth. P(\text{at least one} < 1\text{ hour})=.
The Probability that at least one trip will last less than one hour =7/8
What is probability?It refers to the ratio of favorable outcome to the total possible outcome.
The possibility of happening an event is probability.
How to calculate probability of the given question?Probability of staying in the alternative time for more than an hour is 8
each trip is likely to last for more than one hour so probability of at least one trip will last more than an hour =1/8
Now, probability of at least one trip will last less than one hour = 1-1/8
7/8
hence, the result is 7/8
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Quetion
a. Write the formula for the area A of a trapezoid. Ue b1 and b2 for the length of the bae, and ue h for the height. A=
b. Solve the formula for h. H=
c. Ue the new formula to find the height h of the trapezoid. The height of the trapezoid i
centimeter
The formula for the area A of a trapezoid [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex], the formula for the height of the trapezoid is [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] , and the height of the given trapezoid is 6cm.
(a) let us find the formula for the area A of a trapezoid as follows-
As b₁, b₂ being the lengths of the bases and 'h' is the height.
So, the formula for the area A of a trapezoid is given by-
[tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]
(b) Let us solve for the formula for the height h of the trapezoid as follows-
As the formula for the area A of a trapezoid is [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]
So, the formula for height h of the trapezoid can be given by -
[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]
(c) Let us find the new formula to find the height h of the trapezoid as follows-
Using, [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] to find the height h of the trapezoid.
So,
[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]
[tex]h= \frac{2(72)} {16 +8}[/tex] --------(substituting the values of b₁ = 16, b₂ = 8, A = 72cm²)
h = 144/24
h = 6 cm
Hence, the height of the trapezoid is 6cm.
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The complete question is -
a. Write the formula for the area A of a trapezoid. Use b1 and b2 for the length of the base, and use h for the height. A=
b. Solve the formula for h. H=
c. Use the new formula to find the height h of the trapezoid. The height of the trapezoid in centimeters.
Mustafa walks 15 km east and then 10 km south. How far is Mustafa from the starting point? Is in which direction
Answer:
25 kilometres West direction
a van full of storm chasers is driving along a straight road at 94 kilometers per hour in hopes of filming a tornado. the tornado, 7 kilometers away, is traveling along the same road and moving directly toward them, traveling at 69 kilometers per hour. if neither the van nor the tornado changes course, how long will it be before they meet?
The time taken to traveled the van and the tornado before they meet as per the speed of the van and the tornado is equal to 2.6 minutes.
As given in the question,
Speed of the van along the straight road = 94 kilometers per hour
After travelling distance of 7 kilometers
Speed of the tornado along the same road = 69 km/hour
Total relative speed of van and tornado = 94 + 69
= 163km/hour
Distance travelled between two different speed = 7km
Time used to traveled before they meet = distance / speed
= 7 / 163
= 0.043 hours
= 2.58minutes
= 2.6minutes
Therefore, the time required to traveled the van and the tornado before they meet is equal to 2.6 minutes.
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