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3 years ago

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a runner warms up for ten minutes and then takes seven minutes to run each mile. the total time after r miles in 45 minutes. how

manymiles are run

1 answer:

Alika [10]3 years ago

6 0

45=10+7x
35=7x
5=x

Answer: they ran 5 miles

Hope this helps:)

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You stand a known distance from the base of the tree, measure the angle of elevation the top of the tree to be 15â—¦ , and then

gogolik [260]

Answer:

The maximum possible error of in measurement of the angle is $d\theta_1 =(14.36p)^o$

Step-by-step explanation:

From the question we are told that

The angle of elevation is $\theta_1 = 15 ^o = \frac{\pi}{12}$

The height of the tree is h

The distance from the base is D

h is mathematically represented as

$h = D tan \theta$ Note : this evaluated using SOHCAHTOA i,e

$tan\theta = \frac{h}{D}$

Generally for small angles the series approximation of $tan \theta \ is$

$tan \theta = \theta + \frac{\theta ^3 }{3}$

So given that $\theta = 15 \ which \ is \ small$

$h = D (\theta + \frac{\theta^3}{3} )$

$dh = D (1 + \theta^2) d\theta$

=> $\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta$

Now from the question the relative error of height should be at most

$\pm p$ %

=> $\frac{dh}{h} = \pm p$

=> $\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p$

=> $d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p$

So for $\theta_1$

$d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p$

substituting values

$d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p$

=> $d\theta_1 = 0.25 p$

Converting to degree

$d\theta_1 = (0.25* 57.29) p$

$d\theta_1 =(14.36p)^o$

4 0

3 years ago

Hello can some one please help me

Artemon [7]

It’s 4/25 because 2/5 times 2/5 the numerator is 2 times 2 which is four and the denominator is 5 times 5 which is 25

8 0

2 years ago

Read 2 more answers

Evaluate the expression when a=3 and b=-6.<br> -a +6b

Tcecarenko [31]

Answer:

Step-by-step explanation:

-a + 6b = -3 + 6 * (-6) = -3 - 36 = -39

5 0

3 years ago

Read 2 more answers

Can the sides of a triangle have lengths 3, 3, and 10?

Bingel [31]

Answer:

No

Step-by-step explanation:

According to the property of the triangle ,

sum of any two sides should we greater then third side of the triangle.

Here, Measurement of three sides are given as 3,3,5 .

So, sum of the measurement of first two sides is 6.

And third side equals 10.

Clearly 6 is less than 10. So . it violates the property sum of any two sides should we greater then third side of the triangle.

Thus , Sides of a triangle can't be 3,3,10.

8 0

3 years ago

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What whole number dimensions would allow the students to maximize the volume while keeping the surface area at most 160 square f

ycow [4]

Answer:

The whole number dimension that would allow the student to maximize the volume while keeping the surface area at most 160 square is 6 ft

Step-by-step explanation:

Here we are required find the size of the sides of a dunk tank (cube with open top) such that the surface area is ≤ 160 ft²

For maximum volume, the side length, s of the cube must all be equal ;

Therefore area of one side = s²

Number of sides in a cube with top open = 5 sides

Area of surface = 5 × s² = 180

Therefore s² = 180/5 = 36

s² = 36

s = √36 = 6 ft

Therefore, the whole number dimension that would allow the student to maximize the volume while keeping the surface area at most 160 square = 6 ft.

6 0

3 years ago