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Natasha2012 [34]
2 years ago
9

In driving down to Salem, Nathan strictly followed the speed limit. He drove 55 mph for 15 minutes in the city and then 65 mph f

or 25 min through the countryside.
What was Nathan’s average speed for the whole trip?
Mathematics
1 answer:
Rashid [163]2 years ago
7 0

61.25MPH

55*15+65*25=2450

2450/40=61.25MPH

ANSWER IS 61.25 MPH

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Assume that y varies directly with x then solve y = 2.5 x = .5 when x = 20
velikii [3]

Step-by-step explanation:

y=2.5| ?

x=0.5| 20

It'll be criss-crossed then it'll be:-

2.5×20=50

5 0
2 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
What is the volume of this cone?
olchik [2.2K]

Answer:

The volume of the cone is approximately 453.0 cm³

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and radius.  That gives us  1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length.  We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length.  You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

a^2 = b^2 + c^2

So we can find the height of the cone with that:

10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = \sqrt{61.88}\\h \approx  7.9

Now that we have the cone's height, we can solve for its volume:

v = \frac{1}{3} \pi r^2 h\\v = \frac{1}{3} \pi \times 7.4^2  \times 7.9\\v = \frac{1}{3} \pi \times 54.76 \times 7.9\\v = \frac{1}{3} \pi \times 432.6\\v = \pi \times 144.2\\v \approx 453.0 cm^3

5 0
3 years ago
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The radius of a circle is 6 in. Find the circumference to the nearest tenth.
ycow [4]

Answer:

37.7

Step-by-step explanation:

The orginal answer is 37.699

But you want to round the tenth

So 9 to the 6 you want to rasie the score

6 turns into a 7 and the numbers behind it (9 and the other 9) turn into a zero

37.7 or 37.700

8 0
2 years ago
In finance the notion of expected value is used to analyze investments for which the investor has an estimate of the chances ass
blagie [28]

Answer:

Step-by-step explanation:

The expected return is given as

Expected Return = SUM (Return i x Probability i). i=1,2,3.....

First investment

Probability of 0.7, it returns 60cents per dollars

Second investment

Probably of 0.3, it loses 20cents per dollar.

Expected return=(0.7×60)-(0.3×20)

Excepted return= 42-6

Excepted return=36cents

To dollars, 1cents is 0.01dollars

Then, 36cents = 0.36dollars

Expected return=$0.36

7 0
2 years ago
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