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STALIN [3.7K]
3 years ago
5

Evaluate Integral: 2sin(2x) from 0, pi/2

Mathematics
1 answer:
Neko [114]3 years ago
8 0
Integral of 2sin(2x) is -cos(2x)
from 0 to pi/2 (sub pi/2 minus sub 0 for x) and then solve
= -cos(2*pi/2)-(-cos0)
= -cos pi + cos 0
= 1 + 1
= 2 
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A vehicle travels 250 feet every three seconds find the value of the ratio, the unit rate, and the constant proportionality. How
lidiya [134]

Answer:

The ratio, the unit rate and the constant of proportionality are same but with different name.

Step-by-step explanation:

A vehicle travels 250 feet every three seconds.

(i) So, the ratio is \frac{250}{3}  feet/seconds.

(ii) The unit rate means the rate of change of distance with respect to unit time,

The vehicle in three seconds moves by 250 feet.

Hence, the vehicle in one second will move by \frac{250}{3} feet.

Therefore, the unit rate is \frac{250}{3} feet/seconds.

(iii) The relation between the distance traveled (d) and the time of travel (T) is proportional.

So, D ∝ T, ⇒ D = kT ......... (1) {Where, k is the constant of proportionality}

Since D = 250 feet at T = 3 seconds

So, from equation (1), k = \frac{D}{T} = \frac{250}{3}  feet/seconds.

Therefore, from the above explanation it is clear that the ratio, the unit rate and the constant of proportionality are same but with different name. (Answer)

8 0
3 years ago
I’m so confused, can somebody help me do this?
ValentinkaMS [17]

Answer:

1. -2=-x - 9,   7=-x,  -7=x

2. -1=-x - 9,   8=-x,  -8=x

3. 0=-x - 9,   9=-x,   -9=x

4. 1=-x - 9,   10=-x,    -10=x

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7 0
2 years ago
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A box has the shape of a rectangular prism with height 30 cm. If the height is increased by 0.9 ​cm, by how much does the surfac
crimeas [40]

Answer:

The corresponding increase in surface area of the rectangular prism for an increase of 0.9 cm in height is given by

ΔS = [1.8 (L + B)] cm

where L = length of the rectangular prism

B = Breadth of the rectangular prism

Step-by-step explanation:

A rectangular prism is essentially a cuboid.

The surface area of the cuboid is given as

S = 2[LB + LH + BH]

where

L = length of the rectangular prism

B = Breadth of the rectangular prism

H = Height of the rectangular prism

S = 2LB + 2LH + 2BH

Derivative explains that, for small changes in the two quantities,

(∂S/∂H) = (ΔS/ΔH)

ΔS = ΔH × (∂S/∂H)

S = 2LB + 2LH + 2BH

(∂S/∂H) = 2L + 2B = 2(L + B)

ΔH = 0.9 cm

ΔS = ΔH × (∂S/∂H)

ΔS = 0.9 × 2(L + B) = 1.8 (L + B)

A rectangular prism is essentially a cuboid.

The surface area of the cuboid is given as

S = 2[LB + LH + BH]

where

L = length of the rectangular prism

B = Breadth of the rectangular prism

H = Height of the rectangular prism

S = 2LB + 2LH + 2BH

If the height of the rectangular prism increases by 0.9 cm

S(new) = (2×L×B) + 2L(H + 0.9) + 2B(H + 0.9)

S(new) = 2LB + 2LH + 1.8L + 2BH + 1.8B

S(new) = 2LB + 2LH + 2BH + 1.8L + 1.8B

The old surface area, S = 2LB + 2LH + 2BH

Hence, the change or increase in surface area is S(new) - S

[2LB + 2LH + 2BH + 1.8L + 1.8B] - [2LB + 2LH + 2BH] = 1.8L + 1.8B = 1.8 (L + B)

Still the same increase in surface area as obtained by the first method.

Hope this Helps!!!

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3 years ago
One number is 2 more than another. The difference between their squares is 52. What are the numbers?
kirza4 [7]
The numbers are 12 and 14.
4 0
4 years ago
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A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/4 of what remained. How many copies do
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Answer:

30

Step-by-step explanation:

1/3 of 60 is 20

40 would be left

1/4 of 40 is 10 so 30 would be left

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