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2 years ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Mathematics

1 answer:

Troyanec [42]2 years ago

8 0

Answer: 300

Step-by-step explanation:

Let the number be represented by x.

Therefore, based on the information given in the question, this can be expressed as:

36% of x = 108

36/100 × x = 108

0.36 × x = 108

0.36x = 108

x = 108/0.36

x = 300

Therefore, the number is 300

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The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correc

masya89 [10]

Answer:

Therefore the angle of intersection is $\theta =79.48^\circ$

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

$r_1(t)=(2t,t^2,t^4)$

and $r_2(t)=(sin t , sin5t, 2t)$

To find the tangent of a carve , we have to differentiate the carve.

$r'_1(t)=(2,2t,4t^3)$

The tangent at (0,0,0) is [ since the intersection point is (0,0,0)]

$r'_1(0)=(2,0,0)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{2^2+0^2+0^2} =2$

Again,

$r'_2(t)=(cos t ,5 cos5t, 2)$

The tangent at (0,0,0) is

$r'_2(0)=(1 ,5, 2)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{1^2+5^2+2^2} =\sqrt{30}$

If θ is angle between tangent, then

$cos \theta =\frac{r'_1(0).r'_2(0)}{|r'_1(0)|.|r'_2(0)|}$

$\Rightarrow cos \theta =\frac{(2,0,0).(1,5,2)}{2.\sqrt{30} }$

$\Rightarrow cos \theta =\frac{2}{2\sqrt{30} }$

$\Rightarrow cos \theta =\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =cos^{-1}\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =79.48^\circ$

Therefore the angle of intersection is $\theta =79.48^\circ$ .

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2 years ago

Inscribe a circle in a unit square and to r= 1000 random.

Oduvanchick [21]

Step-by-step explanation:

area of square = 1

area of a circle in square = $\pi r^2 = \pi *(1/2)^2 = \frac{\pi }{4}$

bu estimate $p^ = X/n = 760/1000 = 0.76Therefore, 
[tex]\frac{\pi }{4} \approx 0.76$

$\pi \approx 0.76*4 =3.04$

b) if n tend to infinity

$\pi will approach 3.14$

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2 years ago

tara needs 216 blocks. each box had 10 bags. each bag has 10blocks how many boxes bags and single blocks does she need to make 2

Fed [463]

2 boxes, 1 bag, and 6 blocks

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pochemuha

Answer:

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