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3 years ago

Find 1 plus +2 plus +3 plus +4 plus +... plus + 50 50, the sum of the first 50 50 natural numbers.

Mathematics

1 answer:

anygoal [31]3 years ago

3 0

Answer:

1275

Step-by-step explanation:

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50 never get tired of counting

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Starting from 50 feet away your friend skates towards you and then passes you. She skates at a constant speed of 10 feet per sec

Kitty [74]

12 sec..............

6 0

4 years ago

Two distinct solid fuel propellants, type A and type B, are being considered for a space program activity. Burning rates of the

Finger [1]

Answer:

C.I. = (2.297, 11.703)

Step-by-step explanation:

The t-statistic for difference of mean is given by,

$t=\frac{\bar{x_{1}}-\bar{x_{2}}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$

Here, $\bar{x_{1}}$ = 84

$\bar{x_{2}}$ = 7

s₁ = 4

n₁ = 12

s₂ = 6

n₂ = 18

Substituting all value in formula,

We get, t = -3.541 at 28 degree of freedom.

Using this formula, we get, t = 1.5342

Therefore, based on the data provided, the 99% confidence interval for the difference between the population means $\bar{x_{1}}-\bar{x_{2}}$ is: 2.297 < $\bar{x_{1}}-\bar{x_{2}}$ < 11.703

which indicates that we are 99% confident that the true difference between population means is contained by the interval (2.297, 11.703)

6 0

3 years ago

Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

5 0

3 years ago

11) MZHGF = 16x + 4, m EGF = 110°,<br> and MZHGE = 3x + 11. Find x.<br> G<br> H<br> F<br> E

Darya [45]

<h3>Answer: x = 9</h3>

=======================================================

Explanation:

The smaller angles HGE and EGF combine to form the largest angle HGF.

This is an example of the angle addition postulate.

(angle HGE) + (angle EGF) = angle HGF

(3x+11) + (110) = 16x+4

3x+121 = 16x+4

121-4 = 16x-3x

117 = 13x

13x = 117

x = 117/13

x = 9 which is the final answer

We can stop here.

--------------------

Extra info (optional section)

Use this x value to find each angle shown below

angle HGE = 3x+11 = 3*9+11 = 27+11 = 38 degrees
angle HGF = 16x+4 = 16*9+4 = 144+4 = 148 degrees

Then notice how,

(angle HGE)+(angle EGF) = 38+110 = 148

which is exactly the measure of angle HGF

This confirms that the equation

(angle HGE) + (angle EGF) = angle HGF

is true for that x value of x = 9. Therefore, the answer is confirmed.

6 0

3 years ago

Read 2 more answers

The distances in a children’s traithlon are swimming 1/4 mile,running 3/4 mile,and biking 3/4 mile.What is the total length of t

Marina86 [1]

Answer:

Step-by-step explanation:

1/4+3/4+3/4= 7/4

Now, we need to express as a mixed number.

7/4 = (4+3)/4 = (4/4) + (3/4) = 1 + 3/4 = 1 3/4

Answer C.

4 0

3 years ago

Find 1 plus +2 plus +3 plus +4 plus +... plus + 50 50​, the sum of the first 50 50 natural numbers.

Find 1 plus +2 plus +3 plus +4 plus +... plus + 50 50, the sum of the first 50 50 natural numbers.