Find the base in the following problem. 100 is 19% of what number?

What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47+ ...?

Alex

Answer:

$\huge\boxed{18,475}$

Step-by-step explanation:

The terms of this sum make the arithmetic sequence.

The fomula of a sum of n terms of an arithmetic sequence:

$S_n=\dfrac{[2a_1+(n-1)d]\cdot n}{2}$

We have

$a_1=2\\d=17-2=32-12=47-32=15\\n=50$

Substitute:

$S_{50}=\dfrac{[2\cdot2+(50-1)\cdot15]\cdot50}{2}=(4+49\cdot15)\cdot25=(4+735)\cdot25\\\\=739\cdot25=18,475$

3 0

3 years ago

A spring with a spring constant k of 100 pounds per foot is loaded with 1-pound weight and brought to equilibrium. It is then st

shutvik [7]

Answer:

Equation of movement y(t)

$y(t)=sin(10t-\pi/2)$

Amplitude: 1 inch

Period: 0.628 seconds

Step-by-step explanation:

If there is no friction, the amplitude will be the length it was streched from the equilibrium. In this case, this value is 1 inch

$A=1\,inch$

The period depends on the mass and the spring constant.

The formula for the period is:

$T=\frac{1}{f} =\frac{2/pi}{\omega} =2\pi\sqrt{\frac{m}{k}}=2\pi\sqrt{\frac{1}{100}}=2\pi*0.1=0.628\, s$

The model y(t) for the movement of the mass-spring system is

$y(t)=A\cdot sin(\omega t +\phi)\\\\A=1\\\\\omega=\sqrt{k/m} =\sqrt{100/1}=10\\\\y(0)=Asin(\phi)=-A\\\\ \phi=arcsin(-1)=-1.571=-\pi/2\\\\\\y(t)=sin(10t-\pi/2)$

8 0

3 years ago

Which ordered pair is a solution of the equation -3x - y = 6

e-lub [12.9K]

Hello there!

The correct answer is option B (-3,3)

-3x - y = 6

-3(-3) - 3 = 6

9 - 3 = 6

6 = 6

Thus, the correct answer is option B

Good luck with your studied!

8 0

3 years ago

Multiply and give the answer in scientific notation:

kakasveta [241]

Step-by-step explanation:

given

$(1.5 \times {10}^{4} )(8 \times {10}^{8} )$

in order to make multiplication easier we need to change the 1.5 into a whole number form.

thus

$(15 \times {10}^{ - 1} \times {10}^{4} )(8 \times {10}^{8} )$

$= (15 \times {10}^{4 - 1} )(8 \times {10}^{8} )$

First law of indices applied there

=(15×10^3)(8×10^8)

=(15×8)(10^3×10^8)

=120×10^3+8 ( first law of indices, which states that , numbers of the same base multiplying each other, take one of the base and add the exponent. and clearly both 15 and 8 are in base 10

=120×10^11

=1.20×10^2 ×10^11

=1.20×10^11+2

=1.20×10^13

so the answer is alt B

7 0

3 years ago

Find the number whose arithmetic square root is 0.6

slavikrds [6]

Answer: 0.36

Step-by-step explanation:

6/10 x 6.10= 36/100

5 0

3 years ago