Thirty three ten thousandths=

Inga [223]

(a+b)^7= a^7+ 7a^7b+ 21 a^6b²+ 35a^5b³+ 35 a⁴b⁴+ 21 a³b^5 + 7a²b^6 + b^7

8 0

3 years ago

"You are dating Moon rocks based on their proportions of uranium-238 (half-life of about 4.5 billion years) and its ultimate dec

Olenka [21]

Step-by-step explanation:

a.

Initial mass of the isotope = x

Time taken by the sample to decay its mass by 41% = t

Formula used :

$N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}$

where,

$N_o$ = initial mass of isotope = x

N = mass of the parent isotope left after the time, (t) = 59% of x = 0.59x

$t_{\frac{1}{2}}$ = half life of the isotope = 4.5 billion years

$\lambda$ = rate constant

Now put all the given values in this formula, we get

$0.59x=x\times e^{-(\frac{0.693}{\text{4.5 billion years}})\times t}$

t = 3.4 billion years

The age a rock is 3.4 billion years.

b.

Initial mass of the isotope = x

Time taken by the sample to decay its mass by 35%= t

Formula used :

$N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}$

where,

$N_o$ = initial mass of isotope = x

N = mass of the parent isotope left after the time, (t) = 65% of x = 0.65x

$t_{\frac{1}{2}}$ = half life of the isotope = 4.5 billion years

$\lambda$ = rate constant

Now put all the given values in this formula, we get

$0.65x=x\times e^{-(\frac{0.693}{\text{4.5 billion years}})\times t}$

t = 2.8 billion years

The age a rock is 2.8 billion years.

5 0

4 years ago

If theta is a positive acute angles find theta when 2 sin^2 theta + 3 cos theta =3

MArishka [77]

Answer:

Theta = 0, 60 degrees.

Step-by-step explanation:

2 sin^2 theta + 3 cos theta = 3

Using the identity sin ^2 theta = 1 - cos^2 theta :

2(1 - cos^2 theta) + 3 cos theta = 3

2 - 2cos^2 theta) + 3 cos theta = 3

2 cos^2 theta - 3 cos theta + 3 - 2 = 0

2 cos^2 theta - 3 cos theta + 1 = 0

(2 cos theta - 1)(cos theta - 1) = 0

cos theta = 1/2 , cos theta = 1

Theta = 60 degrees or theta = 0

6 0

3 years ago

Solve the simultaneous equation : 4x+2y=17 3x+2y=14

enot [183]

Answer:

(x, y) = (3, 5/2)

Step-by-step explanation:

$4x+2y=17\\3x+2y=14$

I'll solve by elimination here. If you invert the second equation and add it to the first, 2y and -2y would cancel out.

$4x+2y=17\\-(3x+2y=14)$

Now just add those from top to bottom.

$\rightarrow (4x-3x)+(2y-2y)=17-14\\\rightarrow x=3$

Nothing else needs to be done for that part. Now, you can pick either equation and use the known value of x to solve for y.

$4x+2y=17\\\rightarrow 4(3)+2y=17\\\rightarrow 12+2y=17\\\rightarrow 2y=5\\\rightarrow y=\frac{5}{2}$

(x, y) = (3, 5/2)

6 0

3 years ago

Anyone wanna help ....

just olya [345]

Answer:

$d \approx 12.6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra II

Distance Formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point (-4, -6)

Point (8, -10)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute [DF]: $d = \sqrt{(8+4)^2+(-10+6)^2}$
Add: $d = \sqrt{(12)^2+(-4)^2}$
Exponents: $d = \sqrt{144+16}$
Add: $d = \sqrt{160}$
Simplify: $d = 4\sqrt{10}$
Evaluate: $d = 12.6491$
Round: $d \approx 12.6$

7 0

3 years ago