Find the sum of the first 7 terms of the following series, to the nearest integer. 125,50,20,...

A circular dance stage has a perimeter of 28(3.14) feet. What is the area, in square feet, of this dance stage?

tiny-mole [99]

The perimeter (circumference) = 28 * PI.
This means the diameter = 28.
The area = PI*radius^2
area = PI * 14^2
area = PI * 196 
area = 615.7521601036 square feet

4 0

3 years ago

If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

The sum of two numbers is 28. one number is 14 more. find the numbers

ruslelena [56]

The numbers are: "7 " and "21 " .
_______________________________________
Explanation:
_______________________________________
The numbers are: "x" and "x + 14" .

x + (x + 14) = 28 . Solve for "x" ; and then solve for "x + 14" .
_______________________________________
→ x + (x + 14) = 28 ;

Rewrite as:

→ x + x + 14 = 28 ;

→ 1x + 1x + 14 = 28 ;

→ 2x + 14 = 28 ;

Subtract "14" from each side of the equation;

→ 2x + 14 − 14 = 28 − 14 ;

 → 2x = 14 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 2x / 2 = 14 / 2 ;

→ x = 7 .
_________________________________________
So; one of the numbers is: " 7 " .

The other number is: " x + 14 " ; which equals: " 7 + 14 = 21".

The other number is: "21 " .
_________________________________________
The numbers are: "7 " and "21 " .
_________________________________________

5 0

3 years ago

The diameter of a circle is 50 inches.The radius of the circle is A) 100 inches B) 25 inches C) 157 inches D) 45 inches ...so wh

klasskru [66]

The answer is B, 25 inches.

7 0

3 years ago

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Luda [366]

Bfukbcfjm jejejand keke a snow d chaka disks

4 0

3 years ago