A trapezoid with area of 195cmhas bases 7 cm long and 32cm long. What is

1^2 +2^2+••••+n^2=1/6n(n+1)(2n+1) using maths induction

crimeas [40]

Hello,

$if\ n=1\ then\ 1^2=1\ and\ \dfrac{1}{6}*1*2*3=1:\ true\ for\ n=1\\$

We suppose the property true for n:

1²+2²+...+n²=n(n+1)(2n+1) / 6

and we are going to demonstrate that the property is true for n+1:

1²+2²+..+(n+1)²=(n+1)*(n+2)*(2n+3)/6

$1^2+2^2+...+n^2+(n+1)^2\\\\=n*(n+1)*(2n+1)/6+(n+1)^2\\\\=(n+1)/6*[n(2n+1)+6n+6]\\\\=(n+1)/6*(2n^2+7n+6)\\\\=(n+1)(n+2)(2n+3)/6\\$

5 0

3 years ago

Help me solve this problem please

Anton [14]

Answer:

y=-5x thats it so ype it in ir whatevet

4 0

3 years ago

Read 2 more answers

Calculate the side lengths a and b to two decimal places.

navik [9.2K]

Answer:

D. a = 11.71 and b = 15.56

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Trigonometry

All angles in a triangle add up to 180°

Pre-Calculus

Law of Sines: $\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}$

Step-by-step explanation:

Step 1: Define

AC = b

CB = a

AB = 7

m∠A = 45°

m∠B = 110°

m∠C = ?

Step 2: Find missing ∠

Set up equation: m∠C + 45° + 110° = 180°
Combine like terms: m∠C + 115° = 180°
Isolate unknown: m∠C = 25°

Step 3: Find measure of b

Substitute: $\frac{sin(25)}{7} =\frac{sin(110)}{b}$
Cross-multiply: $bsin(25)=7sin(110)$
Isolate b: $b=\frac{7sin(110)}{sin(25)}$
Evaluate: $b=15.5645$
Round: $b \approx 15.56$

Step 4: Find measure of a

Substitute: $\frac{sin(25)}{7} =\frac{sin(45)}{a}$
Cross-multiply: $asin(25)=7sin(45)$
Isolate a: $a=\frac{7sin(45)}{sin(25)}$
Evaluate: $a=11.7121$
Round: $a \approx 11.71$

6 0

3 years ago

*PLSSSSS HELP*

klemol [59]

Answer: 39 untits 2

Step-by-step explanation:

Hi, to answer this question, first we have to calculate the perimeter (sum of sides) of the triangle:

Perimeter: 7+6+9.22 = 22.22 units

Then we have to apply the circumference (C) formula:

C = π x diameter

Since C = perimeter of the triangle:

22.22 = 3.14 d

22.22 /3.14 =d

7.08 = d

Finally, we apply the next formula:

Area of a circle = π (d/2)^2

Replacing:

A = 3.14 (7.08/2)^2 = 39.30 units2 = 39 units 2

4 0

3 years ago

John took a 5 ½ mile walk to his friend’s house. He left at 11 a.m. and arrived at his friend’s house at 1 p.m. What was John’s

olganol [36]

Answer:

5.5 miles over 2 hours--> 5.5/2= 2.75 miles per hour was his average walking speed. 5.5 miles over 2.5 hours --> 5.5/2.5= 2.2 miles per hour on the return trip meaning that his average speed was (2.75-2.2= 0.55) 0.55 miles per hour lower on the return trip

Step-by-step explanation:

I hope this helps you :)

-KeairaDickson

7 0

3 years ago