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3 years ago

What is the sum of the arithmetic sequence 6, 14, 22, if there are 26 terms

1 answer:

3 0

Sum of nth term of arithmetic sequence is given by Sn = n/2[2a + (n - 1)d]
Here, a = 6, n = 26 and d = 14 - 6 = 8
S26 = 26/2[2(6) + (26 - 1)8] = 13[12 + 25(8)] = 2,756

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The length of a rectangular garden is 9 feet longer than its width. If the garden’s perimeter is 182 feet, what is the area of t

Ivanshal [37]

Answer:

1660.75 square feet

Step-by-step explanation.

Width=x

Length =x+9

((x)+(x+9))×2=182 feet

(2x+9)×2=182

18+4x=164

x=36.5

Width=36.5 feet

Length=45.5 feet

Area=36.5×45.5

=1660.75 square feet

8 0

3 years ago

Find the angle between u = (-2,-5) and v = (5,2)

OleMash [197]

The angle between u = (-2,-5) and v = (5,2) is 134 degrees approximately.

Solution:

Given, two vectors are u = (-2, -5) and v = (5, 2)

We have to find the angle between two vectors.

We know that,

$a. b=\|a\| .\|b\| \times \cos \theta$

where $\theta$ is angle between vectors a and b

$\text { Now vectors are }(-2 \vec{\imath}-5 \vec{\jmath}) \text { and }(5 \vec{\imath}+2 \vec{\jmath})$

$(-2 \vec{\imath}-5 \vec{\jmath}) \cdot(5 \vec{\imath}+2 \vec{\jmath})=\sqrt{(-2)^{2}+(-5)^{2}} \times \sqrt{5^{2}+2^{2}} \times \cos \theta$

$\text { since }\|a\|=\sqrt{x^{2}+y^{2}} \text { for } a=x \vec{\imath}+y \vec{\jmath}$

$\begin{array}{l}{-10-10=\sqrt{29} \times \sqrt{29} \times \cos \theta} \\\\ {-20=29 \times \cos \theta} \\\\ {\cos \theta=\frac{-20}{29}} \\\\ {\theta=\cos ^{-1} \frac{-20}{29}} \\\\ {\theta=133.60}\end{array}$

Hence, the angle between given two vectors is 134 degrees approximately.

3 0

3 years ago

This year’s school population in Waterloo is 135 percent of last year’s school population. This year’s student population is 756

sp2606 [1]

Answer:560

Step-by-step explanation:

Let a be the number of students the school have last year

135% of a=756

135/100 x a=756

135a/100=756

Cross multiplying we get

135a=756 x100

135a=75600

Divide both sides by 135

135a/135=75600/135

a=560

6 0

2 years ago

4 less than half a number is 21

svlad2 [7]

I think the number is 50

7 0

2 years ago

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Your friend operates a business and has the following demand curve. Complete the table, and use the information provided to find

hichkok12 [17]

A demand curve shows the quantity demanded of a product at each price.

<h3>What is a demand curve?</h3>

Your information is incomplete as the table isn't given. Therefore, an overview will be given.

A demand curve simply means a graphical representation of the relationship between price and quantity demanded.

In this case, a demand curve shows the quantity demanded of a product at each price. The profit maximizing price is when the marginal cost equals marginal revenue.

Learn more about demand curve on:

brainly.com/question/1486483

3 0

2 years ago

Read 2 more answers