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Sunny_sXe [5.5K]
3 years ago
14

Find the dot product of v=-7i+4j and w=-6+5j

Mathematics
1 answer:
Anna35 [415]3 years ago
6 0
V•w = (-7i +4j)•(-6i +5j) = (-7)×(-6) +4×5 = 42 +20
v•w = 62
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How many terms are there in a geometric series if the first term is 4, the common ration is 3 and the sum of the series is 160
Marina CMI [18]
\bf \qquad \qquad \textit{sum of a finite geometric sequence}
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S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
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a_1=4\\
r=3\\
S_n=160
\end{cases}

\bf 160=4\left( \cfrac{1-3^n}{1-3} \right)\implies 160=4\left( \cfrac{1-3^n}{-2} \right)\implies 160=-2(1-3^n)
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160=2(3^n-1)\implies \cfrac{160}{2}=3^n-1\implies 80=3^n-1
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81=3^n~~
\begin{cases}
81=3\cdot 3\cdot 3\cdot 3\\
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3 0
3 years ago
2. The rectangular floor of a garage has an area of 198 square feet. Andy knows that the floor is 7
Charra [1.4K]

Answer:

length = 18 ft

Step-by-step explanation:

Let w = width

L = w+7

Area = l*w

198 = (w+7) (w)

Distribute

198 = w^2 +7w

Subtract 198 from each side

0 = w^2 +7w -198

Factor

What 2 numbers multiply to -198 and add to 7

18* -11 = -198

18+-11 = 7

0=(w+18) (w-11)

Using the zero product property

w+18 =0  w-11=0

w= -18   w=11

We cannot have negative width  so w=11

We want the length

l = w+7

l = 11+7 = 18

6 0
3 years ago
What is the slope of the line passing through the points (−3, −5) and (−1, −6)
inessss [21]

slope = (y2-y1)/(x2-x1)

m= (-6--5)/(-1--3)

m = (-6+5)/(-1+3)

m=-1/2

4 0
3 years ago
Use a single digit times a power of 10 to express the number 866,214,000,000
BartSMP [9]

Answer:

8.66214 x 10^11

Step-by-step explanation:

question may ask to round, so the answer may be simplified to 9 x 10^11

3 0
3 years ago
J.k. Rowling and R.L. Stone are both ready hunger games . J.k. Reads 35 pages every 2 hours and R.L. Reads 45 pages every 3 hour
san4es73 [151]

Answer:

The rate of change for each reader is :

For J K Rowling :  17 and a half pages per hour

For R L Stone :  15   pages  per hour

Step-by-step explanation:

Here the reading rate of each reader is given as:

J.K. Reads 35 pages every 2 hours.

So, the number of pages read by J K  in 2 hours  = 35 pages

⇒ The number of pages read per hour  =  35 / 2  = 17 . 5 pages

So, the pages read by J K Rowling in 1 hour is 17 and a half pages.

R L Stone reads 45 pages every 3 hours.

So, the number of pages read by R L  in 3 hours  = 45 pages

⇒ The number of pages read per hour  =  45 / 3  = 15 pages

So, the pages read by R L Stone in 1 hour is 15 pages.

Hence, the rate of change for each reader is :

For J K Rowling :  17 and a half pages  per hour

For R L Stone :  15   pages  per hour

5 0
3 years ago
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