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2 years ago

1) Simplify the expression

Mathematics

1 answer:

bazaltina [42]2 years ago

4 0

Answer:

21 + 12i

Step-by-step explanation:

Given

(3 - 4i)(1 + 5i) - (2 - i) expand the product of factors

= 3 + 11i - 20i² - 2 + i

= 3 + 11i + 20 - 2 + i collect like terms

= 21 + 12i

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Which of these shows the following expression factored completely? 6x2 – 13x +5

stiks02 [169]

Answer:

Step-by-step explanation:

That's my guess.

7 0

3 years ago

Find the average velocity of the function over the given interval.

snow_lady [41]

Answer:

Average velocity of the function over the given interval

= $log(\frac{7}{4} ) -2$

Step-by-step explanation:

Explanation:-

Given function y = 3/x -2 ...(i)

The average velocity of the function over the given interval

Average velocity = $\frac{1}{b-a} \int\limits^b_a {(\frac{3}{x} -2)} \, dx$

= $\frac{1}{7-4} \int\limits^7_4 {(\frac{3}{x} -2)} \, dx$

now integrating

= $\frac{1}{3}( \int\limits^7_4 {(\frac{3}{x} )} \, dx-2\int\limits^7_4 {1} \, dx )$

= $\frac{1}{3} (3 (log x) - 2 x )_{4} ^{7}$

= $\frac{1}{3}( (3 (log 7) - 14 )-(3 log 4 -8))$

by using formulas

log a-log b = log(a/b)

on simplification , we get

= $\frac{1}{3}( (3 (log 7) -3 log 4 ) - \frac{1}{3} (6)$

= $log(\frac{7}{4} ) -2$

Average velocity of the function over the given interval

= $log(\frac{7}{4} ) -2$

6 0

2 years ago

Identify the volume of a cone with base area 64π m2 and a height 4 m less than 3 times the radius, rounded to the nearest tenth.

melomori [17]

V=basearea times 1/3 times height
basearea=64π m2
hmm, they try to make it difficult

basearea=circle=pir^2
pir^2=64pi
divide by pi
r^2=64
sqrt
r=9

h is 4 les than 3 time r
h=-4+3(8)
h=-4+24
h=20

v=1/3*64pi*20=1280pi/3 m^3=1350.4

C

4 0

3 years ago

A rectangular garden is extended 4% on the long sides and 8% on the short sides. To the nearest hundredth of a percent, by what

liq [111]

Answer: 12.32%

Step-by-step explanation:

1. $x$ is the original long side and $y$ is the original short side.

2. The area of the original rectangle is $xy$ .

3. The rectangle is extended 4% on the long sides and 8% on the short sides. therefore, the new long side is:

$\frac{104}{100}x=\frac{26}{25}x$

4. And the new short side is:

$\frac{108}{100}y=\frac{27}{25}y$

5. The new area is:

$(\frac{26}{25}x)(\frac{27}{25}y)=\frac{702}{625}xy$

6. The percentage of increase is calculated by substracting the new area and the original area:

$\frac{702}{625}xy-xy=0.1232xy$

7. The result is:

(0.1232)(100)=12.32%

3 0

3 years ago

Juan rode 72 km on his bike in 4 hours. Find the unite rate.

Westkost [7]

Answer:

18 km/hr

Step-by-step explanation:

To find the unit rate, we must find the rate in kilometers per hour.

Let’s divide the total kilometers by the total number of hours.

unit rate = kilometers/hours

Juan rode 72 kilometers in 4 hours.

unit rate = 72 kilometers/ 4 hours

unit rate = 72 km/4 hrs

unit rate = 18 km / hr

The unit rate is 18 kilometers per hour.

3 0

3 years ago