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2 years ago

HELP DUE SOON EMERGENCY

Mathematics

1 answer:

algol [13]2 years ago

5 0

Answer:

The sum of the series is 44.

Step-by-step explanation:

Sigma notation. I just had a test on this, so this is pretty good timing.

Below the sigma, we see that k = 1. This means that 1 is the number you would substitute for k into the expression on the right to get the first term. In this case, the first term is -2. (2(1)² - 4)

Now, we can also find out the number of terms in the series by subtracting 1 (taken from k = 1) from the number on top of the sigma, 4, and then adding 1 to it.

4 - 1 + 1 = 4. This means there are 4 terms in the series.

See the remaining work in the attached file. You should get that the sum of the series is 44.

Hope this helps!

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If there are 48 boys and 64 girls and the teachers decided to put them each in in equal rows only boys or girls will be in each

german

Answer: 16

Step-by-step explanation:

The question seeks to know the largest number of people that can sit in each row.

To answer this, find the Highest Common Factor of the numbers 48 and 64.

Factors of 48 ⇒ 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

Factors of 64 ⇒ 1, 2, 4, 8, 16, 32 and 64

Because the teacher wants the rows to be equal with either only boys or only girls sitting in them, the highest number of people that can sit in a row will be 16.

There will be 7 rows in total.

Boys ⇒ 48/ 16 = 3 rows

Girls ⇒ 64/16 = 4 rows

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3 years ago

The following question find the value of the variables. If your answer is not an integer leave it in simplest radical form

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Answer:

option 4

Step-by-step explanation:

using the sine/ cosine ratios in the right triangle and the exact values

cos30° = $\frac{\sqrt{3} }{2}$ , sin30° = $\frac{1}{2}$ , then

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{x}{20\sqrt{3} }$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2x = 20 $\sqrt{3}$ × $\sqrt{3}$ = 20 × 3 = 60 ( divide both sides by 2 )

x = 30

and

sin30° = $\frac{opposite}{hypotenuse}$ = $\frac{y}{20\sqrt{3} }$ = $\frac{1}{2}$ ( cross- multiply )

2y = 20 $\sqrt{3}$ ( divide both sides by 2 )

y = 10 $\sqrt{3}$

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2 years ago

Questions are in the pictures

Elan Coil [88]

The values of h and r to maximize the volume are r = 4 and h = 2

<h3>The formula for h in terms of r</h3>

From the question, we have the following equation

2r + 2h = 12

Divide through by 2

r + h = 6

Subtract r from both sides of the equation

h = 6 - r

Hence, the formula for h in terms of r is h = 6 - r

<h3>Formulate a function V(r)</h3>

The volume of a cylinder is

V = πr²h

Substitute h = 6 - r in the above equation

V = πr²(6 - r)

Hence, the function V(r) is V = πr²(6 - r)

<h3>The single critical point</h3>

V = πr²(6 - r)

Expand

V = 6πr² - πr³

Integrate

V' = 12πr - 3πr²

Set to 0

12πr - 3πr² = 0

Divide through by 3π

4r - r² = 0

Factor out r

r(4 - r) = 0

Divide through by 4

4 - r = 0

Solve for r

r = 4

Hence, the single critical point on the interval [0. 6] is r = 4

<h3>Prove that the critical point is a global maximum</h3>

We have:

V = πr²(6 - r)

and

V' = 12πr - 3πr²

Determine the second derivative

V'' = 12π - 6πr

Set r = 4

V'' = 12π - 6π* 4

Evaluate the product

V'' = 12π - 24π

Evaluate the difference

V'' = -12π

Because V'' is negative, then the single critical point is a global maximum

<h3>The values of h and r to maximize the volume</h3>

We have

r = 4 and h = 6 - r

Substitute r = 4 in h = 6 - r

h = 6 - 4

Evaluate

h = 2

Hence, the values of h and r to maximize the volume are r = 4 and h = 2

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brainly.com/question/1869299

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2 years ago

If 3x – 2 = 13, what is the value of x?

inessss [21]

Answer:

x = 5

Step-by-step explanation:

$3x - 2 = 13 \\ 3x = 13 + 2 \\ 3x = 15 \\ x = \frac{15}{3} \\ \huge \red{ \boxed{ x = 5 }}$

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3 years ago

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On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at platform A and zip to each o

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Answer:

We have to travel 26.93 units from platform B to C.

Step-by-step explanation:

Length of a segment having coordinates $(x_1,y_1)$ and $(x_2,y_2)$ is determined by the formula,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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= $\sqrt{725}$

= $5\sqrt{29}$

= 26.93 units

Therefore, we have to travel 26.93 units from platform B to C.

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4 years ago

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