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3 years ago

10

What is the product in lowest terms?

2 answers:

BaLLatris [955]3 years ago

8 0

I don't know what lowest terms means but the answer is -416216.

Gala2k [10]3 years ago

7 0

-539 is the lowest term out of your answers

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I don’t know this one

Taya2010 [7]

74 degrees, because angle 1 and 8 add up to 73 degrees, so to make 180 you subtract 180-73 degrees, which makes 112 degrees for angle 9. Angle 9 and 12 are supplementary so they should both add up to 180. That means that angle 12 must be 68. Angles 12, 7, and 6 must add up to 180, so 38+68=106. 180-106=74. Therefore, angle 6 is 74 degrees

3 0

3 years ago

You have been asked to design a can shaped like right circular cylinder that can hold a volume of 432π-cm3. What dimensions of t

rosijanka [135]

Answer:

$Height = 12cm$

$Radius = 6cm$

Step-by-step explanation:

Given

Represent volume with v, height with h and radius with r

$V = 432\pi$

Required

Determine the values of h and r that uses the least amount of material

Volume is calculated as:

$V = \pi r^2h\\$

Substitute 432π for V

$432\pi = \pi r^2h$

Divide through by π

$432 = r^2h$

Make h the subject:

$h = \frac{432}{r^2}$

Surface Area (A) of a cylinder is calculated as thus:

$A=2\pi rh+2\pi r^2$

Substitute $\frac{432}{r^2}$ for h in $A=2\pi rh+2\pi r^2$

$A=2\pi r(\frac{432}{r^2})+2\pi r^2$

$A=2\pi (\frac{432}{r})+2\pi r^2$

Factorize:

$A=2\pi (\frac{432}{r} + r^2)$

To minimize, we have to differentiate both sides and set $A' = 0$

$A'=2\pi (-\frac{432}{r^2} + 2r)$

Set $A' = 0$

$0=2\pi (-\frac{432}{r^2} + 2r)$

Divide through by $2\pi$

$0= -\frac{432}{r^2} + 2r$

$\frac{432}{r^2} = 2r$

Cross Multiply

$2r * r^2 = 432$

$2r^3 = 432$

Divide through by 2

$r^3 = 216$

Take cube roots of both sides

$r = \sqrt[3]{216}$

$r = 6$

Recall that:

$h = \frac{432}{r^2}$

$h = \frac{432}{6^2}$

$h = \frac{432}{36}$

$h = 12$

Hence, the dimension that requires the least amount of material is when

$Height = 12cm$

$Radius = 6cm$

3 0

3 years ago

A science class began recording the height of a plant each day. On day 10, it was 20 cm tall. On day 35, it was 57.5 cm tall. Wh

Simora [160]

The plant grew 1.5 cm each day.

4 0

3 years ago

Read 2 more answers

What is the elevation of skiier at the top of the mountain?

tatuchka [14]

The elevation of the skiier at the top of the mounting is given by 2,395 - 642 = 1,753.

4 0

3 years ago

Plz I NEEEEED HELP NOWWWW PLZ PLZ PLZ

Liula [17]

<h2>○=> <u>Correct option</u> :</h2><h2> $\color{hotpink}\bold{ (a) \: 130}$ </h2><h3>○=> <u>Steps to derive correct option</u> :</h3>

Angle (p+7)° and angle (3p+1)° are a linear pair so their sum will be equal to 180°.

Which means :

$=\tt 3p + 1 + p + 7 = 180$

Let us solve that equation to find the value of p and the two angles :

$=\tt 3p + 1 + p + 7 = 180$

$=\tt 3p + p + 1 + 7 = 180$

$=\tt 4p + 8 = 180$

$= \tt4p = 180 - 8$

$= \tt4p = 172$

$=\tt p = \frac{172}{4}$

$\hookrightarrow \tt \color{plum}p = 43$

Thus, value of p = 43

Measure of angle (p+7)° :

$=\tt 43 + 7$

$\tt\color{plum}angle \: (p + 7)° =\tt 50°$

Measure of angle (3p+1)° :

$=\tt 43 \times 3 + 1$

$= \tt129 + 1$

$\tt\color{plum}angle \: (3p + 1)° = 130°$

Thus, the measure of the larger angle = 130°

Therefore, the correct option is <em>(a) 130</em>

3 0

2 years ago