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3 years ago

Help asap show work i will make u brainlest.

Mathematics

1 answer:

o-na [289]3 years ago

4 0

Answer: (5) D (6) D (7) B (8) B (9) C

Step-by-step explanation:

5) 2 - 3n < 17 and 6n + 4 < 58

-2 -2 -4 -4

-3n < 15 6n < 54

÷ -3 ↓ ÷ -3 ÷6 ÷6

n > -5 and n < 9

-5 < n < 9

6) 6x + 5 > -49 and 7 - 4x ≥ -21

-5 -5 -7 -7

6x > -54 -4x ≥ -28

÷6 ÷6 ÷ -4 ↓ ÷ -4

x > -9 and x ≤ 7

-9 < x ≤ 7

7) -69 ≤ 6x - 9 ≤ -45

+9 +9 +9

-60 ≤ 6x ≤ -36

÷6 ÷6 ÷6

-10 ≤ x ≤ -6

8) -93 ≤ 9n - 3 < -84

+3 +3 +3

-90 ≤ 9n < -81

÷9 ÷9 ÷9

-10 ≤ n < -9

9) 4k - 6 ≤ -6 + 6k or -3k - 5 ≥ -2k + 10

-6k -6k +2k +2k

-2k - 6 ≤ -6 -k - 5 ≥ 10

+6 +6 +5 +5

-2k ≤ 0 -k ≥ 15

÷ -2 ↓ ÷ -2 ÷ -1 ↓ ÷ -1

k ≥ 0 or k ≤ -15

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A sphere has a volume of Vequals=3600 in cubedin3. Find its surface area.

Mice21 [21]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad 
\begin{cases}
r=radius\\
------\\
V=3600
\end{cases}\implies 3600=\cfrac{4}{3}\pi r^3
\\\\\\
3600=\cfrac{4\pi r^3}{3}\implies \sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}=\boxed{r}\\\\
-----------------------------\\\\
\textit{surface area of a sphere}\\\\
S=4\pi r^2\implies S=4\pi \left(\boxed{\sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}} \right)^2$

simplify away

8 0

3 years ago

A firework is launched at the rate of 10 feet per second from a point on the ground 50 feet from an observer. to 2 decimal place

Kazeer [188]

The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.

First we will draw a right angle triangle ΔABC, where ∠B = 90°

Lets, assume the height(AB) = h and base(BC)= x

If the angle of elevation, ∠ACB = α, then

tan(α) = $\frac{AB}{BC} = \frac{h}{x}$

Taking inverse trigonometric function, α = tan⁻¹ ( $\frac{h}{x}$ ) .............(1)

As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :

$\frac{d\alpha}{dt}=[\frac{1}{1+ \frac{h^2}{x^2}}]*(\frac{1}{x})\frac{dh}{dt}$

Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,

that means h = 40 feet and $\frac{dh}{dt}$ = 10 feet/second.

C is the observer's position which is 50 feet away from the point B, so x = 50 feet.

$\frac{d\alpha}{dt}= [\frac{1}{1+ \frac{40^2}{50^2}}] *\frac{1}{50} *10\\ \\ \frac{d\alpha}{dt} = [\frac{1}{1+\frac{16}{25}}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt} = [\frac{25}{41}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt}= \frac{5}{41} =0.1219512$

= 0.12 (Rounding up to two decimal places)

So, the rate of change of the angle of elevation is 0.12 radians/second.

5 0

3 years ago

Which arrangement shows 318 , 3.7, 334 , and 3.89 in order from least to greatest?

Stolb23 [73]

Answer: OPTION D.

Step-by-step explanation:

<h3> The complete exercise is: "Which arrangement shows $3\frac{1}{8}$ , 3.7, $3\frac{3}{4}$ , and 3.89 in order from least to greatest?"</h3><h3> </h3>

Convert from mixed numbers to decimal numbers.

The steps to do this, are the following:

1. You must divide the numerator of the fraction by the denominator.

2. Then you must add the quotient obtained to the whole number part.

Applying this procedure, you get that:

$3\frac{1}{8}=3+0.125=3.125$

$3\frac{3}{4}=3+0.75=3.75$

Now that you have all the numbers in decimal form, you can order from least to greatest:

$3.125,\ 3.7,\ 3.75,\ 3,89$

Therefore, you can conclude that the correct arrangement is:

$3\frac{1}{8},\ 3.7,\ 3\frac{3}{4},\ 3,89$

3 0

3 years ago

Read 2 more answers

What is the value of the underlined digit 1,711,799.

Varvara68 [4.7K]

I don't know which one is underlined so I will write it out in words.
One million seven hundred and eleven thousand and seven hundred ninety-nine.

Hope I helped :)

3 0

3 years ago

Sin167cos107-cos167sin107

insens350 [35]

Sin 167 = 0.22495

cos 107 = -0.29237

cos 167 = -0.97437

sin 107 = 0.95630

(sin 167)(cos 107) - (cos 167)(sin 107)

(0.22495)(-0.29237) - ( -0.97437)(0.95630)

= 0.86602

hope this helps :)

6 0

3 years ago