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3 years ago

Enter an inequality that represents the description, and then solve.

Mathematics

1 answer:

natta225 [31]3 years ago

5 0

Answer:

X >= 7

Step-by-step explanation:

7x + 8 >= 57

7x >= 57-8

7x >= 49

x >= 49/7

x >= 7

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Glven: F(x) = 2x - 1; G(X) = 3x + 2; H(x) = x2 Find F/G/H(2) 121 27 71

Sergio039 [100]

Answer:

3/32

Step-by-step explanation:

One approach to doing this probelm is to evaluate all three functions F, G and H at x = 2:

F(2) = 2(2) - 1 = 3

G(2) = 3(2) + 2 = 8

H(2) = (2)^2 = 4

3/8

Then (F/G)(2) = (3/8), and (F/G/H) = -------- = 3/32

8 0

3 years ago

You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

3 years ago

Help with spheres! I don't have to do question 3

Katena32 [7]

Question 1.

$d:$ diameter of the sphere

$r:$ radius of the sphere:

As we know,

$r=\dfrac{d}{2}\\ \\ r=\dfrac{15}{2}~\mathrm{in}$

Formula for the volume of a sphere, given its radius:

$V=\dfrac{4\pi r^{3}}{3}\\ \\ \\ V=\dfrac{4\pi\cdot (\frac{15}{2})^{3}}{3}\\ \\ \\ V=\dfrac{4\pi}{3}\cdot \dfrac{15^{3}}{8}\\ \\ \\ V=\dfrac{\diagup\!\!\!\! 4 \pi}{3}\cdot \dfrac{(3\cdot 5)^{3}}{\diagup\!\!\!\! 4\cdot 2}\\ \\ \\ V=\dfrac{\pi}{3}\cdot \dfrac{3^{3}\cdot 5^{3}}{2}\\ \\ \\ V=\dfrac{\pi}{\diagup\!\!\!\! 3}\cdot \dfrac{\diagup\!\!\!\! 3\cdot 3^{2}\cdot 5^{3}}{2}\\ \\ \\ V=\pi \cdot \dfrac{9\cdot 125}{2}\\ \\ \\ \boxed{\begin{array}{c} V=\dfrac{1\,125\pi}{2}\mathrm{~in^{3}} \end{array}}$

Question 2.

$r=6.8~\mathrm{ft}$

The volume of a hemisphere is given by

$V=\dfrac{2\pi r^{3}}{3}\\ \\ \\ V=\dfrac{2\pi\cdot (6.8)^{3}}{3}\\ \\ \\ V=\dfrac{2\pi\cdot 314.432}{3}\\ \\ \\ V \approx \dfrac{2*3.14*314.432}{3}\\ \\ \\ \boxed{\begin{array}{c} V \approx 658,2\mathrm{~ft^{3}} \end{array}}$

6 0

3 years ago

Write formula for arithmetic sequence when first term is not given

SashulF [63]

An = am + (n – 1)d.
i feel like this can work

8 0

3 years ago

The relation shown in the table represents what a local electrician charges each hour of work. The electrician charges 30$ servi

drek231 [11]

Answer:

the 30$ service fee is the independent

Step-by-step explanation:

because it doesn't rely on hours worked. and it's a separate fee.

7 0

3 years ago