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3 years ago

Solve the equation using square roots. X^2+16=0

Mathematics

2 answers:

alexgriva [62]3 years ago

5 0

Answer:

The answer is :

x₁ = 4

x₂ = -4

Step-by-step explanation:

Let's solve the equation using square roots.

X^2+16=0

x² + 16 = 0

x² = -16 (Adding 16 at both sides of the equation)

√x² = i√16 (Square root to both sides of the equation)

x = +/- 4i (Roots of the solution)

x₁ = 4i

x₂ = -4i

bazaltina [42]3 years ago

4 0

Answer:

$\displaystyle 4i = x$

Step-by-step explanation:

$\displaystyle x^2 + 16 = 0 → \sqrt{-16} = \sqrt{x^2} \\ \\ 4i = x$

I am joyous to assist you anytime.

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The radius, R, of a sphere, is 6.3cm. Calculate the sphere's volume, V.

sleet_krkn [62]

Answer:

V = 1046.9

Step-by-step explanation:

The equation for volume is (4/3)pi r^3

substitute 3.14 in for pi and 6.3 in for r so (4/3)*3.14*6.3^3

6 0

2 years ago

1. Let f(x, y) be a differentiable function in the variables x and y. Let r and θ the polar coordinates,and set g(r, θ) = f(r co

Olenka [21]

Answer:

$g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}\\$

Step-by-step explanation:

First, notice that:

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}cos(\frac{\pi}{4}),\sqrt{2}sin(\frac{\pi}{4}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(\sqrt{2}(\frac{1}{\sqrt{2}}),\sqrt{2}(\frac{1}{\sqrt{2}}))\\$

$g(\sqrt{2},\frac{\pi}{4})=f(1,1)\\$

We proceed to use the chain rule to find $g_{r}(\sqrt{2},\frac{\pi}{4})$ using the fact that $X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta)$ to find their derivatives:

$g_{r}(r,\theta)=f_{r}(rcos(\theta),rsin(\theta))=f_{x}( rcos(\theta),rsin(\theta))\frac{\delta x}{\delta r}(r,\theta)+f_{y}(rcos(\theta),rsin(\theta))\frac{\delta y}{\delta r}(r,\theta)\\$

Because we know $X(r,\theta)=rcos(\theta)\ and\ Y(r,\theta)=rsin(\theta)$ then:

$\frac{\delta x}{\delta r}=cos(\theta)\ and\ \frac{\delta y}{\delta r}=sin(\theta)$

We substitute in what we had:

$g_{r}(r,\theta)=f_{x}( rcos(\theta),rsin(\theta))cos(\theta)+f_{y}(rcos(\theta),rsin(\theta))sin(\theta)$

Now we put in the values $r=\sqrt{2}\ and\ \theta=\frac{\pi}{4}$ in the formula:

$g_{r}(\sqrt{2},\frac{\pi}{4})=f_{r}(1,1)=f_{x}(1,1)cos(\frac{\pi}{4})+f_{y}(1,1)sin(\frac{\pi}{4})$

Because of what we supposed:

$g_{r}(\sqrt{2},\frac{\pi}{4})=f_{r}(1,1)=-2cos(\frac{\pi}{4})+3sin(\frac{\pi}{4})$

And we operate to discover that:

$g_{r}(\sqrt{2},\frac{\pi}{4})=-2\frac{\sqrt{2}}{2}+3\frac{\sqrt{2}}{2}$

$g_{r}(\sqrt{2},\frac{\pi}{4})=\frac{\sqrt{2}}{2}$

and this will be our answer

3 0

3 years ago

Sorry if it is blurry but can someone help me 14 through 18

garri49 [273]

I believe number 14 is asking where the points are located. If so D (-3,-3) E(-3,-2) G(4,1) F(4,2)

5 0

3 years ago

you have 20 cookies with the ratio is 2 chocolate chip for every 3 sugar. how many sugar cookies do you have?

skad [1K]

Total number of parts:
2+3=5.

Each part is:
20 cookies/ 5 parts= 4 cookies/part.

Number of chocolate cookies is:
4 cookies/part* 2 parts= 8 cookies.

Number of sugar cookies is:
4 cookies/part* 3 parts= 12 cookies.

There are 8 chocolate cookies and 12 sugar cookies~

4 0

4 years ago

Read 2 more answers

Question 8

daser333 [38]

9514 1404 393

Answer:

42.9 ft

Step-by-step explanation:

The relevant trig relation is ...

Tan = Opposite/Adjacent

where Opposite in this case is the height of the tree, and Adjacent is the distance to the tree.

tan(47°) = height/(40 ft)

height = (40 ft)·tan(47°) . . . . . multiply both sides by (40 ft)

height ≈ 42.9 ft

The tree is about 42.9 feet tall.

7 0

3 years ago