What's a number or expression using a base and exponent?

Which type of data is BEST described by a continuous model?

LUCKY_DIMON [66]

D the temperature of an engine

6 0

4 years ago

Let <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20-%5Csqrt%7Bxy%7D%3D0" id="TexFormula1" title="\frac{dy}{dx} -\sq

miss Akunina [59]

Answer:

E

Step-by-step explanation:

dy/dx - sqrt(x/y) = 0

dy/dx = sqrt(x) ÷ sqrt(y)

y^½ .dy = x^½ .dx

Add 1 to the power and divide by the new power

(⅔)y^(3/2) = (⅔)x^(3/2) + c

x = 1, y = 0

0 = ⅔ + c

c = ⅔

(⅔)y^(3/2) = (⅔)x^(3/2) + ⅔

y^(3/2) = x^(3/2) + 1

At y = 73

73^(3/2) = x^(3/2) + 1

622.7122734 = x^(3/2)

x = 622.7122734^⅔

x = 72.9219527

Approximately 73

3 0

4 years ago

A menu in a restaurant allows you to pick some items from Column A and some from Column B. Column A has 24 items. Column B has 1

Darya [45]

You can each order from: Column A- 6 times, Column B- 4 times

5 0

4 years ago

In T-ball, the distance to each successive base is 50 feet. If the distance from home plate to the pitcher’s mound is 38 feet, h

JulijaS [17]

Answer:

<h2>The distance from the pitcher's mound and to second base is 37.99 approximately.</h2>

Step-by-step explanation:

The diamond is a square, which in this case has 50 feet long each side, and from home to pitcher is 38 feet. Notice that home is a vertex of the square and the pitcher's mound is the intersection of the diagonals, where they cut half.

We can find the distance from the pitcher to first base using Pythagorean's Theorem, where 50 feet is the hypothenuse.

$50^{2} =38^{2}+x^{2}\\x^{2}=50^{2}-38^{2}\\x=\sqrt{2500-1444}\\ x=\sqrt{1056}\\ x \approx 32.5 \ ft$

Therefore, the distance from the pitcher to first base is 32.5 feet, approximately.

Now, we can use again Pythagorean's Theorem to find the distance from pitcher to second base, where the hypothenuse is 50 feet.

$50^{2}=32.5^{2}+y^{2}\\y^{2}=50^{2}-32.5^{2}\\y=\sqrt{2500-1056.25}\\ y =\sqrt{1443} \approx 37.99$

Therefore, the distance from the pitcher's mound and to second base is 37.99 approximately.

<em>(this results make sense, because the diagonals of a square intersect at half, that means all bases have the same distance from pitcher's mound, so the second way to find the distance asked in the question is just using theory)</em>

8 0

3 years ago

6. A sector of a circle is a region bound by an arc and the two radii that share the arc's endpoints. Suppose you have a dartboa

Aliun [14]

Given the dartboard of diameter $20in$ , divided into 20 congruent sectors,

The central angle is $18^\circ$

The fraction of a circle taken up by one sector is $\frac{1}{20}$

The area of one sector is $15.7in^2$ to the nearest tenth

The area of a circle is given by the formula

$A=\pi r^2$

A sector of a circle is a fraction of a circle. The fraction is given by $\frac{\theta}{360^\circ}$ . Where $\theta$ is the angle subtended by the sector at the center of the circle.

The formula for computing the area of a sector, given the angle at the center is

$A_s=\dfrac{\theta}{360^\circ}\times \pi r^2$

<h3>Given information</h3>

We given a circle (the dartboard) with diameter of $20in$ , divided into 20 equal(or, congruent) sectors

<h3>Part I: Finding the central angle</h3>

To find the central angle, divide $360^\circ$ by the number of sectors. Let $\alpha$ denote the central angle, then

$\alpha=\dfrac{360^\circ}{20}\\\\\alpha=18^\circ$

<h3>Part II: Find the fraction of the circle that one sector takes</h3>

The fraction of the circle that one sector takes up is found by dividing the angle a sector takes up by $360^\circ$ . The angle has already been computed in Part I (the central angle, $\alpha$ ). The fraction is

$f=\dfrac{\alpha}{360^\circ}\\\\f=\dfrac{18^\circ}{360^\circ}=\dfrac{1}{20}$

<h3>Part III: Find the area of one sector to the nearest tenth</h3>

The area of one sector can be gotten by multiplying the fraction gotten from Part II, with the area formula. That is

$A_s=f\times \pi r^2\\=\dfrac{1}{20}\times3.14\times\left(\dfrac{20}{2}\right)^2\\\\=\dfrac{1}{20}\times3.14\times10^2=15.7in^2$

Learn more about sectors of a circle brainly.com/question/3432053

8 0

3 years ago