All categories

3 years ago

A number is divided by 3. Then, 5 is added to the quotient, and the result is 8. What is the number?

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

8 0

Answer:

D. 9

Step-by-step explanation:

1. 9/3 = 3

2. 3+5 = 8

Result = 8

You might be interested in

HELP ME PLEASEEEEEEEE ASAPPPP !!

OLEGan [10]

Answer:

C and D

Step-by-step explanation:

Mathematically, a unit circle is one in which the value of the radius is 1 unit

Generally, for a unit circle we have it that;

r^2 = x^2 + y^2

where (x,y) represents the coordinates of a point on the unit circle

But from above, r = 1

Thus:

x^2 + y^2 = 1

Looking at option C, by squaring each coordinate, we have

(6/7)^2 = 36/49 and the second as 13/49

by adding both, we have

36/49 + 13/49 = 49/49 = 1

Thus, we have this as a coordinate on the unit circle

For the last option;

(5/13)^2 = 25/169 and (12/13)^2 = 144/169

Adding both, we have;

25/169 + 144/169 = 169/169 = 1

So this is also a point on the unit circle

5 0

3 years ago

Diego is collecting dimes and nickels in a jar. He has collected $22.25 so far. The relationship between the numbers of dimes an

svet-max [94.6K]

Answer:

Correct options are:

a) ( 0 , 445 )

d) ( 118 , 209 )

e) ( 172 , 101 )

Step-by-step explanation:

A nickel is worth 5 cents $0.05

A dime is worth 10 cents = $0.10

The relationship between the numbers of dimes and nickels, and the amount of money in dollars is represented by the equation 0.10d+0.05n=22.25. Select the THREE values (d,n) that could be solutions to the equation.

a) ( 0 , 445 )

b) ( 0.50 , 435 )

c) ( 233 , 21 )

d)( 118 , 209 )

e)( 172 , 101 )

Verifying the options

a) ( 0 , 445 )

0.10d+0.05n=22.25.

= 0.10(0) + 0.05(445) = 22.25

= 22.25 = 22.25

Options a) is correct

b) ( 0.50 , 435 )

0.10d+0.05n=22.25.

= 0.10(0.50) + 0.05(435) = 22.25

= 21.8 ≠ 22.25

Option b is incorrect

c) ( 233 , 21 )

0.10d+0.05n=22.25.

= 0.10(233) + 0.05(21) = 22.25

= 24.35 ≠22.25

Option c is incorrect

d) ( 118 , 209 )

0.10d+0.05n=22.25.

= 0.10(118) + 0.05(209) = 22.25

= 22.25 = 22.25

Option d) is correct

e) ( 172 , 101 )

0.10d+0.05n=22.25.

= 0.10(172) + 0.05(101) = 22.25

= 22.25 = 22.25

Option e) is correct

5 0

3 years ago

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 4xzj + ex

natima [27]

Answer:

The result of the integral is 81π

Step-by-step explanation:

We can use Stoke's Theorem to evaluate the given integral, thus we can write first the theorem:

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

Finding the curl of F.

Given $F(x,y,z) = < yz, 4xz, e^{xy} >$ we have:

$curl \vec F =\left|\begin{array}{ccc} \hat i &\hat j&\hat k\\ \cfrac{\partial}{\partial x}& \cfrac{\partial}{\partial y}&\cfrac{\partial}{\partial z}\\yz&4xz&e^{xy}\end{array}\right|$

Working with the determinant we get

$curl \vec F = \left( \cfrac{\partial}{\partial y}e^{xy}-\cfrac{\partial}{\partial z}4xz\right) \hat i -\left(\cfrac{\partial}{\partial x}e^{xy}-\cfrac{\partial}{\partial z}yz \right) \hat j + \left(\cfrac{\partial}{\partial x} 4xz-\cfrac{\partial}{\partial y}yz \right) \hat k$

Working with the partial derivatives

$curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(4z-z\right) \hat k\\curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k$

Integrating using Stokes' Theorem

Now that we have the curl we can proceed integrating

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot \hat n dS$

where the normal to the circle is just $\hat n= \hat k$ since the normal is perpendicular to it, so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S \left(\left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k\right) \cdot \hat k dS$

Only the z-component will not be 0 after that dot product we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3z dS$

Since the circle is at z = 3 we can just write

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3(3) dS\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 9\int \int_S dS$

Thus the integral represents the area of a circle, the given circle $x^2+y^2 = 9$ has a radius r = 3, so its area is $A = \pi r^2 = 9\pi$ , so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = 9(9\pi)\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 81 \pi$

Thus the result of the integral is 81π

5 0

3 years ago

The length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°. What is the approxima

Olin [163]

The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

<h3>What is a circle?</h3>

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

Length of the arc of a circle:

s = 7.34 units

The measure of central angle:

θ = 81 degrees = 1.413 radians

s = rθ

r is the radius of the circle

7.34 = r(1.413)

r = 5.19 ≈ 5.2 units

Thus, the radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

Learn more about circle here:

brainly.com/question/11833983

#SPJ1

6 0

2 years ago

Think about how to find the area of a rectangle. A=LW and a triangle 1/2B*H. Create a problem using each formula.

WITCHER [35]

Given expressions:

Area of a rectangle = L W

Area of a triangle = $\frac{1}{2} B H$

Problem;

Create problems using the formula;

Solution:

Problem 1; Find the area of a rectangle whose length is 10cm and the width is half the size of the length?

Given parameters:

Length of rectangle = 10cm

Width of rectangle = $\frac{1}{2}$ x length = $\frac{1}{2}$ x 10 = 5cm

So, the area of the rectangle = 10cm x 5cm = 50cm²

2. A triangle with a base length of 30cm and a height of 2cm will have an area of what?

Given parameters:

base length = 30cm

height = 2cm

Solution:

Area of a triangle = $\frac{1}{2}$ x b x h

Area of a triangle = $\frac{1}{2}$ x 30 x 2 = 30cm²

The area of the triangle will be 30cm²

6 0

3 years ago