dy
If x= 15t2 and y= 10t2, find
dx
​

Answer:

Step-by-step explanation:

Use the Law of Sines for this. Set it up as follows:

[tex]\frac{sin(x)}{6}=\frac{sin(61)}{6.2}[/tex]  Cross multiply:

6.2sin(x) = 6sin(61) and solve for the term with the unknown in it:

[tex]sin(x)=\frac{6sin(61)}{6.2}[/tex]

Work on the right side first. Plug that into your calculator to get

sin(x) = .8464061682

Now the problem comes down to "what angle has a sine of .8464061682?" This requires the use of the inverse button on your calculator. Hit 2nd, then sin, and you will see on your screen:

[tex]sin^{-1}([/tex]

After that open parenthesis enter that big long decimal and hit equals. You should get an angle measure of 57.822 degrees. Not sure what you are rounding to.

Answer:

5/14 = 0.36

7/10 = 0.7

5/6 = 0.83

11/15 = 0.73

19/21 = 0.9

(round to the tenth)

so the answer is;

5/14, 7/10, 11/15, 5/6, 19/21

Step-by-step explanation:

Hope it helps!

Answer:

86

Step-by-step explanation:

x+x+1+x+2+x+3+x+4+x+5 = 519

6x+15 = 519

6x = 504

x = 84

Third number = x+2 = 86

Answer:

86

Step-by-step explanation:

khan

Answer:

A translation 3 units to the right and a 90-degree clockwise rotation

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

width of picture 7 3/5 cm. to fit in the frame the picture cannot be more than 7 3/10 cm. how much should the picture be trimmed

Given that :

Original Width of picture = 7 3/5 cm

Width required for picture to fit into frame=7 3/10

For picture to fit into frame:

(7 3/5 - 7 3/10) must be trimmed off from the frame.

(7 3/5 - 7 3/10)

(7 - 7) = 0

(3/5 - 3/10)

Taking the L. C. M

(6 - 3) / 10

= 2 / 10

= 1/5

THEREFORE, 1 / 5 of the width should be trimmed in other to ensure the picture fits into the frame.

Answer:

A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3

Step-by-step explanation:

Solution A= 4 cups

Solution B= 2 cups

Total cups of the mixture=4+2=6

A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.

Solution A= 4 cups

Mixture=6 cups

Solution A : Mixture =4 : 6

=2:3

Option A is true

B. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2.

Solution A= 4 cups

Mixture=6 cups

Solution A : Mixture =4 : 6

=2:3

Option B not true

C. There are 3 cups of solution A for every 6 cups of mixture.

Option C states that:

Solution A=3 cups

Mixture=6 cups

Solution A : Mixture=3:6=1:2

This is not true

D. For each cup of solution A, there are 2 cups of solution B.

Option D states:

Solution A= 1 cups

Solution B= 2 cups

This is not true

It is rather

Solution A= 2 cups

Solution B= 1 cups

Therefore, option A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3 is the correct statement

5 buses is the answer pls mark me brainliest

Least number of bus require for trip = 5 buses

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

Total number of classes = 9

Number of student in each class = 25

Number of teacher = 4

Number of chaperones = Double of teacher

Bus hold = 45 people

Now,

Total number of student = 9 × 25

                                         = 225

Number of chaperones = 4 × 2

                                         = 8

Total people = 225 + 8 + 4

                     = 237

Least number of bus require for trip = Total people / Bus hold

= 237 / 45

= 5.266

Learn more about unitary method here:

https://brainly.com/question/22056199

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Answer:

This means you would plug in g(x) into f(x).

Step-by-step explanation:

It would look like this:

[tex]3(x^{2} + 1) + 2[/tex]

Answer:

2, 18/b

Step-by-step explanation:

if you divide by the number of bags you will get the number of cookies in each bag.

Answer:2,18/b

Step-by-step explanation:If you multiply the cookies in a bag by b, you will get 18

Answer:

y = 2 x − 1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

We can find the slope from the slope equation

m = (y2-y1)/(x2-x1)

   = ( 1- -3)/(1 - -1)

   = (1+3)/(1+1)

   = 4/2

  =2

Answer:

68.06 sq. feets

Step-by-step explanation:

Area of room's floor

11.33 × 7 = 79.33

Area of tiled floor

4.83 × 2.33 = 11.278

Area of floor needed to be carpeted

79.33-11.278= 68.06

Answer:

Below

Step-by-step explanation:

● Orders of 8 gallons or more can be modeled as: x》 8

● For each gallons in the situation above the company charges 11.99 per gallon so: 11.99x

● For orders that are less than 8, the comapny charges 14.78 per gallon

● => 14.78x for x < 8

So the function that represent the situation is the second one

Answer:

a) 4⁻³ = 1/64 = 0.015625

b)13⁻² = 1/169 = 0.0059171598

c)(-3)⁻² = 1/-3² = 0.1111111111

Step-by-step explanation:

To solve the question above, when we have an integer ( positive or negative) that is raised to a negative power, this means the reciprocal of that integer raised to the positive power

Example:

a⁻ⁿ = 1/aⁿ

a) 4⁻³ = 1/4³

= 1/(4 × 4 × 4)

= 1/64

= 0.015625

b) 13⁻² = 1/13²

= 1/(13 × 13)

= 1/169

= 0.0059171598

c)(-3)⁻² = 1/-3²

= 1/(-3 × -3)

= 1/9

= 0.1111111111

Answer:

10.5 pounds of apples

Step-by-step explanation:

4 devided by 14 = 3.5

3.5* 3 = 10.5

Answer:30%

Step-by-step explanation:you divide 18 by 100 and then multiply that by 30 and it gives you 5.4 which is close to 5 players. So 30% is the answer

Answer: R = (4, 5)

Step-by-step explanation: Midpoint is simply the center of a line. So, the equation for it is ((x1+x2)/2, (y1+y2)/2). Hence for this,

x coordinate- (6+x)/2=5

                        x=4

y coordinates- (9+y)/2=7

                         y=5

And therefore R is (4, 5)

Answer:

It is so easy u should get this right.

First draw a circle and there is an arc that is like forming a triangle inside a circle and then ab angle is 100 degree and outside is the center of the circle. And since u try to find how much is outside it most likely means that 100-60=40

so it b 40.

Step-by-step explanation:

The number of degrees in ∠ABO is 50°. Therefore, option A is the correct answer.

Given that, in a circle whose centre is O, arc AB contains 100°.

We need to find the number of degrees in ∠ABO.

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

According to the theorem ∠ABO=1/2 × arc AB.

So, ∠ABO=1/2 × 100°=50°

The number of degrees in ∠ABO is 50°. Therefore, option A is the correct answer.

Learn more here about arc of a circle here:

https://brainly.com/question/15448382.

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Answer:

310 metres

Step-by-step explanation:

The lowest point in Asia is the Dead Sea, which is =396 meters below sea level.

The lowest point in the USA is Death Valley, a= 86 meters below sea level.

Therefore,

diference in their heights = 396-86 metres =310 metres

Answer:

310 meters higher

Step-by-step explanation:

396-86=-310

The difference btween -396 and -86 is the same as |396| and |86| so you can just subtract the positive numbers.

Answer:

k = 45

Step-by-step explanation:

We can put this into an equation form:

k - 10 = 35

We can solve for k by adding 10 to both sides:

k = 45

Answer:

k-10=35

k=45

Step-by-step explanation:

Let's write this as an equation.

"10 less than k" means subtract 10 from k.

k-10

"is 35" means equals 35.

k-10=35

If we want to solve for k, we have to get k by itself on one side of the equation.

k-10=35

10 is being subtracted from k. The inverse of subtraction is addition. Add 10 to both sides of the equation.

k-10+10=35+10

k=35+10

k=45

Answer:

23×x

=23x

Hope it helps

Answer:

23x

Step-by-step explanation:

"The product of" indicates that we will be multiplying the two quantities. 23 multiplied by x can be written as 23 * x which simplifies to 23x.

Answer:

Approximately 13.4 units.

Step-by-step explanation:

To find the distance between two points, use the distance formula. The distance formula is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

x₁ and y₁ is one coordinate while x₂ and y₂ is the other.

Let (-3,10) be x₁ and y₁ and let (3,-2) be x₂ and y₂. Plug in the numbers and simplify:

[tex]d=\sqrt{(3-(-3))^2+(-2-10)^2}\\ d=\sqrt{6^2+(-12)^2} \\d=\sqrt{36+144} \\d=\sqrt{180}\\ d=\sqrt{36\cdot5}=6\sqrt{5}\approx13.4164[/tex]

Edit: Typo

Answer:

100

Step-by-step explanation:

Answer:

dL/dt  = - 2,019 m/h

Step-by-step explanation:

L²  =  x²  +  y²   (1)    Where  x, and  y are the legs of the right triangle and L the hypotenuse

If the base of the triangle, let´s call x is increasing at the rate of 2 m/h

then  dx/dt =  2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h

If we take differentials on both sides of the equation (1)

2*L*dL/dt = 2*x*dx/dt  + 2*y*dy/dt

L*dL/dt  = x*dx/dt + y*dy/dt         (2)

When  the base is 9  and the height is 22 according to equation (1) the hypotenuse is:

L = √ (9)² + (22)²       ⇒    L = √565       ⇒  L  = 23,77

Therefore we got all the information to get dL/dt .

L*dL/dt  = x*dx/dt + y*dy/dt

23,77 * dL/dt  = 9*2 + 22* ( - 3)

dL/dt  =  ( 18 - 66 ) / 23,77

dL/dt  = - 2,019 m/h

Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.

The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:

[tex]h^2 = x^2 + y^2[/tex]

In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:

[tex]h^2 = 9^2 + 22^2[/tex]

[tex]h = \sqrt{9^2 + 22^2}[/tex]

[tex]h = 23.77[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

Simplifying by 2:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].

We want to find [tex]\frac{dh}{dt}[/tex], hence:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]

[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]

[tex]\frac{dh}{dt} = -2.02[/tex]

The hypotenuse is changing at a rate of -2.02 meters per hour.

A similar problem is given at https://brainly.com/question/19954153

Answer:

                   JUSTIFICATION↓

∠1 ≅ ∠2 (∵ Vertically-opposite angles are equal)

Step-by-step explanation:

Since ∠1  lies vertically opposite to  ∠2 and vice -versa , therefore ∠1 and  ∠2 are equal to each other

Answer: 24$

Step-by-step explanation: First, you need to do 3/5*60 which is  36$.

Then you need to find 2/3 of 36$ which is 24$. So Brittany now has 24$ after going to the movies. I hope this helps you!

Answer:

[tex]\large\boxed{x=-\frac{5}{6}}[/tex]

Step-by-step explanation:

f(x) is the same value as y. Therefore, y = 17. We can place this into slope intercept form (except with a defined value for y) and solve for x.

Start by subtracting 7 from both sides. Then, divide by -12 to solve for x. Finally, simplify the fraction.

17 = -12x + 7

10 = -12x

-10/12 = x

-5/6 = x

[tex]\large\boxed{x=-\frac{5}{6}}[/tex]

Answer:

Option a.

Step-by-step explanation:

In the given triangle angle A is a right angle so triangle ABC is a right angled triangle.

Opposite side of right angle is hypotenuse. So, CB is hypotenuse.

From figure it is clear that CA is shorter that segment BA.

All angles are congruent to itself. So angle C is congruent to itself.

We know that, if an altitude is drawn from the right angle vertex in a right angle triangle it divide the triangle in two right angle triangles, then given triangle is similar to both new triangles.

So, triangle ABC is similar to triangle DBA if segment AD is an altitude of triangle ABC.

Therefore, the correct option is a.

Answer:

(2, 3 )

Step-by-step explanation:

Given the 2 equations

2x - 3y = - 5 → (1)

5x + 4y = 22 → (2) [ rearranged equation ]

Multiplying (1) by 4 and (2) by 3 and adding will eliminate the term in y

8x - 12y = - 20 → (3)

15x + 12y = 66 → (4)

Add (3) and (4) term by term to eliminate y, that is

23x = 46 ( divide both sides by 23 )

x = 2

Substitute x = 2 in either of the 2 equations and evaluate for y

Substituting into (2)

5)2) + 4y = 22

10 + 4y = 22 ( subtract 10 from both sides )

4y = 12 ( divide both sides by 4 )

y = 3

Solution is (2, 3 )

Answer:

  D.  $2071.20

Step-by-step explanation:

The table tells you that Bob's monthly payment on a 4-year loan at 6.5% will be $23.71 per thousand borrowed. The sum of those 48 payments is ...

  48 × $23.71 = $1138.08

That means, Bob pays $138.08 in total finance charge for each $1000 he borrows. He is borrowing 15 times $1000, so his total finance charge will be ...

  finance charge = 15 × $138.08 = $2071.20 . . . matches choice D

Answer:

Graph D

Step-by-step explanation:

(h)t = -16t^2 + 80

At time t = 0 the screwdriver is at 0+80 =80 ft

As time increases the height will decrease so we can eliminate graph B

We know this is a downward parabola by the - in front of the t^2 so we can eliminate graph A

We need to find where it meets the x axis

0 = -16t^2 + 80

-80 = -16t^2

5 = t^2

t = sqrt(5)

t =2.23

This is Graph D

Answer:

Step-by-step explanation:

_____ / 9

2/12

Multiply the divisor (9) by the quotient (12) and to the result add the remainder (2).

9 × 12 + 2 =

108 + 2 = 110

110 is the number divided.

110/9

20/12

2