what is the gcf of 40 and 70​

Answer:

6·108 ≥ 3·106

Step-by-step explanation:

6·108=  648

3·106= 318

648 ≥ 318

The volume of the solid enclosed by the hyperboloid and the plane is 4π² (√3 - 7) cubic units.

To find the volume of the solid enclosed by the hyperboloid −x^2 − y^2 + z^2 = 46 and the plane z = 7, we can use polar coordinates to simplify the calculations.

In polar coordinates, we express the variables x, y, and z as functions of the radial distance ρ and the angle θ. The conversion from Cartesian coordinates to polar coordinates is given by:

x = ρ cos(θ)

y = ρ sin(θ)

z = z

Let's rewrite the equation of the hyperboloid in terms of polar coordinates:

−(ρ cos(θ))^2 − (ρ sin(θ))^2 + z^2 = 46

−ρ^2 cos^2(θ) − ρ^2 sin^2(θ) + z^2 = 46

−ρ^2 + z^2 = 46

Since we are interested in the region above the plane z = 7, we need to find the limits of integration for the variables ρ and θ. The radial distance ρ ranges from 0 to a value that satisfies the equation −ρ^2 + 49 = 46. Solving this equation, we get ρ = √3.

The angle θ ranges from 0 to 2π since we want to cover the entire solid.

Now, we can express the volume of the solid using polar coordinates. The volume element in polar coordinates is given by dV = ρ dz dρ dθ.

To find the volume, we integrate the volume element over the appropriate range:

V = ∫∫∫ dV

= ∫∫∫ ρ dz dρ dθ

= ∫₀²π ∫₇ᵛᵛ₃ ∫₀²π ρ dz dρ dθ

Simplifying the integral, we have:

V = ∫₀²π ∫₇ᵛᵛ₃ 2πρ (z) dz dρ

= 2π ∫₀²π ∫₇ᵛᵛ₃ ρ (z) dz dρ

Evaluating the inner integral, we have:

V = 2π ∫₀²π [(z|₇ᵛᵛ₃)] dρ

= 2π ∫₀²π [z|₇ᵛᵛ₃] dρ

= 2π ∫₀²π [(7 - √3) - 7] dρ

= 2π ∫₀²π [√3 - 7] dρ

= 2π (√3 - 7) ∫₀²π dρ

= 2π (√3 - 7) [ρ|₀²π]

= 2π (√3 - 7) [2π - 0]

= 4π² (√3 - 7)

By using polar coordinates, we simplify the given solid's representation and express the volume as an integral in terms of ρ, z, and θ. We determine the limits of integration and perform the necessary calculations to find the final result.

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Answer:

Step-by-step explanation:

If you are rounding to the whole number you are rounding to ones so you need to look at the tenth digit:

2<5 so 7 stays the same  (rounding down)

7.21 ≈ 7

The nearest whole number for the given number is 7.

To change a number into an approximation having fewer significant digits. For example :-

Round off 15.4 to 15, round off 15.51 to 15.5 or to 16, round off 0.499 to 0, and round off 970,000 to 1 million.

Given is a number 7.21,

We know that,  if the digit is less than 5, round down and if the digit is 5 or more than 5, round up.

Since, numbers after the decimal is not greater than 5, therefore, it will not change and will remain 7.

Hence, the required whole number is 7.

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The expression used to calculate the sale price is given as follows:

S(p) = 0.65p.

The expression used to calculate the sale price is obtained applying the proportions in the context of the problem.

The price was 35% off, meaning that there was a discount of 35%, meaning that a percentage of 100 - 35 = 65% of the total price was paid, hence the expression used to calculate the sale price is given as follows:

S(p) = 0.65p.

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Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

Answer:

67 1/2

Step-by-step explanation:

67 5/10

67 1/2

135 over 2  =67 and 1 over 2 =67.5  Answer:(67  1/2)

The second-order partial derivatives of the given function are; \(hxx = 0, \\hxy = (4e^y)\\ hyx = (4e^y) \\hyy = 0\)

The second-order partial derivative of this equation

\(h(x,y) = 4x e^y + 2y +6\)

we need to differentiate the function twice with respect to x and y, respectively by using the product rule and chain rule.

For instance, to find hxy, we differentiate h(x,y) with respect to x first, taking y as a constant

\(∂/∂x (h(x,y)) = 4e^y\)

We can also differentiate this result with respect to y, when x is considered as a constant:

\(∂/∂y (∂/∂x (h(x,y))) = ∂/∂y (4e^y) = 0\)

When we do similar differentiation to get this hxx, hyx, hyy

we have the second-order derivatives as follow;

\(hxx = 0\\hxy = (4e^y)\\hyx = (4e^y)\\hyy = 0\)

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The diameter of the given circle with a circumference of 28.6 centimeters is approximately 9.11 cm.

The circumference of a circle is given by the simple formula: C = πd, where C is the circumference, π is the constant pi and d is the diameter of the circle.

Given that the circumference of the circle is 28.6 cm, we can use the formula to find the diameter:

28.6 = πd

d = 28.6/π

Using 3.14 as an approximation for π, we get:

d ≈ 28.6/3.14 ≈ 9.11

Therefore, the diameter of the circle is approximately 9.11 cm.

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Answer:

No

Step-by-step explanation:

1 Kilo = 1000 Grams. There are only 1837 Grams. This means that there is no way it is 2 kilos.

Answer:

2 and 9

Step-by-step explanation:

The correct solution for x is,

x = 513

Now, for the equation 4{x} = x + [x] , where x is a real number, we can use the fact that {x} = x - [x].

Substituting this expression into the equation yields:

4(x - [x]) = x + [x]

Expanding the left side gives:

4x - 4[x] = x + [x]

Bringing the terms containing [x] to one side and simplifying, we get:

3[x] = 3x

Dividing both sides by 3, we obtain:

[x] = x

This means that x is an integer.

Therefore, the possible solutions of the equation are values of x that satisfy this condition.

Of the options provided, only option B;

x = 513, is a possible solution, since it is an integer and satisfies the equation.

The other options do not satisfy the equation because they are not integers.

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Answer:

a) 7x-5

b )7(100)-5 = 695

The time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.

The total amount of diesel into the tank = 1700 gallons

The mixture is added at the rate of 0.28 ounces per gallon.

The mixture is added at the rate of 25 gallon per minute.

Let us consider that the time taken is t minutes.

A mixture is a substance made up of two or more distinct chemical components that are not chemically bonded together. A mixture is a mixture of two or more substances that retain their identities while being mixed in the form of solutions, suspensions, and colloids.

Now in t minutes the mixture = 25 × .28 ×t = 7t

Now we will use the second part of the equation as:

The rate of 20gal/min. if there should be 14oz of additive for every 120 gallons of diesel fuel, how long will it take to reach the right mixture

Now we will use the mixture formula to calculate the e amount of diesel in the mixture.

Hence 0.20 × 14×120=336  × 65.11 = 21877.3

Now the diesel mixture will have

Therefore the equation formed is :

336t +7t = 21877.3

Solving we get t=21877.3.

Hence the time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.

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The plane intercepts on the x,y, z axes are 1, ∞, and 1/2. Hence, the Miller indices for the plane inside the cubic unit cell is (102).

Miller indices are used to specify planes and directions. These planes and directions could be in lattices or crystals. The number of indices will correspond to the size of the lattice or crystal.

In the given graph, the plane intercepts are:

x-intercept : 1

y-intercept : ∞  (since the planes does not intercept y-axes)

z-intercept = 1/2

Take the reciprocal:

1/1 = 1

1/∞ = 0

1/(1/2) = 2

Hence, the miller indices are (102)

The graph in your question is missing. Most likely it was like on the attached picture.

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Answer:

3 loaves of bread

Step-by-step explanation:

2/3*3=6/3= 2 cups of oil

m mean slope in parallel lines and it is always same in two parallel lines.

Given:

Linear equations are generally described by the slope-intercept

represented by the equation y = mx+b

where m = slope

b = y-intercept.

In parallel lines:

Slope is always same means that two parallel lines have same slopes because those are not intersect at any point.

Example:

y = 3x + 4

here slope m = 3

The parallel line to this equation is also have the same slope.

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We can use the formula for simple interest:

I = Prt

To understand the calculation, we can break it down. The principal amount is $1600, and the interest rate is 5.25%, which is expressed as a decimal (0.0525). The time period is 18 months. Multiplying these values together gives us the simple interest earned over the given time period.

where I is the interest earned, P is the principal or initial investment, r is the interest rate per year as a decimal, and t is the time in years.

In this case, P = 1600, r = 0.0525 (since 5.25% is the annual interest rate), and t = 1.5 years (since 18 months is half of a year). Plugging in these values, we get:

I = 1600 x 0.0525 x 1.5

= 126

Therefore, the simple interest earned is $126.

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Answer:

16,384

Step-by-step explanation:

Answer:

A. 5x^2 - 2x - 12 = 0

Step-by-step explanation:

The base is x feet.

The height is 2 less that 5 times the base.

The height is 5x - 2.

The area is 12.

The area is base * height / 2.

area = bh/2

area = x * (5x - 2) = 12

5x^2 - 2x = 12

5x^2 - 2x - 12 = 0

Answer:

\( {5x}^{2} - 2x - 24 = 0\)

Step-by-step explanation:

\(area \: a = \frac{base \times height}{2} = \frac{bh}{2} \)

let b = x and h = (5x - 2) then

\(a = \frac{x(5x - 2)}{2} = 12 {ft}^{2} \\ a = \frac{ {5x}^{2} - 2x}{2} = 12 {ft }^{2} \\ a = 2 \times \frac{ {5x}^{2} - 2x}{2} = 12 {ft}^{2} \times 2 \\ a = {5x}^{2} - 2x = 24 {ft}^{2} \\ a = {5x}^{2} - 2x - 24 = 0\)

Answer: there should be 80 blacks

Step-by-step explanation:

i promise

Answer:

Step-by-step explanation:

76/100 of 250

cancel out the zeroes

multiply and divide

76*250/100

=190

Answer:

190

Step-by-step explanation:

76%=76/100

so 76% of 250 can be written as :

76/100 * 250/1 =19000/100

you can simplify that and you get the answer 190

The jump from -25 to -15 is +10

The jump from -15 to -5 is also +10

The jump from -5 to 5 is also +10

Unfortunately, this pattern doesn't hold up. The jump from 5 to 10 is +5

Because the gap isn't the same each time, this tells us the sequence is not arithmetic.

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We can show the sequence isn't geometric either. Pick any term to divide it over its previous term

-15/(-25) = 0.6

-5/(-15) = 0.333 approximate

The result isn't the same, so we don't have a common ratio and that's why this sequence isn't geometric.

----------------

It seems like your teacher made a typo. Please double check with them to make sure that they typed the correct sequence. I have a feeling that 10 should be 15, but I'm not entirely sure.

Answer: x=59

Step-by-step explanation:

360-296=(x-24)+29

         64=x+5

         59=x

Answer:

1. This means that the actual park size is 50 times larger than the size of the park on the map.

2. If a pathway is 7 inches long on the map, it will be 50 times larger in real life;

= 7 * 50

= 350 inches

3. 1 foot is 12 inches so 350 inches will be;

= 350/12

= 29.2 feet

4. The real life length of the car is;

= 5 * 67

= 335 inches

5. The real life length in feet is;

= 335/12

= 27.9 feet

6. Speed = Distance / time

The time should be converted to hours;

= 10/60 minutes

= 1/6

Speed = 9 / (1/6)

= 54 miles per hour

= 54 mph

Answer:

What are the equivalent expressions?

Two expressions are said to be equivalent if they have the same value regardless of the value of the variable(s) in them.

Step-by-step explanation:

Answer:

-14

Step-by-step explanation:

Answer:

-14

Step-by-step explanation: