How many cubic yards of soil are needed to fill a planter that is 20 feet long by 3 feet wide by 4 feet tall

Answer:

doctorate salary:  d = $71,000

bachelor salary:     b = $55,000

Step-by-step explanation:

doctorate salary:  d

bachelor salary:     b

relationship between b and d:  d = 2b - $39,000

Unfortunately, your "1 + 126,000" could not be correct.  I'm going to assume that the total of the two salaries is $126,000.  If that's the case, then:

bachelor salary + (2 times bachelor salary less $39,000) = $126,000.  In symbols,

b + 2b - $39,000 = $126,000

Consolidating the 'b' terms results in 3b - $39,000 = $126,000, and so:

3b = $126,000 + $39,000 = $165,000

Dividing both sides by 3 yields the bachelor salary:  b = $55,000

Then the doctoral salary is 2b - $39,000 = 2($55,000) - $39,000, or $71,000.

Check:  Does b + (2b - $39,000) = $126,000?  Yes.

Then the doctoral salary is d = $103,000, and the bachelor salary $29,000

Answer:

The equations for the value V in terms of t is [tex]V(t)=-16000\cdot t+1000000[/tex] and the value of the building

after 1 year is $984,000

after 2 years is $968,000

after 20 years is $680,000

Step-by-step explanation:

With the straight-line depreciation method, the value of an asset is reduced uniformly over each period until it reaches its salvage value(It is the value of the asset at the end of its useful life).

We know from the information given the year = 0 the building costs $1,000,000 and a the year = 25 it costs $600,000.

With this information, you can calculate the decrease in value of the building due to age. We use the slope of a line formula because is a straight-line depreciation.

If (0, $1,000,000) is the first point and (25, $600,000) is the second point. we have

[tex]m=\frac{V_{2} -V_{1}}{t_{2}-t_{1}} =\frac{600000-1000000}{25-0} =-16000 \frac{\$}{years}[/tex]

To find the equation for the value V in terms of t, we use the point-slope form, this expression let you calculate the value of the building at the end of the year (t)

[tex]V-V_{0}= m(t- t_{0})\\V-1000000=-16000(x-0)\\V=-16000\cdot t+1000000[/tex]

To find the value after 1 year, after 2 years, and after 20 years. We put the year into the equation [tex]V(t)=-16000\cdot t+1000000[/tex]

[tex]V(1)=-16000\cdot (1)+1000000=\$984,000\\V(2)=-16000\cdot (2)+1000000=\$968,000\\V(20)=-16000\cdot (20)+1000000=\$680,000[/tex]

Answer:

a) It is the set of point in the the circumference with equation [tex](x-4)^2+y^2=8[/tex].

b) (10.6, 0, -6 )

Step-by-step explanation:

a) The centre of the sphere is (4,0,-6) and the radio of the sphere is [tex]\sqrt{44} \sim 6.6[/tex]. Since |-6|=6 < 6.6,  then the sphere intersect the xy-plane and the intersection is a circumference.

Let's find the equation of the circumference.

The equation of the xy-plane is z=0. Replacing this in the equation of the sphere we have:

[tex](x-4)^2+y^2+6^2=44[/tex], then [tex](x-4)^2+y^2=8[/tex].

b) Observe that the point (7,0,-6) has the same y and z coordinates as the centre and the x coordinate of the point is greater than that of the x coordinate of  the centre. Then the point of the sphere nearest to the given point will be at a distance of one radius from the centre, in the positive x direction.

(4+[tex]\sqrt{44}[/tex], 0, -6)= (10.6, 0, -6 )

Answer:

The equation of circle is [tex]x^2+y^2=65[/tex].

Step-by-step explanation:

It is given that the circle passes through the point (8,1) and center at the origin.

The distance between any point and the circle and center is called radius. it means radius of the given circle is the distance between (0,0) and (8,1).

Distance formula:

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

Using distance formula the radius of circle is

[tex]r=\sqrt{\left(8-0\right)^2+\left(1-0\right)^2}=\sqrt{65}[/tex]

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]         .... (1)

where, (h,k) is center and r is radius.

The center of the circle is (0,0). So h=0 and k=0.

Substitute h=0, k=0 and [tex]r=\sqrt{65}[/tex] in equation (1).

[tex](x-0)^2+(y-0)^2=(\sqrt{65})^2[/tex]

[tex]x^2+y^2=65[/tex]

Therefore the equation of circle is [tex]x^2+y^2=65[/tex].

The equation of a circle centered at origin and passing through the point (8,1) can be determined using principles of geometry. Calculate the radius using the Pythagorean theorem and then substitute it into the general equation of a circle (x-h)² + (y-k)² = r², where h and k are 0 since the circle is centered at the origin. The equation for the circle is x² + y² = 65.

The subject of this question is a circle in mathematics, particularly geometric principles. The given condition is that the circle's center is at the origin and it passes through the point (8,1). From our understanding of a circle, we know that the radius is the distance from the center to any point on the circle. Since our center is at the origin (0,0), the radius r can be calculated using the Pythagorean theorem as the distance from the origin to the point (8,1), which is sqrt((8-0)² + (1-0)²) = sqrt(65). Therefore, the equation of the circle in terms of x and y based on its center (h,k) and radius r is (x-h)² + (y-k)² = r². Given that the circle's center is at the origin, h and k equal to 0, which simplifies the equation to x² + y² = r², or in our case, x² + y² = 65.

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Step-by-step explanation:

Consider the provided information.

For the condition statement [tex]p \rightarrow q[/tex] or equivalent "If p then q"

The rule for Contrapositive is: Negative both statements and interchange them. [tex]\sim q \rightarrow \sim p[/tex]

Part (A) If you are taller than 6 ft, then it is unpleasant for you to travel in economy class.

Here p is "you are taller than 6 ft, and q is "it is unpleasant for you to travel in economy class".

It is given that Your contrapositive must not contain explicit references to negation. Assume that the negation of "unpleasant" is "pleasant".

Contrapositive: If it is pleasant for you to travel in economy class then you are not taller than 6 ft then.

Part (B) "If x ≥ 0 and y ≥ 0 then xy ≥ 0" where x, y are real numbers.

Here p is "xy≥ 0, and q is "x ≥ 0 and y ≥ 0"

The negative of xy≥ 0 is xy<0, x ≥ 0 is x<0 and y ≥ 0 is y<0.

Remember negative means opposite.

Contrapositive: If xy < 0 then x<0 and y<0.

Final answer:

The contrapositive of a statement involves switching the positions of the subject and the complement, and negating both.

Explanation:

To rephrase the given statement in contrapositive form, we need to switch the positions of the subject and the complement, and negate both.

(a) The contrapositive of the statement 'If you are taller than 6 ft, then it is unpleasant for you to travel in economy class' is:

'If it is pleasant for you to travel in economy class, then you are not taller than 6 ft.'

(b) The contrapositive of the statement 'If x ≥ 0 and y ≥ 0 then xy ≥ 0' is:

'If xy < 0, then at least one of x or y is less than 0.'