the volume of pyramid a is the volume of pyramid b. if the heigh of pyramid b increases to twice that of pyramid a the new volume of pyramid b the volume of pyramid a

9514 1404 393

Answer:

  5.423 miles

Step-by-step explanation:

Let x represent the distance to run. Then the remaining distance to the point that is closest to the island is (6-x) miles. The straight-line distance (d) to the point x from the island is given by the Pythagorean theorem:

  d² = 1² +(6 -x)² = x² -12x +37

  d = √(x² -12x +37)

The total travel time is the sum of times running and swimming. Each time is found from ...

  time = distance/speed

  total time = x/4 + d/2 = x/4 +(1/2)√(x² -12x +37)

__

The total time will be minimized when its derivative with respect to x is zero.

  t' = 1/4 +(1/4)(2x -12)/√(x² -12x +37) = 0

Multiplying by 4 and combining fractions, we can see the numerator will be ...

  √(x² -12x +37) +2x -12 = 0

Subtracting the radical term and squaring both sides, we get ...

  4x² -48x +144 = x² -12x +37

  3x² -36x +107 = 0

The quadratic formula tells us the smaller of the two roots is ...

  x = (36 -√(36² -4(3)(107)))/(2(3)) = (36 -√12)/6 ≈ 5.423 . . . mi

You should run 5.423 miles west to minimize the time needed to reach the island.

__

A graphing calculator solves this nicely. The attached graph shows the time is a minimum when you run 5.423 miles.

Answer:

b

Step-by-step explanation:

A proportional relationship is a straight line.  Is must also go through the point (0,0)

b

Answer:

Step-by-step explanation:

A proportional relationship is a straight line.  Is must also go through the point (0,0)

Answer:

Devaughn = 31, Sydney = 25

Step-by-step explanation:

(56-6)÷2= 25

So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31

ATQ

[tex]\\ \sf\longmapsto x+x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x=56-6[/tex]

[tex]\\ \sf\longmapsto 2x=50[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto x=25[/tex]

Answer:

D.

Step-by-step explanation:

D. This contains an x^2 and is called a parabola ( curved line like a U).

Answer:D

Step-by-step explanation: d is the correct answer

Answer:

ΔT = -75°F

Step-by-step explanation:

ΔT = T₁ - T₀ = 350 - 425 = -75°F

y = 2/3 x - 2

Or

y + 2 = 2/3 ( x )

Answer:

y= 2/3x - 2

hope this helps :)

The exponential function that models the number of trees after t years is given by:

[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]

Hence, after 2 years, 450 trees will be remaining, as the graph at the end of this answer shows.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem:

Then, the equation is:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 800(1 - \frac{1}{4})^t[/tex]

[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]

After 2 years:

[tex]A(2) = 800\left(\frac{3}{4}\right)^2 = 450[/tex]

450 trees will be remaining.

You can learn more about exponential functions at https://brainly.com/question/25537936

The equation of the circle is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] . The option C is the correct option.

Given that the centre of the circle is (2,3) and circle has radius 4.

To find the equation of the circle, use the general equation of the circle as:

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

Where (h, k) is the centre of the circle and r is the radius of the circle.

Since, h = 2, k = 3 and radius r = 4.

Therefore, the equation of the circle:

[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-3)^2=4^2\\(x-2)^2+(y-3)^2=16[/tex]

The equation of the circle cantered at (2,3) and has a radius of 4 is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .

Therefore, The equation of the circle cantered at (2,3) and has a radius of 4 is  [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .

Learn more about Diameter here:

https://brainly.com/question/32968193

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Answer:

N(t) = 0.188t + 22.76

Step-by-step explanation:

Number of licensed drivers in 2004 = 22.76 million

Number of licensed drivers in 2009 = 23.7 million

Number of licensed drivers, N as a function of t since year 2004 ;

General form of a linear function :

y = mx + c

c = intercept ; m = slope

Intercept c = value of y ; when x = 0

Here, population after uerssmmx,

Hence,

In 2004 ;

22.76 = mx + c

x = 0

22.76 = c

Number in 2009

x = number of yesrs after 2004 ; x = 2000 - 2004 = 5years

We can find the slope :

y = m*5 + 22.76

y = 23.7 in 2009

23.7 = 5m + 22.76

23.7 - 22.76 = 5m

m = 0.94 / 5

m = 0.188

Hence, the linear function can be written as :

N(t) = 0.188t + 22.76

Answer:

h.

[tex] \frac{9 {x}^{10}(y. {x}^{3}) {}^{2} }{y.x(3 {x}^{3}) {}^{3} } \\ \\ = \frac{9 {x}^{10}(y {}^{2} )( {x}^{6} ) }{3y. {x}^{10} } \\ \\ = \frac{ {3}^{2} {x}^{16} {y}^{2} }{3y {x}^{10} } \\ \\ = 3y {x}^{6} [/tex]

j.

[tex] \frac{(3x. {y}^{7} ) {}^{2}. {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{3 {x}^{2} . {y}^{14} . {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{ {3x}^{7} {y}^{14} }{3 {x}^{7} {y}^{4} } \\ \\ = {y}^{10} [/tex]

Answer:

loses  14 cents

- $0.14

Step-by-step explanation:

90%  $0.30   $(0.30)  $(0.27)

9%  $1.00   $0.40   $0.04  

1%  $10.00   $9.40   $0.09  

   $(0.14)

Answer:

8. -2a+14

9. w=3/2

Step-by-step explanation:

8.

The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.

For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as

-2 * a + (-2) * (-7) = final answer

= -2 * a + 14

We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out

9.

Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in

(-2/3)w = 4-5 = -1

Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get

w = (-3/2)

To check this, we can plug (-3/2) for w in our original equation, so

(-2/3) * (-3/2) + 5 = 4

-1 + 5 = 4

4 = 4

This works!

Answer:

x2  1-

Step-by-step explanation:

Answer:

x ≥ 0

Step-by-step explanation:

Domain of a function is the x values of a function

The graph extends from 0 to positive infinity.

Since the point at x=0 is closed, the graph includes 0

Answer:

y = 6

I hope this helps you out!

Answer:

C.

Step-by-step explanation:

Science questions are T/F. That's .5 or [tex]\frac{1}{2}[/tex] chance to get it right.

7 questions. Each with a [tex]\frac{1}{2}[/tex].

That's [tex](\frac{1}{2})^{7}[/tex]  

[tex](\frac{1}{2})^{7}[/tex] = [tex]\frac{1}{128}[/tex] = .0078 = .008 rounded

English questions are multiple choice. 4 choices. That's .25 or [tex]\frac{1}{4}[/tex]

3 questions. Each [tex]\frac{1}{4}[/tex]

That's [tex](\frac{1}{4})^{3}[/tex]

[tex](\frac{1}{4})^{3}[/tex] = [tex]\frac{1}{64}[/tex] = .0156 = .016 rounded

The probability of getting all questions correct is 0.004 which is lower than for science (0.016).

Science questions are said to have a 6 out of 6 correct answer range and a 0.5 chance of being answered properly.

So, P(6) = 0.5⁶

P(6) = 0.016

We are informed that there are 4 out of 4 correct answers for English, with a 0.25 chance of getting it right.

Thus; P(4) = 0.25⁴ = 0.004

Thus, we conclude that they will have to study English.

Learn more about Probability here:

brainly.com/question/251701

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Answer:

Slope: 1

Y-intercept: (0,3)

Step-by-step explanation:

The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.

Y intercept: (0, 3)

For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]

From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.

Slope: 1

Hope this helped.

Answer: 1

Step-by-step explanation: got it right on edge

please mark this answer as brainlist

To solve this question, the real rate of return formula is used, and we apply the data given in the exercise into the formula to find the real rate of return.

Formula for the real rate of return:

[tex]R = \frac{1 + N}{1 + i} - 1[/tex]

In which N is the nomial rate and i is the inflation rate, as decimals.

A certificate of deposit offers a nominal interest rate of 2.5 percent annually.

This means that [tex]N = 0.025[/tex]

Inflation is 1 percent

This means that [tex]i = 0.01[/tex]

What is the real rate of return:

Now we apply the formula:

[tex]R = \frac{1 + 0.025}{1 + 0.01} - 1[/tex]

[tex]R = 1.0149 - 1[/tex]

[tex]R = 0.0149[/tex]

0.0149*100% = 1.49%

Thus, the real rate of return is of 1.49%.

For another example of a similar problem, you can check https://brainly.com/question/20164190

Answer:

0.0005m^3

Step-by-step explanation:

V=1/3hπr²

h=6m

d=12m

r=12÷2=6m

V=1/3×6×(3.14)×36

V=1/2034.72

V=0.0005m^3

Answer:

y-3 = -4(x+2)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-3 = -4(x --2)

y-3 = -4(x+2)

Answer:

csc = 6/5= 1.2

cot = √(11)/5= 0.6633

sin = 5÷6= 0.83333

9514 1404 393

Answer:

  $70

Step-by-step explanation:

Four relationships are given among four unknowns. Define the following variables: p, c -- the cost of a pie and a cake, respectively. q, d -- the number of pies and cakes, respectively.

  q/d = 5/2 . . . . . the ratio of pies to cakes sold

  pq +cd = 3780 . . . . revenue from the sales

  p = c -35 . . . . . a pie is $35 less than a cake

  cd = pq -420 . . . . revenue from cakes is $420 less than for pies

__

The equations are non-linear, so we're making up this process as we go along. We observe that 'pq' and 'cd' are involved in relations that give us their sum and difference, so these products are easily found. Their ratio can let us take advantage of our knowledge of q/d.

Substituting for cd in the second equation, we get ...

  pq +(pq -420) = 3780

  2pq = 4200

  pq = 2100

  cd = 2100 -420 = 1680

Now, we can write ...

  pq/cd = 2100/1680 = 5/4

  (p/c)(q/d) = 5/4 = (p/c)(5/2) . . . . substitute for q/d

  p/c = 1/2 = (c -35)/c . . . . . . . . . . substitute for p

  c = 2(c -35) . . . . multiply by 2c

  c = 70 . . . . . . . . add 70-c

The cost of a cake is $70.

_____

Additional comment

24 cakes were sold at $70 each. 60 pies were sold at $35 each.

Answer:

f(3) = 6

Step-by-step explanation:

If f(1)=10, then f(1+1)=f(1)-2

f (2) = 10 - 2 = 8

Therefore f(3) = f(2) - 2 = 8 - 2 = 6

Answer:

the slope -3, slope meaning rate of change and y intercept is 1.

hope that answers your question

(used desmos to graph, good stuff!!!)

I believe your answer is D

Answer:

option(d)

Step-by-step explanation:

5/12 + 4/12 + 3/12 + 2/12 + 1/12

=> (5+4+3+2+1)/12

=> 15/12 ≠ 10/12

Answer:

21

Step-by-step explanation:

you divide 10.50 by 50

Answer:

✔ positive

✔ 1

✔ closely

✔ increases

ED2021