The hiking path to the top of a mountain makes, at the steepest place, an angle of 20° with the
horizontal, and it maintains this constant slope for 500 meters, as illustrated below. Which of the
following is the closest approximation to the change in elevation, in meters, over this 500-meter
section?
500 meters
20
A 20
B) 170
180
D 250

Answer:

The volume of the solid is 243[tex]\sqrt{2} \ \pi[/tex]

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0  ≤ ρ²   ≤   81

0  ≤ ρ   ≤  9

The intersection that takes place in the sphere and the cone is:

[tex]x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81[/tex]

[tex]2(x^2 + y^2) =81[/tex]

[tex]x^2 +y^2 = \dfrac{81}{2}[/tex]

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

[tex]z = \sqrt{x^2+y^2}[/tex]

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; [tex]\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}[/tex]

Thus, volume: [tex]V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi[/tex]

[tex]V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho[/tex]

[tex]V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}[/tex]

[tex]V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ][/tex]

V = 243[tex]\sqrt{2} \ \pi[/tex]

Answer:

A expression is a number, variable, or a combination of numbers and variables and operation symbols. A equality is a relationship between 2 quantities or more . Hope it helps:)))

Step-by-step explanation:

I think u got right answer...

Answer:

a. yes it is a binomial experiment

b. success is that baby recovers

c. n = 6

d. p = 0.5

e. q = 0.5

f. X: 0,1,2,3,4,5,6

Step-by-step explanation:

a.

the answer is yes this is a binomial experiment. This is true because we have a finite number of babies and these babies are independent of each other. there are two possible outcomes. 1. baby recovers 2. baby does not recover.

b.

success: baby recovers

c.

n = number of babies born with ailment. n = 6

d.

p = 50% = 0.5

e.

q = 1-p = 1-0.5

q = 0.5

f.

possible values of X: 0,1,2,3,4,5,6

Answer: -1 1/8 -3/4 -1/2 3/8

Answer:

c

Explanation:

Just because

Answer:

3080mm = 3.08 meters

3080mm = 308 centimeters

Step-by-step explanation:

1 meter = 1000 mm

3080mm = 3080/1000 = 3.08 meters

1 centimeter = 10 mm

3080mm = 3080/10 = 308 centimeters

Answer:

1400

Step-by-step explanation:

Answer:

Equal???

Step-by-step explanation:

Answer:

The probability is [tex]P(X = 0) =  0.6997[/tex]

Step-by-step explanation:

From the question we are told that

   The  mean is  [tex]\mu = 2.8[/tex]

Generally the Poisson distribution constant  [tex]\lambda[/tex] is mathematically represented as

        [tex]\lambda = \frac{1}{\mu }[/tex]

=>     [tex]\lambda = \frac{1}{2.8 }[/tex]

=>     [tex]\lambda = 0.3571[/tex]

Generally the probability distribution for Poisson distribution is mathematically represented as  

     [tex]P(X = x) =  \frac{(\lambda t)^x e^{-t \lambda}}{x!}[/tex]

Here  t =  1 day

Generally the probability  that no babies are born today is mathematically represented as

       [tex]P(X = 0) =  \frac{(0.3571 * 1 )^0 e^{-1 * 0.3571}}{0!}[/tex]

=>    [tex]P(X = 0) =  0.6997[/tex]

Answer:

d

Step-by-step explanation:

.................have a great day

Answer:

x=4

Step-by-step explanation:

As the two angles are clearly congruent because of the bisector, we set them equal to each other:

7x=3x+16

4x=16

x=4

Therefore, the value of x is 4 and not 9

Answer:

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Step-by-step explanation:

hope its right

Answer:

h(-3)=-1

Step-by-step explanation:

Replace all x in h(x)= -3x-10 by -3:

h(-3)=-3(-3)-10

Now multiply -3 and -3:

h(-3)=9-10

Simplify 9 and -10 (aka add 9 and -10 together):

h(-3)=-1

Answer: h(-3)=-1

Hope this helps!

Answer:

-1

Step-by-step explanation:

If h(x)= -3x-10 and we want to solve for h(-3) then we have to plug in -3 for all x variables. h(-3)= -3(-3)-10, then solve using PEMDAS.

First multiple h(-3)= 9-10, multiple -3*-3 to get 9.

Then subtract, h(-3)=-1

Answer:

$3,780

Step-by-step explanation:

27*140=3780

Answer:

look go search Math - way its a calculator and type in your question ir really helps gives you the answer

Step-by-step explanation:

Answer:

14.5 feet

Step-by-step explanation:

the midpoint is halfway from 30 to 45 so be(bart elevation) b.e = 45 - 30 / 2

7.5 m above sea level

__________________________________________________________

We are given:

The elevation of Homer = -30 feet                         [30 feet below sea level]

The elevation of Marge = +45 feet                         [45 feet above sea level]

The elevation of Bart is at the exact mid-point of the elevations of Homer and Marge

The elevation of Bart:

We are given that the elevation of Bart is at the exact mid-point of the elevations of Homer and Marge

So, Half the distance between the elevation of Homer and Marge is the elevation of Bart

Elevation of Bart (with respect to the elevation of Homer) =

(elevation of Marge - Elevation of Homer) / 2

replacing the variables with the suitable values:

(+45 - (-30))/2

(45 + 30) / 2

75 / 2

Elevation of Bart (w.r.t. Homer) = 37.5 feet

Since this is the elevation of Bart with respect to Homer, we can say that Bart is 37.5 m above Homer

So, we can say that:

Elevation of Bart (w.r.t Homer) = Elevation of Bart - Elevation of Homer

replacing the values

37.5 = Elevation of Bart -(-30)

37.5 = Elevation of Bart + 30

Elevation of Bart = 7.5 m above sea level [subtracting 30 from both sides]

Answer:

[tex]1764 = 2^2 \times 3^2 \times 7^2[/tex]

Step-by-step explanation:

Divide by the prime numbers in increasing order until you find all the prime factors.

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17

1764/2 = 882

882/2 = 441

441/3 = 147

147/3 = 49

49/7 = 7

7/7 = 1

[tex]1764 = 2^2 \times 3^2 \times 7^2[/tex]

Answer:

Step-by-step explanation:

This is the combination of 5 experiments out of 12

Formula to find the combination:

So this can be arranged in 95040 ways

Answer:

The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].

Step-by-step explanation:

From statement we understand that parabola has its axis of symmetry in an axis parallel to y-axis. According to Analytical Geometry, the minimum distance between focus and directrix equals to twice the distance between vertex and any of endpoints.

If endpoints are (-5, 5) and (-5, -1), respectively, then such distance ([tex]r[/tex]), dimensionless, is calculated by means of the Pythagorean Theorem:

[tex]r = \frac{1}{2}\cdot \sqrt{[-5-(-5)]^{2}+[5-(-1)]^{2}}[/tex]

[tex]r = 3[/tex]

And the location of the vertex ([tex]V(x,y)[/tex]), dimensionless, which is below the focus, is:

[tex]V(x,y) = F(x,y)-R(x,y)[/tex] (1)

Where:

[tex]F(x,y)[/tex] - Focus, dimensionless.

[tex]R(x,y)[/tex] - Vector distance, dimensionless.

If we know that [tex]F(x,y) = (-5,5)[/tex] and [tex]R(x,y) = (0,3)[/tex], then the location of the vertex is:

[tex]V(x,y) = (-5,5)-(0,3)[/tex]

[tex]V(x,y) =(-5,2)[/tex]

In addition, we define a parabola by the following expression:

[tex]y-k = \frac{(x-h)^{2}}{4\cdot r}[/tex] (2)

Where:

[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.

[tex]r[/tex] - Distance of the focus with respect to vertex, dimensionless.

If we know that [tex]h = -5[/tex], [tex]k = 2[/tex] and [tex]r = 3[/tex], then the equation of the parabola is:

[tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex]

The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].

Answer:

si

Step-by-step explanation:

la longitud mayor es menor que la suma de las otras 2 longitudes que es 10

Answer:

R = 118

Step-by-step explanation:

Given

Represent the polynomial with P and the divisor with D

[tex]P = 19x^2 + 15x + 12[/tex]

[tex]D = x -2[/tex]

Required

Determine the remainder

We start by equating the divisor to 0

i.e.

[tex]D = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

Substitute 2 for x in the polynomial.

This gives remainder (R)

[tex]R = 19*2^2 + 15*2 + 12[/tex]

[tex]R = 19*4 + 15*2 + 12[/tex]

[tex]R = 76 + 30 + 12[/tex]

[tex]R = 118[/tex]

Hence, the remainder is 118

Answer:

B dilation

Step-by-step explanation:

the shape didnt move but it got bigger

Answer:

y=2

Step-by-step explanation:

that's the answer hope u understand it

Answer:

[tex]y = 2[/tex]

Step-by-step explanation:

Sure.

[tex]y - \frac{2}{5} = 1 \frac{3}{5} \\[/tex]

Convert to improper fraction

[tex]y - \frac{2}{5} = \frac{8}{5}[/tex]

Combine like terms

[tex]y - \frac{2}{5} = \frac{8}{5} \\[/tex]

[tex]+\frac{2}{5}[/tex] from both sides

[tex]y = \frac{8}{5} + \frac{2}{5} \\y = 2[/tex]

Love from Nepal :)

Answer:

$48

Step-by-step explanation:

Multiply 200 by 0.08 or 8%. That is how much interest he will earn in a year. Then multiply the product by 3.

Answer:

9:5

Step-by-step explanation:

Answer:

slope-6

y-intercept-(0,-3)

Step-by-step explanation:

Answer:

(4x−3)(x−2)=0

Step-by-step explanation:

Step-by-step explanation:

4x²-11+6=0

4x²-5=0

x²=5

4

x=√5

4

hope it help u