This is the graph of a function in the form f(x)=a•b^x what’s the function

The sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8) is y = 5 sin(π/2(x - 3)) + 3

We are given that;

Minimum point= (3,-2)

Maximum point= (7, 8)

Now,

To construct a sinusoidal function that rises from a minimum point at (3,-2) to a maximum point at (7, 8), we can use the following steps:

Find the amplitude A. The amplitude is the distance from the midline of the function to the maximum or minimum point. The midline is the average of the maximum and minimum values, which is (8 + (-2))/2 = 3. The distance from 3 to 8 or -2 is 5, so A = 5.

Find the period P. The period is the length of one cycle of the function, or the horizontal distance between two consecutive maximum or minimum points. In this case, the period is 7 - 3 = 4. The constant B is related to the period by the formula B = 2π/P, so B = 2π/4 = π/2.

Find the horizontal shift C. The horizontal shift is the amount that the function is shifted left or right from its standard position. In this case, we want the function to have a minimum point at x = 3, so we need to shift it right by 3 units. This means that C = 3.

Find the vertical shift D. The vertical shift is the amount that the function is shifted up or down from its standard position. In this case, we want the function to have a midline at y = 3, so we need to shift it up by 3 units. This means that D = 3.

Putting it all together, we get:

y = 5 sin(π/2(x - 3)) + 3

Therefore, by the function the answer will be y = 5 sin(π/2(x - 3)) + 3.

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Answer:

what?

Step-by-step explanation:

Answer: $9,000 is invested in the 5% bond, and $24,000 is invested in the 6.5% bond.

Step-by-step explanation: x + y = 33,000 (the full sum contributed)

We too know that the yearly intrigued earned is $2,010.00, which is the whole of the intrigued earned from each bond. Utilizing the equation for basic intrigued:

intrigued = principal x rate x time

ready to calculate the intrigued earned from each bond:

0.05x (for the 5% bond)

0.065y (for the 6.5% bond)

So we have another condition:

0.05x + 0.065y = 2,010

Presently we have two conditions with two factors, which we are able illuminate utilizing substitution or end.

Let's utilize substitution:

x + y = 33,000 --> y = 33,000 - x

0.05x + 0.065y = 2,010 --> 0.05x + 0.065(33,000 - x) = 2,010

Streamlining:

0.05x + 2,145 - 0.065x = 2,010

-0.015x = -135

x = 9,000

So the sum contributed within the 5% bond is $9,000, and the sum contributed within the 6.5% bond is:

y = 33,000 - x = 33,000 - 9,000 = $24,000

The equation of tangent plane to the surfacez = 8x² - 9y² at the point (2,1,23) is 32(x - 2) - 18(y - 1) -1(z - 23) = 0

Here, the equation of the surface is

z = 8x² - 9y²

Let us assume that f(x, y, z) =  8x² - 9y² - z

The partial derivative of f(x, y, z) would be:

[tex]\frac{\partial f}{\partial x}[/tex] = 16x

[tex]\frac{\partial f}{\partial y}[/tex] = -18y

[tex]\frac{\partial f}{\partial z}[/tex] = -1

At point (2, 1, 23) the partial derivative of f(x, y, z),

[tex]\frac{\partial f}{\partial x}[/tex] = 32

[tex]\frac{\partial f}{\partial y}[/tex] = -18

[tex]\frac{\partial f}{\partial z}[/tex] = -1

So, the equation of tangent plane would be,

32(x - 2) - 18(y - 1) -1(z - 23) = 0

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Answer:

116

Step-by-step explanation:

Given that the diameter of a circle is 8.4 inches.

The radius (r) of the circle can be found by dividing the diameter by 2:

r = d/2 = 8.4/2 = 4.2 inches

The area (A) of a circle can be found using the formula:

A = πr^2

Substituting the value of r, we get:

A = 3.14 x 4.2^2 = 55.3896 ≈ 55.39 square inches

The circumference (C) of a circle can be found using the formula:

C = 2πr

Substituting the value of r, we get:

C = 2 x 3.14 x 4.2 = 26.3896 ≈ 26.39 inches

Therefore, the area of the circle is approximately 55.39 square inches and the circumference of the circle is approximately 26.39 inches.

We know that the area of a circle is given by the formula A = π×r²

Given the diameter of the circle = 8.4 in

Therefore radius of the circle = 8.4/2 = 4.2 in    (diameter/2 = radius)

Now Area of the circle = π × 4.2²

                                     = 3.14 × 17.64
                                     = 55.3896

                                     = 55.39   (round up to the nearest hundredth)

Circumference of the circle = 2 × π × r

                                              = 2 × 3.14 × 4

                                              = 26.376

                                              = 26.38 (round up to the nearest hundredth)

Therefore the area of the circle is 55.39 in² and the circumference is 26.38 in.

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Brenda's class left for the field trip at 10:16 A.M.

We have,

Let's break down the time of Brenda's class field trip:

50 minutes to drive to the museum

3 hours and 45 minutes (or 225 minutes) at the museum

56 minutes to drive back to school

Adding up all of these times, we get:

50 + 225 + 56 = 331 minutes

So the field trip took a total of 331 minutes.

If the class arrived back at school at 3:47 P.M., and we subtract 331 minutes from 3:47 P.M., we can determine the time they left for the field trip:

3:47 P.M. - 331 minutes

= 10:16 A.M.

Therefore,

Brenda's class left for the field trip at 10:16 A.M.

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Answer:

  (d)  5i -j

Step-by-step explanation:

You want the value of the expression 2u -v where u=3i and v=i+j.

Use the given definitions of u and v, and simplify in the usual way.

  2u -v = 2(3i) -(i+j)

  = 6i -i -j . . . . . . . . . eliminate parentheses

  = 5i -j

__

Additional comment

The unit vectors i and j can be treated as though they were variables. The usual properties of equality and (scalar) arithmetic apply.

The value of SV, given that point J is the centroid, would be A. 9.

Seeing as we have point J as the centroid for triangle SZU, we can then tell that JV would be:

JV = 1 / 3 x SV

Knowing this, we can make SV the subject of the formula to become:

(JV = 1 / 3 x SV ) / 1 / 3

3 x JV = SV

SV = 3 JV

SV would then be:

SV = 3 x JV

SV = 3 x 3

SV = 9

In conclusion, SV would be 9.

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Answer:

answer is B. 9 :)

Step-by-step explanation:

Answer:16.484

Step-by-step explanation:

find the area of a regular polygon with n sides and radius r, we can use the formula:

Area = (n * r^2 * sin(2*pi/n)) / 2

where pi is the mathematical constant pi (approximately equal to 3.14159).

Plugging in n = 14 and r = 1, we get:

Area = (14 * 1^2 * sin(2*pi/14)) / 2

= (14 * sin(pi/7)) / 2

≈ 16.484

Therefore, the area of the polygon with 14 sides and a radius of 1 unit is approximately 16.484 square units.

The value of sin 75 without using a calculator is 1/4(√2 +√6)

From the question, we have the following parameters that can be used in our computation:

sin(75)

This can be expanded as

sin(75) = sin(45 + 30)

Using the sine rule, we have

sin(75) = sin(45)sin(30) + cos(45)cos(30)

Evaluate the trigonometry ratios

So, we have

sin(75) = √2/2 * 1/2 + √2/2 * √3/2

So, we have

sin(75) = √2/4 + √6/4

Evaluate the sum

sin(75) = 1/4(√2 +√6)

Hence, the value is sin(75) = 1/4(√2 +√6)

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Answer:

  2035.8 ft³

Step-by-step explanation:

You want to know the volume of a cylinder with radius 6 ft and height 18 ft.

The volume of a cylinder is given by the formula ...

  V = πr²h

For the given dimensions, the volume is ...

  V = π(6 ft)²(18 ft) ≈ 2035.8 ft³

The volume of the cylinder is about 2035.8 cubic feet.

__

Additional comment

If you use 3.14 for π, you get 2034.7 cubic feet.

<95141404393>

Answer:

$1092

Step-by-step explanation:

[tex](2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}[/tex]

The missing length is 4 in.

The volume of a rectangular prism is 32 in³.

We have,

Since the two faces of the blocks are squares.

The face that has the missing length can be considered as a square face.

i.e

The front and back faces are squares.

So,

The missing length is 4 in.

Now,

The volume of a rectangular prism.

= length x width x height

= 4 x 2 x 4

= 32 in³

Thus,

The missing length is 4 in.

The volume of a rectangular prism is 32 in³.

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The monthly payment will be $618.71

We know that the formula for the loans are:

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}}[/tex]

where

P₀ is principal

d is monthly payment, annual payment

r is the annual interest rate in decimal form.

k is the number of compounding periods in one year.

and N is the length of the loan, in years.

Here, P₀ =  $32,000

r = 0.06

N = 5

k = 12

Using above formula of loan we need to find value of d.

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}} \\\\32000 =\frac{d(1-(1+\frac{0.06}{12} )^{-60})}{\frac{0.06}{12}}\\\\32,000 =\frac{d(1-(1+0.005)^{-60})}{0.005} \\\\32000\times 0.05=d(1-(1.005)^{-60})\\\\160=d\times (1-0.7414)\\\\d = 160/0.2586\\\\d=618.72[/tex]

Therefore, the monthly payment = $618.71

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Answer:

  15

Step-by-step explanation:

You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).

The table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).

The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.

The remainder theorem tells you that is also the value of the function for x = k.

The remainder from f(x) ÷ (x +1) is 15.

<95141404393>

Answer:

V = 62.8 m[tex]^{3}[/tex]

Step-by-step explanation:

V = pi × (radius)[tex]^{2}[/tex] × height

V = [tex]\pi[/tex] × [tex]r^{2}[/tex] × h

V = (3.14 × [[tex]2^{2}[/tex]]) × 5

V = (3.14 × 4) × 5

V = 12.56 × 5

V = 62.8 m[tex]^{3}[/tex]

The vertices of the feasible region is (4, 3)

From the question, we have the following parameters that can be used in our computation:

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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The volume of the large solid is equal to 8/25 cm³.

In Mathematics, the volume of a cube can be calculated by using the following formula:

V = m³

Where:

By substituting the given points into the formula for the volume of a cube, we have the following;

Volume of cube, V = m³

Volume of cube, V = (1/5)³

Volume of cube, V = 1/125 cm³.

For the volume of the large solid, we have:

Volume of large solid = 5 × 2 × 4 × 1/125

Volume of large solid = 8/25 cm³.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The required pair of points that are both located less than 3 units from points (3, 8) is (2, 7).

Following the condition given in the question,
Assuming there are 3 points on the graph beside (3, 8) are (2, 7), (5, 5), and (6, 10)

The distance formula between two points is given by:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

So, for each point, we can plug in the coordinates and simplify the following:

Point (2, 7):

d = √[(2 - 3)² + (7 - 8)²]

d = √[1² + 1²]

d = √2  (<3)

Points (6, 10):

d = √[(6 - 3)² + (10 - 8)²]

d = √[3² + 2²]

d = √13  (>3)

Point (5, 5):

d = √[(5 - 3)² + (5 - 8)²]

d = √[2² + 3²]

d = √13   (>3)

Point (1, 1):

d = √[(1 - 3)² + (1 - 8)²]

d = √[(-2)² + (-7)²]

d = √53  (>3)

Thus, the pair of points that are both located less than 3 units from points (3, 8) is (2, 7).

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Result:

sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).

For us to write the expression, we shall use this formular formula:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

where:

a = tan⁻¹(x)

b = tan⁻¹(y)

Next, we have:

tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))

= (x - y) / (1 + xy)

From both sides, we have sine:

sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))

So, sin(tan⁻¹(x) - tan⁻¹(y))  

= sin(tan⁻¹(x) - tan⁻¹(y))

= (x - y) / (1 + xy) in terms of x and y.

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Answer:

Step-by-step explanation:

Answer:

log(10)

Step-by-step explanation:

We can use the product property for logarithms:

log(a)+log(b)=log(ab)

In our case, a=5 and b=2. We can multiply a and b now to get the new number we're taking the logarithm of.

log(2)+log(5)=log(2×5)=log(10)

The expression 16x⁹y¹⁸√3xy is equivalent to √769x¹⁹y³⁷

If a > O and y > 0, which expression is equivalent to √769x¹⁹y³⁷

Factor and rewrite the radicand in exponential form:

√16²×3x¹⁸×xy³⁶×y

Simplify the radical expression:

16x⁹y¹⁸ √2²×3xy

Factor and rewrite the radicand in exponential form:

8x⁹y¹⁸√2²×3xy

8x⁹y¹⁸.2√3xy

Multiply the monomials:

16x⁹y¹⁸√3xy

Hence, the expression 16x⁹y¹⁸√3xy is equivalent to √769x¹⁹y³⁷

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