s=ut+ 1/2 at²
u=10 a= -2 t= 1/2
work out the value of s

By evaluating the polynomial, we will see that the sign on the interval [-4, 2] is negative.

Here we have the polynomial:

f(x) = (x - 2)*(x + 4)*(x + 5).

You can see that the roots of the polynomial are at:

x = 2

x = -4

x = -5.

Then, on the interval [-4, 2], the sign of the polynomial don't change. So to get the sign of f(x) on that interval we can just evaluate it in any value of x that belongs to the interval, for example, x = 0.

f(0) = (0 - 2)*(0 + 4)*(0 + 5) = -2*4*5 = -40

With this, we can conclude that the sign of f(x) on the given interval is negative.

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Answer:

always negative

Step-by-step explanation:

Approximation of cos(15) from linear approximation: L(15) ≈ cos(1) - 15sin(1) ≈ 0.540302305868 - 15(0.841470984808) ≈ -11.0905365065

We cannot estimate the value of csc(0.2) using linear approximation without any computational aid.

First, let's find the derivative of g(y) with respect to y:

g'(y) = -sin(y+1)

Next, we evaluate g'(y) at y = 0:

g'(0) = -sin(0+1) = -sin(1)

The linear approximation to g(y) at y = 0 can be expressed as:

L(y) = g(0) + g'(0)(y - 0)

Since g(0) = cos(0+1) = cos(1), the linear approximation becomes:

L(y) = cos(1) - sin(1)y

To approximate the values of cos(2) and cos(15) using the linear approximation, we substitute the respective values of y into L(y):

Approximation of cos(2):

L(2) = cos(1) - sin(1)(2) = cos(1) - 2sin(1)

Approximation of cos(15):

L(15) = cos(1) - sin(1)(15) = cos(1) - 15sin(1)

To compare the approximated values to the exact values, we need to compute the exact values of cos(2), cos(15), and csc(0.2).

cos(2) ≈ 0.41614683654 (approximated using a calculator)

cos(15) ≈ 0.96592582629 (approximated using a calculator)

csc(0.2) ≈ 5.02553333034 (approximated using a calculator)

Now we can compare the approximated values using the linear approximation to the exact values:

Approximation of cos(2) from linear approximation: L(2) ≈ cos(1) - 2sin(1) ≈ 0.540302305868 - 2(0.841470984808) ≈ -1.14264104833

Error: |exact value - approximation| = |0.41614683654 - (-1.14264104833)| ≈ 1.55878788487

Approximation of cos(15) from linear approximation: L(15) ≈ cos(1) - 15sin(1) ≈ 0.540302305868 - 15(0.841470984808) ≈ -11.0905365065

Error: |exact value - approximation| = |0.96592582629 - (-11.0905365065)| ≈ 12.0564623328

For csc(0.2), we need to use a different approach as it involves the cosecant function. The linear approximation is not directly applicable to this trigonometric function. Therefore, we cannot estimate the value of csc(0.2) using linear approximation without any computational aid.

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The triangular pyramid has a greater surface area than the square pyramid.

The surface area of a pyramid depends on the shape and dimensions of its base as well as its height and slant height. In this case, the square pyramid has a square base with sides of length 10 cm and four equilateral triangular faces with a height of 8.66 cm. The triangular pyramid has an equilateral triangular base with sides of length 10 cm and three identical equilateral triangular faces, each with a height of 8.66 cm.

To calculate the surface area of the square pyramid, we can first find the slant height of each triangular face using the Pythagorean theorem:

slant height = sqrt(10^2 + (8.66/2)^2) = 10.82 cm

Then, we can calculate the area of each triangular face as:

area = (1/2) * base * height = (1/2) * 10 cm * 8.66 cm = 43.3 cm^2

And finally, the total surface area of the pyramid is:

total surface area = area of base + 4 * area of triangular faces

= 10 cm * 10 cm + 4 * 43.3 cm^2

= 600.8 cm^2

To calculate the surface area of the triangular pyramid, we can use the formula:

surface area = area of base + 1/2 * perimeter * slant height

The area of the equilateral triangular base is:

area = (sqrt(3)/4) * base^2 = (sqrt(3)/4) * 10 cm^2 ≈ 21.65 cm^2

The perimeter of the base is simply 3 times the length of a side, or 30 cm. The slant height of each triangular face is 8.66 cm, so the surface area of the pyramid is:

surface area = 21.65 cm^2 + 1/2 * 30 cm * 8.66 cm

= 21.65 cm^2 + 130.0 cm^2

= 151.65 cm^2

Therefore, the triangular pyramid has a greater surface area than the square pyramid.

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Step-by-step explanation:

(30 men, 56 days, 6 hours daily)

=> (30 men, 48 days, 7 hours daily)

=> (45 men, 32 days, 7 hours daily)

Hence it will take 32 days.

Answer:

Gradient

Step-by-step explanation:

The slope represents the gradient of a line

One solution for the given linear equation is the poiont (1, 1)

We want to find a solution for the linear equation:

y = 2x - 1

A solution will be any pair (x, y), such that when we replace these values in the equation, it becomes true.

To find a solution we can evaluate the equation in some value of x, for example, if x = 1

y = 2*1 - 1

y = 2 - 1

y = 1

(1, 1) is a solution for the line.

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Answer:

525

Step-by-step explanation:

f(x)=(x)(2x+5)

f(x)=2x^2+5x

f(15)=2*(15)^2 + 5*15

= 2*225 + 75

=450 + 75

=525

The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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Using the fundamental theorem of calculas the derivative of function g(x)=\(xt^{3}+t^{5}\) at x=0 is \(t^{3}\).

Given a function g(x)=\(xt^{3}+t^{5}\).

We are required to find the derivative of the function g(x) at x=0.

Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.

g(x)=\(xt^{3}+t^{5}\)

Differentiating with respect to x.

d g(x)/dx=\(t^{3}\)+0  [Differentiation of x is 1 and differentiation of constant is 0]

=\(t^{3}\)

Hence using the fundamental theorem of calculas the derivative of function g(x)= \(xt^{3}+t^{5}\) at x=0 is \(t^{3}\).

The function given in the question is incomplete. The right function will be g(x)=\(xt^{3}+t^{5}\).

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.

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

Because angles 1 and 2 are close to one another, they are neighboring angles.

A They share a side and are near to each other, making them neighboring angles.

B. The angles are complimentary (add to 90 degrees) False—Angle 2 has a 90 degree angle.

C. They are additional angles. (add to 180) They do not create a straight line, which is untrue.

D. Vertical angles describe them. (Contrary angles) False, they are not created through the intersection of lines.

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

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Answer:

Yes

Step-by-step explanation:

Yes, that is exactly what Sarah did wrong. Apparently, she tried to divide both the numerator and denominator in this problem by 2 (half) but divided the numerator incorrectly. 26 divided by 2 would equal 13 but Sarah mistakenly calculated it as 14 which would give her a totally different value when divided by the new denominator. If were to have divided correctly it would give her \(\frac{13}{4}\) which is the same as \(\frac{26}{8}\)

The given linear programming problem aims to maximize the objective function \(Z = 3x1 + 2x2\), subject to four constraints: x1 ≤ 4, x2 ≤ 6, 3x1 + 2x2 ≤ 18, and x1 ≥ 0, x2 ≥ 0.

The objective of linear programming is to optimize (maximize or minimize) a linear objective function while satisfying a set of linear constraints. In this case, the objective is to maximize \(Z = 3x1 + 2x2\).

The constraints in the problem define the feasible region, which is the set of all points that satisfy the constraints. The constraints state that x1 must be less than or equal to 4, x2 must be less than or equal to 6, and the linear combination \(3x1 + 2x2\) must be less than or equal to 18. Additionally, both x1 and x2 must be greater than or equal to zero.

To solve this linear programming problem, graphical methods or optimization algorithms such as the simplex method can be employed. The feasible region is determined by graphing the constraints and finding the overlapping region. The optimal solution is the point within the feasible region that maximizes the objective function.

The explanation of the solution, including the optimal values of x1 and x2, the maximum value of Z, and the graphical representation of the problem, can be provided based on the chosen method of solving the linear programming problem.

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Answer:

It's (8/3) 6  I took the test and that was the answer. Your Welcome!!!!!!!!!!!!!

Answer:

Its 83 the power of 6. Also Please choose my anwer as brainliest

Answer:

So we have: \((8x+16)-(3x^2-3x-15)\)

We will start operating the parenthesis, so we will have to pass the - to the members of these  (we will have to change their sign):

\((8x+16)-3x^2+3x+15\)

We can also removee the first parenthesis, as it doesn't change the meaning if it's or if it isn't::

\(8x+16-3x^2+3x+15^\)

Now, we will group the numbers

\(-3x^2+8x+3x+16+15\)

And we can now do the operations:

\(-3x^2+8x+3x+16+15=-3x^2+11x+16^\)

The expression (8x + 16) – (3x² – 3x – 15)  is equivalent to the expression 31 + 11x – 3x².

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

⇒ (8x + 16) – (3x² – 3x – 15)

Simplify the expression, then we have

⇒ (8x + 16) – (3x² – 3x – 15)

⇒ 8x + 16 – 3x² + 3x + 15

⇒ 31 + 11x – 3x²

The expression (8x + 16) – (3x² – 3x – 15)  is equivalent to the expression 31 + 11x – 3x².

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Answer:

\( x = 20 \)

Step-by-step explanation:

\( \frac{3}{5}x - \frac{1}{4}x = 7 \)

The LCD is 20, so multiply both sides of the equation by 20.

\( 20(\frac{3}{5}x - \frac{1}{4}x) = 20 \times 7 \)

\( 4 \times 3x - 5 \times x = 140 \)

\( 12x - 5x = 140 \)

\( 7x = 140 \)

\( x = 20 \)

Answer:

8

Step-by-step explanation:

Since the two horizontal lines are parallel, we have that triangle CDG and triangle CEF are similar (corresponding points in that order). Therefore, using similarity, CD/CG = CE/CF. Therefore 3/4 = 9/(4+x).

So 12 = 4+x, and x = 8.

10 procent

Step-by-step explanation:

150 / 150 = 10

Answer:10%

Step-by-step explanation:

Answer:

Answer:

5. 18

6. 13.75 all the arrows for 6 is just explaining how 13,75 is the answer

5 2 11 8 35 32

if i helped brainliest is appreciated :)

The given differential equation is given byy′=√2−16.

Let's find the solution of the differential equation:We can write the given differential equation asy′=1√2−16.

Using integration by substitution, let's integrate it as follows:∫1√2−16dx=12ln⁡|√2−16+x|+C

Now, applying the initial condition y(x)=yo at

x=0

yo=12ln⁡|√2−16|+C

=>C=yo−12ln⁡|√2−16|

Therefore, the solution of the given initial value problem is

y=12ln⁡|√2−16+x|+yo−12ln⁡|√2−16|

Hence, option (c) yo = 4 is the correct answer.

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a)There are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

a)Set A has m elements and set B has n elements

Firstly determine the number of elements A*B by using the multiplication rule

Number of elements\(=A*B=m*n=mn\)

For each element, \(A*B\) we have two option

First element 2 ways

Second element 2 ways

mn element 2 ways

By using the multiplication rule

\(2*2*2......=2^m^n }\)

Then there are \(2^m^n\) possible relation

b)Similarly \(n^m\)

c)\(\frac{n^m}{2^m^n}\)

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From the picture we knwo that the minor arc MN is:

Now we have to notice that segment LM is tangent to the circle, this means that the angle 6 have to be half the value of minor arc MN, therefore:

Infinitely many position vectors with length 2 in xyz-space are orthogonal to the nonzero position vector v. (D)

A position vector in xyz-space is a vector that starts at the origin and ends at a point in xyz-space. The length of a position vector is the distance from the origin to the point it ends at.

If we want to find position vectors with length 2 that are orthogonal (perpendicular) to a given nonzero position vector v, we can use the dot product.

Let w be a position vector with length 2 that is orthogonal to v. Then, the dot product of v and w must be zero, since they are orthogonal. That is, v · w = 0. Since the length of w is 2, we can write w as 2u for some unit vector u. Thus, v · w = v · (2u) = 2(v · u) = 0.

This means that v and u are orthogonal as well, since the dot product of two vectors is zero if and only if they are orthogonal.

There are infinitely many unit vectors u that are orthogonal to v, and therefore, there are infinitely many position vectors with length 2 that are orthogonal to v. Therefore, the answer is (d) infinitely many.

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The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

Answer: D. line d

Step-by-step explanation:

Answer: D. line d

A function is general describe as y = mx + b, so we need to set this function in y form.

2x + 5y = -10

       5y = - 2x - 10             (Subtract 2x from both side, to make sure there are only y value in the left side)

         y = - 2/5x -10/5       (Divide by 5 from both side)

         y =  -2/5x - 2           (Simplified)

-2/5x was the m or the slope, it shows how the line was change. -2/5x is negegative, which means is decreasing, and going downward, only line b and d fits.

-2 is the y-intercept, where y is equal to 0, (-2,0)

The y-intercept for line b is (2,0), so it can't be. Thus, the y-intercept for line d is (-2,0), so it fit.

Answer:

Step-by-step explanation:

yes

The statement that is also true to ΔQSR ≅ ΔYXZ is  ΔQRS ≅ ΔYZX.

Two triangles are defined to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. In other words, triangles are congruent when they have exactly the same three sides and exactly the same three angles.

Therefore,

ΔQSR ≅ ΔYXZ

Therefore, another statement that is equal to the congruency of the triangle is as follows:

ΔQRS ≅ ΔYZX

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The derivative of the function is \($\boxed{y' = 6x^{5}(1+\ln x)}$\).

The given function is \($y=x^{6x}$\).

We are to use logarithmic differentiation to find the derivative of the function.

Logarithmic differentiation refers to a method of finding the derivative of a function by applying logarithmic differentiation to both sides of the equation and then differentiating.

Let us take the logarithm on both sides of the equation.\($$\ln y = \ln(x^{6x})$$\\$$\ln y = 6x\ln x$$\\$$\ln y = \ln x^{6x}$$\\$$y = x^{6x}$$\)

Differentiating both sides of the equation with respect to $x$ gives, \($$\frac{d}{dx}(y) = \frac{d}{dx}(x^{6x})$\\$Let $f(x) = x^{6x}$.\)

Using the logarithmic differentiation formula, \($$\ln y = 6x\ln x$$\\$$\frac{y'}{y} = 6x \frac{1}{x} + 6 \ln x$$\)

\($$\frac{y'}{y} = 6 + 6\ln x$$\\$$y' = 6x^{6-1}y(1+\ln x)$$\\$$y' = 6x^{5}(1+\ln x)$$\)

Therefore, the derivative of the function is \($\boxed{y' = 6x^{5}(1+\ln x)}$\).

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Using the given information and what we know about linear equations, we will find the sketch below.

Here we need to analyze each part separately.

In a coordinate axis where the y-axis represents distance and the x-axis represents time, we will have that:

First, we know that he rides for 30 minutes at a given speed, this will be represented with an increasing linear function.

Then he stops for 20 minutes, this is represented with a horizontal line.

Finally, he returns the motion, but slower than before, so the slope of this line will be smaller than the first one.

So for 0 to 30 we have an increasing linear equation, then for 30 to 50 we have a constant horizontal line, then for 50 to 80 we have another increasing linear equation

The sketch can be seen below.

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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