Evaluate f(t)=-2t2+ 1 for f(-3)

The numbers are 26 and 9 respectively.

An algebraic expression can best be defined as an arithmetic or mathematical expression that is known to consist of variables, coefficients, constants, factors as well as terms.

These expressions said to contain numerous arithmetic operations, which includes;

From the information given, we have that

Let the small number be x

The large number be y

y < 3x    (1)

Also,

x + y = 35    equation 2

x = 35 - y

Substitute the value of x in equation 1

y < 3(35 - y)

expand the bracket

y < 105 - 3y

collect like terms

y + 3y < 105

4y < 105

Make 'y' the subject

y < 105/4

y < 26. 25

y = 26

substitute the value of y

x + y = 35

x + 26 = 35

x = 9

Hence, the values are 26 and 9

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

The solution for the initial value problem is \(y_{g} = e^{-2x} (-12cos(x) + 5sin(x)) + 7e^{-4x}\)

Given,

y" + 4y' + 5y = 35\(e^{-4x}\)

y(0) = -5

y'(0) = 1

Solve this homogenous equation to get \(y_{h}\)

According to differential operator theorem,

\(y_{h}\) = \(e^{ax}\)( A cos (bx) + B sin (bx)), where A and B are constants.

Therefore,

y" + 4y' + 5y = 0

(\(D^{2}\) + 4D + 5)y = 0

D = -2± i    

\(y_{h} = e^{-2x} ( A cos (x) + B sin (x))\)

Now, solve for \(y_{p}\)

A function of the kind \(ce^{-4x}\) is the function on the right, we are trying a solution of the form \(y_{p} =ce^{-4x}\), here c is a constant.

\(y_{p} " + 4y_{p} ' + 5y_{p} = 35e^{-4x} \\=16ce^{-4x} -16ce^{-4x} +5ce^{-4x} = 35e^{-4x} \\= 5ce^{-4x} =35e^{-4x} \\c=\frac{35}{5} =7\\y_{p} =7e^{-4x}\)

Then the general solution will be like:

\(y_{g} =y_{h} +y_{p} \\\)

    = \(e^{-2x} (Acos(x)+Bsin(x))+7e^{-4x}\)

\(y_{g}(0)=-5=A+7=-12\\y_{g} '(0)=e^{-2x} (-Asin(x)+Bcos(x))-2e^{-2x} (Acos(x)+Bsin(x))-28e^{-4x} \\y'_{g} (0)=1=B-2A-28\\\)

       B = 1 - 24 + 28 = 5

Then the solution for the given initial value problem is

\(y_{g} =e^{-2x} (-12cos(x)+5sin(x))+7e^{-4x}\)

Learn more about initial value problem here: https://brainly.com/question/8599681

#SPJ4

Answer:

100 hours

Step-by-step explanation:

To find the amount of liters in one hour, you divide 10 by 1000, which gives 0.01 liters each hour. From here, the 1 is in the hundredths place, so if you multiply by 100 hours, if will be at 1 liter.

The x-intercept is (735, 0) and y-intercept is (0, 490)

The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. To graph this equation, we can rearrange it into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

2x + 3y = 1,470

3y = -2x + 1,470

y = (-2/3)x + 490

We can use the intercepts method to graph the line. For x-intercept, y = 0 and solve for x:

2x + 3(0) = 1,470

2x = 1,470

x = 735

Therefore, the x-intercept is (735, 0).

For y-intercept, x = 0 and solve for y:

2(0) + 3y = 1,470

3y = 1,470

y = 490

Therefore, the y-intercept is (0, 490). We can plot both intercepts and draw a straight line through them to represent Sal's profits last month.

Learn more about Graph here

https://brainly.com/question/17267403

#SPJ1

Given a sector with radius, r,

In this case,

then

Take

Then,

Therefore the area of the sector is 12.01 square units

Step-by-step explanation:

simple answer mate..

under root 2 is right because angle are same.. option d

Answer:

√2

Step-by-step explanation:

Angle ( θ ) = 45

Hypotenuse side = 2

Opposite side = x

Formula : -

sin θ = Opposite side / Hypotenuse side

Note :

The value of sin 45 = 1/√2

sin 45 = x/2

1/√2 = x/2

Cross multiply,

x*√2 = 2*1

x√2 = 2

2 can be simplified as √2 * √2

x√2 = √2*√2

Divide √2 on both sides,

x = √2

Answer:

279.987

this is da answer

Step-by-step explanation:

There are 280.035 lbs in 127 kilograms. The answer is obtained by applying the unit conversion.

What is unit conversion?

A unit conversion is used to express the same property in a different unit of measurement. For instance, you could use minutes instead of hours to represent time or feet instead of miles to indicate distance. It commonly occurs when measurements are provided in one system of units, such as feet, but are required in a different system, such as chains.

Now,

we have been given 127 kilograms which are to be converted into pounds and to be represented in lbs.

We know that 1 kilogram = 2.205 lbs (approx)

Therefore,

⇒127 kilograms = 127 * 2.205

⇒127 kilograms = 280.035 lbs

Hence,

          There are 280.035 lbs in 127 kilograms.

Learn more about unit conversion from the given link

https://brainly.com/question/4158962

#SPJ4

The two given angles add together to make a linear pair, which is 180 degrees.

(2x + 8) + (2x) = 180

4x + 8 = 180

4x = 172

x = 43

Angle ABC = 2(43) + 8 = 86 + 8 = 92 degrees

Hope this helps!! :)

a) To find the value of k such that the lines and are perpendicular, we need to find the dot product of their direction vectors and set it equal to zero.

The direction vector of the first line is (3, -1, k), and the direction vector of the second line is (2, -2, 5). Taking their dot product, we have:

(3, -1, k) · (2, -2, 5) = 3*2 + (-1)*(-2) + k*5 = 6 + 2 + 5k = 8 + 5k

For the lines to be perpendicular, the dot product must be zero. Therefore, we have:

8 + 5k = 0

Solving this equation, we find:

5k = -8

k = -8/5

So the value of k that makes the lines perpendicular is k = -8/5.

b) To determine parametric equations for the plane through the points A(2, 1, 1), B(0, 1, 3), and C(1, 3, −2), we first need to find two vectors in the plane. We can take the vectors AB and AC. The vector AB is obtained by subtracting the coordinates of point A from those of point B: AB = (0-2, 1-1, 3-1) = (-2, 0, 2). Similarly, the vector AC is obtained by subtracting the coordinates of point A from those of point C: AC = (1-2, 3-1, -2-1) = (-1, 2, -3).

Now, we can express any point (x, y, z) in the plane as a linear combination of these vectors:

(x, y, z) = (2, 1, 1) + s(-2, 0, 2) + t(-1, 2, -3)

where s and t are parameters. These equations represent the parametric equations for the plane through the points A, B, and C.

c) To determine a vector equation for the plane that is parallel to the xy-plane and passes through the point (4, 1, 3), we can use the fact that the normal vector of the xy-plane is (0, 0, 1). Since the plane we are looking for is parallel to the xy-plane, its normal vector will be the same.

Using the point-normal form of a plane equation, the vector equation for the plane is:

(r - r0) · n = 0

where r is a position vector in the plane, r0 is a known point in the plane, and n is the normal vector. Plugging in the values, we have:

(r - (4, 1, 3)) · (0, 0, 1) = 0

Simplifying, we get:

(0, 0, 1) · (x - 4, y - 1, z - 3) = 0

0*(x - 4) + 0*(y - 1) + 1*(z - 3) = 0

z - 3 = 0

Therefore, the vector equation for the plane that is parallel to the xy-plane and passes through the point (4, 1, 3) is z - 3 = 0.

Learn more about perpendicular here:
https://brainly.com/question/11707949

Answer:

The scale factor is 20.

Explanation:

The scale factor is the ratio of the corresponding side lengths (or areas or volumes) of the two similar figures. In this case, we are given the areas of the front sides of the toy building and the real building, and we want to find the scale factor between them.

Let x be the scale factor. Then, the area of the front side of the real building is x^2 times the area of the front side of the toy building. We can set up the equation:

x^2 * 1 square foot = 400 square feet

Solving for x, we get:

x^2 = 400

x = sqrt(400)

x = 20

Therefore, the scale factor between the toy building and the real building is 20.

Given that μ = 9.1, σ = 0.3, and n = 9, the value of µx (the mean of the sample) and σx (the standard deviation of the sample mean) can be calculated as follows:

µx = μ = 9.1 (since the sample mean is equal to the population mean)

σx = σ/√n = 0.3/√9 = 0.3/3 = 0.1

Therefore, µx is 9.1 and σx is 0.1 (rounded to the nearest hundredth).

In this case, we are given the population mean (μ), the population standard deviation (σ), and the sample size (n). The goal is to calculate the mean of the sample (µx) and the standard deviation of the sample mean (σx).

Since the population mean (μ) is provided as 9.1, the sample mean (µx) will be the same as the population mean. Therefore, µx = 9.1.

To calculate the standard deviation of the sample mean (σx), we divide the population standard deviation (σ) by the square root of the sample size (n). In this case, σ is given as 0.3 and n is 9.

Using the formula σx = σ/√n, we substitute the values:

σx = 0.3/√9 = 0.3/3 = 0.1

Therefore, the calculated value for σx is 0.1 (rounded to the nearest hundredth).

The mean of the sample (µx) is 9.1 and the standard deviation of the sample mean (σx) is 0.1 (rounded to the nearest hundredth). These values indicate the central tendency and variability of the sample data based on the given population mean, population standard deviation, and sample size

To know more about mean visit:

https://brainly.com/question/1136789

#SPJ11

Since the calculated test statistic (2.836) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that more than half of internet users have posted photos or videos online.

To test the hypothesis that more than half of internet users have posted photos or videos online, we can use a one-sample proportion test. Let p be the true proportion of internet users who have posted photos or videos online. The null and alternative hypotheses are:

H0: p <= 0.5

Ha: p > 0.5

We will use a significance level of 0.05.

Using the given information, we have:

n = 855

x = (56/100) * 855

= 479.6 (rounded to nearest whole number, 480)

The sample proportion is:

p-hat = x/n

= 480/855

= 0.561

The test statistic is:

z = (p-hat - p0) / √(p0 * (1 - p0) / n)

where p0 is the null proportion under the null hypothesis. We will use p0 = 0.5.

z = (0.561 - 0.5) / √(0.5 * (1 - 0.5) / 855)

= 2.836

Using a standard normal distribution table or calculator, the critical value for a one-tailed test at a 0.05 level of significance is approximately 1.645.

To know more about hypothesis,

https://brainly.com/question/11560606

#SPJ11

Answer: long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend

Step-by-step explanation:

To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.

Lengthy divide as you'll with entire numbers, but positioned the decimal point in the answer at the equal place it's miles at within the dividend

What is a decimal ?

Decimal can be defined as a number in which it contains whole and fractional part.

performing long department with decimals may be very just like acting long department with entire numbers, with a few more steps along the way. The manner we technique an extended department trouble concerning decimals will rely on in which in the equation the decimal range appears; either in the dividend (the quantity under the lengthy department bracket), the divisor (the range to the left of the lengthy division bracket), or each. the position of the decimal factor within the quotient (answer) can be depending on the placement of the decimal factor within the dividend.

Therefore, lengthy divide as you'll with entire numbers, but positioned the decimal point in the answer at the equal place it's miles at within the dividend

To learn more about Decimal from given link.

https://brainly.com/question/29765582

#SPJ4

Answer:

2.24units

Step-by-step explanation:

Let the coordinate be A(3, -5) and A'(2, -3)

Using the formula for calculating the distance between two points

D = √(x2-x1)²+(y2-y1)²

AA' = √(2-3)²+(-3-(-5))²

AA' = √(-1)²+(-3+5))²

AA' = √1+2²

AA' =√5

AA' = 2.24 units

Note that the coordinate points are assumed

Answer:

It’s C

Step-by-step explanation:

Just did the quiz

Answer:

that answer is 7 is bigger then 1.9

Step-by-step explanation:

so 7 is a whole and 1.9 is a decimal

Answer: 2.65 <  1.9

Step-by-step explanation:

The square root of 7 is 2.65

2.65 is larger than 1.9 so that is why

it is "< "

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Learn more about cross product visit:

brainly.com/question/29097076

#SPJ11

Answer:

-1 7/8

Step-by-step explanation:

Linear equation is the equation in which the highest power of the unknown variable is always 1.The equation which helps determine the distance x on each side of the mirror is ,

\(x+3+x=18\).

The length of the mirror is 36 inches.

The length of the wall is 18 feet.

The linear equation has to find out for the distance x.

Linear equation is the equation in which the highest power of the unknown variable is always 1.

As one feet is equal to the 12 inches. Thus the length \(l\) of the mirror in the feet is,

\(l=\dfrac{36}{12}\)

\(l=3\)

The mirror is 3 feet wide.

The distance on each side of the mirror is x. This distance is equal at both side as the mirror is centered. The distance on each side of the mirror is,

\(=x+x\).

Now the the wall is 18 feet wide which is equal to the distance each side of the mirror and the distance of the mirror. As the mirror is 3 feet wide. Thus the equation which determine the distance x on each side of the mirror can be given as,

\(x+3+x=18\)

Hence the equation which helps determine the distance x on each side of the mirror is ,

\(x+3+x=18\).

Learn more about the linear equation here;

https://brainly.com/question/2263981

The point estimate that can be used to estimate the true mean population is 11.97 inches.

To find the point estimate that can be used to estimate the true population mean, we need to take the sample mean of the given observations. The formula for the sample mean is:

Mod(X)= (Σx) / n

where Mod(X)  is the sample mean, Σx is the sum of all the observations, and n is the size.

Using the given observations, we can calculate the sample mean as follows:

Mod(X) = (11.3 + 10.7 + 12.4 + 15.2 + 10.1 + 12.1 + 16.2 + 10.5 + 11.4 + 11.0 + 10.7 + 12.0) / 12

Mod(X) = 11.97

Therefore, the point estimate that can be used to estimate the true mean population is 11.97 inches.

Learn more about mean:

https://brainly.com/question/30112112

#SPJ4

The most accurate statement about the mean absolute deviation (MAD) is that it is measured in the same units as the original data. MAD is the arithmetic mean of the absolute deviations from the mean, which means that it measures the average distance between each data point and the mean. It is different from standard deviation, which measures the spread of the data around the mean, and is calculated by taking the square root of the arithmetic mean of the squared deviations from the mean. MAD can only be a positive number, as it measures distances. Therefore, the correct answer is C.
C. It is measured in the same units as the original data.

The mean absolute deviation (MAD) is a measure of dispersion or variability in a dataset. It is calculated by finding the arithmetic mean of the absolute deviations from the mean of the dataset. Since the absolute deviations are in the same units as the original data, the MAD is also measured in the same units as the original data.

To learn more about deviation : brainly.com/question/13905583

#SPJ11

Answer:

80/100 and 0.8

Step-by-step explanation:

Answer:

5/10 in fraction form and 0.5 in decimal form

Step-by-step explanation:

The carbon cycle is a natural process that involves the movement of carbon atoms between the atmosphere, organisms, rocks, sediments, and the ocean.

The carbon cycle is a crucial process for maintaining the balance of carbon in the Earth's ecosystems. Carbon dioxide (CO2) is taken up by plants during photosynthesis, converting it into organic carbon compounds that are stored in plant tissues. When plants die and decompose, or when animals respire or decompose, carbon is released back into the atmosphere as CO2. Additionally, carbon can be stored in rocks and sediments over long periods of time.

Deforestation, the clearing of forests on a large scale, can significantly disrupt the carbon cycle. When forests are cut down, the stored carbon in trees and vegetation is released into the atmosphere as CO2 through the process of decomposition or burning. This contributes to increased greenhouse gas emissions and can contribute to climate change.

Furthermore, deforestation reduces the number of trees available to absorb CO2 through photosynthesis, leading to decreased carbon uptake from the atmosphere. The loss of forests also means the loss of carbon sinks, as trees are natural carbon storage systems. Without these sinks, more carbon remains in the atmosphere, further exacerbating the greenhouse effect.

In addition to these changes, deforestation can also impact the water cycle, which in turn affects the carbon cycle. Trees play a vital role in regulating water flow and moisture levels in ecosystems. When forests are removed, there is a higher risk of soil erosion and decreased water retention. These changes can affect the growth and survival of plants, ultimately impacting carbon uptake and storage.

In summary, deforestation disrupts the carbon cycle by releasing stored carbon into the atmosphere, reducing carbon uptake, and altering carbon storage patterns. These changes contribute to increased greenhouse gas emissions, climate change, and overall environmental imbalance.

To learn more about carbon Click Here:  brainly.com/question/22741334

#SPJ11

Answer:

no

Step-by-step explanation:

i dont

X can be anything bigger than 7, and numbers go on forever so infinite

Answer:

Infinite solutions

Step-by-step explanation:

Inequalities are statements that express the value of a variable in relation to another number.

This inequality states that x must be greater than 7. To find the number of solutions it is important to remember that numbers continue for infinity. This means that every number has a number greater than it. For this reason, there are an infinite number of numbers greater than 7. So, there are infinite solutions that satisfy this inequality.

Answer:

cam has b-7

Step-by-step explanation:

Answer:

the answer is B 7

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the boat's path and the direction of the lifeguard tower form a right angle, so we can use the theorem to find the distance between them.

First, we need to find the length of the boat's path after it turns N 20 W. To do this, we can use trigonometry. Since the boat is traveling at an angle of 20 degrees west of north, we can use the sine and cosine functions to find the horizontal and vertical components of its motion:

cos(20) = adjacent/hypotenuse
hypotenuse = adjacent/cos(20)
hypotenuse = 5/cos(20)
hypotenuse ≈ 5.26 miles

sin(20) = opposite/hypotenuse
opposite = hypotenuse*sin(20)
opposite ≈ 1.8 miles

So the boat travels approximately 1.8 miles north and 5.26 miles west from its starting point. To find the distance between the boat and the lifeguard tower, we can use the Pythagorean theorem:

distance² = 3² + (5.26)²
distance² = 9 + 27.6
distance² ≈ 36.6
distance ≈ 6.05 miles

Therefore, the distance from the boat to the lifeguard tower at this time is approximately 6.05 miles.

Visit here to learn more about Pythagorean theorem  : https://brainly.com/question/14930619
#SPJ11

Answer:

106.95

Step-by-step explanation:

there are 31 days in july so if multiply 3.45 and 31 you get your answer