From the top of a building, 30.15m high, the angle of depression of a point on the ground level 25.88'm from the base is B° find B​

Since f(x) is a cubic polynomial, it has at most 3 distinct roots. If f(x) has 3 real roots, then f(x) = 0 for more than one instance of x.

But if f(x) is one-to-one, then there must be only one real root and the other two are non-real. Let a + bi and a - bi be these non-real roots and c the single real root; then we can factorize f(x) as

[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x - (a + bi)) (x - (a - bi)) (x - c)[/tex]

Expand the right side to get

[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x^2 - 2ax + a^2+b^2) (x - c)[/tex]

[tex]f(x) = x^3 - kx^2 + 12x + 7 = x^3 - (2a + c) x^2 + (a^2 + 2ac + b^2) x - (a^2c + b^2c)[/tex]

from which it follows that

[tex]\begin{cases}k = 2a + c \\ 12 = a^2+2ac+b^2 \\ 7 = -a^2c-b^2c\end{cases}[/tex]

Since f(x) has only one root, its graph will have no turning points/extrema. If f(x) has a critical point, it must be a saddle point. Differentiating f(x) yields

[tex]f'(x) = 3x^2 - 2kx + 12[/tex]

Solve for the critical point:

[tex]f'(x) = 3x^2 - 2kx + 12 = 0[/tex]

[tex]x^2 - \dfrac{2k}3 x = -4[/tex]

[tex]x^2 - \dfrac{2k}3 x + \dfrac{k^2}9 = \dfrac{k^2}9-4[/tex]

[tex]\left(x - \dfrac k3\right)^2 = \dfrac{k^2}9-4[/tex]

[tex]x = \dfrac k3 \pm \sqrt{\dfrac{k^2}9-4}[/tex]

There is at most one real critical point, so either the square root term vanishes or it produces a non-real number. This happens for

[tex]\dfrac{k^2}9 - 4 \le 0 \implies k^2 \le 36 \implies -6 \le k \le 6[/tex]

So, if f(x) is one-to-one, then

[tex]k \in \left\{\kappa \in \Bbb R \mid -6 \le \kappa \le 6\right\}[/tex]

The computation of the word problem shows that the oranges will John have in 12 weeks will be 70 oranges.

The word problem will be that John has 10 oranges and buys 5 more oranges every week. How many oranges will John have in 12 weeks.

The computation will be:

= 10 + 5x

where x= number of weeks.

= 10 + 5x

= 10 + 5(12)

= 10 + 60

= 70 oranges

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Answer:AA , BB , and CC are parallel to MN.

Step-by-step explanation:

Answer:

there are 3 ferrets,15 dogs,27 cats

Step-by-step explanation:

the ratio of the three

9:5:1

the ferrets,1/15 * 45= 3

the dogs,5/15 * 45= 15

the cats, 9/15 * 45=27

Answer:

6

Step-by-step explanation:

When you have a proportion (fraction=fraction), you can crossmultiply to solve. See image.

Step-by-step explanation:

the united set of A and B contains every element of both sets without listing any element twice.

so, it is

{1, 2, 4, 5, 7, 8, 11}

Answer:

[tex] \frac{43}{110} [/tex]

Step-by-step explanation:

43 is the total amount of junior students

while 110 is the total amount of students who use Company B

and... in probability it's never more than one that's why it isn't

[tex] \frac{110}{43} [/tex]

Hope it helps

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

Translate into an algebraic equation:-

The quotient of a number and 5.

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

✳︎ First, the word "quotient" indicates that we divide.

Here, we have the quotient of a number and 5, so we divide the number by 5; let the number be d.

So the quotient of d and 5 looks as follows:-

[tex]\bold{\dfrac{f}{5}}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

i belive 7

Step-by-step explanation:

becuse 3+6 in one line = 9 so 2 + 7= 9

Answer: 2/sqrt6

Step-by-step explanation:

tan theta=perpendicular/base so

cot theta =base /perependicular=sqrt2/2

while sin theta=perpendicular/hypotenous=2/x

here x is unkown to find it we will use pythagoras theorem

(hypoteneous)^2=(Base)^2+(perependicular)^2

                            =(sqrt 2)^2+(2)^2

                            =2+4

  (hypoteneous)^2=6

  hypotenous   =sqrt6

so

sin theta=2/sqrt6

Answer:

(4:-4)

Step-by-step explanation:

the graphs y- axis starts at 4 and ends at -4

Answer:

The Answer is: 0.744747

Step-by-step explanation:

cos 45 + sin 160

0.525322 + 0.219425

0.744747

hope this helps if it wasn't too late lol

The capital gross is calculated by doing subtracting purchase price from selling price option first “selling price-purchase price” is correct.

The entire value of gross fixed capital formation, changes in inventories, and acquisitions less disposals of assets for a unit or sector is used to calculate gross capital formation.

As we know, deducting the asset's or portfolio's acquisition price from the selling price yields the capital gain formula.

Thus, the capital gross is calculated by doing subtracting purchase price from selling price option first “selling price-purchase price” is correct.

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Answer:

no picture

Step-by-step explanation:

just search it up

Answer:

the answer is 63.59m²

Step-by-step explanation:

[tex]radius = \frac{diameter}{2} \\ = \frac{3}{2} \\ = \frac{9}{2} (since \:1cm = 3m \: so \: 3cm = 9m) \\ = 4.5 \\ area \: of \: circle = \pi {r}^{2} \\ = 3.14 \times (4.5) {}^{2} \\ = 3.14 \times 20.25 \\ = 63.585 {m}^{2} [/tex]

Answer:

  resistance must quadruple

Step-by-step explanation:

You want to know the change in resistance required to quadruple the amount of heat if heat is proportional to the square of voltage, inversely proportional to resistance, and the voltage is quadrupled.

Let H represent the heat generated for voltage V and resistance R. We want to find R, the new resistance required, when V is replaced by 4V, and H is replaced by 4H.

  H = V²/R

  4H = (4V)²/R'

  4(V²/R) = 16V²/R'

  R' = (16/4)R . . . . . . . multiply by RR'/(4V²)

  R' = 4R

The resistance must quadruple if the amount of heat is to be quadrupled.

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Answer:

√10z^3(z - 1)(z + 1).

Step-by-step explanation:

The GCF is √10z* z^2

= √10z^3

So factoring we get

√10z^3(z^2 - 1)           The expression in brackets is difference of 2 squares so:

= √10z^3(z - 1)(z + 1)

Answer:

Below in bold.

Step-by-step explanation:

7,16,10,16,9,13,14

Arrange in ascending order:

7 9 10 13 14 16 16

The median = middle value

= 13 pounds.

Mean = (7+9+10+13+14+16+16)/7

= 12.14 pounds.

Answer:

The measure of its complementary angle is 3.

Step-by-step explanation:

Answer:

There are many ways to describe a data set using a single measure. Some common ways are to find the mean, median, or mode of the data set.

Step-by-step explanation:

A single measure can be used to describe a data set in the form of a statistic. This statistic can be used to measure the central tendency, dispersion, or shape of the data set. For example, the mean can be used to describe the central tendency of a data set, while the standard deviation can be used to describe the dispersion of a data set.

Answer:

x = 30

Step-by-step explanation:

x = 90 - 60 = 30

x = 30

.................................................

Answer:

Its d

Step-by-step explanation:

Answer:

by 3% percent

Step-by-step explanation:

i hope this helps ._.

So in January he could do 12 pushups..
4 months later, he could do 3 more..
A total of 15 in 4 months would make a 25% increase with 6.25% every month as 3 pushups represent 1/4 of the 12 he used to do

Answer:

the answer is C :) hope it helps

Answer:its actually 9.1 ft

Step-by-step explanation: i just took the same test

[tex]{\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}[/tex]

Answer:

diameter of the circle

Step-by-step explanation:

A chord that passes through a circle's centre is a diameter of the circle.

The attached figure represents the scatter plot for the data

The table of values is given as:

Height: 5 ft 0” 5 ft 1” 5 ft 2” 5 ft 3” 5 ft 4” 5 ft 5”

Weight: 9.1        9.5     9.8       10         10.4  10.8

Next, we convert the heights to feet

So, we have:

Height: 5     5.08  5.17   5.25   5.33  5.42

Weight: 9.1    9.5    9.8      10    10.4  10.8

Next, we plot the scatter plot (see attachment) where the heights are plotted on the x-axis, and the weights are plotted on the y-axis

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Answer:

option  A

first graph.

Answer:

8km 323m

Step-by-step explanation:

The total distance given by summing up all the distances traveled using different means.

Distance by bus = 5km 28m

Distance by car = 2 km 265 m

Distance on foot = 1 km 30 m

(1km + 2 km + 5km) + (30m + 265m +28m) = 8km + 323m

Step-by-step explanation :

Here we have been given with the distance travelled by Abhishek through bus , car and foot. We're asked to calculate the total distance travelled by him.

But we will first convert the distance which is in kilometres into metres in order to do that. And after that we will add them all.

• Distance travelled by bus :

> Bus = 5km 28m

> Bus = 5 × 1000 + 28

> Bus = 5000 + 28

> Bus = 5028 m

• Distance travelled by car :

> Car = 2km 265m

> Car = 2 × 1000 + 265

> Car = 2000 + 265

> Car = 2265m

• Distance travelled by foot :

> Foot = 1km 30m

> Foot = 1 × 1000 + 30

> Foot = 1000 + 30

> Foot = 1030m

★ Now, total distance would be calculated as follows :

>> Total distance = (5028 + 2265 + 1030) m

>> Total distance = (7293 + 1030) m

>> Total distance = 8323 m

Therefore,